Download Optical Trapping Techniques Applied to the Study of Cell Membranes

Optical Trapping Techniques
Applied to the Study of Cell
Membranes
DISSERTATION
Presented in Partial Fulfillment of the Requirements for the Degree Doctor of
Philosophy in the Graduate School of The Ohio State University
By
Andrew J. Morss, B.S.
Graduate Program in Physics
The Ohio State University
2012
Dissertation Committee:
Gregory Lafyatis, Advisor
Ralf Bundschuh
Michael Poirier
Ratnasingham Sooryakumar
c Copyright by
Andrew J. Morss
2012
Abstract
Optical tweezers allow for manipulating micron-sized objects using pN level optical forces.
In this work, we use an optical trapping setup to aid in three separate experiments, all
related to the physics of the cellular membrane.
In the first experiment, in conjunction with Brian Henslee, we use optical tweezers to
allow for precise positioning and control of cells in suspension to evaluate the cell size
dependence of electroporation. Theory predicts that all cells porate at a transmembrane
potential VT M of roughly 1 V. The Schwann equation predicts that the transmembrane
potential depends linearly on the cell radius r, thus predicting that cells should porate at
threshold electric fields that go as 1/r. The threshold field required to induce poration is
determined by applying a low voltage pulse to the cell and then applying additional pulses
of greater and greater magnitude, checking for poration at each step using propidium iodide
dye. We find that, contrary to expectations, cells do not porate at a constant value of the
transmembrane potential but at a constant value of the electric field which we find to be
692 V/cm for K562 cells.
Delivering precise dosages of nanoparticles into cells is of importance for assessing toxicity of nanoparticles or for genetic research. In the second experiment, we conduct nanoelectroporation—a novel method of applying precise doses of transfection agents to cells—by
using optical tweezers in conjunction with a confocal microscope to manipulate cells into
contact with 100 nm wide nanochannels. This work was done in collaboration with Pouyan
Boukany of Dr. Lee’s group. The small cross sectional area of these nano channels means
that the electric field within them is extremely large, 60 MV/m, which allows them to
electrophoretically drive transfection agents into the cell. We find that nano electropoii
ration results in excellent dose control (to within 10% in our experiments) compared to
bulk electroporation. We also find that, unlike bulk electroporation, nano-electroporation
directly injects nanoparticles, such as quantum dots, to the cell interior, bypassing the cell
membrane without the need for endocytosis.
The aging of RBC’s can render them rigid, an issue for the survivability of transfusion
patients. This rigidity can be assessed by examining the fluctuations in the cell membrane.
In the third experiment, we use back focal plane detection—an interferometric detection
scheme using an optical tweezers setup—to measure the membrane fluctuations of RBC’s
and K562 cells. Membrane fluctuations have long been observed in RBC’s and a well
developed theory exists linking them to the cells internal viscosity η, the membrane bending
modulus k and the surface tension of the membrane σ. We use back focal plane detection
to measure the effect of ascorbic acid treatment on RBC aging and find no improvement
in cell flexibility. K562 cells differ from RBC’s in that they possess an actin cortex which
the membrane attaches to. We demonstrate that K562 cells exhibit as much as an order of
magnitude more variation in their fluctuations than RBC’s do.
iii
Dedicated to my wife, Kate, and my mother, Diane. Without their love, kindness and
support, none of this would have been possible.
iv
Acknowledgments
This thesis would not have been possible without the assistance of my advisor, Dr. Gregory
Lafyatis, whose advice, technical support and guidance have been crucial in the completion
of this work. I would also like to take this opportunity to thank the rest of my committee
members: Dr. Ralf Bundschuh, Dr. Michael Poirier and Dr. Ratnasingham Sooryakumar.
I would also like to thank Dr. James Lee of the Nanoscale Science and Engineering
Center for Affordable Polymeric Biological Devices(NSEC-CANPBD), whose guidance and
support was critical. This thesis is the result of collaboration with Dr. James Lee and the
students and post docs of the NSEC-CANPBD group, in particular Brian Henslee, Pouyan
Boukany, Yun Wu, Wei-ching Liao and Bo Yu. Dr. Andre Palmer and his group, notably
Jorge Fontes and Uddyalok Banerjee, were instrumental to the section on red blood cells
in Chapter 6. Dr. Samir Ghardiali and his student Yan Huang were also helpful for their
insight and assistance with the latrunculin portions of Chapters 4 and 6.
I would like to thank the NSF and NSEC-CANPBD for their financial support throughout my graduate studies.
Finally, I would like to thank my wife, Kathleen Morss, my parents, Peter and Diane
Morss, and my sister, Laura Morss, for giving me the support and inspiration without which
this work would not have been possible.
v
Vita
June 2000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Solanco High School, Quarryville, PA
May 2004 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B.S., Math, Physics, Penn State University, State College, PA
AU 2004 to SP 2006 . . . . . . . . . . . . . . . . . . . . . . . . . . . Graduate Teaching Assistant, Physics Department, Ohio State University
SU 2006 to Present . . . . . . . . . . . . . . . . . . . . . . . . . . . . Graduate Research Assistant, Physics Department, Ohio State University
Publications
Brian E. Henslee, Andrew Morss, Xin Hu, Gregory P. Lafyatis, and L. James Lee. Electroporation dependence on cell size: an optical tweezers study. Analytical Chemistry, 83:39984003, 2011.
Pouyan E. Boukany, Andrew Morss, Wei-ching Liao, Brian Henslee, HyunChul Jung, Xulang Zhang, Bo Yu, Xinmei Wang, Yun Wu, Lei Li, Keliang Gao, Xin Hu, Xi Zhao, O.
Hemminger, Wu Lu, Gergory P. Lafyatis, and L. James Lee. Nanochannel electroporation
delivers precise amounts of biomolecules into living cells. Nature Nanotechnology, 6:747-754,
2011.
Bross, A.L.; Lafyatis, G; Ayachitula, R; Morss, A; Hardman, R.; Golden, J. Robust, efficient grating couplers for planar optical waveguides using no-photoacid generator SU-8
electron beam lithography. Journal of Vacuum Science & Technology B: Microelectronics
and Nanometer Structures, 27:2602, 2009.
I. Albert, J.G. Sample, A.J. Morss, S. Rajogopalan, A-L Barabasi and P. Schiffer. Granular
drag on a discrete object: Shape effects on jamming. Physical Review E, 64:061303, 2001.
Fields of Study
vi
Major Field: Physics
vii
Table of Contents
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Page
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xi
. xiii
. xiv
1 Electroporation: Historical Summary
1.1 Mechanism of Permeabilization . . . . . . . .
1.1.1 Planar Membrane Experiments . . . .
1.1.2 Electromechanical Collapse . . . . . .
1.1.3 Electroporation . . . . . . . . . . . . .
1.2 Factors Affecting Permeabilization Threshold
1.3 Asymmetric Breakdown . . . . . . . . . . . .
1.4 Effect of the Cytoskeleton . . . . . . . . . . .
1.5 Transfection of Large Molecules . . . . . . . .
1.6 Electrofusion . . . . . . . . . . . . . . . . . .
1.7 Resealing and Memory . . . . . . . . . . . . .
1.8 Micro Electroporation . . . . . . . . . . . . .
1.9 Outline of This Work . . . . . . . . . . . . . .
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Abstract . . . . . .
Dedication . . . .
Acknowledgments
Vita . . . . . . . .
List of Figures .
List of Tables . .
Acronyms . . . .
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Chapters
2 Optical Trapping
2.1 Principles of Trapping . . . . . . . . . . . . . .
2.1.1 Ray Optics Description . . . . . . . . .
2.1.2 Point Dipole Description . . . . . . . . .
2.2 Optical Tweezers: Basic Design Considerations
2.2.1 Objective Lens . . . . . . . . . . . . . .
2.2.2 Laser . . . . . . . . . . . . . . . . . . .
2.2.3 Sample Manipulation . . . . . . . . . .
2.2.4 Position Detection . . . . . . . . . . . .
2.2.5 Multiple Trapping . . . . . . . . . . . .
viii
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3 Technical
3.1 Experimental Setup . . . . . . . . .
3.2 Position Detection . . . . . . . . . .
3.2.1 Calibration . . . . . . . . . .
3.2.2 Transmission . . . . . . . . .
3.3 Additional Optical Trapping Setups
3.3.1 Confocal System . . . . . . .
3.3.2 Touch Screen System . . . . .
3.4 Flow Cell Construction . . . . . . . .
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4 Bulk Electroporation Experiments
4.1 Experimental Setup . . . . . . . . . . . . .
4.2 Results . . . . . . . . . . . . . . . . . . . . .
4.3 Effect of the Laser on Measurements . . . .
4.4 Effect of Pulsing History on Measurements
4.5 Effect of the Actin Cortex on Poration . . .
4.6 Discussion . . . . . . . . . . . . . . . . . . .
4.7 Conclusion . . . . . . . . . . . . . . . . . .
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5 Nano-Electroporation Experiments
5.1 Methods . . . . . . . . . . . . . . . . . . . . .
5.2 Delivery and Dosage Control . . . . . . . . .
5.3 Nanoparticle Delivery . . . . . . . . . . . . .
5.4 Theory . . . . . . . . . . . . . . . . . . . . . .
5.4.1 Modeling NEP as an Electrical Circuit
5.4.2 Finite Element Simulations . . . . . .
5.5 Conclusions . . . . . . . . . . . . . . . . . . .
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6 Membrane Experiments
6.1 Theory . . . . . . . . . . . . . . . .
6.1.1 Surface Tension Term . . .
6.1.2 Curvature Term . . . . . .
6.1.3 Derivation of the PSD . . .
6.2 Experimental Methods . . . . . . .
6.3 Red Blood Cell Experiments . . .
6.3.1 Red Blood Cell Preparation
6.3.2 Results . . . . . . . . . . .
6.4 K562 Cell Experiments . . . . . . .
6.4.1 Electroporation . . . . . . .
6.4.2 Latrunculin A . . . . . . . .
6.4.3 Results . . . . . . . . . . .
6.5 Conclusions . . . . . . . . . . . . .
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7 Conclusion
131
7.1 Future Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
7.1.1 Evaluating Cell Size Effects on Electrical Breakdown of the Membrane 133
7.1.2 Nano-Electroporation (NEP) of Large Cell Populations . . . . . . . 133
ix
7.1.3
Evaluation of RBC Aging Using Large Scale Deformations . . . . . .
Bibliography
135
137
Appendices
A Manual for 3rd Optical Tweezer System
x
151
List of Figures
Figure
Page
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
Diagram Showing a Cell in an Electric Field . . . . . . . .
An Example of Poration in a K562 Cell . . . . . . . . . .
The Results of Molecular Dynamics Simulations by Tarek
Results from Krassowska . . . . . . . . . . . . . . . . . . .
Symmetric and Asymmetric Membrane Permeabilization .
Asymmetric Poration Observed by Djuzenova et al. . . . .
Effect of Poration on the Cytoskeleton . . . . . . . . . . .
Electrointernalization . . . . . . . . . . . . . . . . . . . .
An Example of MEP . . . . . . . . . . . . . . . . . . . . .
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2
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2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
Optical Trapping Diagram . . . . . . . . . . . . . . . . .
A diagram of a typical inverted light microscope . . . .
A simple optical trapping setup . . . . . . . . . . . . . .
The numerical aperture of a thin lens . . . . . . . . . .
Spherical aberration . . . . . . . . . . . . . . . . . . . .
Photodamage in E. coli as a function of laser wavelength
Optical Trapping Interferometry . . . . . . . . . . . . .
The Back Focal Planes of a Lens . . . . . . . . . . . . .
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26
28
29
31
32
34
39
40
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10
3D Piezoelectric Stage Calibration . . . . . . .
Optical Beampath . . . . . . . . . . . . . . . .
Back Focal Plane Detection Optical Beampath
Calibration curve for a 3 µm bead. . . . . . . .
Triangle Wave Calibration . . . . . . . . . . . .
Power Spectrum Calibration . . . . . . . . . . .
Confocal Microscopy . . . . . . . . . . . . . . .
Beam path in the 2nd and 3rd unit . . . . . . .
GUI of the 3rd unit . . . . . . . . . . . . . . .
Schematic of flow cell design . . . . . . . . . . .
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45
47
48
51
52
53
56
56
58
59
4.1
4.2
Diagram of the Bulk Electroporation Experiment . . . . . . . . . . . . . . .
Diagram of the Channel Used in the Bulk Electroporation Experiment . . .
62
63
xi
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4.3
4.4
4.5
4.6
4.7
4.8
Threshold Electroporation . . . . . . . . . . . . . . . . . . . . . . . . .
Bulk Electroporation Results . . . . . . . . . . . . . . . . . . . . . . .
Critical Transmembrane Potentials . . . . . . . . . . . . . . . . . . . .
Results of the Actin Cortex Experiment . . . . . . . . . . . . . . . . .
Electric Field Strength . . . . . . . . . . . . . . . . . . . . . . . . . . .
Example Of Poration Images for Cells Without Latrunculin Treatment
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65
66
68
74
75
75
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
NEP Device . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Comparison of NEP with BEP and MEP . . . . . . . . . . .
ODN Delivery: Dose Control with NEP . . . . . . . . . . . .
Leukemia Patient Cell ODN Transfection . . . . . . . . . . .
GAPDH Molecular Beacon Delivery: Dose Control with NEP
Delivery of QD’s by NEP, MEP and BEP . . . . . . . . . . .
Delivery of Plasmids by NEP, MEP and BEP . . . . . . . . .
Mesh Geometries for the Finite Element Analysis . . . . . . .
NEP Theory . . . . . . . . . . . . . . . . . . . . . . . . . . .
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82
83
85
86
87
89
91
95
96
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
6.10
6.11
6.12
6.13
6.14
6.15
6.16
The Results of Betz et al. . . . . . . . . . . . . . . . . . . . .
Membrane Fluctuation Experiment Diagram . . . . . . . . .
Red Blood Cell Results . . . . . . . . . . . . . . . . . . . . .
Example of 15 Data Sets Before Averaging . . . . . . . . . .
The data from the experimental RBC groups . . . . . . . . .
The data from the control RBC groups . . . . . . . . . . . . .
Red Blood Cell Results . . . . . . . . . . . . . . . . . . . . .
K562 Electroporation Fluctuation Experiment Results . . . .
K562 Fluctuation Results in RPMI 1640 Media . . . . . . . .
K562 Fluctuation Results From the Latrunculin Experiments
K562 Model Fit to Latrunculin Treated Cells . . . . . . . . .
K562 Experiment Results . . . . . . . . . . . . . . . . . . . .
K562 ATP Depletion Results . . . . . . . . . . . . . . . . . .
K562 Laser Power Results . . . . . . . . . . . . . . . . . . . .
K562 Cell Growth Cycle Results . . . . . . . . . . . . . . . .
K562 Cell Variation . . . . . . . . . . . . . . . . . . . . . . .
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101
109
112
113
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115
116
119
120
121
122
123
125
126
127
129
7.1
7.2
Centrifugal Loading of an NEP Chip . . . . . . . . . . . . . . . . . . . . . .
Two Potential RBC Deformation Experiments . . . . . . . . . . . . . . . .
134
136
xii
List of Tables
Table
Page
4.1
4.2
The average threshold fields required to induce poration . . . . . . . . . . .
Results of the pulsing history experiments . . . . . . . . . . . . . . . . . . .
68
71
5.1
Results of the finite element simulations. The final two rows are the time it
takes a quantum dot to traverse the length of the channel and the velocity
of the quantum dot as it exits the channel. . . . . . . . . . . . . . . . . . .
97
Results of the fits for the K562 membrane fluctuation experiments . . . . .
118
6.1
xiii
Acronyms
AOD acousto optic deflector. 35, 36, 43, 69
BEP bulk electroporation. 21, 60, 63, 79, 80, 84, 85, 88–90, 94, 98, 131
BFP back focal plane. 38–42, 48, 49, 100, 109, 110, 114, 117, 125, 128, 132, 135
BSA bovine serum albumin. 84
DI deionized. 81, 84
DIC differential interference contrast. 38
DPBS Dulbecco’s phosphate buffered saline. 64
EGDMA ethylene glycol dimethylacrylate. 81, 82
EOD electro optic deflector. 35, 36, 43
GAPDH glyceraldehyde 3-phosphate dehydrogenase. 85, 87
GFP green fluorescent protein. 18, 19, 89, 90
HEMA hydroxyethyl methacrylate. 81
MEP micro-electroporation. 22, 80, 84, 88–90, 94, 97, 98, 131
MES mouse embryonic stem. 64, 67
mRNA messenger RNA. 85, 87
NA numerical aperture. 24, 25, 28, 30, 31, 33, 54
NEP Nano-Electroporation. ix, xii, 54, 55, 57, 80–82, 84, 85, 87–90, 92, 94, 97, 98, 131–134
ODN oligodeoxynucleotide. 84, 85
PBS phosphate buffered saline. 70, 93, 111, 117, 121, 124
xiv
PDMS polydimethylsiloxane. 81
PI propidium iodide. 14, 15, 18, 46, 63, 64, 72, 84, 117, 133
PKC protein kinase C. 100, 101
PSD power spectral density. 100, 101, 106, 107
QPD quadrant photo-diode. 37, 39, 40, 48–50, 54, 100, 110
xv
Chapter 1
Electroporation: Historical
Summary
Cells, the basic building block of life, are surrounded by a cellular membrane, a selectively
permeable lipid bilayer which separates the cell interior from the external environment. This
membrane has small channels in it to allow the transport of smaller molecules and ions, but
in general, larger molecules cannot pass through it. Researchers attempting to insert larger
molecules into the cell interior first have to determine how to get those molecules through
the membrane of the cell. One common method of doing this is by electropermeabilization.
Electropermeabilization, or electroporation, as it is often also known, is a process in
which an applied external electric field creates a reversible breakdown of a cell membrane.
Electropermeabilization was first observed in the laboratory of Alex Hope in the 1960’s [1],
and its discovery has had a major impact in all manner of cellular research fields. Along
with other techniques, such as microinjection and viral vectors, electropermeabilization is a
common method of transfecting cells with drugs, genes or dyes for a variety of experiments
in a laboratory setting. Although to date, viruses are by far the most efficient method
of experimentally transfecting cells with genes, electropermeabilization is still extremely
popular in gene therapy research, since virus based techniques are generally regarded to be
unsafe due to the potential for immune system responses and viral mutations [2–5].
Despite its common use in laboratories across the world, the physics behind electroporation are still poorly understood [2, 6–8]. The accepted model of events is to treat the
cell membrane as an insulating spherical shell which isolates the cell interior from its exte1
rior environment [2, 6, 9–11]. Both the cell interior and the exterior are good conductors.
Permeabilization occurs when the applied electric field induces an electric potential across
the cell membrane (hereafter referred to as the ”transmembrane potential”) that exceeds a
certain threshold ”breakdown” value Vperm . The value of Vperm is a matter of some debate,
but measured values fall in a range between 200 mV and 1.5 V [6, 9]. The cell membrane is
typically approximately 6 nm in thickness [1], so the electric field strength across the membrane is on the order of 108 V/m. Many bulk dielectric materials will experience breakdown
at these kinds of electric field strengths [1].
Figure 1.1: The geometry of the cell described in Eq. (1.2). The angle θ is the angle with
the axis of the applied electric field E.
The transmembrane potential can be calculated using Laplace’s equation under the
quasi-static approximation. At time t = 0, an electric potential V is applied across parallel
plate electrodes separated by a distance x, creating an electric field E = V /x in the medium,
where x is the spacing of the electrodes. Assuming both the cell interior and exterior are
conductors, the induced transmembrane potential then becomes:
Vinduced = 1.5f grEcos(θ)(1 − e−t/τ )
(1.1)
where f is a geometrical factor that is 1 for spheres, r is the radius of the cell membrane
and τ is the time constant for charging the cell membranes capacitance [2, 6]. The factor
2
g allows for correction for non-insulating membranes and is given by
1
1+Gm r(0.5ρe +ρi )
where
Gm is the membrane conductance per unit area, and the resistivity of the cell interior and
exterior are ρi and ρe , respectively [6]. In most cases, the conductivity of the cell membrane
is small, and g can be taken to be 1. When g and f are taken to be 1, this equation is
known as the Schwan equation.
In addition to the induced transmembrane potential, the cell also has a resting transmembrane potential Vrest . Adding this to the induced potential yields the total transmembrane potential as:
VT M = 1.5f grEcos(θ)(1 − e−t/τ ) + Vrest .
(1.2)
It is important to note that this equation is not valid once permeabilization has occurred as,
at that point, the assumption that the cell membrane is an insulator ceases to be true. The
conductivity of the cell membrane increases sharply as a consequence of permeabilization [6].
Eq. (1.2) predicts that the maximum transmembrane potential of a cell in an applied
field E depends linearly on the cell radius r. This is because, since the conductivity of
the cell membrane is small compared to the conductivity of the cell interior, most of the
potential dropped across the cell is dropped across the membrane. As a result, the interior of
the cell is shielded from the applied field. In the case of a membrane with zero conductivity,
the field in the cell is also zero. As the cell gets larger and larger, the shielded region
also increases, and thus, in order for the line integral of the electric field between the two
electrodes to remain constant, the transmembrane potential must increase linearly with r.
Eq. (1.2) was tested directly by Hibino et al. [12]. By binding the voltage sensitive
fluorescent dye RH292 to the cellular membrane of sea urchin eggs, they were able to
visualize the transmembrane potential using fluorescence microscopy. By imaging cells
with submicrosecond time resolution, they were able to confirm the cos(θ) dependence of
the transmembrane potential, as well as the timing constant τ , which they found to be 1.2 µs
in sea water. In addition, they found that the transmembrane potential was asymmetric.
This is due to the resting transmembrane potential of the cell, which points in the radial
direction and thus reinforces the induced transmembrane potential on one side of the cell,
3
Figure 1.2: An example of electropermeabilization in a K562 cell. In this experiment PI
dye was placed in solution with the cell. Following permeabilization the dye leaks into the
cell and lights up. Note that poration occurs only at the poles, agreeing with the prediction
of Eq. (1.2) that the transmembrane potential is largest at the poles.
while it opposes it on the other side of the cell.
Teissié et al. broke electropermeabilization up into 5 steps [8]:
1. Induction step: The external field induces an increase in the transmembrane potential
until some critical value is reached.
2. Expansion step: Permeablization of the cell membrane begins and continues to increase as long as the transmembrane potential is kept over the critical value.
3. Stabilization step: After the applied field decreases, as soon as the transmembrane
potential is lower than the threshold value, a stabilization process takes place.
4. Resealing step: A slow resealing then occurs on the scale of seconds and minutes. If
the applied field is too large or the pulse is too long, this step may not occur, leading
to cell lysis.
5. Memory effect: Cell viability is preserved, and the membrane reseals, but some internal features may take several hours to return to normal functioning.
4
1.1 Mechanism of Permeabilization
Several models have been offered to describe what occurs in the electropermeabilization
process. The most commonly accepted explanation is that, during electropermeabilization,
small pores open in the cell membrane to allow electric current to pass through the cell and
thus minimize the free energy of the membrane (hence the common term electroporation) [7,
10, 11]. Under this model, the appearance of pores in the cell membrane is a phase change,
with the creation of pores being similar to the nucleation of vapor bubbles during the boiling
of a fluid. Before looking in detail at why this is the consensus picture, it is important to
discuss several important results from planar membrane experiments.
1.1.1 Planar Membrane Experiments
Artificially created lipid planar membranes have been used in a number of experiments to
gain further insight into the process of electroporation [13, 14]. These have a few advantages
over using cells [11]. In planar membrane experiments with pulses longer than the membrane charging time τ , all the voltage between electrodes is dropped across the membrane
prior to poration. Once poration occurs, only some fraction of the voltage drop will be
across the membrane. The charging time for planar membranes is generally on the order of
microseconds. Planar membranes created in the lab are also far more homogeneous than
cells, where the membrane is embedded with a large number of proteins.
In the simplest experiment, a membrane in a buffer solution is suspended across an
aperture and placed between two electrodes, and a potential difference is applied across
them. Measurements of the transmembrane current find that, after the application of
a square voltage pulse, the current increases to a steady state value. After this time,
large fluctuations in the current occur, until, finally, after some time, the current reaches
a final saturation level [13]. This saturation level corresponds to irreversible membrane
breakdown, a fact which can be confirmed by lowering the voltage and confirming that the
current is the same as the situation where no membrane is present. The time it takes for this
saturation current to be reached is thus defined as the membrane lifetime tm . Repeating the
5
experiment with a new membrane reproduces the qualitative behavior of the experiment,
but the membrane lifetime will, in general, be different. This critical result suggests that,
even for an artificial planar membrane, the electroporation process is stochastic [11]. In
general, the exact behavior of a single membrane cannot be predicted based on previous
measurements.
One question we can ask of electropermeabilization is whether or not the phenomenon
is dominated by large scale deformations of the membrane, such as a change in membrane
thickness [11]. The presence of such deformations in thickness can be determined by measuring the membrane capacitance, much like in the case of a parallel plate capacitor. The
capacitance of the membrane Cm changes rapidly by a small amount during experiments.
Specifically, it was found that:
∆Cm = Cm,0 [1 + αV 2 ],
(1.3)
where V is the voltage applied across the electrodes, α = 0.02V −2 , Cm,0 is the rest capacitance of the membrane and ∆Cm is the change in the membrane capacitance induced by
that voltage [11, 15]. This result is important, because it demonstrates that the thickness
of the membrane does not change by more than a few percent throughout the process [11].
This puts restrictions on what models can account for the permeabilization process.
1.1.2 Electromechanical Collapse
One of the earliest models proposed to explain electropermeabilization is electromechanical
collapse [16]. The following description of the model follows that of Weaver [11]. Electromechanical collapse treats the membrane as a capacitor filled with an elastic dielectric
material. When an electric field is applied, the capacitor begins to charge, and the dielectric
begins to compress. The pressure on the membrane caused by the field is the same pressure
as the pressure between two plates in a parallel plate capacitor: pe = Vm2 /2h2 where Vm is
the transmembrane potential, is the dielectric constant inside the membrane and h is the
6
membrane thickness. The elastic force per unit area pm is given by:
Z
h
pm = −Ym
h0
∆h 0
dh
h0
(1.4)
where h is the membrane thickness, h0 is the membrane thickness for Vm = 0, ∆h is the
thickness deformation and Ym is the Young’s modulus of the membrane. The equilibrium
between these two pressures occurs at:
Ym Log(
h0
V2
) = m2 .
h
2h
2 = 0.368
This equation has no roots if Vm > Vmc where Vmc is given by Vmc
(1.5)
Ym h20
.
