Download Lecture 12 (3/03/10) "Magnetic Tweezers and (Optical) Microscopes"

Today’s Announcements
1. HW (really!) assigned today (