Using mea-
sured values for the various constants involved, the equation gives a value of Vmc of about 5
V, which is higher than what is observed. More importantly, though, the electromechanical
collapse theory is inconsistent with experiment for two primary reasons. First of all, the
theory predicts changes in the membrane thickness h on the order of 39% [11], which, as
mentioned in the previous section, are not observed in experiment. Secondly, the model
predicts a value for the critical transmembrane potential of about 5 V, which is much larger
than the observed value of about 1 V. Most importantly however, the electromechanical
collapse model is deterministic in the case of planar lipid membranes. Experimental results, however are decidedly stochastic. As soon as the transmembrane voltage exceeds
the predicted critical value, the membrane should reproducibly become permeable, but,
in fact, what is observed is that the membrane exists in a non-permeable state for some
indeterminate amount of time that varies from experiment to experiment.
1.1.3 Electroporation
The most frequently used model for the permeabilization assumes that, during permeabilization, small pores open up in the cell membrane, a process called electroporation. In fact,
this model is so widely used that the terms electropermeabilization and electroporation are
often used interchangeably in the literature [6]. No other model of permeabilization yet
proposed fully accounts for all the key features of experimental results. Despite this, it is
important to note that the evidence for electroporation is largely indirect. The small size of
7
the pores involved, along with the short time scale of permeabilization, makes direct imaging of the pores difficult. Pores have been imaged using electron microscopy after poration
experiments have been conducted [17], but those results are more likely artifacts of the
imaging process than evidence of physical pores resulting from electropermeabilization [6].
Weaver describes electroporation as follows [11]: Poration can be thought of as a phase
change in the cell membrane, and the creation of pores is a type of nucleation. Assuming
that the membrane of the cell has a surface tension associated with it, then the creation of
the cell membrane requires work. Introducing a pore works to reduce the free energy of the
system by an amount πr2 Γ (where Γ is the energy per unit area of the membrane, and r is
the pore radius) by decreasing the membrane area. This decrease in free energy is offset by
the line tension 2γπr (where γ is the energy per unit length along the circumference of the
pore) required to insert a hole into the membrane. The work required to create a pore of
size r in the cell membrane, at a transmembrane potential of zero, is then given by:
∆W = 2γπr − πr2 Γ.
(1.6)
For small pore sizes, the line tension is larger than the energy gained by the reduction in
area of the cell membrane, which creates a large barrier to the creation of pores. As a result
of this large barrier, pore formation cannot occur at zero transmembrane potential.
In the presence of an external electric field, the membrane acquires a transmembrane
potential and acts as a capacitor. The creation of pores in the membrane then alters the
stored energy of the capacitor by changing the dielectric constant of portions of the capacitor
from that of the lipids to that of water. This introduces a third term in above equation,
changing it to:
∆W = 2γπr − πr2 Γ − 0.5∆Ca Vm2 πr2
(1.7)
where ∆Ca is the change in capacitance per unit area resulting from a switch in dielectric
constant from that of the lipid to that of water. Since ∆Ca is positive, this third term
serves to lower the barrier to pore formation significantly. Stable pores have a minimum
possible radius given by the point at which ∆W is equal to zero.
8
Unlike the breakdown model, electroporation predicts a stochastic process, which is
consistent with the results seen in bilayer membrane experiments [11]. For small values of
Vm , thermal fluctuations are expected to provide the energy needed to exceed the barrier
to pore formation.
Theoretical Treatment of Pore Formation
Attempts to model electroporation using molecular dynamics simulations are difficult, primarily due to the large processing power required. Simulations are forced to restrict both
the size of the system simulated and the duration of the simulation. Tarek has perfomed
the most complete simulation to date, simulating the effects of an applied electric field on
a lipid bilayer for 10 ns [7]. Tarek found that: “The simulations have evidenced that the
electroporation process takes place in two stages. First, water molecules organized in single
file like wires penetrate the hydrophobic core of the bilayer. This water penetration is apparently favored by local defects in the lipid headgroup region. Then, the water wires grow
in length and expand into water-filled pores. These pores are stabilized by lipid headgroups
that migrate from the membrane-water interface to the middle of the bilayer.” [7] Tarek
found that, once the applied field was removed, the lipid bilayer resealed itself within a few
nanoseconds.
Limitations in computer processing make molecular dynamics simulation of electroporation over long timescales or for large systems impractical. Krassowska and Filev modeled
the pore density resulting from electroporation using the differential equation:
N
dN
2
= αe(Vm /Vmc ) (1 −
)
dt
Neq (Vm )
(1.8)
where N (t, θ) is the pore density, θ is the same as in Fig. 1.1, α is a constant, Vmc is the
critical transmembrane potential and Neq is the equilibrium pore density given by:
2
Neq = N0 eq(Vm /Vmc )
(1.9)
where q is a constant [10]. The differential equation was then solved based on the initial
condition that N (0, θ) = 0 (no pores at no voltage). This equation not only describes pore
9
Figure 1.3: The results of Tarek’s molecular dynamics simulations. The equilibrium bilayer
is shown in (a). In (b) water wires (O red, H white) begin to appear within the bilayer. In
(c) these wires have expanded into pores. The images in (d) and (e) show the topology of the
pores from the top and the side respectively. Reprinted from Biophysical Journal, Vol 88,
Mounir Tarek, Membrane Electroporation: A Molecular Dynamics Simulation, 4045-4053,
Copyright (2005), with permission from Elsevier [7].
formation, but the resealing process as well, as, once the field is turned off,
dN
dt
becomes
negative, and the pore density begins to decrease. Pore size for the jth pore was modeled
as:
drj
D
Vm2 Fmax
r∗ 1
=
(
+ 4β( )4 − 2πγr + 2πσef f r)
dt
kT 1 + rh /(r + rt )
r r
(1.10)
where the above equation is valid for r > r∗ where r∗ is minimum radius of hydrophilic
pores. In the above equation, D is a diffusion coefficient, Fmax is the maximum electric
force for Vm = 1V , rh and rt are constants, β is the steric repulsion energy, γ is the edge
energy and σef f is the membranes effective surface tension. Values for all these constants
can be found in Krassowska and Filev.
Krassowska and Filevs model finds that when a cell is exposed to a 1 ms pulse, pore
nucleation occurs on a time scale of microseconds. In simulations, pore nucleation was
more or less complete after 1.43 µs. After pore formation was complete, pores continued
to expand in size for the duration of the 1 ms pulse, although, by the end of the pulse,
additional changes in pore sizes were small. Since the transmembrane potential peaks after
10
Figure 1.4: Some results from Krassowska and Filevs model of single cell electroporation.
a) The transmembrane potential as a function of θ at various times. The dotted line
corresponds to the steady state solution given by Eq. (1.2). b) Number of all pores K θ
θ as a function of θ at 1 ms. Note the different scales for K θ and
and all large pores Klg
θ . c) Radii of selected pores at the depolarized pole of the cell. Note that pores fall
Klg
into two distinct groups by 1 ms, small pores and large pores. Adapted from Biophysical
Journal, Vol 92, Krassowska and Filev, Modeling Electroporation in a Single Cell, Pages
No. 404-417, Copyright (2007), with permission from Elsevier [10].
the membrane capacitor finishes charging (which happens within microseconds), the pore
evolution is heavily driven by the cells surface tension. As pores grow, the overall surface
tension of the cell decreases, lowering system energy. Pores that were produced by the
model were divided into two groups, large pores and small pores, as shown in Fig. 1.4 c.
Small pores were those pores whose radius was approximately 1 nm, while large pores were
those pores whose radius was much larger than 1 nm.
Since the transmembrane potential depends on θ (Fig. 1.4 a, Eq. (1.2)), the angle with
the applied electric field, the poration starts at the poles of the cell, as one might expect.
Poration continues throughout those portions of the membrane where the transmembrane
potential exceeds the threshold value. In the simulations, there are no pores in regions
11
near the equator, as the transmembrane potential never reaches the threshold value. The
model found that, somewhat counterintuitively, very few large pores existed near the poles
of the cell. Instead, small pores dominated near the poles, and most of the large pores were
located near the edge of the porated region, nearer the equator.
The model predicted that, as expected, the number of pores increases as the applied
field increases, but that, except for those fields very close to the poration threshold, this
was due almost exclusively to an increase in the size of the small pore population. The
large pore population levels off and does not increase after a certain value of the applied
field (roughly 25 kV/m).
Following the pulse, pore sizes decrease rapidly, leading to the elimination of the large
pore population within microseconds. Pore resealing takes longer, on the order of seconds.
This matches well with the experimental observation that, while the membrane is generally
only permeable to larger molecules for the duration of the pulse, the membrane may remain
permeable to smaller molecules for several seconds afterwards [10, 18–20].
1.2 Factors Affecting Permeabilization Threshold
Cell membranes generally permeabilize at a transmembrane potential of around 1 V; however, this threshold value can be affected by a number of different factors. Somewhat
surprisingly, it is not affected strongly by the type of cell, as cells from entirely different
kingdoms exhibit the same 1 V permeabilization threshold at room temperature [6]. Cell
permeabilization can be evaluated by the penetration of flourescent dyes into the cell interior, the tendency of chemotactic bacteria (bacteria which are attracted to certain chemicals
usually found in the cell interior) to gather near permeabilized portions of the cell membrane
or by the electrofusion of two cells in contact (see Section 1.6).
The permeabilization threshold is greatly affected by temperature. Coster and Zimmermann conducted repeated poration experiments on a single Valonia utricularis cell at a
variety of temperatures over the course of 5 hours and found that the breakdown voltage
varies from a value of about 1 V at 4 ◦C to a value of about 640 mV at 30 ◦C [21].
12
The osmotic pressure on the cell membrane can also affect the permeabilization threshold, a fact which is unsurprising in the light of Eq. (1.6). Zimmermann et al. measured the
critical breakdown potential of Valonia utricularis cells as a function of turgor pressure and
found that the critical potential decreases linearly with the pressure [22]. This fact may explain why bacteria experience permeabilization at significantly lower thresholds than what
is predicted by theory [6].
The stage of the cell growth cycle also appears to affect permeabilization threshold [6].
Zimmermann et al. found that the permeabilization threshold of Friend cells (mouse erythroblasts transformed by the Friend virus) depended on the cell growth cycle [23]. E. coli
permeabilization thresholds also depended on the cell growth cycle, with cells exhibiting an
increase in the average permeabilization threshold during the transition from the logarithmic to the stationary growth phase [23]. The mechanism for this observation is not well
understood but may be due to changes in the cell cytoskeleton or membrane fluidity [6].
In most cells, the ratio of lipids to proteins in the cell membrane is approximately
1:1 [6]. Adjusting this ratio appears to affect the permeabilization threshold. In developing
chloroplasts, the permeabilization threshold is observed to be smaller by 20% [24]. Since
developing chloroplasts have higher protein content membranes, this suggests that breakdown may occur at the protein/lipid junctions [6]. This is supported by the observation
that plant vacuoles, which have a lower protein content than the mentioned 1:1 ratio, have
a higher permeabilization threshold [6, 25].
1.3 Asymmetric Breakdown
If the resting transmembrane potential Vrest is small compared to the induced potential,
then Eq. (1.2) implies that membrane breakdown should be symmetrical; that is, breakdown
should occur in both hemispheres of a cell exposed to a pulse exceeding the threshold value.
On the other hand, if Vrest is large compared to the induced field, then one expects to
observe asymmetric breakdown of only one hemisphere. Assuming that the rest electric
field in the membrane points inward towards the center of the cell (which in the usual
13
Figure 1.5: Diagram showing symmetric (a) and asymmetric (b) membrane permeabilization. The applied electric field E adds with the cells rest field (represented by the arrows)
near the anode but subtracts near the cathode.
case is negatively charged), then the induced field and the rest field add in the hemisphere
facing the anode but subtract in the side facing the cathode [6]. As a result, in the case
of asymmetric breakdown, we expect to see poration on the anode-facing side but not on
the cathode-facing side. Once poration occurs on the anode side of the cell, however, the
transmembrane potential across the membrane on cathode side of the cell will increase as
a greater portion of the applied voltage is dropped across that side, once the anode side
becomes conductive.
Several experiments have observed asymmetric breakdown of the cell membrane during
permeabilization and appear to confirm its dependence on the cells resting transmembrane
potential. Asymmetric breakdown of the anode side has been observed in a variety of experiments across a variety of cell types [6]. Djuzenova et al. observed the asymmetry of uptake
of propidium iodide (PI) dye in murine myeloma cells while adjusting the concentration
of K+ ions in the surrounding media [26]. The rest transmembrane potential of the cell
depends on this concentration. At low K+ concentrations, the membrane transmembrane
potential is expected to be large, while at high K+ concentrations, the rest transmembrane
potential approaches 0. Djuzenova et al. found that, as expected, at low K+ concentrations,
the cells experienced strongly asymmetric dye uptake on the anode side of the cell, while
at high concentrations, the dye uptake became symmetrical (see Fig. 1.6). Mehrle et al.
used chemotactic bacteria to observe poration in isolated plant vacuoles, which are unique
in being positively charged with respect to their suspension medium, and found that they
14
exhibited poration in the cathode facing side [25]. When the polarity of the electrodes in
this experiment was reversed, the result was breakdown in the other hemisphere (now facing
the new cathode).
Figure 1.6: Asymmetric uptake of PI dye in murine myeloma cells. The left image takes
place in 30 mM NaCL (no K+ ions), while the right image takes place in 30 mM KCl. The
left image corresponds to a high rest transmembrane potential, while the right corresponds
to a low rest transmembrane potential. Reprinted from Biochimica et Biophysica Acta Biomembranes, Vol 1284, Djuzenova et al., Effect of medium conductivity and composition
on the uptake of propidium iodide into electropermeabilized myeloma cells, Pages No. 143152, Copyright (1996), with permission from Elsevier [26].
Despite these results, asymmetric breakdown is not a straightforward phenomenon.
Sowers et al. observed that in erythrocyte ghosts—red blood cells that have lost their
hemoglobin—breakdown was observed to occur preferentially in the cathode-facing hemisphere, even though these cells should have no rest transmembrane potential [6, 27]. Zimmermann states that, in mouse myeloma cells, asymmetry of breakdown was found to depend on the osmolarity of the suspension medium [6]. For most such cells in a iso-osmolar
medium, PI dye preferentially entered the cell through the anodic side while, in a hypoosmolar solution, the cathodic side was preferred. In the case of mouse L-cells, however,
the reverse occurred. In poorly conductive media, breakdown was symmetric in all cases.
These osmotic effects could be explained if the rest transmembrane potential depends on
15
the osmolarity if the solution. It is known that, for plant cells, the magnitude and direction
of the rest transmembrane field depend on the membrane tension (and consequently on the
osmolarity of the solution) [28]. It is possible a similar effect is in place in other cells [6].
It is also possible to imagine situations where poration in fact occurs on both sides
of the membrane but is only detected on one side. The model of Krassowska and Filev
predicts that, even when poration occurs on both the anode side and the cathode side, the
results will be asymmetrical, with the anode side possessing more pores while the cathode
side possesses larger pores [10]. This could manifest in dye entering the cell preferentially
through the anode side for small dyes, while larger dyes may only enter through the cathode
side.
1.4 Effect of the Cytoskeleton
In order for cells to function properly, they need to be able to maintain their shape, interact mechanically with their environment and be properly structured internally. They
need to be able to rearrange internal components as they grow and adapt to changing circumstances [29]. Eukaryotic cells achieve these functions through a complex network of
filaments known as the cytoskeleton. The cytoskeleton is a dynamic structure composed
of three primary components, intermediate filaments, microtubules and actin filaments.
Generally speaking, intermediate filaments provide the cell with mechanical strength, while
microtubules determine the positions of cell organelles and direct intracellular transport.
Actin filaments, arranged in a mesh known as the actin cortex, determine the shape of the
cell membrane.
As the cytoskeleton interacts with the cell membrane, it is reasonable to expect that
it may affect the electroporation process. The conventional description of electroporation
assumes that the cell interior is a homogeneous conductor. As a result the cytoskeleton,
which defines the cells internal structure, may lead to deviations from theory in experimental
observations [30].
The impact of tubulin, the primary component of microtubules, on electroporation in
16
Chinese hamster ovary (CHO) cells was examined by Rols and Teissie [31]. Treatment
of the cells with colchicine, known to depolymerise the microtubules of CHO, cells was
found to have no measurable effect on the formation of pores or on their expansion but did
substantially increase the speed of the resealing process. Similar results were found when
cells were undergoing mitosis, when tubulin is rearranged in mitotic spindles [32]. When
the spectrin-actin network of erythrocytes was disrupted by heat, however, a small change
in critical transmembrane potential from 1.0 to 1.2 kV/cm was observed [31].
Electroporation has been observed to disrupt the cytoskeleton on several occasions [30].
Harkin and Hay examined the effects of electoroporation on chick embryo corneal fibroblasts
suspended in a collagen gel. They found that, following electroporation, the cells displayed
uncoordinated pseudopodia and were unable to migrate effectively [33]. They attributed
this to depolymerization of the cells microtubules or the perinuclear collapse of vimentin
filaments caused by Ca2+ ions from the culture media. They found that conducting the
experiment instead in a buffer which resembled the cellular interior, the cells maintained
the cytoskeleton, and the cells continued to migrate. Kanthou et al. observed the impact
of electroporation on the cystoskeleton of endothelial cells in M199 culture medium using
fluorescent dyes. They found that the actin network and the microtubules of the cytoskeleton were reversibly disorganized [34]. Reorganization took roughly 1 hour. Although the
cytoskeleton was disorganized, they found that cytoskeletal proteins were not degraded by
the poration process.
1.5 Transfection of Large Molecules
Although smaller dyes and ions can enter the cell directly as a result of electroporation, the
majority of interesting molecules are considerably larger. DNA fragments, quantum dots
and other nanoparticles, which are much larger than dyes and ions, are unable to diffuse
directly through the cell membrane during electroporation. These molecules can still enter
the cytosol following electroporation in an endocytosis like process that Zimmermann calls
electrointernalization [6].
17
Figure 1.7: The effect of electroporation on the cytoskeleton. a) Microtubule structures in
a cell prior to electroporation. b) Microtubule structures immediately after poration by a 60
V pulse. Fine features are lost, and fluorescence becomes more diffuse as the cytoskeleton
breaks down. Adapted by permission from the American Association for Cancer Research:
Kanthou et al., The endothelial cytoskeleton as a target of electroporation-based therapies,
Molecular Cancer Therapies, 2006, vol. 5 issue 12, pages 3145-3152, doi: 10.1158/15357163.MCT-06-0410 [34].
Following permeabilization, portions of the cell membrane can be engulfed by the cytosol
and incorporated into the cell interior, a process called endocytosis [6]. During this process,
large molecules such as DNA fragments, which have adhered to the membrane, may also
be internalized. Internalization of these molecules can be observed by labeling them with
fluorescent dyes [6, 35]. When small dyes, such as PI, diffuse through the cell membrane,
they are evenly distributed through the cell. By contrast, when large molecules are internalized by endocytosis, fluorescence is observed to occur in patches or adhered to the inner
cell membrane. This indicates that the internalized molecules are contained in complexes
together with the internalized membrane sections [6, 36]. Internalization of large molecules
is most effectively achieved by pulses that are long in duration, in the ms range [30, 35].
Golzio et al. looked at this process extensively using Chinese hamster ovary cells and
green fluorescent protein (GFP) plasmids stained with TOTO-1 dye [35]. GFP plasmids are
pieces of DNA that code for green fluorescent protein. Once they enter a cell, they migrate
towards the cell nucleus, at which point the cell begins producing GFP, which can be seen
using fluorescence microscopy. Golzio et al. found that, following electropermeabilization,
the plasmids form localized aggregates on the cell membrane but only on the side of the cell
facing the cathode. This is consistent with the explanation that electrophoretic forces bring
18
Figure 1.8: The results of electrointernalization experiments by the Golzio group. a)
Plasmid flourescence 1 s after electroporation. The DNA is stuck to the outside of the
membrane. b) Plasmid fluorescence 30 minutes after poration. The DNA is now internalized
but exists in discrete pockets instead of being evenly diffused throughout the cell. c) GFP
fluorescence in a single cell after 24 hours, demonstrating the plasmids eventually worked
their way to the nucleus and were transcribed by the cell. Adapted from Golzio et al., Direct
visualization at the single-cell level of electrically mediated gene delivery, PNAS, vol. 99,
pages 1292-1297, copyright (2002) National Academy of Sciences, USA [35]
the negatively charged DNA particles into contact with the permeabilized cell membrane.
The aggregates cannot be destroyed by reverse polarity pulses. The plasmids enter the
cytosol within about 30 minutes, and within 24 hours, GFP expression is observed.
19
1.6 Electrofusion
During reversible electroporation, pores form in the cell membrane which eventually reseal,
but if two cells held in contact with each other (for example, through dielectrophoresis) are
porated, then their membranes can fuse. If this happens, the two cells can join together
topologically, leaving only a single pore that provides a connection between the cytoplasm
of the two cells. This process is called electrofusion and essentially joins two cells together
to form one larger cell. In order for the fusion to occur, contact between the two membranes
must be made within a few minutes of poration [30]. Electrofusion has a higher required
critical voltage than conventional electroporation [30] and is sometimes used as an indicator
of whether or not electroporation has occurred, much like transfection of dyes [37]. It is
also an important step in cloning procedures for mammals [1].
1.7 Resealing and Memory
The speed of the resealing process depends strongly on temperature. Cells kept at 4◦ C can
remain permeable for several hours [8]. Conversely, at high temperatures (above 30◦ C in
mammalian cells), the speed of resealing increases [6]. Cells suffering from ATP depletion
also have a slower resealing process [38]. These facts, together with the cytoskeleton’s impact
on resealing times, suggest that pore resealing is the result of active membrane processes.
The temperature dependence of the pore resealing process is likely strongly influenced by
the fact that the various enzymes in the cell are most active at higher temperatures [6].
Resealing also depends on the fluidity of the cell membrane. Zimmermann observes resealing
of artificial planar lipid bilayers (which have very high membrane fluidity) occurs on a
microsecond timescale [23]. By comparison, resealing of cells can take minutes [6, 8].
Even after the cell membrane has resealed, it may be sometime before the cell completely
returns to its normal pre-pulse state. These so-called ”memory” effects can persist for several
hours [8]. Two examples of such effects that have already been discussed in previous sections
are large disorganizations of the cytoskeletal network and the endocytosis of permeabilized
sections of the cell membrane.
20
Another example is “flip flop” of phospholipids. The cell membrane is a bilayer of phospholipids and proteins. Initially, in many cells, phospholipids are distributed asymmetrically
between the two monolayers of the membrane [6]. Electroporation leads to greatly enhanced
mobility of phospholipids between the two layers of the membrane, which leads to a partial
disturbance of this asymmetry that can last up to an hour [39, 40]. This can be easily
understood under the electroporation model. In cell membranes, phospholipids are very
mobile in the lateral directions, hopping 1 nm on average once every microsecond [8]. If
the membrane has toroidal pores, only short lateral movements along the inner surface are
required to place a phospholipid in a region of the membrane that will become the exterior
after pores are resealed [11].
Electroporation also affects surface proteins on the cell membrane. Antibody staining
of surface immunoglobulin is reduced by strong applied field pulses (4 kV/cm 3 pulses of
5 µs duration at 4◦ C) in lipopolysaccharide stimulated B lymphoblasts [41]. This could
be due to either electrointernalization of the associated proteins or electric field induced
conformational changes in the proteins [6].
1.8 Micro Electroporation
Electroporation is a common laboratory technique that is frequently used for a variety of
biological experiments. The vast majority of electroporation done in laboratories around
the world is bulk electroporation (BEP). In BEP, a solution of free floating cells is simply
placed between two electrodes (usually parallel plate electrodes), and then an electric pulse
is applied, permeabilizing the cell membranes. Commercial apparatuses exist to fill the need
for conducting BEP quickly and easily. A typical commercial BEP apparatus then simply
consists of a cuvette with parallel electrodes hooked up to a pulsing power supply.
This system, though widely used, has several downsides [42]:
• Eq.(1.2) predicts that large cells will porate at lower values of applied field than small
cells. This leads to a situation where large cells are prone to being exposed to field
that are too large and thus lysing, and small cells being exposed to fields that are too
21
Figure 1.9: A diagram showing the MEP setup used by Kurosawa. A cell is held in place
over a micropore in an insulating membrane. Reprinted from Measurement Science and
Technology, Vol 17, Kurosawa et al., Electroporation through a micro-fabricated orifice and
its application to the measurement of cell response to external stimuli, Pages No. 3127-3133,
Copyright (2006), with permission from IOP Publishing [42]
small and thus not porating at all.
• Non-uniformities in the field caused by local features (such as other cells) can lead to
potentially large differences in the local electric field each cell sees.
• For non-spherical cells, the transmembrane potential depends on the cell shape and
orientation.
• For reasonably sized cuvette (several mm across), high voltages are required (several
hundred volts). This causes electrolysis, leading to large bubbles in the solution which
distort the electric field.
All of these factors conspire to decrease both the efficiency of transfection and also the
degree to which the dosage of transfection agents can be controlled.
A number of potential solutions to these issues exist, including capillaries, micropore
filters and micro-electro-mechanical systems [42]; however, the most relevant solution to the
rest of this work is micro-electroporation (MEP). MEP works by placing a cell next to a
micrometer-sized orifice that is smaller than the cell itself. The cell can be manipulated into
contact with the orifice using electrophoresis or vacuum loading [42, 43]. This orifice serves
22
to constrict the local electric fields, leading to high local field strengths near the cell. This
has the benefit of guaranteeing that, for a given pulse, the local electric field near the cell,
as well as the induced transmembrane potential, is always the same. Additionally, since the
local fields are so high, very low applied voltages (as low as 1 V) are required to porate the
cell, leading to minimal joule heating and electrolysis [42, 43].
1.9 Outline of This Work
The rest of this work will describe the results of experiments where optical trapping techniques have been used to examine various properties of the cell membrane. Chapter 2 will
provide a brief overview of the optical trapping technology which will be used in the experiments that follow. Chapter 3 will provide a description of the experimental setups and
techniques used in these experiments, including a description of the three optical trapping
setups used. In Chapter 4, we will test Eq. 1.2 and the assumption that cells porate at
a fixed transmembrane potential. Chapter 5 will introduce nano-electroporation, a novel
method of reproducibly transfecting cells with precise doses and allows for the transfection
of large molecules that bypasses endocytosis. Finally, in Chapter 6, we will use laser position detection to measure the thermal fluctuations of the cell membrane. This will allow
us to extract information on the membranes surface tension, bending rigidity and the cells’
effective viscosity. We will use this technique to measure the effects of ascorbic acid on red
blood cell aging. We will also attempt to determine the differences between the mechanics
of red blood cell membranes and those of K562 cells, which, unlike red blood cells, are
bound to an actin cortex.
23
Chapter 2
Optical Trapping
Optical trapping was pioneered by Arthur Ashkin in the 1970’s and 1980’s [44]. In 1970,
he first demonstrated that lasers could levitate micron-sized particles [45], and, by 1971, he
developed a stable three dimensional trap based on counter propagating beams [46]. The
single beam optical gradient trap, commonly referred to as “optical tweezers”, was first
demonstrated by Ashkin and Chu in 1985 [47] and is the basis for modern biological optical
trapping systems. Ashkin went on to use optical trapping in a wide range of experiments,
including the cooling and trapping of neutral atoms [48], as well as the manipulation of live
cells [49], bacteria [50], viruses [50] and cell organelles [51].
Since the invention of optical tweezers, a number of techniques for measuring the positions of trapped particles with nanometer precision have been developed [52–56]. By
assuming that the trap follows Hooke’s law, a position measurement can then be used to
measure applied forces. The ability of optical tweezers to exert piconewton forces on micronsized objects, and accurately measure their positions and the forces applied, has lead to its
use as a tool in a large number of interesting biophysics experiments, such as assessing the
mechanical properties of biopolymers, such as DNA [57–60], colloids [44], measuring the
viscoelastic properties of cells [61], and characterizing molecular motors [44, 52, 62].
2.1 Principles of Trapping
Single beam optical traps are created by passing a laser through a high numerical aperture
(NA) lens. A dielectric particle in the vicinity of the laser focus experiences an optical force,
24
which is usually decomposed into two components: a scattering force which points in the
direction of the laser propagation and a gradient force which points in the direction of the
lasers intensity gradient [44].
The scattering force is the more intuitive of the two. Incoming light which strikes the
particle scatters in a variety of directions, but some portion of the light becomes absorbed,
resulting in a net transfer of momentum in the direction of beam propagation. The scattering force can be thought of as the force resulting from forward momentum transfer of a
“fire hose” [44] of photons. In most situations, the scattering force is the dominant force.
The gradient force is less intuitive and is the force utilized to create the optical tweezer
effect. A dielectric object in the path of a laser beam will develop a net oscillating dipole
moment induced by the electric field created by the laser. A dipole in an inhomogeneous
electric field then experiences a force in the direction of the field gradient. The stronger the
gradient in intensity, the stronger the force. This is the reason for focusing the beam through
a high NA lens—the greater the NA of the lens, the greater the spatial intensity gradient.
There are two basic ways of quantitatively describing the gradient force. The first is the
ray optics approach, which is valid when the particle is large compared to the wavelength
of light. The second is the point dipole approach, which is valid when the particle is small
compared to the wavelength of light. Unfortunately, many of the interesting experiments
involve particles that are roughly the same size as the light wavelength. In these situations,
obtaining an exact solution for the trapping force is more difficult [63].
For stable, three dimensional trapping to occur, the maximum axial component of the
gradient force pulling the object towards the focus must be larger than the scattering force;
otherwise, the scattering force will simply push the object forward in the direction of beam
propagation. For stable, three dimensional trapping, the object will be trapped at a point
some small distance down-beam from the laser focus where the scattering force and the
axial component of the gradient force cancel [44].
25
Figure 2.1: Ray optics description of the trapping force. Two representative rays of the
laser beam are shown. As ray 1 enters the microbead, it is refracted at the surface of the
bead causing a change in momentum of the beam. By Newton’s third law, this results in
the force F1 on the bead. Likewise, ray 2 results in the force F2. In this diagram, the
lateral components of each force cancel, leaving only the axial components, which point
back towards the focus. In this case, this force counters the scattering force, which points
in the direction of beam propagation.
2.1.1 Ray Optics Description
The ray optics description may be used when the wavelength of the light is much smaller
than size of the object being trapped. As seen in Fig. 2.1, when the laser beam passes
through the object, the light is bent, imparting a momentum change (and thus a force) to
the laser beam. By Newtons third law, this in turn imparts a force on the trapped particle.
In the case where the index of refraction of the particle is higher than the surrounding
solution, the results are a force that pushes the trapped object in the direction of the
intensity gradient. The force is also proportional to intensity. In the case of a sphere,
this force can be readily calculated[64]. The extremal rays—that is, those rays farthest
26
from the center—contribute most to the gradient force. Likewise, those near the center will
contribute the most to the scattering force, since the scattering components of individual
rays do not cancel nearly as much due to the rays traveling at a smaller angle to the direction
of propagation. As a result of these facts, when constructing an optical trapping apparatus,
it is desirable to use a beam expander to overfill the back aperture of the objective lens in
order to maximize the ratio of gradient force to the scattering force.
2.1.2 Point Dipole Description
The point dipole approach may be applied when the wavelength of the light is much larger
than the particle size. In this limit, the particle may be treated as a point dipole, for which
well known solutions exist. Starting with the equation for the force on a charge distribution
in an electric field and ignoring time dependence [65]:
F~ =
Z
~
E(x)ρ(x)dx
(2.1)
we can Taylor expand the electric field to get:
∂ ~
~
~
E(x)|xi =0
E(x)
= E(0)
+ xi
∂xi
(2.2)
substituting this into equation 1 and integrating yields:
~ + p~ · ∇E(x)
~
F~ = q E
+ ...
(2.3)
where the total charge of the particle, q, is 0. Assuming the dipole moment depends linearly
on the field, the use of a vector identity yields:
1
F~ = α∇E 2
2
(2.4)
where α is the polarizeability of the trapped particle. One can see from this result that the
trapping force is proportional to the intensity gradient of the trapping laser as well as the
laser power.
27
2.2 Optical Tweezers: Basic Design Considerations
Figure 2.2: Schematic of a typical light microscope set up for fluorescent microscopy.
Commonly, optical trapping setups intended for biological trapping are built around a
commercial inverted light microscope [44]. These microscopes are ideal for trapping because
they allow for easy imaging of trapped objects, and their high NA objective lenses are ideal
for creating traps. The commercial microscope also usually provides a stage which can
hold the sample in place during trapping. Most modern research microscopes are so-called
infinity conjugate microscopes. In these systems, the objective lens forms an image of the
object at infinity which is then refocused by a second lens, called a tube lens, for the CCD
or the eyepiece. A diagram of a simple infinity conjugate inverted microscope can be seen
in Fig. 2.2. The primary optical components of the microscope are the objective lens, the
28
Figure 2.3: A simple optical trapping setup. The red line is the optical path of the laser,
while the blue region is the optical train of the microscope.
condenser lens and a tube lens. The condenser lens focuses light from the illumination
source at the specimen plane, and an image of the specimen is formed at the CCD by the
objective lens and the tube lens.
Commercial light microscopes also often feature additional components in order to allow
for epi-fluorescence microscopy: a light source and a fluorescence filter block. The filter block
consists of three primary elements: an excitation filter, which passes only that portion of
the illumination source which is at the excitation wavelength, a dichroic, which reflects
the excitation wavelength but passes the emission wavelength and an emission filter, which
passes only the emission wavelength and blocks the excitation wavelength.
The trapping laser can usually be easily inserted into the optical path of the microscope
by replacing the fluorescence filter block with a dichroic mirror, which passes visible light
but reflects the laser wavelength. In order to minimize the impact of local vibrations, an
29
optical table is also generally used [44]. Beyond that, all that is required is a suitable laser,
a beam expanding telescope and beam steering optics. Adding additional capabilities, such
as the position detection, multiple traps or the ability to control the trap location, will
require additional elements.
A diagram of a basic optical trapping system can be seen in Fig.2.3. Taken together, the
illumination source, condenser lens, objective lens and tube lens form an optical microscope
which creates an image of the trapped object at the CCD camera. A laser passes through a
beam-expanding telescope, formed by lenses L1 and L2, to ensure that it overfills the back
aperture of the objective lens and is introduced to the optical train of the microscope by the
dichroic mirror. The two mirrors, M1 and M2, provide the beam-steering optics required
for beam alignment. By adjusting the angle of M1, one can change the position of the trap
in the specimen plane. In general, a change in angle of M1 will result in a change of position
of the beam at the back aperture of the objective lens, which will lead to clipping of the
beam (and thus a loss of power). In order to avoid this, M1 should be placed at a plane
optically conjugate to the back aperture of the objective lens. In this way, changes in angle
of the beam at M1 will also manifest purely as changes in angle at the aperture, and, thus,
no clipping will occur.
2.2.1 Objective Lens
The objective lens is the most important component of an optical trapping system. In order
to obtain strong trapping, it is necessary that the objective possess a high NA, generally
higher than 1, although we have had success trapping with NA as low as 0.8. Given that
trapping forces are proportional to the intensity of the trapping laser, the strength of an
optical trap will also be affected by the transmittance of the objective lens at the trapping
wavelength.
The NA of a lens is given by N A = nSin(θ), where θ in this case is the maximum
angle that a ray of light can make with the optical axis and still be accepted by the lens,
and n is the index of refraction of the medium the lens is immersed in. One can see that
NA is proportional to the immersion index of refraction. In particular, since Sin(θ) has an
30
Figure 2.4: The NA of a lens is defined by the half angle θ of the maximum cone of light
that can enter the lens. The point F is the focal point of the lens.
upper bound of 1, in order for a lens to have a NA greater than 1, it must be immersed
in a medium with an index of refraction that is greater than 1. The NA of the objective
also determines the resolution of a microscope, so manufacturers have great incentive to
push it as far as possible, and, as a result, a variety of lenses with NA greater than 1 are
commercially available. These lenses fall into two primary types: oil immersion lenses and
water immersion lenses. Immersion oils typically have indices of refraction greater than 1.5,
while water has an index of refraction of 1.33. As a result, oil immersion lenses tend to
have higher NA than water immersion lenses. Despite this fact, water immersion lenses are
generally preferred by the optical trapping community. Most optical trapping experiments
are done in water, and the difference in index of refraction between the immersion oil and
the trapping medium results in spherical abberations [44]. An example of spherical aberration can be seen in Fig. 2.5. Spherical aberrations decrease trapping strength and get
progressively worse the deeper into the solution one tries to trap. In addition to spherical
aberrations, oil immersion lenses tend to have shorter working distances than water immersion lenses. The working distance of a lens defines the distance between the front element
of the objective lens and the surface of the coverslip when the specimen is in focus. Nikon
31
oil immersion lenses, such as the CFI PLAN APO 100X (part number 93110), tend to have
working distances of around 0.13 mm, while the working distances on their water immersion
lenses, such as the CFI PLAN APO 60X (part number 93109), are generally greater than
0.2 mm. The smaller working distances of oil immersion lenses, coupled with their greater
propensity for spherical abberations, mean oil immersion lenses can only effectively trap to
a depth of about 20 µm) [44, 66].
Figure 2.5: The top lens exhibits no spherical abberation, while the bottom lens exhibits
strong aberation. In optical trapping, spherical aberration can result from a difference in
index of refraction between the lens immersion medium and the trapping medium.
Objective lenses are often complex multi-element optics designed with transmittance
of visible light in mind. As a result, the anti-reflective coatings applied to them often
32
considerably attenuate transmission in the near infrared wavelengths that optical trapping
lasers usually operate at [67]. Objective lens manufacturers may not report transmittance
coefficients in the infrared. Objective lenses purposefully built for general fluorescence microscopy, and those built for infrared transmission, tend to perform better than others [44].
Transmission coefficients at 1064 nm can vary from as little as 0.32 to as much as 0.59 for
1.4 NA oil immersion lenses from the same manufacturer [68]. Given such large differences,
the transmittance of any objective lens should be verified. One way to measure transmittance of an objective lens is simply to place a power meter in front of the lens output;
however, because of the potential for specular reflection of a highly focused laser beam at
the specimen plane, this results in a underestimation of the transmittance [44]. A more
reliable method of measuring transmittance is to use a second, identical, objective lens to
collimate the output, which can then be measured using a power meter [67].
2.2.2 Laser
When choosing a laser for optical trapping, there are five primary considerations: output
power, output power stability, pointing stability, wavelength and mode quality (Gaussian,
TEM00 ) [44]. The optimal laser choice will need to take all these factors into consideration
together with cost. Fluctuations in output power will lead to fluctuations in trap stiffness,
while fluctuations in pointing stability result in fluctuations in trap location. A Gaussian
beam provides the smallest diameter beam at the focal point, leading to the most efficient
trap.
Together with the transmission of the optical system and the NA of the objective lens,
the output power of the laser will determine the strength of the optical trap [44]. How
much trapping force one gets for a given laser power depends additionally on the size of
the trapped object and its index of refraction. Calculating the trapping power for objects
roughly the size of the laser wavelength is problematic [63]. As an example, from our lab,
using a 1.2 NA lens and trapping a 3 µm polystyrene bead, we obtain a trap stiffness of
4.2 pN/nm per W of laser power in the specimen plane.
When selecting an appropriate laser wavelength for trapping of biological specimens, a
33
primary concern is the risk of ”opticution”, the death of cells due to the trapping laser.
Given the large intensities involved in optical trapping, the laser has the potential to do
considerable damage to cellular functions. Proteins tend to absorb light strongly in the
visible range, while water absorbs light strongly in the far infrared [67]. As a result, most
lasers used for optical trapping are in the near infrared, where absorption in cells is at its
lowest. Even within this range, large variations in cell mortality are observed. Neuman et
al. studied cell mortality due to opticution in E. coli and found minima at roughly 830 nm
and 970 nm (Fig. 2.6) [68]. In addition to opticution, the choice of laser wavelength should
depend on the transmission of the objective lens. The ND:YAG laser, which emits at
1064 nm, is the most commonly used laser in optical trapping experiments, due to nearinfrared wavelength, as well as its relative cost effectiveness and the availability of lasers
with output powers of 1 W or more [44]. The ND:YAG laser in our lab has a maximum
output power of 10 W.
Figure 2.6: Photodamage in E. coli as a function of laser wavelength. The damage as
minimal around 830 nm and 970 nm. Reprinted from Biophysical Journal, Vol 77, Neuman
et al., Characterization of Photodamage to Escherichia coli in Optical Traps, Pages No.
2856-2863, Copyright (1999), with permission from Elsevier [68].
34
2.2.3 Sample Manipulation
There are two fundamental ways of attaining object manipulation with optical tweezers.
One is to hold the trap position fixed and to manipulate the medium around it. The second
is to hold the medium fixed and manipulate the trap. The first is achieved using a two—
or three—dimensional piezoelectric stage. These can be purchased commercially and can
offer nanometer level spatial resolution. The second can be achieved by changing the laser
pointing, by use of a mirror or by the use of an acousto optic deflector (AOD) or electro
optic deflector (EOD).
Through capacitive position detection, problems with hysteresis have largely been removed from modern piezoelectric stages [44]. Spatial resolution is typically around 0.5 nm
in the more advanced models, and stage ranges are typically on the order of 100 µm. A typical example is the Nano-LPS series from Mad City Labs, which features spatial resolutions
of 0.2-0.6 nm and ranges of 100-300 µm. Calibrated piezo stages have made many aspects
of optical trapping experiments much easier. In addition to allowing programmable sample
manipulation, they also make force calibrations and position calibrations much easier. The
existence of 3d piezoelectric stages that are accurate to 1 nm allow for known displacements
to be applied to samples, which can be used as the basis for calibrations of position detection
equipment, pixel size on CCD’s and more. The ability to accurately control displacements
in the z axis is especially useful, since accurate calibrations in that axis can be more difficult
to obtain and check. Their primary drawback is their high cost. A single axis piezoelectric
stage will typically run about $10,000. They also do not have the frequency response that
AOD’s or EOD’s have, typically being limited to around 50 Hz [69].
The other option is to hold the sample fixed and manipulate the trap by changing the
pointing of the laser. A variety of ways of doing this are possible. Galvanometer mirror
systems are available, which allow for computer control. Step response times on commercial
systems are usually on the order of a few hundred µs’s; typical repeatability is on the order
of 10 µrad. Response times are considerably lower than AOD’s or EOD’s, which makes
them generally unsuitable for fast scanning applications, such as multiple trapping (see
35
section 2.2.5), but throughput is high, and they are useful for slow scanning experiments.
AOD’s work by Bragg diffraction. A piezoelectric transducer is attached to a dielectric
crystal and oscillated, creating a sound wave in the material. This oscillation leads to plane
waves of expansion and compression in the material, which in turn changes the index of
refraction, setting up a diffraction grating. The diffraction angle depends on the wavelength
of the sound, while the diffraction efficiency depends on the amplitude of the sound. This
gives AOD’s the ability to rapidly control both the trap location and the trap strength by
controlling the wavelength and amplitude of the acoustic wave [44]. AOD’s benefit from
an extremely fast response time, limited by the transit time of the sound wave through
the material, and is on the order of 1 µs for typical optical trapping setups [44]. One—
and two—dimensional systems are commercially available. Maximum deflection is usually
around 1 degree. Their primary drawback is that they have a low transmission rate. Power
into the diffracted beam can be as high as 80%, but, in practice, it is often as low as 60%,
especially for two-dimensional systems where the transmission goes as the transmission for a
one-dimensional system squared. Worse, transmission varies with the diffraction angle [44].
EOD’s rely on crystals whose index of refraction varies with an applied electric field. By
setting up a gradient in index of refraction across the crystal, a light beam can be deflected
by an amount ∆θ = KlV /w2 where l is the length of the crystal, V is the applied voltage,
w is the diameter of the aperture and K is a constant. Few commercial systems exist
currently; however, ConOptics produces a system designed specifically for optical trapping
which features a transmission rate of 85%, a maximum deflection angle of 3 mrad’s and a
reaction time of 1 µs at 1064 nm. EOD’s have reaction times comparable to AOD’s, but
possess low deflection ranges and high costs due to the crystals used in their construction.
Despite their drawbacks, they have higher transmission coefficients than AOD’s and have
been successfully utilized in optical trapping setups [70].
2.2.4 Position Detection
Of central importance to optical trapping experiments is the ability to accurately measure
sample position. In addition to providing position information, accurate position read36
ings are necessary to measure forces. A number of position detection schemes have been
conceived.
Video-based detection relies on imaging the trapped particle on a CCD camera and
using a centroid-finding algorithm to locate the object center. For a point source, the
spatial resolution afforded by such algorithms depends heavily on the signal-to-noise ratio
of the image data from the camera and can vary between approximately 2 nm at a S/N
ratio of 10 to resolution no better than that of a pixel at S/N ratio of 4 [55]. Detection
bandwith is ultimately limited by the camera frame rate, however, which typically is on the
order of 50 Hz. High speed cameras (such as CMOS cameras) can improve this considerably,
but limitations in CPU speed prevent real time position detection at much above several
hundred Hz, and limitations in computer storage space prevent the storing of the large
amounts of image files necessary to take data for extended periods of time [44].
Most position detection schemes in present day optical tweezer systems rely on the
use of a quadrant photo-diode (QPD). The simplest of these images a trapped bead onto
a QPD [56]. Unfortunately, this runs into problems with the signal-to-noise ratio, for the
simple reason that it is difficult to get a strong enough signal with conventional illumination
sources. Laser sources are generally poor choices for illumination because light coming from
them is coherent and, therefore, interferes with itself, resulting in a ”speckled” pattern at
the QPD [56]. In addition to direct imaging, two interference-based detection schemes have
been developed. In most cases, one laser is used for both trapping and position detection.
This can be useful for experiments where the position of the trapped sample relative to the
trapping center is the relevant measure, as the trap position and the detection beam are
automatically aligned. It is possible, though, to use separate detection and trapping beams,
provided the detection beam uses a low enough power that it does not result in an added
trapping force on the particle [44]. The addition of a second beam introduces considerable
complexity in the form of spatially overlapping and then separating two beams but can be
particularly useful if the absolute position of the particle (as opposed to its position relative
to the trap center) is the important measure [44]. This can be the case, for example, in
experiments where the trap position moves or when multiple traps are employed.
37
Optical Trapping Interferometry
Optical trapping interferometry was first demonstrated by Denk and Webb in 1990 [71] and
makes use of a microscope equipped for differential interference contrast (DIC) microscopy.
DIC microscopy is a common method of increasing contrast in samples where differences
in index of refraction are small (such as biological samples where the index of refraction
is very near that of water). In a DIC setup, light from the illumination source is first
polarized at 45 degrees and then sent through a Wollaston prism. This splits the light into
two separated but overlapping beams with orthogonal polarizations. As the two beams
pass through adjacent points on the sample with differing indices of refraction, they will
experience different optical path lengths. The beams are recombined at a second Wollaston
prism and experience interference depending on their phase differences, resulting in light
and dark regions which increase the image contrast.
In optical trapping interferometry, as the laser passes through the first Wollaston prism,
it is split into two overlapping beams which form one optical trap. As a trapped microbead
is displaced from the trap center, it retards one of the two beams relative to the other due
to a difference in optical path length. This results in slightly elliptical polarization when
the beams are recombined at the second Wollaston prism. The laser is then sent through a
quarter waveplate, which results in a nearly circular polarization of the beam before being
sent through a polarizing beam splitter. The two resulting beams will have slightly different
intensities due to the ellipticity of the laser caused by the beads displacement from the trap
center. Measuring the two beams with photodiodes and then running the signals through a
normalizing differential amplifier gives a position signal. This detection system is extremely
accurate, down to the picometer range [52, 71] but only offers position detection in one
dimension.
Back Focal Plane Detection
The second major interference based position detection scheme is back focal plane (BFP)
detection [53, 54]. This is the detection scheme used throughout the rest of this work. In
38
Figure 2.7: The principle behind optical trapping interferometry. If the trapped bead is
displaced from the trap center, the recombined laser light after the 2nd Wollaston prism
will be slightly elliptical, leading to slightly different intensities at the two photodiodes.
Adapted by permission from Macmillan Publishers Ltd: Nature, Vol 365, Svoboda et al.,
Direct observation of kinesin stepping by optical trapping interferometry, Pages No. 721727, Copyright (1993) [52].
this scheme, a QPD is used to measure the interference pattern between forward scattered
light from the trapped particle and unscattered transmitted light. The QPD is placed at
the back focal plane of the condenser lens of the microscope, thus leading to the name back
focal plane detection. From ray optics, the intensity pattern of the laser light at the back
focal plane of the condenser lens is independent of the trap position, allowing the trap to be
repositioned without changing the detector response. The BFP instead contains information
about the angular distribution of light leaving the specimen region. As a result, measuring
the intensity pattern at the BFP is akin to doing an angular scattering experiment [54].
Light at radius R in the BFP exits the specimen plane at angle θ where R = f sinθ with
f is the focal length of the lens (see Fig. 2.8). Unlike optical trapping interferometry,
BFP detection can provide information on the location of a trapped particle in both lateral
directions. Accuracy is approximately 1 nm [54], while measurements can be made with
39
bandwidths of up to 100 kHz [54].
Figure 2.8: At the BFP of a lens, all light entering the lens at a give angle arrives at a
single radial position.
The detector response was modeled by Alersma et al. [54] by assuming that the intensity
pattern at the QPD is the result of interference between the unscattered beam and the
scattered light from the particle. Light is defined to be focused at the origin (~r = 0). The
angle with the optical axis, θ, is assumed to be small, and the time dependence of e−iωt is
omitted. The electric field due to the trapping laser at focal plane of the objective lens is:
Ê(~rs ) = Ê(x) =
2
2
2
e−x /w0
√
w0 πs cs
(2.5)
where ~rs is the lateral displacement from the origin. For the same beam, the field far from
40
the focal plane is:
1
−ikw0
exp{ikr − k 2 w02 θ2 }, {r >> w0 }.
Ê(~r) ≈ √
r πs cs
4
(2.6)
In the above equation, k = 2πns /λ with λ being the vacuum wavelength of the trapping
laser. The constants s and ns are the permittivity and refractive index of the solution, cs
is the speed of light in the solvent, and w0 is the beam half-waist at the focus. If a trapped
particle is located at a location ~rs which is displaced laterally from the beam focus by an
amount x, it will scatter light due to the local electric field. At large values of r in the
forward direction, this scattered field is then:
k2 α
Ê(x)exp(ik|~r − r~s |)
r
k2 α
≈
Ê(x)exp(ik[~r − xsin(θ)cos(φ)]),
r
Ê 0 (~r) ≈
(2.7)
(2.8)
where α is the polarizability of the particle. The total electric field at the detector is
then (Ê + Ê 0 )e−iωt (including the previously omitted time dependence). The time averaged
squared real part of this is |Ê + Ê 0 |2 /2, and the change in the intensity I due to the scattered
particle is simply:
δI =
s cs
{|Ê + Ê 0 |2 − |Ê|2 } ≈ s cs Re{Ê Ê 0∗ }.
2
(2.9)
Substituting Eqs. (2.5), (2.6) and (2.8) into Eq. (2.9) and making a small θ approximation
gives:
δI(x) ∼ 2k 4 α −x2 /w02
2 2 2
xe
θcos(φ)e−k w0 θ /4 .
=
Itot
πr2
(2.10)
Integrating over the “+” (−π/2 < φ < π/2)and ”-” halves of the detector and then subtracting the two gives the predicted detector response:
I+ − I− ∼ 16 kα
2
2
(x/w0 )e−x /w0 .
=√
2
I+ + I−
π w0
(2.11)
All the above detection methods measure only lateral positions of the trapped particle.
BFP detection also offers the possibility for axial position detection. As a Gaussian beam
goes through a focus, it picks up a phase shift of η(z) = −arctan( zz0 ) where z0 is the
41
Rayleigh length πw02 /λ and z is the axial distance from the focus [53]. In the far field, this
phase shift is π. The scattered beam, however, continues to propagate with whatever phase
it acquired prior to being scattered. This results in an axial interference pattern between
the scattered and unscattered beam which is the counterpart of the lateral interference
pattern described above and can be measured as the total intensity of the laser at the BFP.
Pralle et al. found that, for a trapped particle located on the optical axis and displaced by
an amount z 0 from the focus, the expected detector response is [53]:
Iz 0
z0
8kα
z0
(z ) =
(1 + ( )2 )−1/2 sin(arctan( )),
2
I
z0
z0
πw0
(2.12)
and more generally a trapped particle at an arbitrary location ~r0 = {x0 , y 0 , z 0 } = {ρ, ϕ0 , z 0 }
generates an axial signal:
Iz 0
2π
ρ2
(~r ) = 2 2 I(z 0 )(r0 sinψ 0 − z 0 −
I
k w0
2R(z 0 ) +
where I(z 0 ) =
z 0 2 −1/2
4k4 α
,
π (1 + ( z0 ) )
ζ(z 0 )
k
),
(2.13)
ψ = arctan(z 0 /ρ) and R(z 0 ) is the Gaussian beam radius
z 0 (1 + (z0 /z 0 )2 ).
2.2.5 Multiple Trapping
In order to conduct experiments involving multiple objects, multiple trapping is sometimes
desirable. One way of doing this is to simply fix one object immobile, either by fixing it
to a coverslip or by holding it in place with a micropipette [57]. Most cells will naturally
attach to a glass coverslip, given time. Failing that, it is also possible to coat a surface with
substances to increase adhesion, such as polylysine.
The other possibility is to construct a setup that allows for multiple optical traps. There
are several ways of accomplishing this. One simple way is a polarization based scheme [72].
By using a polarizing beam splitter, it is possible to split the laser beam into two separate
paths which can then be independently manipulated. A second polarizing beam splitter
can then be used to recombine the two traps and allow them both to be coupled into the
objective lens. A quarter waveplate before the first polarizing beam splitter can allow for
42
control of the relative intensities of the two traps by rotating the linear polarization of the
laser.
Another way to create multiple traps is to quickly scan the laser between multiple trap
locations [72]. This has the advantage of being able to create more than two traps. By
scanning the laser through multiple trap locations more quickly than the timescale for the
trapped particle to move away under Brownian motion, it is possible to ”juggle” several
particles at once. Ultimately, the ability to create multiple traps is limited either by laser
power or by the reaction speed of the scanning device. AOD’s or EOD’s offer the quickest
reaction speeds, but a galvanometer scanning mirror system can sometimes be used to setup
two traps as well [72].
43
Chapter 3
Technical
3.1 Experimental Setup
A Nikon TE2000-U inverted light microscope serves as the microscope for the optical trapping setup for this work. An upstage package has been purchased for the microscope, which
allows for a 2nd fluorescent filter wheel on top of the standard first unit. This allows us
to use the first wheel for standard fluorescent microscopy, while a dichroic mirror in the
2nd wheel allows us to bring in the trapping laser. The objective lens most commonly used
for optical trapping is a 60x, 1.2 NA water immersion objective with a working distance of
0.22 mm, purchased from Nikon.
Cameras are attached to two of the microscopes camera ports, either of which can be
used, depending on the experiment. Both cameras are Photometrics cameras one, a CoolSNAP EZ and the other, a Cascade II 512. The Cascade II is a EMCCD camera with
an adjustable gain and allows for low light applications. The size of each pixel element
at 60x magnification was measured for each camera through the use of a calibration microscope slide with regularly spaced markings on it. The pixel size was found to be 0.188
microns/pixel for the CoolSNAP EZ and 0.266 microns/pixel for the Cascade II.
Sample manipulation is done using a 3d piezoelectric stage from Mad City Labs. This
stage has a range of 50 µm in all three directions. The stage is controlled via three inputs
each with a range of 0-10 V. In order to calibrate the stage, we held the Y axis fixed at
0 V and then sent the X axis through its full 50 µm range in increments of 1 µm. At each
step, the displacement of a fixed feature on a coverslip was measured using the Cascade
44
Figure 3.1: The results of the piezoelectric stage calibration.
II. Once the maximum displacement of 50 µm was reached, the stage was run back down
to 0 µm in 5 µm increments to check for any hysteresis effect. This experiment was then
repeated for the Y axis. The results can be seen in Fig. 3.1. The X axis shows relatively
good agreement with the camera measurements of the coverslip displacement, disagreeing
by less than 10% and also shows little in the way of a hysteresis effect. The Y axis, on the
other hand, disagrees with the camera measurements by 15% and shows a considerably more
pronounced hysteresis curve. As a result, for experiments where the distance calibration of
the stage were critical, the X axis was preferred to the Y axis.
45
The trapping laser is an IPG Photonics fiber laser. The laser has a wavelength of 1064
nm, a common wavelength in optical trapping chosen to reduce the risk of opticution, and
a maximum output power of 10 W, although typically only 1-2 W were actually used in
experiments. In order to assess whether or not damage was being done to a cell when
trapped by the laser, a K562 (leukemia cell line) cell was held in an optical trap with the
laser set to a power of 1.5 W while in a solution of PI dye. PI dye is a dye that fluoresces
once it comes into contact with nucleic acids but usually cannot penetrate the membrane
of a healthy cell. After half an hour in the trap, the cell still was not fluorescing, indicating
that the membrane was still intact, and the cell was still viable.
The optical beam path is outlined in Fig.3.2. The laser passes through an optical isolator before encountering a polarizing beam splitter. The polarizing beam splitter gives us
two independent traps, allowing for the manipulation of two objects simultaneously or the
manipulation of a single object using two “handle” points. The relative power in the two
beams can be adjusted by using a half waveplate to adjust the linear polarization of the
beam. One of the beams bounces off mirrors before hitting the second polarizing beam splitter cube. The other beam goes through a galvanic mirror control system, allowing computer
control of the trap position, before also hitting the second polarizing beam splitter. The
two beams are then recombined and pass through a beam expanding telescope consisting of
L1 and L2. These lenses, which have focal lengths of 7.5 and 40 cm’s respectively, expand
the beam size by a factor of approximately 5. This allows the beam to overfill the 1 cm
back aperture of the objective lens, which allows for greater trapping efficiency, as discussed
in the introduction. Mirrors M7 and M5 are placed at a plane that is optically conjugate
to the back aperture of the objective. This ensures that a change in angle at these mirrors
results only in a change in angle at the aperture. This allows us to change the position of
the beam at the trapping plane while ensuring that the beam still hits the center of the
back aperture of the objective lens, preventing any change in beam power due to clipping
when changing the trap position.
Beam alignment is done by using the microscope to observe the reflection of the beam
off a microscope coverslip. Mirror M7 (or M5 for the second trap) is used to adjust the
46
Figure 3.2: The path taken by the beam as it enters the microscope. PBZ1 and PBZ2 are
polarizing beam splitters. M1-M6 are mirrors. L1 and L2 are lenses with focal lengths of
7.5 and 40 cm.
47
Figure 3.3: The path taken by the beam as it leaves the sample and passes through the
condenser lens on its way to the QPD.
beam position so that it is centered in the microscope field of view, then mirror M4 (or
M3) is adjusted so that the beam profile is symmetrical (this signifies that the beam is
passing straight through the objective). Doing so will change the beam position slightly,
which necessitates adjusting mirror M7 again. This process is iterated several times until
the beam is both centered in the field of view and symmetrical.
3.2 Position Detection
Particle positions and trapping forces are measured using a technique known as BFP detection. This technique is outlined in Chapter 2; however, the basic premise will be summarized
below.
In BFP detection, a QPD is placed at a plane optically conjugate to the back focal plane
of the microscope condenser lens. If a particle or object is placed in the path of the laser
beam, then some fraction of the incident beam is scattered. This scattered light interferes
with the incident beam, creating an interference pattern at the back focal plane of the
condenser lens. As the particle is displaced off the beam center, this interference pattern
shifts, resulting in a linear position signal at the QPD.
The beam path for the position detection part of the apparatus is outlined in Fig.3.3.
The beam passes through the condenser lens of the microscope and then reflects off two
48
dichroic mirrors. The lens L3 then creates a plane optically conjugate to the BFP at the
QPD.
In order for BFP detection to work, the condenser lens must be aligned and positioned
correctly. Following the procedure used to create what is commonly known in microscopy
as “Koehler Illumination” is sufficient for this. The steps for creating Koehler illumination
are as follows:
1. Prepare the microscope for imaging. Turn on the illumination source as well as the
cameras. Place a drop of deionized water on the objective lens and place the sample
you intend to use in the sample holder. Insure that the optical path is set to “EYE”,
and pull the bino and photo selector to photo. Turn on Metamorph and observe the
live image coming from the CoolSnap camera. Bring the specimen into focus.
2. Close the field diaphragm all the way.
3. Turn the condenser focus knob until the field diaphragm comes into focus.
4. Use the condenser centering screws (two silver knobs on the condenser lens mount) to
center the field diaphragm in the field of view.
5. Open the field diaphragm.
Once this is done, the QPD needs to be placed at the plane conjugate to the BFP of the
condenser. This can be done by removing the objective lens of the microscope and allowing
the laser beam to pass directly through the condenser lens. By placing the QPD at the
point where the laser beam is at its tightest focus, it is then ensured that the QPD is at a
plane conjugate to the BFP.
The output signal from the QPD goes into an Ectron E513-2A amplifier before being sent
to a National Instruments data acquisition board. The QPD itself is on a 2d translational
mount. This allows it to be easily centered with respect to the laser interference pattern. If
the QPD is not properly centered, the detector response may feature a large offset or may
be non-linear. Because the condenser lens needs to be centered before every experiment
as part of Koehler illumination, the QPD position also needs to be centered before every
49
experiment. This can be done by turning on the laser in a portion of the sample that is
not near any objects which may scatter the light (a bare section of coverslip) and using the
QPD centering knobs to bring both the x and y detector response to zero while maximizing
the signal coming from the sum of the four quadrants.
3.2.1 Calibration
In order to conduct truly quantitative optical trapping experiments, it is critical to have
an accurate calibration of the position detection. This is important not just for position
measurement, but also because measurement of forces depends on accurate position measurements and the assumption that the trap follows Hooke’s law F = −αx.
Calibration of the position signal can be most easily accomplished by observing the
detector response as a bead, fixed to a coverslip, is scanned across the beam using the 3d
piezoelectric stage. This results in a curve like the one in Fig. 3.4 for a 3 µm bead at 500
mW of laser power as measured at the laser output. In the center of this curve exists a
linear regime from which a calibration constant can be derived.
In order to turn position measurements into force measurements the trap stiffness, α
must be determined. Three different ways of doing this were ultimately used, allowing the
methods to be checked against each other for consistency.
Triangle Wave Measurements
The simplest way, conceptually, to measure the trap strength is by trapping a bead and
then applying a known force to it. By measuring the displacement of the bead from the
trap center, the trap strength can then easily be determined.
This is accomplished by feeding a triangle wave to the 3d piezoelectric stage. This
creates alternating periods of constant drag force on the particle. Since the speed of the
oscillations is known to be that which is sent to the piezo stage, the drag force can be
calculated from Stoke’s law as F = 6πηrv where η is the viscosity of water, r is the radius
of the bead and v is the velocity of the stage motion. An example of the data one obtains
from such a measurement can be seen in Fig. 3.5. Again, the laser power is 500 mW, and
50
Figure 3.4: An example of a calibration curve obtained by scanning the laser over a bead
fixed to a coverslip. The orange curve is a fit to the linear region of the graph with a slope
of 0.01 V/nm.
the bead is (3.0 ± 0.3) µm. In this case, the force on the bead is 2.8 ± 0.3 pN, and the
bead displacement from the trap center is, on average, 36 ± 2 nm, giving a trap stiffness of
0.08 ± 0.01 pN/nm.
Equipartition Principle
The Brownian motion of a bead in an optical trap is dependent only on the trap stiffness
and the temperature. The mean square of fluctuations in one dimension is given by:
< x2 >=
kb T
κ
(3.1)
where x is the bead displacement from the trap center, and κ is the trap stiffness. As a
result, trap stiffness can be determined by measuring the mean square fluctuations of a
bead. This is done by simply holding the bead in a trap and recording the position signal
over a period of time. This method has the advantage that it does not depend on the
viscous drag of the particle. This means that the viscosity of the medium and the particle
51
Figure 3.5: An example of the data taken in a triangle wave calibration. The bead position
was converted into nm using the calibration data in Fig..
shape do not affect the calibration [44]. Returning to our example of the (3.0 ± 0.3) µm
bead at 500 mW of laser power, we obtain a value of 45.3 ± 0.9 nm2 for the mean square
fluctuations, which at room temperature gives a value of 0.093 ± 0.001 pN/nm for the trap
stiffness.
Power Spectrum Roll Off
The final way in which the trap stiffness was determined was by measuring the power
spectrum of the Brownian motion of a trapped bead. This can be done with the same
measurements used in the Equipartition method. The Brownian motion follows a Lorentzian
distribution with a roll off frequency given by [67]:
fc =
κ
.
12π 2 ηr
(3.2)
This method has the advantage that it does not depend on the previous calibration of the
position signal, which allows for an independent check of that calibration. An example
52
Figure 3.6: An example of the data taken in a power spectrum calibration. The blue curve
is a fit to a Lorentzian distribution.
of this for our (3.0 ± 0.3) µm bead case can be seen in Fig. 3.6. In this case, the roll off
frequency is 497 ± 1.2 Hz, yielding a trap stiffness of 0.088 ± 0.009 pN/nm. In this case, all
three calibrations of the trap stiffness agree to within 20%.
3.2.2 Transmission
The transmission of the laser through the OT setup is critical for knowing exactly how much
power is being used for trapping, which can be important when concerned about damage
to biological specimens or when working with samples that could potentially absorb some
fraction of the laser light. In addition, knowing where in the apparatus power is lost is
important for minimizing losses and maximizing trapping force. Transmission was measured
using a Power Max 500D laser power meter. Relative to the power coming straight out of the
optical fiber, transmission was found to be 92% after passing through the optical isolator.
After passing through the first lens of the beam-expanding telescope (lens L1) transmission
had dropped to 54%, again relative to the laser power out of the fiber optic. Transmission
was down to 20% out of the objective lens, but this is probably an underestimation. Power
53
through the objective was measured by placing the power meter directly in front of the
objective lens, and, as described in Chapter 2, this tends to underestimate the actual
transmission due to specular reflection at the specimen plane. Because the condenser lens
has a smaller NA than the objective lens, a great deal of power is lost at the condenser lens,
and transmission to the QPD is thus only about 3%.
3.3 Additional Optical Trapping Setups
Aside from the main trapping setup described above, two additional optical trapping systems were built for use by members of NSEC. These systems lack the options for position
detection and multiple trapping featured by the system used above but are easy to use and
still allow for single object manipulation.
3.3.1 Confocal System
In a standard light microscope, in addition to light from the focal plane, light from out of
focus planes will also show up in the image. This has the effect of introducing a ”fuzz” effect
to the image and making it more difficult to resolve fine features. There are two methods
of dealing with this. The first is to use deconvolution software to adjust the image after the
fact by removing signal from out of focus planes. The second way to deal with the problem
is to use a confocal microscope, which eliminates light from out of focus planes before it
reaches the CCD. In the course of the NEP experiments outlined in Chapter 6, it became
evident that there was a need for three dimensional image stacks of cells made by a confocal
microscope in order to be able to better determine exactly where transfected molecules went
in the cell. Optical trapping was still required for these experiments, however, necessitating
the construction of a optical trapping system for Nanotech West’s confocal microscope
system. The experiments in Chapter 5 were conducted using this confocal optical trapping
setup.
The confocal system at Nanotech West is a Yokogawa CSU22 spin disk confocal system.
Confocal microscopy works using point illumination and a pin hole between the objective
54
lens and the CCD to eliminate out-of-focus light. The pin hole is placed at a plane conjugate
to the focal plane; as a result, light from the image plane is able to pass through, but light
from out-of-focus planes is blocked. Only one point on the sample is illuminated at a time.
In a spin disk confocal system, a spinning disk of pinholes scans over all the points in the
sample to provide a complete 2 dimensional image. The confocal unit at Nanotech West
features two different CCD cameras, a Photron APX RS CMOS camera used for high speed
applications and a Hamamatsu EM-CCD model C9100-02 used for low light applications.
Each of these take advantage of the confocal attachment. The system also features a laser
illumination system for fluorescence microscopy with two solid state laser lines, one at
491 nm, and another at 561 nm. The microscope itself is an Olympus IX81 inverted light
microscope and is fitted with a piezo focusing collar to allow the control of the microscope
focus via software. The microscope’s manipulation stage was replaced with a Semprex stage
with micrometer knobs to allow for accurate sample manipulation.
The optical trap laser is a 1200 mW, 1064 nm laser manufactured by OEM Laser Systems. Although the output power can be controlled with a voltage input, this was left wired
to the lasers +5 V and ground terminals. As a result, the laser power is not adjustable and
is set to maximum output. In order to provide an entry point for the optical trapping laser,
the microscopes Mercury lamp and the associated collimation optics were removed, and a
dichroic mirror was placed in the fluorescence filter wheel. The Mercury lamp is usually
used for fluorescence illumination but is not necessary here because of the laser illumination
sources. The beam path to the microscope is shown in Fig. 3.8. Alignment is handled in
the same way as described above.
3.3.2 Touch Screen System
The third optical trapping system was designed to be cheap, simple and easy to use. The
system’s primary purpose was to be utilized in additional NEP experiments, specifically
with an eye towards gathering data on a large number of cells in order to alleviate concerns
about small sample size. As such, ease of use was defined as being able to conduct as
many NEP experiments as possible, in as short a time as possible, with as small a training
55
Figure 3.7: a) The principle of confocal microscopy b) Diagram showing how the various
pieces of the confocal microscope connect to each other
Figure 3.8: The beam path of the trapping laser before entering the microscope for both
the 2nd and 3rd unit. Lens L1 has a focal length of 5 cm while lens L2 has a focal length
of 20 cm. M1 through M3 are mirrors. M2 and M3 are used alignment of the system.
56
requirement as possible.
The laser used was the same OEM Laser Systems model as was used in the confocal
unit. As with the confocal unit, the control to the output power was left wired to +5 V and
ground, giving a constant 1200 mW output beam. The beam path into the system is shown
in Fig. 3.8. The apparatus was built around a Nikon TE2000-S microscope. The TE2000-S
is very similar to the TE2000-U used in the setup described at the beginning of this chapter.
As with the TE2000-U in the beginning of the chapter, an upstage kit was purchased to
give the microscope a second fluorescence wheel. This wheel was then fitted with a 1064 nm
dichroic mirror which was used to couple in the laser light, while the first wheel remained
free for standard fluorescence microscopy. Alignment of the laser was again handled in the
same fashion as outlined in the beginning of the chapter. Sample manipulation was handled
by a microscope stage fitted with two ZST25B drives from ThorLabs, while the camera was
a CoolSnapHQ Photometrics camera.
In order to make the system as easy to use for NEP experiments as possible, a Labview
program was written to control the manipulation of the cells by computer. The program
allows for real time control of the stage position using the mouse by clicking on a live feed
from the camera. When the user clicks on a position on the camera feed, the stage moves
so that location is now at the center of the image. The program also has the ability to
store a recall point that can automatically be returned to with the press of a button, so,
for example, a user can tag a nanochannel location as a recall point, trap a cell, and then
return to the channel with a button press. As an added feature, since the nanochannels are
arranged in a repeatable array, the program can calculate the location of all channels given
the location of one channel and the size of the channel spacing. These calculated channel
locations can all then be used as recall points. A screenshot of the program interface can
be seen in Fig. 3.9. The system also features a touch screen, allowing manipulation of
cells to be handled either with the mouse or by pressing locations on the screen. While
the ThorLabs ZST25B drivers come with Labview support, Photometrics does not supply
Labview support for its line of cameras, so the third party SITK application was required
in order to get the camera to interface with Labview.
57
Figure 3.9: The user interface of the 3rd optical trapping unit. In this screenshot the
camera is off and the live feed is replaced with a checkerboard pattern.
3.4 Flow Cell Construction
Most experiments were done using a simple flow cell. The steps for creating these flow cells
are as follows:
1. One starts with a glass microscope cover slip. This is the “bottom” of the flow cell.
2. Take two layers of parafilm wax and cut a rectangular channel out of the middle using
a knife.
3. Place the parafilm channel on top of the coverslip.
4. On top of this, place a microscope slide with two holes drilled in it to allow for fluid
inlet/outlet.
5. Heat the flow cell on a hot plate until the parafilm begins to melt. This seals the
channel. Turn off the hotplate.
A drawing of the process, as well as a photo of a finished flow cell, can be seen in Fig. 3.10.
58
Figure 3.10: a) The top layer of the flow cell is a glass slide with two holes drilled for fluid
inlet/outlet. The bottom layer is a glass coverslip which may be coated in polylysine if the
experiment calls for it. In between, two layers of parafilm, with a rectangle cut out of the
middle, form the channel. b) A finished flow cell. This flow cell has copper tape electrodes
on the glass coverslip to allow for electroporation.
For some experiments, it is desirable for cells to adhere to the surface of the coverslip,
which forms the bottom of the channel. For these experiments, a few drops of a 4 mg/ml
solution of polylysine was placed on the center of the coverslip and allowed to evaporate,
leaving behind a polylysine coating. Cells, such as red blood cells and K562 cells, will
adhere to this polylysine coating.
Electroporation experiments required flow cells with electrodes. In cases where a uniform
field was not required, the above flow cell design was modified by placing a strip of copper
tape on the coverslip. A middle section of the tape, measuring 1 mm across, was then cut
away, creating the two electrodes required for electroporation. A photo of this can be seen
in Fig. 3.10.
59
Chapter 4
Bulk Electroporation
Experiments
Standard electroporation, here referred to as BEP, is a common laboratory technique, but
the physics behind it are poorly understood [2, 6–8, 11]. Previous attempts to study single
cell electroporation have relied on cells fixed to surfaces, leading to non-spherical geometry,
and have used non-uniform electric fields [35, 73]. The intent of the work in this chapter
is to test the predictions of Eq. (1.2) with single cell experiments in an environment that
minimizes these concerns.
In BEP, cells are placed in suspension between two parallel plate electrodes and then
subjected to electric fields of several hundred V/cm for durations of several ms. The ideal
single cell BEP then would evaluate the poration of a single cell in suspension, and that
poration would be created by an electric pulse in the ms time range, which would create
a uniform electric field in the solution. Studying cells in suspension has been problematic
because, during the electroporation process, bubbles are usually formed at the surfaces of
the electrodes through electrolysis. This effect causes cells in suspension to be scattered
and makes it difficult to track them. We found that optical trapping allows us to hold cells
fixed in the solution so long as the viscous drag force caused by electrolysis is not larger
than ∼ 100 pN. This situation was found to be satisfied, provided the length of the pulses
was kept below 3 ms.
60
Recall from Chapter 1 Eq. 1.2:
Vinduced = 1.5f grEcos(θ)(1 − e−t/τ ).
Theory predicts that cells should porate at a critical value of the transmembrane potential
of around 1 V. If this is true, then the applied field at which cells porate should depend on
the cell radius r and go as 1/r. We test this by measuring the poration threshold field for
single cells as a function of their radius. The time constant τ depends on the conductivities
of the buffer, and the cell and in our case was less than 1 µs, after which time a steady
state solution is applicable. The cells used in our experiment were chosen such that they
would be spherical in solution; thus, the geometric factor f was taken to be 1. Likewise, the
conductivity of the cell membranes were small compared to the conductivity of the cellular
interior and the exterior, so g was also taken to be 1. The electric field E was simply the
potential difference applied across the electrodes V , divided by the electrode spacing d.
In order to get an expression for the total transmembrane potential, one must add to
this the rest transmembrane potential. This value is typically taken to be about 100 mV,
with the cell interior being a lower voltage than the exterior. The total transmembrane
potential of an impermeable cell in our experiments was thus given by:
Vtrans (θ) = Vrest + 1.5r
V
cos(θ).
d
(4.1)
Electroporation occurs for those parts of the cell membrane where Vtrans (θ) exceeds the
breakdown voltage. The above equation predicts that:
• The transmembrane potential is largest near the poles of the cell which face the
electrodes.
• Because of the Vrest term, the transmembrane potential will be highest on the side of
the cell which faces the anode.
• The transmembrane potential should be highest for those cells which have the largest
radii. As a result, large cells will porate at lower fields than small ones.
While the existing literature on electropermeabilization is truly vast, apparently, there
61
Figure 4.1: Diagram showing how the optical tweezers apparatus integrates with the bulk
electroporation experiment. Reprinted from Analytical Chemistry, Vol 83, Henslee et al.,
Electroporation dependence on cell size: an optical tweezers study, Pages No. 3998-4003,
Copyright (2011), with permission from Elsevier [9].
have been no previous definitive experimental studies of the relationship between cell size
and electropermeabilization parameters. We summarize relevant previous work below. Frequently, the cell radius dependence of Eq. (4.1) is assumed and used as a basis for subsequent
analysis in experiments.
4.1 Experimental Setup
Because a uniform field was desired, the channel design described in the technical chapter
was replaced with a channel type created by Brian Henslee of the Lee group. A 15 mm
long, 1 mm by 1 mm channel was milled into a piece of PMMA. Copper tape was then
placed along the walls of this channel, creating electrodes that were 1 mm in height. Glue
was then used to fix a glass coverslip to the bottom of the device.
Roughly 600 mW of laser power, as measured at the specimen plane, was used by
the optical tweezer system to hold cells in place throughout the electroporation process.
Cells were brought towards the middle of the channel in order to minimize any fringing
of the electric field that might be occuring near the electrodes. The optical tweezers also
62
Figure 4.2: a) Schematic showing the BEP channel. Notice that the copper tape runs
up the side of the channel (inset). b) A photograph of a channel. This particular channel
features thinner copper tape than most of the channels used.
allowed us to move cells far away from other cells in solution, thus minimizing any cell-cell
interaction effects. Cells were held roughly 20 µm above the surface of the coverslip. Given
enough time, cells eventually adhere to the surface of the flow cell, at which point the laser
cannot manipulate them. The amount of time required for this to happen depended on cell
type. Of the cells tested, K562 cells were found to be the least sticky and usually could be
manipulated for at least 15 minutes after being inserted into the flow cell. Other cells, such
as mouse embryonic stem cells, adhered to surfaces very quickly, requiring experiments to
be done quickly after adding the solution to the flow cell.
A Bio-Rad GenePulser Xcell was used to provide the pulses needed to induce electroporation. Typical rise times for this system were 1 µs. A series of pulses of increasing
voltage were applied to each cell. The pulses started at a voltage well below that required
to induce poration and continued until poration was observed. Pulses were usually on a
ms timescale, with at least 1 minute between each pulse to allow time to assess whether
poration occurred.
Poration was determined using PI dye. PI dye typically has low fluorescence in solution.
However, once it comes into contact with RNA, which is present in the cellular interior,
63
its fluorescence increases by a factor of roughly 30. It is commonly used in live/dead
tests on cells because it cannot normally pass through the cellular membrane. Following
electroporation, the dye leaks into the cell, binds with RNA in the cytoplasm and fluoresces,
making it easy to determine when poration has occurred [74].
Our primary test cell was K562, a type of immortalized leukemia cell line, purchased from
American Type Culture Collection (catalog number CCL-243). Additional experiments
were also done with NIH-3T3 cells and mouse embryonic stem (MES) cells. Culture media
and additives were purchased from Invitrogen. Cells were cultured in RPMI 1640 medium,
with 10% newborn calf serum (heat-inactivated), 2 mM L-glutamine and 1 mM sodium
pyruvate. Cells were cultured in 25 cm2 T-flasks incubated at 37◦ C under an atmosphere
of 5% CO2.
Frequently cells were found to be permeable to PI dye and, thus, fluorescent prior to any
poration attempt. This problem was found to be heavily dependent on the cell growth cycle.
Cells harvested when the cell concentration was very high or very low were almost always
found to be fluorescent. To minimize this prior to each experiment, cells were harvested
during their growth phase (< 80% confluence). The cells were then centrifuged and washed
in Dulbecco’s phosphate buffered saline (DPBS). The cells were then resuspended in a
mixture of DPBS and 100 mM PI dye.
4.2 Results
An example of a typical single cell electroporation near the minimum field required for
poration can be seen in Fig. 4.3c. As predicted, the dye enters through the cells anodefacing pole. Usually, we observe dye entering a cell near-symmetrically, but we never have
seen it enter preferentially from the cathode-facing side.
The results of the size dependence experiments can be seen in Fig. 4.4. Rols and
Teissie [75] claim that, while the basic fact of poration is determined solely by the amplitude of a pulse, the degree of poration can be affected by the length of a pulse. In
order to test this, in addition to 1 ms pulses, we also conducted tests with 100 µs pulses.
64
Figure 4.3: (a) Diagram of a cell in an applied poration field. The radial angle, θ , on
the cell membrane is measured relative to the direction of the electric field. (b) Schematic
top view of a permeabilization cuvette. Cells were held by the optical tweezers midway
between the electrodes and about 20 µm above the coverslip defining the bottom sidewall.
(c) Sequence showing propidium iodide fluorescence of a K562 cell permeabilized by a nearthreshold electric field applied at t = 0. Shown are times (i) t = 0, (ii) t = 5 s, (iii) t =
20 s, and (iv) t = 60 s (note that the fluorescence signal shows saturation in (iii) and (iv)).
Reprinted from Analytical Chemistry, Vol 83, Henslee et al., Electroporation dependence on
cell size: an optical tweezers study, Pages No. 3998-4003, Copyright (2011), with permission
from Elsevier [9].
65
Figure 4.4: Minimum applied electric field to induce poration vs. cell radius. Red: K562,
Blue: MES cells, Green: NIH-3T3 cells, Empty Circle: K562 single 1 ms pulse, Filled Circle:
K562 sequence of 10 1 ms pulses, +: K562 single 100 µs pulse, Empty Diamond: MES
single 1 ms pulse, Filled Diamond: MES sequence of 10 1 ms pulses, Triangle: 3T3 single
1 ms pulse. Reprinted from Analytical Chemistry, Vol 83, Henslee et al., Electroporation
dependence on cell size: an optical tweezers study, Pages No. 3998-4003, Copyright (2011),
with permission from Elsevier [9].
66
Our results confirm these predictions, as the poration thresholds for the 100 ms pulses are
indistinguishable from the 1 ms pulses. In order to address the concern that single pulse
measurements may miss successful poration because the degree of poration may be below
our detection sensitivity, we also conducted measurements using ten one millisecond pulses
separated by 100 ms intervals. Much like the 100 µs pulses, these results are indistinguishable from the single 1 ms pulses. In all successful porations, the final fluorescence signal
was at least an order of magnitude larger above our minimum detection sensitivity. This
leads us to the conclusion that we observe all successful attempts.
The data show that electroporation is a stochastic process; that is to say that seemingly
identical cells will porate at different threshold electric field values. This is unsurprising; it
was previously found that this was the case in similar experiments by other researchers on
planar lipid membranes [11, 13, 14].
Especially striking, though, is that the data fails to offer any support for the notion that
the field needed to porate a cell depends on cell size. The predicted inverse dependence on
cell size is clearly not observed. To test whether or not this was an oddity of the K562 line,
we conducted further experiments on the MESc and 3T3 cells. The electric field needed
to induce poration varied between the three cell types, but all confirmed the lack of size
dependence. In particular, the large size variance of the MESc allowed a factor of 5 range
in cell radii. Instead of the expected result that our experiment would reveal a critical value
for the transmembrane potential, what we actually found was that a critical value of the
electric field determined the success of poration. The results can be seen in Table 4.1.
An alternative way to examine the issue is to assume that Eq. (4.1) is correct and to
plot the critical transmembrane potential Vc resulting from the applied critical value of
the electric field Ec . We assume the rest transmembrane potential to be small and, thus,
that Vc = 1.5rEc cos(θ). Again, in the literature, the critical value of the transmembrane
potential has been believed to be constant, but that is not the case here; instead, the critical
field is constant, leading to the result that Vc is roughly linear in r. It is interesting to note
that all the measured values for Vc fall within the range of 200-1500 mV, which is the range
reported in the literature.
67
Figure 4.5: Critical transmembrane potentials implied by our data. Also included are the
results of Zimmerman et al. which can be seen to also potentially fit the same pattern. Red:
K562, Blue: MES cells, Green: NIH-3T3 cells, Empty Circle: K562 single 1 ms pulse, Filled
Circle: K562 sequence of 10 1 ms pulses, +: K562 single 100 µs pulse, Empty Diamond:
MES single 1 ms pulse, Filled Diamond: MES sequence of 10 1 ms pulses, Triangle: 3T3
single 1 ms pulse, X: Zimmerman data (Zimmerman report cell sizes in terms of volumes,
for this figure we assume spherical cells.) Reprinted from Analytical Chemistry, Vol 83,
Henslee et al., Electroporation dependence on cell size: an optical tweezers study, Pages
No. 3998-4003, Copyright (2011), with permission from Elsevier [9].
Cell Line
K562
MESc
3T3
Average Threshold Field
(V/cm)
692
555
509
Standard Deviation
(V/cm)
32.0
30.1
22.2
Table 4.1: The average threshold fields required to induce poration
68
4.3 Effect of the Laser on Measurements
One possible objection to the above results is that the trapping laser may affect the electroporation process in some unforseen way. In order to evaluate this possibility, three tests
were undertaken.
1. Normally, in taking the data, the laser power at the specimen plane was kept at roughly
600 mW in order to ensure that the cell was held tightly though out electroporation.
With the 10 pulse data, in particular, maximum trap power was necessary to ensure
that the cell was not knocked free by the bubbles created in the solution near the
electrodes by the pulsing sequence. In order to determine if the laser was affecting
results, we repeated the measurement of the critical electric field outlined above but
kept the laser power at the absolute minimum required to manipulate the cell, reducing
the laser power by a factor of 10. Because the laser power was so much lower, only
data for one pulse experiments could be obtained. Over the course of four trials, we
found the threshold field needed to induce poration to be 685 V/cm, which matches
well with the value of 692 V/cm that we found for the high laser power experiments.
2. As a second test, we turned the laser off for the 1 ms period that the pulse was applied.
The laser was shut off using an IntraAction model DTD-274HD6 AOD as a switch.
The poration was done using a custom power supply created by Professor Lafyatis.
Both the power supply and the AOD were controlled with a computer output and
handled with a Labview program. The average measured threshold field as a result of
this experiment, was 683 V/cm, again agreeing with the value of 685 V/cm obtained
in the original experiment.
3. As a final test, we used 3T3 cells which attached to the surface of the glass coverslip.
These cells did not move throughout the poration process, even in the presence of
significant bubbles, since they were well adhered to the surface of the glass. We
conducted experiments with the laser on and focused on a cell and with the laser
completely blocked throughout the entire process. No substantial difference was found.
69
An additional concern was whether our data depended on the interval between permeabilization attempts. In order to assess this, we measured the threshold field for intervals
ranging from 15 s to 2 minutes and found no dependence.
Electroporation is known to be temperature dependent. In order to determine whether
the current through the device as a result of the pulsing was causing heating of the channel,
we used a Victory Engineering model 42A29 small diameter thermistor to measure the
temperature of the solution in a channel through a series of pulses. The channel was
filled with phosphate buffered saline (PBS) and pulsed with 10 1 ms pulses at 70 V. The
experiment was then repeated at 2 V intervals, all the way up to 84 V (840 V/cm field),
waiting 1 minute between pulses. Throughout the entire sequence, the temperature of the
device increased by less than 2◦ C.
4.4 Effect of Pulsing History on Measurements
The experimental procedure for all the above measurements includes a series of pulses
whose amplitudes are incremented upwards until a poration event is observed. A natural
question that arises from this is what, if any, impact the pulsing history in our experimental
procedure has on the poration threshold. The effect of repeated sub threshold, pulses on
a cell are not understood, and it is possible that the previous pulses might act to lower,
or even raise, the threshold field required for poration. A full investigation of this issue
would require a huge amount of data, so we instead conducted an experiment to determine
whether any effect that might exist would have a large impact on our results. The intent is
to conduct two experiments. In the first, we pulse the cell repeatedly with pulses 2 standard
deviations below the previously measured threshold field. In the second, we pulse the cell
with a pulse 2 standard deviations above the previously measured threshold field. If the
pulsing history impacts the data, we expect to see that, in the low field tests, the cell will
eventually porate, even though the measured threshold value is never exceed. Likewise,
in the high field test, we would expect the cells to require multiple pulses to porate, even
though the measured threshold is exceeded with the very first pulse.
70
Measurement
Below Threshold
Applied
Field
(V/cm)
415
Number of
Cells
(V/cm)
6
Mean
Size
(µm)
17
Above Threshold
575
8
16
Results
1 cell porated on 1st pulse, others
failed to porate after 8 or 9 pulses
all cells porated on 1st pulse
Table 4.2: Results of the pulsing history experiments
First, in order to set a control, we established an average threshold field for a population
of K562 cells, using the same method used in the above experiments. Because this experiment was carried out roughly a year after the first set of experiments, and used a different
cell population, we found that the average values found in the above experiments were no
longer applicable, forcing us to evaluate them a second time.
With this done, we then carried out two experiments. First, we applied a series of
pulses to cells separated in time by 1 minute; however, instead of incrementing the pulses
upward each time as in the other experiments, all pulses were carried out at a voltage 2
standard deviations below the measured average threshold for poration (which corresponds
to a field or voltage roughly 20% smaller than the threshold one). In the second experiment,
we exposed cells to voltage pulses two standard deviations above the measured average
threshold.
The results are outlined in Table 4.2 and suggest that the pulsing history does not
strongly influence the results. In the 6 cases of cells exposed to pulses below the threshold,
1 of them porated on the first pulse, but the remaining 5 stayed unporated for as long as
they were held by the tweezers (typically 8 or 9 pulses, at which point bubbles began to
fill the channel). This leads to the conclusion that previous pulsing history cannot result
in a decrease in threshold field of more than 20%. In the 8 cases of cells pulsed at above
threshold, pulses all porated on the first pulse, again suggesting that the pulsing history
has no more than a 20% impact.
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4.5 Effect of the Actin Cortex on Poration
Eukaryotic cells, like K562 cells, possess a rigid cytoskeletal network. This cytoskeleton
provides structure to the cell and is also used by the cell for intracellular transport and a
variety of other functions [29]. The cytoskeletal network is comprised of three different types
of proteins, which work together to provide structure thoughout the cell. But, of particular
importance to electroporation, is actin, which forms a mesh-like cortex in the interior of the
cell that the membrane attaches to [29]. The impact that this cortex has on electroporation
is not well understood. Eq. (4.1) assumes that the cell membrane is a thin, insulating
layer and that the cell interior is a homogeneous conducting medium. The electroporation
description of the electropermeabilization process laid out by Weaver [11] and used by
Krassowska [10] assumes that permeabilization is a membrane phenomena. Neither take
into account non-membrane aspects of the cell, like the actin cortex. Previous experiments
by other groups using similar dye-based techniques have found that the actin cortex is at
least partially destroyed during successful poration [34], so perhaps that breakdown plays
some role in permeabilization. Previous results by Rols and Teissie [31] disrupted the
spectrin-actin network of red blood cells (an elastic mesh in red blood cells that the cell
membrane attaches to) and found a small change in the critical transmembrane potential
from 1.0 kV/cm to 1.2 kV/cm but did not address size dependence specifically. We are
aware of no results examining the actin cortex of eukaryotic cells specifically.
In order to assess whether or not the actin cortex was responsible for the striking lack of
size dependence in our results, we performed an additional experiment. An electroporation
chamber was made in the manner laid out in Chapter 3, by placing a piece of copper tape
over a glass coverslip and cutting away the middle 1.3 mm. A channel several mm wide
was then cut in a double layer of parafilm, which was used to create a seal with a piece
of PMMA with holes drilled in it to allow for inlet and outlet of media. MESCs were
prepared in a solution of cell media and PI dye and then added to the electroporation
chamber. The MESCs were allowed to attach to the surface of the glass coverslip, and
a series of incremented voltage pulses were applied across the electrodes. Much like the
72
other experiments in this chapter, the pulses were 1 ms long and were separated in time by
1 minute. The first pulse was at 50 V, while each subsequent pulse was 10 V higher than the
last. After each pulse, a fluorescence image of the cells was taken in order to asses poration.
Once it was apparent no more cells were being porated, the pulses stopped. Afterwards,
the individual cell sizes, location in the channel and the voltages at which they porated
were recorded from the image file. Because the field in the electroporation chamber was not
uniform, it was necessary to perform an additional step to turn the recorded voltages into
electric field values. The electric field in the chamber was modeled in MATLAB, and the
model was then used in conjunction with the recorded data on cell location and poration
voltage to generate a poration field strength for each cell. This experiment was then repeated
with the added change that, prior to electoroporation, the cells were incubated for 1 hour
at 37 degrees Celsius with 0.5 µ M of Latrunculin A, a compound which inhibits actin
formation. This had the effect of effectively destroying the actin cortex. The results can be
seen in Fig. 4.6.
While the control experiment clearly follows the previous pattern with the poration field
not depending on size, the Latrunculin treated cells may follow a 1/r fit. More data for the
Latrunculin treated cells is needed to be able to come to a conclusion on this.
4.6 Discussion
Comparing data with previous experiments is notoriously difficult in the electroporation
field. The literature is vast, and experimental parameters other than cell size, most notably pulse length and total number of pulses, vary considerably from one experiment to
another. Some have even suggested that different mechanisms may be responsible for permeabilization, depending on whether longer pulses or shorter pulses (pulse lengths << 1
ms) are used [6, 76]. Other experimental parameters are only loosely controlled in many
experiments. Electrolysis bubbles, fringing fields and cells attached to surfaces are common
features of most experiments. Some of these features may correlate with cell size in some
non-obvious way. Experiments also evaluate the success of electroporation using a variety of
73
Figure 4.6: a) Poration data for the Latrunculin treated cells. The curve is a 1/r fit. b)
Poration data for the non-Latrunculin treated cells. Again the curve is a 1/r fit. One can
clearly see that the data matches the experiments earlier in this chapter in that the poration
field does not appear to depend on size.
74
Figure 4.7: The calculated electric field strength in the channel used for the actin experiment as a function of position for a 100 V pulse.
Figure 4.8: Example of poration images from the actin experiment. Cells shown are those
that were not treated with Latrunculin. a) Cells after an 90 V pulse b) Cells after a 100 V
pulse c) Cells after a 110 V Pulse.
75
methods. These include measuring the cells electrical properties (such as conductance) [77],
observed expression of reporter genes [35], successful electrofusion of two adjacent cells [37]
and the penetration of various sized molecules into the cellular interior [78].
Experiments dealing directly with cell size dependence are few and far between. Those
that do exist are mostly statistical measurements of cell populations, as opposed to single
cell experiments. Puc et al. [79] measured permeabilization yield as a function of applied
electric field for a population of DC-3F cells (a line of Chinese hamster fibroblasts) and
found that they got good agreement with theory, assuming that cell size was the only
source of threshold field variation. Hojo et al. [80] measured permeabilization efficiency of
Saccharomyces Cerevisiae (a type of yeast) cells as a function of cell size and found that
permeabilization rates were higher for small cells than they were for large cells, which is
the opposite of what theory would predict. Most recently, the University of Pittsburgh
group carried out single cell studies on the role of cell size in permeabilization, but direct
comparison with the work outlined here is not currently possible.
The only directly relevant single cell measurements to compare with this work is Zimmermann’s double Coulter counter experiment carried out shortly after the discovery of
electropermeabilization [77]. In a Coulter counter, two chambers containing conducting
media are connected by a micro channel. A pump is then used to create a flow through
the micro channel containing cells to be sized. As non conducting cells pass through the
channel, they cause an increase in the resistance across the microchannel. The size of this
increase can be used to determine the volume of the cell. If one then ramps the potential
difference across the channel while the cell is still in the channel, it was found that there
will come a voltage at which the resistance of the channel drops. This drop was identified
with electropermeabilization of the cell membrane. This device was used to measure the
size dependence of the threshold breakdown voltage of guard cell protoplasts in Vicia faba.
The results are included on our Fig.4.5. While the data fit with the accepted model of a
constant threshold transmembrane potential and a threshold field that depends on cell size,
their errors are large enough that it could equally well fit a model with a threshold field
that does not depend on cell size. Thus, the results do not have the precision to distinguish
76
between accepted theory and the alternative model we suggest.
There are several possible explanations for why the results in this chapter do not agree
with the theory laid out in the introduction. Certainly, to the extent that the cell can be
modeled as an insulating shell with a conducting interior, Eq. (4.1) accurately describes the
steady state transmembrane potential. In the past, it has been assumed that the critical
transmembrane potential is relatively constant across different cells, certainly at least within
the same cell line, but perhaps this is not the case. If smaller cells have a lower critical
transmembrane potential than larger cells, then that could explain the results we see. This
could be reasonable if, for example, smaller cells have a higher surface tension. Then,
according to theory, that would result in a lower critical transmembrane potential.
Assuming that critical transmembrane potential does not depend on size, another possibility is that the commonly held view that permeabilization is just a matter of increasing
transmembrane potential above a threshold value is inaccurate. Eq. (4.1) is only applicable in the steady state. It does not accurately describe the situation that exists during
the membranes initial capacitive charging, nor does it apply after poration occurs, and
the membrane becomes electrically conductive. The initial electric field within the cell is
independent of radius, and, during the charging process, large current densities flow, and
screening ion gradients form within the cell. It is possible that some process crucial to
permeabilization requires the cell to have a large internal electrical field during this initial
charging period, thus making the permeabilization process independent of cell size. In the
light of the results of the actin cortex experiments, this seems especially plausible; perhaps
field induced change in the cytoskeleton is necessary for permeabilization to occur. A third
possibility is that the field induced breakdown of the membranes electrical insulation and
its permeability to molecules such as PI dye do not occur simultaneously. Generally, it is
assumed that the same permeabilization process that leads to the membrane’s electrical
conductivity also results in it’s permeability to dyes like PI, but these two things have
never been demonstrated to occur coincidentally. Perhaps electrical breakdown is accurately described by Eq. (4.1), but some further process is required to allow for molecules
at least as large as PI to penetrate the cell interior. Again, it is possible that some change
77
in the cytoskeleton is required here. Perhaps a partial breakdown of the cytoskeleton is
a necessary precondition for dye to enter the cell, and this process is independent of cell
size. Finally, cell membranes are not homogeneous insulators [81], and the cell interior is
not a homogeneous conductor. Membranes feature large numbers of channels, transporters,
other protein structures and variant lipid rafts, while the cell interior features a variety of
internal structures and compartments. Within the generally accepted theory, these presumably have a role in determining threshold permeabilization potentials for a particular cell
lines. We suggest that perhaps these have a broader role that is missed in the first order
modeling the cell membrane as a homogenous insulator, and that is what is being seen in
our measurements.
4.7 Conclusion
While these results have turned up a surprising scaling relationship for electropermeabilization, at this time little can be said about what it tells us about permeabilization as a
process. The simplicity of the scaling of the applied threshold permeabilization field with
cell radius—it is constant—leads us to suspect that there is a fundamental feature important
to the permeabilization process that has yet to be uncovered. Experimentally, an important
future direction is to investigate other parts of parameter space for the electropermeabilization process. Notably, experiments utilizing shorter pulse lengths would be especially
interesting. Additional data are also needed on the impact that the actin cortex has on the
permeabilization process. A further potential avenue of research is to evaluate what the
relationship is between a cell membranes electrical breakdown and its permeabilization to
molecular dyes.
78
Chapter 5
Nano-Electroporation
Experiments
The last chapter addressed bulk electroporation, a common laboratory method of transfecting cells. In BEP, cells are placed in solution between two parallel plate electrodes and
subjected to a uniform electric field. BEP is an easy-to-perform process that requires little
preparation time or training and yields high transfection rates. As a result, it is an extremely popular experimental technique used in laboratories around the world to transfect
genes and drugs through the cell membrane [6, 35, 82]. Despite this, it has limitations.
Notably, it is extremely difficult to obtain true dose control with bulk electroporation. According to current theory, in BEP, pores are opened up in the cell membrane, at which point
small molecules can diffuse into the cell. Factors such as cell size, local non-uniformities in
the electric field, cell to cell variations and the stochastic nature of electroporation can all
lead to differences in porated area and, thus, to differences in the degree of transfection.
Further, because of the stochastic nature of diffusion, transfecting small numbers of copies
of molecules like, DNA, with repeatability has proved impossible, and, as a result, BEP experiments use large numbers of copies of genes (> 108 ) [83]. Achieving precise dose control
is critical for a number of research and therapeutic applications, such as evaluating drug
efficacy for cancer treatment.
Another problem with BEP is that larger molecules such as DNA or quantum dots do
not penetrate the cell membrane directly, but, instead, are gradually internalized over the
course of hours in an endocytosis process [6, 35]. Additionally, as the transfected molecules
79
do not pass directly through the membrane, there is the concern that, even once they reach
the cell interior, they may be enclosed in an endosome and be ineffective.
Micro-electroporation, or MEP, transfection was discussed in Chapter 1 and is an alternative to BEP. MEP works by pressing the cell up against a micrometer sized channel
through which the applied electric field must pass. Recently, MEP experiments have been
done by a variety of researchers [42, 43, 84–88]. MEP can porate cells using lower fields
and can attain lower cell mortality than BEP, but MEP delivery mechanisms are similar to
that in BEP [89–92]; the process is still diffusion, driven and large molecules still enter the
cell via endocytosis. As a result, MEP cannot address either of these two issues with BEP.
In nanochannel electroporation, the technique we developed, a cell is placed up against a
channel no more than a couple hundred nanometers across. Because the cross sectional area
of the channel is so small, the electric field reaches extremely large values (≈ 6 ∗ 107 V/m in
our experiment) due to the compression of the electric field lines as they enter the channel.
NEP thus exposes a small area of the cell membrane to an extremely high electric field.
Unlike MEP or BEP, NEP does not work by diffusion of the transfection agent, but, instead,
electrophoretically drives molecules through the cell membrane using the enormous electric
field through the channel. These unique features of NEP allow for cell mortality rates of
nearly zero while allowing for dose control repeatable to within 10%. Additionally, large
molecules transfected using NEP pass through the cell membrane nearly instantaneously,
avoiding endocytosis and ensuring that they are chemically active in the cytosol.
5.1 Methods
The NEP device used throughout this chapter consists of two microchannels connected by
a nanochannel several microns in length (Fig. 5.1). The diameter of the nanochannel in
our experiments was approximately 90 nm. One microchannel holds the cell, while the
other contains the transfection agent to be delivered. Optical tweezers are used to position
a cell precisely at the end of the first microchannel, thus ensuring good contact with the
nanochannel. A series of pulses, each lasting several ms, is then used to simultaneously
80
porate the cell and electrophoretically drive the molecule to be transfected into the cell.
Dose control is achieved by controlling the duration or number of pulses.
The devices were made by Pouyan Boukany of Dr. Lee’s group using a DNA combing and imprinting (DCI) method first described in 2010 [93]. The technique can be used
to form an array of laterally ordered nanochannels interconnected to microchannels with
controllable sizes and rounded shape over arbitrarily large surface areas (Fig. 5.1). The
process starts with a microridge patterened polydimethylsiloxane (PDMS) stamp. A solution of 0.5 wt% calf thymus DNA (75 kbp USB Co.) in TE buffer was then “combed”
over the polymer stamp (see Fig. 5.1a). The combing process was done by hand, peeling
the PDMS stamp away from a glass coverslip in the presence of solution, as shown in the
figure. This produces an array of stretched DNA nanostrands across the ridges of the stamp
(see Fig. 5.1a). These nanostrands form the template for the nanochannels. In order to
control the width of the nanochannels, the stamp was then sputter-coated with gold, creating gold coated DNA nanostrands of controllable thickness. The stamp was then placed
face down on a silanized glass substrate and imprinted by the low viscosity resin ethylene
glycol dimethylacrylate (EGDMA) (93 wt% EGDMA, 6 wt% hydroxyethyl methacrylate
(HEMA)). The resin was cured using UV light (wavelength, 365 nm; intensity, 4 mW cm−2 )
for 20 minutes in a nitrogen atmosphere. The stamp was then peeled off the slide, leaving
an array of microchannels connected by gold coated DNA nanostrands. The nanostrands
were removed by soaking the slide in gold etchant (GE8111, Transene Company Inc.) for 48
hours and then thoroughly rinsing them with deionized (DI) water. The chip was soaked in
Piranha solution (H2SO4/H2O2, 7:3) for 3 hours to make it hydrophilic. A PDMS ceiling
is then placed on top of the microchannels, creating a seal and preventing leakage from one
set of channels to the other (Fig. 5.1b).
Each side of the device is then filled with buffer, and electrodes are placed into each. The
distance between these electrodes was 2 mm, but, because more than 99% of the voltage
is dropped across the nanochannel, the spacing is not important. The NEP chip was then
placed in the optical tweezer setup described in Chapter 3. Initial experiments were carried
out on the primary optical tweezer device before later being moved to the confocal setup.
81
Figure 5.1: a)Top: SEM image of a DNA nanostrand after having been combed across two
PDMS ridges. Bottom: The manufacturing process of the NEP device. b)Left: schematic
of an NEP chip, covered by a PDMS lid with electrodes placed in reservoirs. Middle:
optical micrograph of a Jurkat cell in the left microchannel and positioned at the tip of
the nanochannel using optical tweezers. The right microchannel contains gene or drugs.
Right: SEM image of side view cut of a nanochannel. The nanochannel is approximately
90 nm in diameter and approximately 3 µm long. Adapted from Macmillan Publishers Ltd:
Nature Nanotechnology, Vol 6, Boukany et al, Nanochannel electroporation delivers precise
amounts of biomolecules into living cells, Pages No. 747-754, Copyright (2011).
The optical tweezers were used to manipulate cells to the tip of a microchannel, at which
point the cell made contact with the nanochannel. Usually, once the cell made contact with
the tip of the channel, it would stick, removing the need for further optical trapping. The
laser was then moved off the cell for the duration of the poration experiment. Pulses varied
from 1-50 ms and from 150 to 350 V. Between 1 and 10 pulses were applied. The experiments
done in this chapter were largely carried out in conjuction with Pouyan Boukany.
A major difficulty in integrating the NEP chip with the optical tweezers technology was
cell adhesion. Cells readily stuck to the EGDMA surface after only a few minutes, making
it difficult to do multiple experiments in one session. Further, even if cells were free of
adhesion initially, it was very easy for them to stick to the sides of the microchannel when
maneuvering them into position next to the nanochannel. The “gold standard” of combating
82
Figure 5.2: Comparison of NEP with BEP and MEP. a, Left: time dependence of PI dye
uptake for NEP (180 V/2mm, blue curve), BEP (70 V/mm, black) and MEP (150 V/2 mm
for 1 mm (red) and 60V/2 mm for 5mm (green) cases). All used a single 10 ms pulse. Right:
results of the finite-element simulation for the channel, including the maximum electric
field (max(E)), the electrophoretic exit velocity and the channel transit time (assuming an
electrophoretic mobility of 1 1028 m2 V21 s21 for the PI dye). b, Fluorescence micrographs
of a cell after being transfected with PI dye by NEP, MEP (1 mm case) and BEP. Conditions
are as in a. The time series of captured images is specified at the bottom of each image.
Solid white horizontal lines show the location of micro/nanochannels. The loaded cells in
NEP, MEP and BEP devices are specified by dotted circles. The transverse axis was defined
by dotted lines to measure the intensity across the cell section (01 represents the distance
from top to bottom of the cell). c, Fluorescence intensity profile along the transverse axis
of the cell (shown in b) at different times. Adapted from Macmillan Publishers Ltd: Nature
Nanotechnology, Vol 6, Boukany et al, Nanochannel electroporation delivers precise amounts
of biomolecules into living cells, Pages No. 747-754, Copyright (2011).
83
cell adhesion in the literature is, usually, coat the surface of the chip in PEG; however, there
was concern that doing so would cover up the entrance to the nanochannel. Eventually, we
settled on a coating of bovine serum albumin (BSA), which is a much smaller molecule. The
chip was rinsed with DI water three times and soaked in 0.1% BSA containing DI water
for 30 min the night before experiments, and this process largely removed cell adhesion
problems.
Fig. 5.2 compares the transfection of PI dye for NEP, MEP and BEP. MEP experiments
were conducted by Brian Henslee. PI dye is a type of dye which fluoresces in the presence
of nucleic acids (see section 4.1). In the BEP case, a single 10 ms pulse with a field strength
of 70 V/mm resulted in a gradual increase of fluorescence over a time scale of 150 s, as dye
diffused into the cell (this is a repeat of the experiments seen in Section 4.2 and Fig 4.3).
Fluorescence starts at the poles of the cell and gradually creeps into the cell interior. The
MEP case exhibited similar behavior. Dye entered the cell through a 1 µm microchannel
and slowly diffused into the cell over the course of about 25 s (Fig. 5.2). In contrast, during
NEP, the PI dye (which possesses an electric charge) is accelerated by the strong electric
fields in the nanochannel and rapidly flows into the cell. Within 30 ms, fluorescence is seen
in the center of cell, and, by 2.3 s, the entire cell is bright. This unique electrophoretic
effect is what allows for the precise dose control that we observe.
5.2 Delivery and Dosage Control
In order to study dosage control, Jurkat cells (diameter ≈15 µm) were transfected with an 18mer oligodeoxynucleotide (ODN) (G3139), conjugated with the dye Cy3, to allow fluorescent
detection. The NEP was conducted using a single 220 V pulse of varying durations. The
fluorescence of cells after the pulse was measured by reading the pixel values of CCD images
to determine the relative amount of ODN transfected. The amount of ODN transfected was
found to be a nearly linear function of pulse duration for durations of 5 to 20 ms. For pulse
durations greater than 20 ms, intensity increases level off, following a saturating exponential
function (5.3). Similar results were observed for leukemia patient cells with diameters of
84
Figure 5.3: The result of dose control experiments for NEP. a, Jurkat cells transfected with
Cy3-ODN using single 220 V/2 mm pulses of varying durations. Transfection is quantified
by the fluorescence signals, which are normalized to the intensity at 60 ms (scale bar, 15 µm).
The saturating fluorescence fits a saturating exponential function. b, Top: fluorescence
micrographs of five cells transfected by NEP chip (scale bar, 60 µm). Bottom: five cells are
transfected simultaneously (left) and individually (right) by NEP, showing the repeatability
and reliability of the NEP performance. Intensity is expressed in arbitrary units (a.u.). s.d.,
standard deviation. Adapted from Macmillan Publishers Ltd: Nature Nanotechnology, Vol
6, Boukany et al, Nanochannel electroporation delivers precise amounts of biomolecules into
living cells, Pages No. 747-754, Copyright (2011).
approximately 8 µm subjected to 200 V pulses. Fig. 5.4 compares patient cells subjected to
a 10 ms pulse, a 20 ms pulse and 4 10 ms pulses.
In order to assess the repeatability of NEP, two additional tests were undertaken. In the
first, five cells were simultaneously transfected in an NEP array. In the second, another five
cells were individually transfected using identical NEP settings. The cell-to-cell variation in
the amount of ODN delivered for the two experiments was ±10% and ±12%, respectively.
By comparison in, BEP, the amount of ODN delivered to cells varied greatly. Over nine
trials, cells exhibited an average intensity of 41.4, with a standard deviation of 28.4.
As a second study of dosage control, Jurkat cells were transfected with glyceraldehyde 3phosphate dehydrogenase (GAPDH) messenger RNA (mRNA) molecular beacons. mRNA
is the RNA that carries the blueprint for a specific protein from the nucleus, where the
information is stored as DNA, to the ribosome, where it is used to manufacture the protein
itself. GAPDH mRNA is the mRNA which carries the blueprint for the protein GAPDH,
an enzyme involved in the breakdown of glucose. A molecular beacon is a probe with a
fluorophore at one end and a quencher at the other end of a stem hairpin oligonucleotide
85
Figure 5.4: The fluorescent image of a leukemia patient cell held near the tip of a nanochannel connected to a microchannel pre-filled with FITC-ODN (a) before NEP, and after NEP
(200 V/2 mm) with (b) one 10 ms pulse, (c) one 20 ms pulse and (d) four 10 ms pulses.
Adapted from Macmillan Publishers Ltd: Nature Nanotechnology, Vol 6, Boukany et al,
Nanochannel electroporation delivers precise amounts of biomolecules into living cells, Pages
No. 747-754, Copyright (2011).
86
Figure 5.5: The result of dose control experiments for NEP. a, Molecular beacon (MB) before
hybridization shows dye is quenched (top). After hybridization with target, fluorescence is
restored (bottom). b, A Jurkat cell transfected (220 V/2 mm) with GAPDH-MB produced
fluorescence, but a cell transfected with a scrambled sequence remained dark (scale bar,
15 µm). c, Relative MB fluorescence intensities for various pulsing programmes (measured
45 min after NEP). Adapted from Macmillan Publishers Ltd: Nature Nanotechnology, Vol
6, Boukany et al, Nanochannel electroporation delivers precise amounts of biomolecules into
living cells, Pages No. 747-754, Copyright (2011).
structure (Fig. 5.5) [94, 95]. The oligonucleotide structure is designed to be complementary
to the specific type of RNA being probed. Under normal circumstances, the quencher
suppresses the fluorescence of the fluorophore; however, once the beacon comes into contract
with its complementary target, it binds to it, breaking the hairpin structure and separating
the fluorophore from the quencher, restoring fluorescence. Molecular beacons allow for realtime expression and localization of specific mRNA within living cells. Successful delivery of
the GAPDH molecular beacon can be seen in Fig. 5.5. As a control, a randomly scrambled
molecular beacon was also transfected to confirm the selectivity of the GAPDH beacon.
No significant fluorescence was observed with the control beacon. Fig. 5.5c summarizes the
fluorescence intensity inside the cells at different conditions. The GAPDH beacon signal
levels off at long pulse lengths or multiple pulses, indicating that all GAPDH mRNA in the
cell has been detected. Over prolonged time periods (hours), the hairpin structure of the
beacons can break apart, resulting in a false positive. NEPs quick delivery of probes into
the cell avoids this time-dependent fouling of the beacons [94].
87
5.3 Nanoparticle Delivery
A variety of applications require the transfection of large molecules and nanoparticles into
the cell interior. One example is the creation of induced pluripotent stem cells in mice,
which requires the transfection of four different DNA fragments [96]. Another example is
the transfection of nanoparticles directly into the cell interior in order to study the toxicity
of structures such as carbon nanotubes or metal oxide particles. Quantum dots possess
a bright and stable fluorescence that is resistant to photo-bleaching, and their small size
makes them suited to revealing biological mechanisms and processes within the cell at an
unprecedented level of detail. As mentioned in Chapter 1, larger molecules, such as DNA
or quantum dots, typically do not enter the cell interior directly during BEP. Instead,
they attach to the cell membrane and are internalized later through an endocytosis process
Zimmermann calls “electrointernalization” [6, 30, 35] (see Fig. 1.8). These molecules are
often trapped inside endosomes within the cell and thus may not chemically active [36]. As
shown below, despite their small size, quantum dots, in particular, are too large (≈ 10 nm)
to enter the cell through conventional BEP.
We carried out a study comparing the abilities of BEP, MEP and NEP to transfect
cells with quantum dots. The QD’s were conjugated with a COOH group, which both
makes them water soluble and gives them a negative charge, allowing them to be subject
to electrophoretic forces. Attempts to transfect Jurkat cells with QD’s using BEP were
unsuccessful. MEP was used to attempt to transfect QD’s into K562 cells and likewise was
unsuccessful (160 V, electrodes separated by 2 mm, 1 µm). In both cases, the quantum
dots remained stuck at the cell membrane, where perhaps later some might enter the cell
via endocytosis (Fig. 5.6). NEP, on the other hand, readily internalized the quantum dots
inside the Jurkat cells. Only 14 seconds after poration, a broad spray of quantum dots
was observed inside the cells, and, after 30 minutes, the quantum dots were uniformly
distributed about the cell interior. Other biomolecules, such as DNA, RNA and molecular
probes, can be conjugated onto quantum dots and delivered into cells in a similar way [97–
100]. Fig 5.6. shows that small numbers of quantum dots can also be controllably delivered
88
Figure 5.6: The delivery of QD’s to Jurkat and K562 cells. Quantum dots delivered
by BEP, MEP (1 µm channel) and NEP at 600, 60 and 14 s after poration respectively.
Location of channels is specified by solid white lines. Adapted from Macmillan Publishers
Ltd: Nature Nanotechnology, Vol 6, Boukany et al, Nanochannel electroporation delivers
precise amounts of biomolecules into living cells, Pages No. 747-754, Copyright (2011).
by NEP, a fact which is important for the prospects of using NEP to assess cytotoxicity of
nanoparticles.
Transfection of still larger agents was demonstrated using Cy3 labeled GFP plasmids (3.5
kbp). GFP plasmids are circular segments of DNA that encode for green fluorescent protein.
After being internalized, the plasmids migrate to the nucleus, and the cell begins producing
the protein. The produced GFP can then be seen using fluorescence microscopy. In both
BEP and MEP, the GFP plasmids did not penetrate the membrane initially. Instead, they
attached to the cell membrane and were internalized by endocytosis. In the case of BEP,
this took over an hour, while, for MEP, it took more than 60 s. These results are consistent
with previous observations [35]. Migration to the nucleus and the production of visible
GFP required many hours. Even 18 hours after transfection, no GFP fluorescence could be
observed. In the case of NEP, however, within 40 s of poration, significant Cy3 fluorescence
was observed in the cell interior. Migration of the DNA and GFP fluorescence were observed
within 6 hours. For quicker gene transfection, we found that simultaneous transfection of
genes with nanoparticles, such as gold or quantum dots, can be used to facilitate delivery.
This is roughly analogous to the role of the needle in micro-injection. This result has
not been observed in any previous experiment we are aware of, and the reason for it is
not understood. Fig. 5.7 shows the NEP transfection of a Jurkat cell using a mixture of
quantum dots and GFP plasmids. These plasmids were not attached to the quantum dots.
89
This procedure led to GFP expression within 3 h. We ran a viability/cytotoxicity assay and
verified that the cells in Fig. 5.7 were alive. The fact that large molecules, such as quantum
dots and GFP plasmids, enter the cytosol so easily during NEP, as compared to BEP and
MEP, suggests that the pores created during NEP are exceptionally large.
5.4 Theory
NEP is a fundamentally different process than BEP and MEP in several respects and
requires a unique theoretical model to understand it. We believe that the following model
captures most of the key observations described above. We note the following key features
of our model:
• All important activity takes place in the immediate vicinity of the nanochannel.
From an electrical standpoint, the microchannels in our microchannel-nanochannelmicrochannel devices are high conductance ”wires”.
• For most of the process, almost all the potential drop is across the high resistance
nanochannels (≈ 600M Ω). The current in the system is given by iN C =
Vapplied
RN C .
As
shown below, this feature helps to explain the near-linearity of the process with pulse
length and the repeatability of the transfection.
• All charged transfection molecules are swept by the electric fields through the
nanochannel and into the cell within 10 µs.
• Significant transfection only occurs during the applied voltage pulse. During that time,
poration is highly intense but localized to the immediate region of the nanochannel.
At the very least, large pores are created that little-impede large transfection agents
during the voltage pulse, and almost all of the transfection occurs at that time.
5.4.1 Modeling NEP as an Electrical Circuit
We will be modeling transfection of COOH conjugated quantum dots. The experimental
setup can be seen in Fig. 5.9. The media used in our experiments has a conductivity of
90
Figure 5.7: The delivery of GFP plasmids to Jurkat cells. a) Z-stack of confocal microscope
images (step size 1.1 µm) of a cell after being subjected to NEP with 3.5 kbp Cy3 labeled
GFP plasmid. The top left image represents the bottom of the cell, and the bottom right
image is the top of the cell. b-e) Comparison of the delivery of GFP plasmids by BEP,
MEP (5 µm channel, 60 V pulses with 2 mm electrode spacing, two 10 ms pulses), NEP
(two 5 ms 260 V pulses) and NEP + quantum dots. Fluorescence images: Cy3 (yellow),
nucleus (DRAQ-5, blue), and GFP (green). BEP was carried out on a NEON transfection
system at 1325 V with three 10 ms pulses for 105 cells. Adapted from Macmillan Publishers
Ltd: Nature Nanotechnology, Vol 6, Boukany et al, Nanochannel electroporation delivers
precise amounts of biomolecules into living cells, Pages No. 747-754, Copyright (2011).
91
1.5 S/m, which drops to 0.8 S/m after the addition of the buffer containing the quantum
dots. The nanochannel has a diameter of 90 nm and a length of 3 µm. The resistance
of the channel is then given by RN C =
l
σbuf f er A
≈ 590M Ω. The two microchannels have
a diameter of approximately 40 µm and a length of approximately 1 mm, giving them a
resistance of approximately 1 MΩ. This is negligible when compared to the resistance of
the nanochannel. We thus model the microchannels as wires and note that the placement
of the electrodes has no meaningful impact on experimental results.
The electrical model of the cell is based on that of Krassowska and Filev [10]. The
cell is assumed to have a diameter of 15 µm, and the interior is, for now, modeled as an
equipotential. The membrane is divided into two parts; Membrane 1 is that section of the
membrane which is adjacent to the nanochannel, while the rest of the cell membrane is
referred to as Membrane 2. Each membrane is modeled as a resistance in parallel with a
capacitance. Values for the membrane conductivity vary by a factor of about 100 in the
literature [101]. Fortunately, while the details of our model based understanding of NEP
depend on this value, the predicted degree of transfection does not. We use the value which
Krassowska and Filev used, 2 S m−2 for the surface conductivity (σ = 1 × 10−8 S m−1 ). The
membrane surface capacitance is more reliably known. We again use the number used
by Krassowska and Fileve of 1 × 10−2 F m2 . This gives the values of the resistance and
capacitance of Membrane 1 as 8 × 1013 Ω and 6 × 10−17 F. For Membrane 2, these values
are 710 MΩ and 7 pF. This model will hold as long as the membranes are intact.
The applied voltage satisfies Vapplied = VN C + VT M 1 + VT M 2 . We assume that, once
the transmembrane potential exceeds a small threshold difference, it porates. The value of
this potential difference does not matter much but is assumed to be roughly 1 V, based on
the literature as laid out in Chapter 1. Upon applying the pulse, almost all the applied
voltage is dropped across Membrane 1. It reaches the threshold transmembrane potential and porates in nanoseconds. Assuming the voltage drop across the porated Membrane 1 is negligible, from that point, Membrane 2 begins charging according to the equaR2
(1 − e−t/(RN C C2 ) ), where t is measured in milliseconds. In this
tion VT M 2 = Vapplied R2 +R
NC
model, Membrane 2 porates in 10’s to 100’s of microseconds. After Membrane 2 porates,
92
the current through the system is given by I ≈ Vapplied /RN C . The current flows until the
end of the pulse, which is typically 20 ms. Since the current is a constant for almost the
entire pulse, if we assume that a constant fraction of the current is accounted for by the
transfection agent, this explains the reproducibility of our results.
Pore Creation
Prior to the poration of Membrane 1, almost all of the applied voltage should be dropped
across that membrane after a few nanoseconds, according to the above model. Typically,
poration occurs when the transmembrane potential exceeds a critical value of around 1 V,
so, under this model, we expect the cell should porate at extremely low applied voltages
(such as a few volts). Despite this, contrary to expectations, no poration was observed
experimentally unless the applied voltage was around 200 V. There are at least two possible
explanations for this:
• It is possible that, at low voltages, the cell does porate, but the degree of poration
and the amount of transfection is below our detection threshold. The area of the cell
membrane exposed to the transfection agent in a cell exposed to a 100 nm nanopore is
only about 1% of that for a cell exposed to a 1 µm micropore. All other things equal,
this would mean an equal decrease in the amount of transfected material, which may
be below our detection sensitivity.
• The transmembrane potentials present at low voltages do not necessarily create large
pores, but, rather, may create a large number of small pores. Krassowska and Filev
write that: ”above 45 kV/m in the cell (transmembrane potential = 3.75 V) large
pores disappear altogether and only small pores (radius = 1 nm) are created” [10].
Perhaps for low voltage pulses (5-10 V), we actually do porate the membrane, but
only small pores are generated, which may be unable to pass the transfection agents
we use.
In either case, any poration current that does occur at low voltages would be carried by
ions in the PBS solution and not by our much larger transfection agents.
93
It is possible that the pore creation mechanism in NEP may be different than the one
that occurs in BEP and MEP. The fields created are enormous (several tens of MV/m)
and far exceed the values usually seen in typical BEP or MEP experiments. The ease with
which large transfection agents enter the cytosol in NEP suggests that extremely large pores
are created in the cell membrane adjacent to the nanochannel opening during the electrical
pulse. It is possible that there is even a complete breakdown or disappearance of the
membrane opposite the channel. Perhaps what occurs during NEP is not electroporation
at all but rather electrocompression [11] or some other mechanism.
At this time, the specifics of NEP are not fully understood. In particular, the mechanism
of pore formation and the number or size of the pores is not known. It is clear from the
experimental results, however, that high enough voltages will permeabilize the membrane
opposite the channel and allow the passing of nanoparticles to the cell interior.
Transfection Agent Transport
Unlike diffusion based techniques, like BEP and MEP, the transport of transfection agents
in NEP is electrophoretically driven. This occurs because of the extremely high fields within
the nanochannel. Since the voltage drop is almost entirely across the nanochannel after the
membrane porates, the electric field in the channel is approximately equal to the applied
voltage divided by the channel length. In our case, this is about 70 MV m−1 . The mobility
of the quantum dot is µQD = −1 ∗ 10−8 m2 V−1 s−1 , which means that the field produces a
drift velocity of about 700 µm s−1 . As a result, quantum dots enter the nanochannel through
a combination of drift and diffusion and are quickly swept into the cell by the field.
5.4.2 Finite Element Simulations
In order to compare NEP with MEP, finite element simulations were carried out on the
system described above, as well as on several different MEP channel designs in COMSOL
by Wei-ching Liao. In all such simulations, axial symmetry was assumed. The cells transmembrane potential, the electric field both in the channels and in the cell and the behavior
of the transfection agent were all modeled.
94
Figure 5.8: Geometries and computational meshes for nano- and microelectroporation
device simulations. (a) NEP from above. (b) MEP, this work. (c) MEP5. (d) MEP6.
The distortion of the cells seen in (c) and (d) are the result of suction from vacuum loading
reported in the literature for those devices. Adapted from Macmillan Publishers Ltd: Nature
Nanotechnology, Vol 6, Boukany et al, Nanochannel electroporation delivers precise amounts
of biomolecules into living cells, Pages No. 747-754, Copyright (2011).
For a cell with no surface charge, the static electric field is governed by Laplace’s Equation:
∇ · (σ∇V ) = 0,
(5.1)
where σ is the conductivity, and V is the electric potential. Once the potential has been
calculated, the electric field is given by E = −∇V . The transmembrane potential VT M then
is given by VT M = V (Sext −Sint ), where S denotes the surface of the membrane, and ext and
int denote the external and internal surfaces. In order to deal with the difficulty of creating
a mesh for the extremely thin cell membrane (5 nm), the concept of contact resistance
in heat conduction was utilized. In this method, the Laplace equation is simplified as a
one-dimensional equation within the membrane, since the electric currents tangential to
95
Figure 5.9: a) Left: a cell in an NEP device. Right: equivalent electrical circuit of the
electroporation system for an intact cell during NEP. b) Transport of transfection agents
into a cell. The zero of the vertical axis is the entrance of the nanochannel. During the
pulse, electric fields in the cell interior drive molecules through the cell membrane and deep
into the cytosol. Adapted from Macmillan Publishers Ltd: Nature Nanotechnology, Vol 6,
Boukany et al, Nanochannel electroporation delivers precise amounts of biomolecules into
living cells, Pages No. 747-754, Copyright (2011).
the surface can be ignored compared to those in the radial direction. In one dimension,
the equation can be solved analytically, which results in a linear voltage distribution across
the membrane. Once this is done, the membrane is modeled as an interface in the finite
element simulation, and the analytical solution for the membrane region is used to generate
boundary conditions for the internal cytoplasm and the cell exterior.
The simulations were used to study the transport of transfection agents through the
channel and into the cell. The computed electric field from the finite element simulation
was taken and used to numerically integrate the equation of motion for a molecule traveling
down the center of the nanochannel. We assume the molecule travels through the membrane
uninhibited. Within the cell, we reduce the quantum dot mobility by a factor of 60, a number
which is consistent with our observations of quantum dot diffusion inside the cell. After
rapidly traveling through the nanochannel, electric fields inside the cell inject the molecule
a significant distance into the cell. The results can be seen in Fig. 5.9b.
96
Channel Diameter
Voltage
∆Vchannel
Max(VT M )
Channel Length
Channel Area
Emax in channel
∆tchannel
v (electrophoretic)
NEP
90 nm
200 V
193 V
2.5 V
3 µm
0.006 µm2
6.43 ∗ 107 V/m
4.7 µs
490 µm ms−1
MEP
5 µm
10 V
0.75 V
2.63 V
5 µm
20 µm2
1.79 ∗ 105 V/m
3.9 ms
0.18 µm ms−1
MEP
1.5 µm
1.5 V
0.3 V
1.15 V
7.5 µm
1.8 µm2
4.65 ∗ 104 V/m
16 ms
0.006 µm ms−1
MEP
4 µm
1V
0.1 V
0.72 V
200 µm
12.5 µm2
531 V/m
35 s
0.002 µm ms−1
Table 5.1: Results of the finite element simulations. The final two rows are the time it takes
a quantum dot to traverse the length of the channel and the velocity of the quantum dot
as it exits the channel.
Comparing NEP with MEP
In addition to our NEP chip, Wei-ching Liao also performed simulations of QD transfection
on three MEP devices. One of these devices was one of our own design, while the other
two were ”low voltage” devices from the literature [42, 43]. The operating parameters and
results are summarized in the table. Usually MEP is carried out with relatively low applied
potential difference and, thus, low fields. This means that these MEP devices are diffusion
dominated, as opposed to electrophoretically driven like NEP. While there is no reason that
the voltages in MEP experiments could not be increased to make it more like NEP, our
own experiments indicate that such high fields are usually fatal to the cell. We believe the
reason these fields are fatal in MEP but not in NEP is that the area of the cell membrane
exposed to high fields in NEP is less than 1% of the corresponding area of an MEP device.
5.5 Conclusions
We have demonstrated that NEP is capable of achieving:
• High precision dose control
• Transfection of nanoparticles directly into the cytosol.
97
Furthermore, it is able to achieve both these things without harming cells. We believe
that dose control is the result of the fact that, during NEP, large electric fields in the
nanochannel accelerate transfection agents and drive them into the cell. After the pulse,
any additional, diffusion driven transfection is limited by the small size of the nanochannel.
This contrasts strongly with BEP and MEP where transfection is the result of diffusion
through the cell membrane. The easy transfection of nanoparticles seems to indicate that,
during NEP, either a single very large pore or several very large pores are created adjacent
to the channel. The low (actually zero in our measurements) cell mortality is likely the
result of the fact that the affected area of the cell membrane is very limited (less than 1%
of the area affected in even a small area MEP device).
Future work is required on both the experimental and modeling sides to better characterize the NEP process. Absolute quantitative calibration of dosage may be accomplished
by comparing fluorescence measurements single cell polymerase chain reaction or with quantitative fluorescence microscopy. Some applications require large cell samples, which will
require either robotic control of the optical tweezer apparatus used to load the channels or
some other type of mechanical loading system capable of handling large volumes of cells.
The question of why we do not see poration at low voltages (applied voltages much less
than 100 V) is still unresolved and may require more detailed modeling of the NEP process
and additional experiments to fully understand.
98
Chapter 6
Membrane Experiments
As far back as 1890 [102], red blood cell membranes have been known to fluctuate in solution.
This fluctuation, known as “flicker”, can be easily observed under an optical microscope.
Attempts to model flicker have assumed that it is the result of thermal fluctuations [103].
The theory follows the model developed by Helfrich for lipid bilayers [104].
The primary requirements for readily observable fluctuations in a membrane are:
1. Low surface tension,
2. Low internal viscosity,
3. Inequality between internal and external indices of refraction.
[103]
Membrane fluctuations are not specific to red blood cells, but they are rarely observed
in other cell populations, because, in general, these three conditions are not necessarily
satisfied [103]. In particular, many cells have a high surface tension, and, in general, the
difference between internal and external indices of refraction are usually small. In addition,
most cell membranes are made more rigid by the presence of the actin cortex, a complex
interconnecting structure of proteins that extends throughout the cell [29]. Red blood cell
membranes, in comparison, are bound by a flexible spectrin mesh which adheres closely to
the membrane [29]. These differences are a result of the red blood cells’ primary function.
Red blood cells need to be extremely deformable in order to pass through capillaries easily
for oxygen transport.
99
Flicker has been measured using a variety of techniques. Brochard and Lennon made the
first quantitative measurements of flicker by using phase contrast microscopy to measure
thickness fluctuations in red blood cells in 1975 [103]. They made three distinct measurements: the mean square fluctuations hδh2 i of the cell thickness, the frequency spectrum
hδh2 (ω)i, which they found to follow a −4/3 power law, and the spatial correlation functions
hδh(r1 )δh(r2 )i for the thickness fluctuations measured at two points on the surface. Since
then, bright field observation, [105] reflection interference contrast microscopy [106] and
stabilized Hilbert phase microscopy [107] have all been used to measure flicker by various
authors.
The above techniques generally rely on a camera for imaging purposes, which effectively
means their frequency spectrum is limited by the camera frame rate. Betz et al. got around
this limitation by using BFP detection, as described in Chapter 2, to measure flicker by
lining the laser position up with the edge of the cell membrane [108]. This has the advantage
of having a sample rate limited by the bandwidth of the QPD, which is much higher than
that of a CCD camera, allowing the observation of a greater range of frequencies of the
flicker phenomenon. This technique is the one used throughout this chapter. Once a time
series of membrane fluctuations is recorded by the QPD, the fourier transform is used to
create a power spectral density (PSD), which can then be fit to theory to extract the surface
tension of the membrane, its bending modulus and the effective viscosity (roughly speaking,
the average of the internal and external viscosities). Betz found that the frequency spectrum
followed a −5/3 power law at high frequencies. The difference between this result and the
−4/3 power law result of Brochard and Lennon is due to a confinement effect caused by
the the finite thickness of the cell adhered to a substrate [109]. At low frequencies (below
10 Hz), Betz et al. were able to determine that the fluctuations were dominated by active
effects, instead of thermal fluctuations, by comparing the fluctuations of cells before and
after ATP depletion, as well as before and after activation of protein kinase C (PKC), an
ATP activated enzyme which controls the spectrin-membrane connection.
100
Figure 6.1: The results of the frequency spectrum measurements of the fluctuations of
red blood cell membranes by Betz et al. Fluctuations follow a −5/3 power law at high
frequencies but are dominated by active effects at low frequencies. The ATP depletion
curve exhibits smaller fluctuations at low frequencies due to the loss of active effects, while
the cells that underwent PKC activation exhibit higher fluctuations in the same range. The
solid lines are fits to the theory outlined in Section 6.1. Reproduced with permission from
Betz et al, ATP-dependent mechanics of red blood cells, PNAS, vol. 106, pages 15312-15317,
copyright (2009) [108].
6.1 Theory
The cell membrane can be described by a free energy functional featuring two primary
terms, a term caused by the surface tension of the membrane and a term caused by the
bending energy of the membrane. Once this free energy functional is determined, it can
be used to obtain a prediction for the PSD of the membranes thermal fluctuations based
on three parameters: the cells membrane bending modulus k, tension σ, and the effective
viscosity of the cell η.
6.1.1 Surface Tension Term
The energy due to the surface tension of a membrane is the tension multiplied by the area.
It can be thought of as the energy stored in the system by expansions in the membranes
total area. We seek to find the free energy due to differences in the area of an undulated
surface compared to a perfectly flat one: σ(A0 − A) where A0 and A are the area of the
101
undulated and flat surfaces, respectively. Much of this discussion follows Safran Chapters
1 and 3 [110].
In order to find an expression for the undulated area A0 , consider a surface defined by
the vector ~r(u, v). The metric for this surface is then:
ds2 = (d~r)2 = (r~u du + r~v dv)2
(6.1)
where the subscripts denote a derivative. Note any tangent vector to the surface can be
written as ar~u + br~v . This metric gives a metric tensor:


E F 
g=

F G
(6.2)
whose determinant is EG − F 2 , where E = r~u 2 , G = r~v 2 and F = r~u · r~v . The area element
dA0 is given by the area of the parallelogram defined by the vectors r~u du and r~v dv, which,
in turn, is given by their cross product. Using Lagrange’s Identity for the cross product, it
can be shown that this is simply:
dA0 =
p
Det[g]dudv
(6.3)
We now choose to represent the surface by parametrization z = h(u, v) = h(x, y). Under
this parametrization (known as the Monge parametrization), the vector ~r then becomes
(x, y, h(x, y)). The vectors r~u and r~v become (1, 0, hx ) and (0, 1, hy ), respectively. The area
element for the surface then becomes:
q
dA = dxdy (1 + h2x + h2y )
0
(6.4)
If we now assume that the curvature is small, so that h2x , h2y << 1, then we can expand the
area element of the undulated surface as dxdy(1 + 21 (h2x + h2y )), and then the additional free
energy due to differences in the area of an undulated surface, compared to a perfectly flat
102
one, becomes simply:
Z
Z
F = σ( dA0 − dA)
Z
Z
1 2
2
= σ( (dxdy(1 + (hx + hy ))) − dxdy)
2
Z
σ
dxdy(h2x + h2y )
=
2
which we write as:
1
F = σ
2
Z
dA(∇h)2 .
(6.5)
6.1.2 Curvature Term
We next look at the curvature term, which was first derived by Helfrich [104]. If the
membrane were constrained to a plane, then the only energy that would be stored in the
system would be the energy due to the surface tension of the membrane; in other words, it
would be entirely determined by the average energy per molecule. Since the membrane can
exhibit out-of-plane deformations, in the form of curvature there can be additional energy
stored in this curvature. Much of this discussion will follow Safran Chapters 1 and 6 [110].
The curvature of a curve on a surface with length ds given by Eq. (6.1) is defined as:
κ = ~r00 · n̂
(6.6)
where the prime denotes differentiation with respect to s and n̂ is the normal. The vector
~r00 is given by:
~r00 = u00~ru + v 00~rv + u02~ruu + v 02~rvv + 2(u0 v 0 )~ruv .
(6.7)
Rewriting Eq. (6.7) using the definition of ds2 in Eq. (6.1), and substituting into Eq. (6.6),
remembering that n̂ · ~ru = n̂ · ~rv = 0, since the normal and tangent vectors are orthogonal,
we get that the curvature is given by:
κ=
Lds2 + 2M dudv + N dv 2
Edu2 + 2F dudv + Gdv 2
(6.8)
where L = −n̂ · ~ruu ,M = n̂ · ~ruv , N = −n̂ · ~rvv and E,F and G are defined as in the previous
section. Noting again that n̂ · ~ru = n̂ · ~rv = 0, we can differentiate these relations to show
103
that, in addition:
L = −nˆu · ~ru , M = −n̂v · ~ru = −n̂u · ~rv , N = −n̂v · ~rv
which allows us to re-write the curvature as:
κ=
−d~r · dn̂
.
d~r · ~r
Now if we describe the surface in its implicit form G(x, y, z) = 0, then n̂ =
(6.9)
∇G
|∇G| ,
and this
allows us to write:
dn̂ = d~r · Q
(6.10)
where Q is given by:
Qij =
where Υ = |∇G| and Gi =
∂G
∂ri
Gi Υj
1
[Gij −
]
Υ
Υ
(6.11)
with ~r = (x, y, z).
Since the free energy of a surface should not depend on rotations of the coordinate
system, we describe Q by its invariants under a similarity transformation P−1 QP. These
are its determinant, its trace and the sum of its principal minors (the 2 by 2 matrices
obtained by eliminating the rows and columns of its diagonal elements). The determinant
of Q is zero. This, in turn, implies that one of its eigenvalues is zero. The remaining two
non-zero eigenvalues are known as the principal curvatures. The sum of its eigenvalues
(the trace) is twice a term that we call the mean curvature H = 21 (κa + κb ) (for obvious
reasons). The final invariant, the sum of the principal minors, is equal to the product of
the eigenvalues and is termed the Gaussian curvature K = κa κb .
So Q can be described in terms of the mean curvature H and the Gaussian curvature
K. One can show from Eq. (6.11) that:
H=
2Υ3 [G
2
xx (Gx
+
G2z
1
− 2Gx Gy Gxy + P erm]
(6.12)
and
K=
1
[Gxx Gyy G2z − G2xy G2z 2G2xz Gx (Gy Gyz − Gz Gyy ) + P erm]
Υ4
(6.13)
where Perm signifies that one should add two additional permutations of each term, where
104
(x, y, z) → (z, x, y) and another where (x, y, z) → (y, z, x). In the Monge parametrization,
these equations simplify to:
H=
(1 + h2x )hyy + (1 + h2y )hxx − 2hx hy hxy
q
2 (1 + h2x + h2y )3
(6.14)
hxx hyy − h2xy
.
(1 + h2x + h2y )2
(6.15)
K=
Finally, if we assume that hx << 1, hy << 1, these become simply:
1
H ≈ (hxx + hyy )
2
(6.16)
K ≈ hxx hyy − h2xy .
(6.17)
If we write an expansion for the free energy per unit area in small curvatures up to
second order in κa and κb , we get:
fc = 2kH 2 − 4kc0 H + k̄K.
(6.18)
The constant c0 is called the spontaneous curvature. If the equilibrium surface is flat, then
c0 must be zero; otherwise, the derivative with respect to curvature of the free energy
would not be zero for the flat surface, and the free energy would not be a minimum. This
expression can be further simplified if we consider the total energy due to the Gaussian
curvature K with fixed boundary conditions (fixed normal vector n̂ on the contour). We
have the free energy functional:
Z
F = k̄
K(hxx , hyy , hxy )dxdy.
This functional is minimized when the Euler Lagrange equation is satisfied:
0=
∂K
∂ ∂K
∂ ∂K
∂ 2 ∂K
∂ 2 ∂K
∂ 2 ∂K
−
−
+ 2
+
+ 2
∂h
∂x ∂hx ∂y ∂hy
∂x ∂hxx ∂x∂y ∂hxy
∂y ∂hyy
0=
∂ 2 ∂K
∂ 2 ∂K
∂ 2 ∂K
+
+
∂x2 ∂hxx ∂x∂y ∂hxy
∂y 2 ∂hyy
105
(6.19)
0=
∂2
∂2
∂2
h
−
2
h
+
hxx .
yy
xy
∂x2
∂x∂y
∂y 2
(6.20)
One can easily see by inspection that this is satisfied for any function h(x, y); as a result,
for fixed boundary conditions, the free energy due to the Gaussian Curvature term is a
constant as a function of the surface and will thus be omitted [104].
This leaves us with the free energy functional:
Z
Fc =
2kH 2 dxdy =
Z
1
k(hxx + hyy )2 dxdy =
2
Z
1
k(∇2 h)2 dxdy
2
(6.21)
combining this with Eq. (6.5) yields:
Z
F =
1
1
( σ(∇h)2 + k(∇2 h)2 )dxdy.
2
2
(6.22)
Betz et al. refer to this as Eq. 3 in their appendix.
6.1.3 Derivation of the PSD
We seek to obtain the PSD of the membrane fluctuations from Eq. (6.22). We start by
rewriting h(x, y) using its Fourier transform [111]:
h(x, y) =
X
hqn eiq~n ·~r .
(6.23)
n
Eq. (6.22) then becomes:
Z
F =
Z
F =
X
X
1
1
( σ(∇
hqn eiq~n ·~r )2 + k(∇2
hqn eiq~n ·~r )2 )dxdy
2
2
n
n
1 X
1 X 2 02
~0
~0
( σ(
−qq 0 hq hq0 ei(~q+q )·~r ) + k(
q q hqhq 0 ei(~q+q )·~r ))dxdy.
2
2
The integral:
Z X
~0
ei(~q+q )·~r dxdy
when taken over a finite area becomes simply:
L2 δq,q0
106
(6.24)
where L2 is the area of the surface, and the delta is the Kronecker delta and implies that
only terms q 0 = −q are nonzero. This leaves:
1 X 2
1 X 4
F = L2
σq hq h−q + L2
kq hq h−q .
2
2
(6.25)
Applying the equipartition theorem to this gives [111]:
kB T
L2
=
(kq 4 + σq 2 )hh2q i
2
2
(6.26)
which can be solved for the mean square amplitude of the fluctuation mode q:
hh2q i =
kB
.
+ σq 2 )
L2 (kq 4
(6.27)
In order to turn the mean square amplitude of the fluctuations into the PSD, we must
find the evolution over time of a given perturbation of the membrane. In order to do this, we
first find the time correlation function hhq (t)hq (0)i. Through a hydrodynamics analysis, one
finds that, for a free lipid bilayer, the amplitude of a membrane fluctuation of wavelength
q will decay as e−ω(q)t , where ω(q) =
(kq 4 +σq 2 )
4ηq
[112, 113]. This yields the time correlation
function [111]:
hhq (t)h−q (0)i = hh2q ie−ω(q)t
(6.28)
with which we can find the variance:
hh2 (t)i =
X
h(hq (t) − hq (0))2 i
(6.29)
X
hhq (t)hq (t) − 2hq (t)hq (0) + hq (0)hq (0)i
X
=2
(hh2q i − hhq (t)hq (0)i)
X
=2
hh2q (1 − e−ω(q)t ).
=
(6.30)
(6.31)
(6.32)
The time Fourier transform of this yields the PSD. Looking up the Fourier transform from
a table, we find:
hδh2 (ω)i = 2
X
hh2q i
107
ω(q)
.
+ ω2
ω 2 (q)
(6.33)
Integrating this equation over all q’s then yields the desired result:
hδh2 (ω)i = 2
noting that q =
2πn
L ,
Z
dn2 hh2q i
ω(q)
.
ω 2 (q) + ω 2
(6.34)
we have:
dq 2
ω(q)
L2
hh2q i 2
2
(2π)
ω (q) + ω 2
Z
ω(q)
L2
qdqhh2q i 2
=
π
ω (q) + ω 2
Z
4ηkB T
dq
=
.
3
π
(kq + σq)2 + (4ηω)2
Z
2
hδh (w)i = 2
(6.35)
(6.36)
(6.37)
Betz refers to this as Eq.8̃ in their appendix. In the limiting cases, as ω → ∞, the PSD
approaches
kB T
,
12π(2η 2 k)1/3 ω 5/3
while, as ω → 0, the PSD approaches
kB T
4σω
[108].
Eq. (6.37) diverges as ω → 0. This is because a flat membrane has fluctuations which
are divergent in its size. In RBCs, these fluctuations are limited by the finite size of the
spherical cell membrane [108]. Betz took this into account using a expansion in spherical
harmonics.
r(Ω) = R(1 +
X
ulm Ylm (Ω)),
(6.38)
l,m
where Ω is the solid angle, R is the cell radius and Ylm (Ω) are the spherical harmonics.
With this, the mean squared fluctuations are:
h|ulm |2 i =
kB T
,
k(l + 2)(l − 1)l(l + 1) + σR2 (l + 2)(l − 1)
(6.39)
and the time correlation function is:
hulm (t)ul0 m0 (0)i = δl,l0 δm,m0 h|ulm |ieωl t ,
(6.40)
k(l + 2)(l − 1)l(l + 1) + σR2 (l + 2)(l − 1)
,
ηR3 Z(l)
(6.41)
with:
ωl =
and:
Z(l) =
(2l + 1)(2l2 + 2l − 1)
.
l(l + 1)
108
(6.42)
Figure 6.2: a) A diagram of the membrane fluctuation experiments. b) A typical calibration
curve result created by scanning the laser across the membrane edge using the piezo stage.
Before taking fluctuation data the stage will be set to the working point noted in the graph
by the dotted line at the center of the linear regime.
The Fourier transform again gives the PSD:
hδu2lm (w)i =
Z
dt
X
h|ulm |ie−ωl t eiωt
(6.43)
l=2,m=−l
=
X
h|ulm |2 i
l=2
ωl2
ωl
2l + 1
.
2
+ ω 2π
(6.44)
This is the equation that was used to fit to experimental data to obtain the cells membrane
bending modulus k, tension σ, and the effective viscosity η.
6.2 Experimental Methods
Experiments are conducted in flow cells of the type described in the technical chapter.
Polylysine coating is applied to the coverslip surface in order to ensure that cells will adhere
to the surface of the coverslip.
The microscope is set up for BFP detection as outlined in the technical chapter. Laser
power is set to a value much less than 1 mW in order to avoid trapping forces affecting the
thermal fluctuations. Betz found that the trapping force did not affect membrane fluctuations for laser powers less than 1 mW [108] (we confirm this in Section 6.4.3). Once a cell
is brought into focus and located, a calibration curve is taken by using the 3D piezoelectric
109
stage to scan the laser over the edge of the cell membrane (see Fig. 6.2). This creates a
position signal from the QPD. Near the edge of the cell, there is a linear regime in this
curve. Using the 3D piezoelectric stage, the cell is then positioned so that it is exactly in
the center of this linear regime.
Once the cell is positioned, fluctuations in the membrane will show up as voltage fluctuations on the QPD. 100 s of fluctuation data is taken using the QPD at 2 kHz. In
Mathematica, the PSD of this data is computed and then log binned in order to reduce
noise. Generally, this is done for at least 15 individual cells. The resulting 15 data sets are
then log averaged. The resulting averaged set of data is then fit to the model described in
the previous section using a Mathematica program.
6.3 Red Blood Cell Experiments
As previously noted, red blood cells readily exhibit membrane flicker to the point where
it can easily be observed under the microscope [102]. Red blood cells are also convenient
because their lack of an actin cortex allows them to be readily modeled using the theory
laid out in the previous section.
Human blood is stored for long periods of time in blood banks around the world for use
in future transfusions. Typically, blood is stored for 120 days before it is discarded. Studies
have shown that patients that receive fresh blood tend to have higher survivability rates
than those who receive blood at the end of its storage cycle [114, 115]. There are many
theories why this is the case, but one explanation is that, over time, red blood cells become
less flexible [116, 117]. Less flexible blood cells are not able to easily make it through the
body’s many narrow capillaries, which, in turn, leads to lower patient survival rates [118].
By using BFP detection, we can directly measure the membrane properties of individual
red blood cells and assess their flexibility over time.
110
6.3.1 Red Blood Cell Preparation
Blood samples were obtained by the Palmer group from the Red Cross. These blood cells
were then split into an experimental group and a control group. The experimental group
was treated with ascorbic acid that was intended to reduce the aging effect, while the control
group was left unaltered. Measurements were taken immediately after receiving the samples
from the Red Cross and then roughly 15, 40, and 50 days later.
Before conducting experiments, blood was diluted about 200 times in PBS. Data was
only taken on discocyte cells (cells which had a toroidal shape). Sometimes at 200 times
dilution, the cells would assume an echinocyte (non-toroidal) shape. Eriksson found that
red blood cell morphology was dependent on cell concentration [119]. Following this advice,
in cases where echinocytes were observed, more blood was added up to 100 times dilution.
Usually, this was sufficient to resolve the issue.
6.3.2 Results
An example of the final, averaged, RBC data for a group of 15 cells can be seen in Fig. 6.3,
while an example of the data before averaging can be seen in Fig. 6.4. Gaps in data of this
graph, as well as the rest of the graphs in this chapter, are the result of electrical noise in
our system. One can see that, as expected, the results fit the model relatively well. The
results of the fit are similar to the results found by Betz. Whereas our fit parameters were
σ = 6 ∗ 10− 7 N/m k = 2 ∗ 10− 19 J and η = 80 ∗ 10− 3 Pa s, Betz found that, for normal
RBCs, σ = 6.5 ∗ 10− 7 N/m k = 2.8 ∗ 10− 19 J and η = 81 ∗ 10− 3 Pa s [108]. Unfortunately,
because of noise in the data and the fact that there are three different parameters to fit, it
is not possible for us to assess these parameters with any certainty, but it does demonstrate
our data is consistent with that of Betz et al. Different values of the parameters may also
yield reasonable fits. At high frequencies, the PSD approaches
kB T
,
12π(2η 2 k)1/3 ω 5/3
which allows
one to simplify the fitting process considerably by looking at the parameter kη 2 . The results
of all experiments are summarized in Fig. 6.7 by the parameter kη 2 . The averaged PSD’s
of the experimental and control groups are shown in Fig. 6.5 and Fig. 6.6, respectively.
111
Figure 6.3: An example of typical averaged RBC data. This particular set is an average
of cells from the day 0 measurement of the experimental group. The blue curve is a fit to
theory with the parameters σ = 6 ∗ 10− 7N/m k = 2 ∗ 10− 19J and eta = 70 ∗ 10− 3P as. The
red curve shows a f −5/3 slope.
112
Figure 6.4: An example of what the RBC data looks like before averaging. This graph
features 15 different individual data sets which are then averaged to create a plot similar
to the one in Fig. 6.3.
113
One can see that, over long time span, the kη 2 parameter increases considerably in
the experimental group. At day 0, it is 12 ± 2.6 ∗ 10−22 J Pa2 s2 , while, by day 49, it is
over 280 ± 96 ∗ 10−22 J Pa2 s2 . For comparison, Betz found that normal RBC’s have a
kη 2 of 18 ± 2.5 ∗ 10−22 J Pa2 s2 , while ATP depleted cells have a kη 2 of 54 ± 11 ∗ 10−22
J Pa2 s2 . The increase in kη 2 signals an increase in the cells bending rigidity or internal
viscosity or both. In any case, it leads to cells that are less flexible on the whole. This
is corroborated by the fact that the integration of the PSD, which yields the total RMS
membrane fluctuations, also decreases as time passes. By comparison, the control group
exhibits only minor increases in the kη 2 parameter over this time. All this indicates that the
cells receiving treatment are actually less flexible after prolonged storage than those that
aren’t; this implies that they would have more difficulty passing through extremely thin
capillaries. It is important to note that this measurement necessarily measures small scale
deformations of the cell membrane; large scale deformations of the type that occur within
capillaries may well behave differently, necessitating that this data be checked against, for
example, large scale deformations of the cell using optical tweezers [116, 117] or microfluidic
experiments [120].
6.4 K562 Cell Experiments
As mentioned before, all cell membranes will experience thermal fluctuations to some degree.
This opens the door to use BFP detection to measure membrane fluctuations in a variety
of situations beyond the typically studied red blood cell example.
Whereas red blood cells possess a spectrin mesh that can be modeled using a membrane
theory other eukaryotic cells possess a network of interconnecting actin filaments that run
throughout the cell [29]. These actin filaments prevent the membrane fluctuations from
being modeled using a pure membrane theory; however, this does not mean that BFP
detection cannot offer any insight to other types of cells.
In order to evaluate the effects of the cytoskeleton on the cells’ membrane mechanics,
measurements identical to the ones conducted on RBC’s were conducted on K562 cells.
114
Figure 6.5: The averaged data for the experimental groups.
Figure 6.6: The averaged data for the control groups.
115
Figure 6.7: The results of the red blood cell experiments.
Two different methods of disrupting the cytoskeleton were tested to evaluate their effects
on membrane fluctuations, electroporation and chemical disruption of the actin cortex using
Latrunculin A.
K562 cells were cultured in RPMI 1640 medium, with 10% newborn calf serum (heatinactivated), 2 mM L-glutamine and 1 mM sodium pyruvate as described in Chapter 3 and
harvested for experiments during their exponential growth phase.
6.4.1 Electroporation
Electroporation has been observed to disrupt the actin cortex. Kanthou et al. fixed cells in
formaldehyde and stained their actin networks using a fluorescent dye before electroporating
them [34]. Prior to electroporation, the actin network of the cells was easily visible under
fluorescence microscopy. However, after electroporation, individual actin filaments became
impossible to resolve.
In order to evaluate the effects of this damage to the cytoskeleton on the cell membrane
mechanics, measurements were taken on K562 cells before and after electroporation. Cells
were placed in electroporation channels like those described in Chapter 3. Electrodes were
made using copper tape on top of a glass coverslip which was fixed to a glass slide by
parafilm. The spacing between the copper electrodes was approximately 1 mm, and a pulse
116
of 200 V was applied to cells for 2 ms. Based on the experiments of Chapter 4, this field
should be much higher than the critical one needed to induce poration, and, indeed, cells
were always observed to porate following the pulse. The applied field for these pulses is an
order of magnitude larger than those used by Kanthou et al. (2.5-20 V/mm) [34]. Electroporation was detected using PI dye as described in Chapter 4. Membrane fluctuations were
observed immediately following the detection of PI dye fluorescence. Measurements take
100 s to carry out, but Kanthou found that cytoskeleton repair occurred over the course of
an hour [34]. All measurements were carried out in cell media.
6.4.2 Latrunculin A
Cells were incubated for 1 hour at 37 degrees Celsius with 0.5 µ M of Latrunculin A in
media. These cells were then taken from the incubator and resuspended in PBS. Their
membrane mechanics were then measured using BFP detection and compared to data from
a control group of cells that had not received the Latrunculin treatment.
6.4.3 Results
The results of the electroporation measurements are shown in Fig. 6.8, while the results
of the fit parameters are in table 6.1. The data from both the control cells and the electroporated cells clearly do not fit the model. Each possess a ”hump” in the PSD between
1 Hz and 10 Hz. This characteristic of the graph was not reproducible in future experiments. An example of K562 data without the hump is shown in Fig. 6.9. There is a clear
difference between the fluctuations measured in the membrane before and after poration
with cells generally exhibiting higher fluctuations before poration over the entire frequency
range. This could be explained if the cytoskeleton is a source of “active” fluctions (see
below). Another possibility is that the difference in fluctuations indicates a change in the
structure of the membrane itself via, for example, phospholipid flip flop (see Section 1.7).
The fluctuations in this data are in general much higher than the fluctuations seen in data
taken later; the reason for this is unknown, but several potential explanations are explored
(see below).
117
Cell Type
Control
Electroporated
k (10−19 J)
14
4
σ (10− 7N/m)
13
30
η (10− 3P as)
130
900
Table 6.1: Results of the fits for the K562 membrane fluctuation experiments
The Latrunculin data is shown in Fig. 6.10. A fit of the theory to the Latrunculin data is
shown in Fig. 6.11. The surface tension of the fit is zero, while k and η were 500∗10−19 J and
500 ∗ 10− 3 Pa s. respectively. The values for k and η are much larger than the values found
in RBC fits, but, as with the RBCs, none of these individual parameters may be known with
any certainty. There is no distinguishable difference between the Latrunculin-treated cells
and the control cells for frequencies less than 100 Hz, which is surprising. Despite this, at
high frequencies, there is a measurable difference. Looking at the high frequency data allows
us to distinguish a difference between the two sets for the value of kη 2 . For the latrunculin
data, kη 2 is 1.79 ± 0.15 ∗ 10−17 J Pa2 s2 , while, for the control group, it is 13.9 ± 1.9 ∗ 10−17 J
Pa2 s2 . Given the lack of a difference between the latrunculin-treated cells and the control
group at lower frequencies, it is reasonable to ask whether the Latrunculin we had exceeded
its shelf life. A future experiment with new Latrunculin is planned.
The model described assumes that:
1. The cells lipid bilayer fluctuations can be modeled as a membrane.
2. The fluctuations can be modeled as equilibrium thermal fluctuations.
Either of these assumptions could be wrong in the case of K562 cells possessing an actin
cortex. On the one hand, the actin cortex provides a 3-dimensional structure to the cell and
confines the lipid bilayer, making the use of a purely membrane model questionable. On the
other hand, it can also induce active fluctuations in the cell membrane. The actin cortex is
constantly changing and rebuilding itself in a living cell, and the membrane detaches and
reattaches to the cortex at various times.
118
Figure 6.8: The results of the K562 cell electroporation experiments. The red data points
are cells prior to electroporation while the green data points are cells immediately after
poration. Each curve is a fit of the model to its same-colored data. The orange curve is
f −5/3 .
119
Figure 6.9: The results of K562 cell experiments in RPMI 1640 media. The hump from
Fig. 6.8 is not reproduced.
120
Figure 6.10: The results of K562 cell Latrunculin experiments in PBS.
Non-Membrane Effects
One potential explanation for the odd hump that we see in the electroporation data is that it
is a result of the actin cortex. Fournier et al. developed a theory to explain the fluctuations
of a membrane coupled to an external system (such as the cytoskeleton) [121]. In this
model, coupling energy is described to a first approximation by a function of the membrane
area coarse grained to a characteristic length scale ξ0 , defined by the cytoskeleton mesh
size. They find that the effective membrane tension exhibits a crossover of magnitude ∆σ
at the length scale ξ0 . This allows one to rewrite Eq. (6.27) as:
hh2q i =
L2 (kq 4
hh2q i =
L2 (kq 4
kB
, For q < ξ0−1 ,
+ (σ + ∆σ)q 2 )
kB
, For q > ξ0−1 .
+ σq 2 )
121
(6.45)
(6.46)
Figure 6.11: A fit of the model to Latrunculin-treated K562 cells. The blue line is a model
fit with paramaters σ = 0, k = 500 ∗ 10−19 J and η = 500 ∗ 10− 3 Pa s
122
Figure 6.12: The results of an attempt to fit the composite membrane theory of Fournier
et al. to the data for normal K562 cells. The fit curve has the parameters k = 10 ∗ 10−19 J,
σ ≈ 0, η = 200 ∗ 10− 3P as, ∆σ = 50 ∗ 10−7 N/m and ξ0 =1 µm
With this, Eq. (6.37) becomes:
4ηkB T
hδh (w)i =
π
2
Z
0
ξ0−1
dq
4ηkB T
+
3
2
2
(kq + (σ + ∆σ)q) + (4ηω)
π
Z
∞
ξ0−1
(kq 3
dq
,
+ σq)2 + (4ηω)2
(6.47)
which can then be fit to the data. The results of this fit can be seen in Fig. 6.12.
Although the values for the fit parameters seem to fall within reasonable ranges the fit
does not appear to be substantially better than the one seen in Fig. 6.8. Certainly the
“hump” in the data is not reproduced. One possible interpretation of this result is that the
unexplained shape of the K562 cell frequency spectrum is not the result of being coupled
to an external system, such as the actin network, something which seems likely given our
inability to reproduce it. Another possibility is that the model described by Fournier et
123
al. does not accurately describe the situation resulting from the K562 cells actin cortex.
The theory assumes that the cytoskeleton takes the form of a spherical mesh to which the
membrane attaches. The actin cortex is a more complex, three-dimensional, structure than
this, with actin fibers running throughout the cell. The theory also assumes that the mesh
has a regular spacing ξ while the actin cortex does not necessarily have a regular, repeating
structure. It may be the case that a more complicated treatment is necessary to capture
the results in these experiments.
Active Effects
The other possibility is that the K562 cell membrane is not in thermal equilibrium. At low
frequencies (<10 Hz), active effects could come into effect. In the model, this would be
seen as a frequency dependent “effective temperature” T (f ). At high frequencies T (f ), will
be approximately 300 K, but, at lower frequencies, T (f ) > 300K as the system begins to
behave as though its temperature has been increased. Recent experiments on RBC’s [108],
hair cells [122], and actin gels [123] have seen such active effects dominate over equilibrium
fluctuations at frequencies less than 10 Hz. It could be the case that something similar is
happening in the case of K562 membrane fluctuations, especially given the results in actin
gels.
The actin gel experiments by Mizuno et al. found that the active fluctuations were
ATP dependent [123]. In order to investigate, this we conducted experiments where we
placed cells through an ATP depletion treatment. Our procedure for ATP depletion follows
that of Thatte et al. [124]. Cells were incubated in glucose-free RPMI 1640 culture media
with 10 mM of 2-deoxyglucose and 10 mM of sodium azide for 3 hours. Cells were then
resuspended in PBS, and measurements were taken. Measurements were taken on two
seperate occasions to assess repeatability.
The results can be seen in Fig. 6.13. Contrary to our expectations ATP, depletion
appeared to increase the membrane fluctuations over the almost entire frequency range. This
result was unexpected, and the reason for it is unknown. It could be the case that the ATP
depletion is not working. In order to test this, we will need to conduct a bioluminescence
124
Figure 6.13: The results of the ATP depletion experiments. The top and bottom figures
correspond to two different runs. In both cases the ATP depleted fluctuations are higher
than the control group over most frequencies.
assay test of the ATP in the cells before and after depletion. Another possibility is that
the ATP depletion is, in fact, working, but some ATP driven process we do not understand
actually increases the rigidity of the cell membrane.
The Effect of the Trapping Laser
One concern, when doing BFP measurements of membrane fluctuations, is that the laser
power must be low enough so that no trapping of the membrane occurs. Betz et al. found
that, for RBCs, trapping did not occur at laser powers of below 1 mW [108], but this may
be different in K562 cells. In order to assess whether we were trapping the membrane, we
conducted measurements of the membrane fluctuations of a single cell at three different laser
intensities corresponding to laser powers at the specimen plane of roughly 0.07 mW, 0.2 mW
and 0.6 mW. The results of the measurements can be seen in Fig. 6.14. To summarize, at
125
Figure 6.14: The effects of laser power on membrane fluctuations.
0.6 mW, there is a slight decrease in total fluctuations across the frequency spectrum, but,
in general, the results are within the error for all three laser powers. All measurements on
K562 cells in this chapter were conducted at laser powers of less than 0.2 mW.
The Effect of Cell Cycle
A major issue over the course of the K562 experiments was reproduceability. An example
of this is the differences not just in shape, but also in magnitude, of the control data
in Fig. 6.8 and Fig. 6.9. One obvious factor that may impact membrane properties is
the cell growth cycle. The cell growth cycle has been shown to impact electroporation
(Section 1.2), so it is possible it affects membrane fluctuations as well. In order to test
this, we conducted measurements of cell membrane fluctuations over the course of a single
growth cycle. Data was taken shortly after splitting a cell population during the so-called
126
Figure 6.15: The effects of the cell growth cycle on membrane fluctuations.
lag phase before exponential growth occurs, during the exponential growth phase, at the end
of the exponential growth phase and after the growth phase, when the population begins to
decrease and die off. The results can be seen in Fig. 6.15. In general, the difference between
data sets was small, except for the lag phase data, which differed from the rest of the data
by a factor of roughly 2 across the frequency spectrum. In order to control for this effect as
much as possible, all data in this chapter was taken during the exponential growth phase.
In addition, control/experimental group pairs were always taken on the same day, usually
within a few hours of each other.
127
The Variation of Measurements of a Single Cell
Closely related to the issue of reproduceability of K562 measurements is the large variations
in membrane fluctuations observed over multiple cells. While RBC measurements would
vary over an order of magnitude at most (see Fig. 6.4), the variations in K562 cells sometimes
approached two orders of magnitudes (Fig. 6.16 a). In order to evaluate whether this is
the result of cell to cell variations or the result of the inability to reproduce membrane
fluctuations in even a single cell, we conducted a series of 15 measurements of a single
cell’s membrane fluctuations. All measurements were taken at the same spot on the cell
membrane; however, in order to ensure that the cell remained centered in the linear regime
of BFP detection, the cell did need to be slightly repositioned several times in between
measurements.
The results can be seen in Fig. 6.16. The single cell results vary over a factor of roughly
4, while the data taken from 15 different cells varies over a factor of as much as 200 in
places, indicating that most of the variation we see is cell-to-cell variation. Even the factor
of 4 variation in the single cell data is significant, however. A likely reason for both the
cell-to-cell variation and the single cell variation in K562 cells is the actin cortex. The
spectrin mesh in RBC’s is a regular structure, while the actin cortex in K562 cells is a
largely irregular structure that also changes over time. It may be the case that membrane
fluctuations in K562 cells depend heavily on the local structure of the actin cortex.
6.5 Conclusions
BFP detection has been shown to be an effective method of measuring membrane fluctuations in RBCs in the past, and our results in these experiments match well with previous
experiments by other researchers. Fluctuation measurements further found that a treatment intended to increase membrane flexibility of RBCs over long storage times probably
was not effective.
BFP detection was also successful in measuring the fluctuations of K562 cells, something
which had not been attempted before. Fluctuations in K562 cells were found to be highly
128
Figure 6.16: a) An example of unaveraged data from a set of 15 different K562 cells. b)
An example of unaveraged data from a single K562 cell measured 15 times.
129
variable compared to RBC’s, a fact which complicated experimental reproduceability. Not
only did K562 cell fluctuation measurements vary greatly from cell to cell, they also varied
significantly for a single cell and from day to day. These variations may be the result of the
local structure of the actin cortex.
The results of experiments measuring the response of K562 cell membrane fluctuations
to cytoskeletal disruption from chemical and electric means are conflicting. In the case of
disruption of the actin cortex by electroporation, membrane fluctuations decrease across
all frequency ranges following poration, while, in the case of destruction of the actin cortex by Latrunculin, there is a difference only at high frequencies, and there fluctuations
actually increase. The difference may be accounted for if the membrane properties themselves change as a result of poration through phospholipid flip flop or some other membrane
memory effect. Another possibility is that the Latrunculin has exceeded its shelf life. Most
puzzling is the response of the cells to ATP depletion. Where there was an expectation
that active fluctuations would disappear, thus leading to frequency dependent decreases of
the fluctuations, what is actually observed is an increase in fluctuations across almost the
entire frequency range. This result is not understood.
Potential future work includes verifying repeatability of all experiments and, in particular, reproducing the Latrunculin results with new Latrunculin. Another future experiment
is to evaluate the membrane fluctuations at various points on the surface of a single cell in
order to evaluate the importance of the local actin cortex structure in K562 cell fluctuation
variations.
130
Chapter 7
Conclusion
We have discussed three experiments using optical tweezer techniques. In the first, optical
trapping was used to manipulate single cells in suspension in order to test the prediction of
the Schwan equation, that the threshold applied electric field necessary to induce electroporation goes as 1/r. What we observed was that the threshold field was, in fact, constant
for a given cell type for our millisecond pulses. Experiments with Latrunculin A, a chemical
that depolymerizes the actin cortex appear to indicate that this departure may be the result
of the cells actin cortex, but more data is needed to confirm this. Important future work
includes determining whether these results also hold for short (microsecond) pulses.
Next, we demonstrated and discussed an improved electroporation technique, NEP.
Here, optical tweezers were used to manipulate and precisely position a cell next to a
nanochannel. We demonstrated that NEP offers two significant advantages over conventional BEP or MEP:
• High precision dose control
• Transfection of nanoparticles directly into the cytosol.
The high precision dose control is believed to be the result of the large electric fields in
the nanochannel, which electrophoretically drive the transfection agents into the cell. This
contrasts with the diffusion driven transfection seen in BEP and MEP. The easy transfection
of nanoparticles directly into the cell, bypassing endocytosis, is believed to indicate that the
high electric fields near the channel create either a single very large pore or several large
131
pores adjacent to the channel. Poration was only observed when the applied voltages were
fairly large, over 200 V. It is still not fully understood why we do not see poration at much
lower applied voltages. The physics of NEP requires further exploration.
Finally, an optics technique developed in conjunction with optical tweezers, called BFP,
position detection was used to measure cell membrane fluctuations. Two primary experiments were undertaken. In the first, the effectiveness of ascorbic acid at maintaining RBC
flexibility over time was assessed by measuring the membrane fluctuations of RBC’s treated
with ascorbic acid over a period of 50 days and comparing them to a control group that received no special treatment. The results for the control group match well with measurement
undertaken by Betz et al. [108], demonstrating that we are obtaining meaningful results.
Unfortunately, the ascorbic acid was not observed to be effective at maintaining membrane
flexibility. Instead, membrane flexibility was found to actually decrease.
In a second experiment, BFP detection was also successful in measuring the membrane
fluctuations of K562 cells, something which, to the best of our knowledge, had not been
attempted before. K562 cells exhibited much greater variations in membrane fluctuations
from cell to cell and from day to day than RBC’s. This feature made drawing meaningful
conclusions from measurements difficult, and, often times, experiments gave conflicting
results. These variations may be the result of the local structure of the actin cortex.
In order to observe the effect of the actin cortex on the membranes mechanical properties, a number of methods were attempted to disrupt the cytoskeleton. Electroporation,
treatment with the chemical agent Latrunculin A, and ATP depletion were all attempted.
In the case of electroporation, membrane fluctuations were observed to decrease across the
entire frequency range following poration. The results for Latrunculin treatment conflict
with this, as no significant difference is seen except at high frequencies. The results of ATP
depletion experiments were most puzzling of all. Depletion of ATP was expected to reduce
fluctuations in the membrane through the removal of active fluctuations from cellular processes, but, instead, the reverse was observed. Independent verification that ATP depletion
has actually occurred would be the next step. The Latrunculin experiments also need to
be repeated, as the shelf life of the Latrunculin may have been exceeded.
132
7.1 Future Experiments
7.1.1 Evaluating Cell Size Effects on Electrical Breakdown of the Membrane
One outstanding issue from Chapter 4 is whether the permeabilization of the membrane
to PI dye necessarily coincides with the electrical breakdown of the membrane. It may be
the case that the cell membrane becomes conductive at applied field values that depend on
the cell size as theory predicts, even though permeability to PI dye appears to occur at a
constant applied field. If this is the case, then electroporation would be a more complicated
process than previously thought.
In general, in the literature, permeabilization of the membrane is determined either
by an increase in its conductivity (for example in Zimmermann’s double coulter counter
experiment [77]) or by its permeability to transfection agents, such as dyes (for example,
in Golzio et al. [35]). In order to confirm that an increase in electrical conductivity necessarily implies membrane permeability to transfection agents such as PI dye it would be
necessary to evaluate both properties simultaneously. This could be done by repeating
Zimmermann’s coulter counter experiment in the presence of PI dye, and watching the cells
under fluorescence microscopy.
7.1.2 NEP of Large Cell Populations
For many experiments, transfections of large numbers of cells is necessary in order to establish statistical significance. The optical tweezers loading method for NEP is practically
limited by loading times and laser powers to small numbers of cells. Loading thousands
or millions of cells using optical tweezers, as described in Chapter 5, is not feasible. One
potential alternative for cell loading to optical trapping, proposed by Dr. Lee, is centrifugation. Centrifugation is an already established method of cell manipulation [125]. In this
proposal, the microchannels in the NEP chip would be considerably shortened so that only
one cell may fit in each channel. Centrifugal forces would then load cells into the channels.
At this point, a pulse would be applied, porating the cells, and centrifugal forces would
133
Figure 7.1: Centrifugal loading of an NEP chip. a) A schematic of the design. b) A
preliminary chip. c) Loaded cells under fluorescence. Channels have 1-3 cells each. Adapted
from Macmillan Publishers Ltd: Nature Nanotechnology, Vol 6, Boukany et al, Nanochannel
electroporation delivers precise amounts of biomolecules into living cells, Pages No. 747-754,
Copyright (2011).
again be used to extract the cells. Students in Dr. Lee’s group have produced some preliminary results here (see Fig. 7.1), but more work is needed in device fabrication. Presently,
multiple cells are loaded into each channel, when, ideally, each channel would have only a
single cell. If successful, though, this process could allow for the simultaneous poration of
50,000 cells or more.
134
7.1.3 Evaluation of RBC Aging Using Large Scale Deformations
In Chapter 6, BFP detection was used to evaluate changes in the membrane properties of
RBC’s as they age in the presence of ascorbic acid. In the body, RBCs must pass through
micrometer-sized capillaries to deliver oxygen to cells. In order to accomplish this feat
RBC’s must be capable of large scale deformations. Even if ascorbic acid has no beneficial
effect on the mechanics of the cell membrane under small thermal fluctuations, it is possible
that it may have a beneficial effect on these large deformations.
One way of examining this possibility would be to use optical tweezers to deform the
cell [116, 117]. By attaching polystyrene beads to opposite ends of a RBC to serve as
“handles” for the optical tweezers, RBC’s can be deformed, and the forces required to
cause those deformations can be measured using BFP detection. Another possibility is to
deform the cell using microfluidics [120]. A fluid flow can be used to drive RBC’s down a
microfluidic tube with a diameter smaller than that of the RBC. The more quickly the cells
reach the other side of the fluidic, the more flexible they are.
135
Figure 7.2: Two possible RBC deformation experiments. In the first, polystyrene beads
(black) are used as handles for optical traps (red dots). One trap is held fixed, while the
second is used to stretch the cell (red arrow). In the second experiment, fluid flow (black
arrows) is used to force an RBC down a narrow microfluidic channel.
136
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Appendix A
Manual for 3rd Optical Tweezer
System
Safety: The Optical Trapping system uses a 1.5 W invisible infrared laser. This is a Class
IV laser, and poses a serious risk to vision in the event of eye contact.
1. Be aware of the beam path. The laser beam passes into the rear of the microscope
and passes out the objective lens through the condenser.
2. At no point should you block the beam path.
3. At no point should you look into the path of the beam.
4. Do not look into the eye piece of the microscope when the beam is on. Always use
the camera to observe your specimen when the beam is on.
5. Always wear laser safety glasses while the beam is on.
Operation:
1. Turn on the computer monitor if it is not on.
2. Make sure that the computer is booted in Windows 7. If it is not then reboot the
computer and login using the username: admin. Leave the password field blank.
3. Rotate the top fluorescence filter wheel of the microscope into the OT position.
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4. Select an appropriate objective lens. Trapping should be done with the 1.2 NA 60x
water immersion lens, the 0.6 NA 40x lens or an oil immersion lens. Trapping will be
difficult with other lenses.
5. Turn on the camera and the illumination source.
6. Double click on the APT User software on the desktop. Click the button that says
home for both of the motorized drives. Wait for them to zero. This may take a couple
minutes.
7. Using the sliding potentiometer on the boxes labeled X and Y roughly center the stage
to your liking.
8. Close the APT User software. It must be closed.
9. Double click on the Labview program Main on the desktop.
10. Click the white arrow near the top-left of the program below the File and Edit menus.
This starts the program.
11. The camera feed should start after a few seconds signifying the program is ready to
use.
12. Click the Setup tab.
13. Click on the drop down box and select your objective lens from the list.
14. Choose an appropriate speed and acceleration for the stage. 0.02 works well for the
speed and 0.1 works for the acceleration. These values can be changed later if you
find things are moving to slow/fast.
15. Make sure you are wearing safety glasses and that nothing is blocking the laser beam
path.
16. Turn on the laser by flipping the red switch next to the laser power cord on the power
strip.
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17. Click on the camera feed near the trap position. The X and Y location of the cursor
will be displayed in the lower left portion of the program. The last trap position
should be recorded on the right hand side of the program. If something is trapped
you can also locate the trap position in that way.
18. Click the Set Trap Position button. This stores the location of the trap on the camera
feed.
19. Click the Run tab.
20. You should now be able to manipulate the stage by clicking on the camera screen
either using the mouse or the touch screen. When you click on a point on the screen
the stage should move so that the trap is in that location. (Note that the stage
position updates when the cursor location changes, not when the mouse button is
pressed, so if you click the exact same location on the screen over and over the stage
will not move.)
Setting Up Return Positions:
You can setup return positions for the stage. This is potentially useful if you are using
the software in conjunction with a NEP array for example.
1. Using the Run move the trap so that it is positioned over the first nanochannel in the
array.
2. Click on the Setup tab. Then click Set First. This stores the first nanochannel location
in memory.
3. Using the Run tab move the trap so that it is positioned over the second nanochannel
in the array.
4. Click on the Setup tab. Then click Set Second. This stores the second nanochannel location in memory. The computer will now subtract the two locations to find
the array spacing and use that number to calculate the locations of the remaining
nanochannels.
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5. Using the Run tab position the stage so that it is located near the cells of the first
microchannel that you marked in step 1.
6. Click on the Setup tab. Then click Set First Cell. This stores the location of the
cells for the first microchannel in memory. The computer will now use the spacing for
the nanochannel array obtained in step 4 to obtain cell locations for the remaining
channels.
7. You can now have the stage automatically go to any of the return positions using
the Run tab. For example to return to the first nanochannel location, enter 0 under
chamber number and click Load Cell. The second nanochannel would be at chamber
number 1 and so on. Negative numbers also work. To use the cell return points enter
the appropriate chamber number and click Go Back to Cells.
When Youre Done:
1. Click the button that says Stop to end the program.
2. Turn off the camera and the illumination source.
3. Turn off the monitor of the computer. Do not turn off the computer.
Troubleshooting
1. The software doesnt run:
Reset the computer. Unplug the power supply to the drives (small black box with power
cords with a ThorLabs logo) and plug it back in. Turn the camera off then turn it back on.
It may not work the first time you do this, but just keep resetting everything and it should
eventually start working.
2.Nothing is trapping.
Make sure that the top fluorescent wheel is set to the OT position and the laser is on.
Make sure you are using a high NA objective lens. Make sure the object you are trying to
trap is near the trap position (which should be somewhere near the center of the screen).
Make sure the object you are trying to trap is not stuck to a surface.
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If none of these resolves the problem the alignment may be wrong. Contact Andrew
Morss at [email protected] or in the Optical Tweezers room of the Biohybrid
lab.
3.The return positions are off.
The drives are not perfectly accurate. After a number of stage movements they eventually will be offset. Reset the return positions as outlined under Setting Up Return Positions.
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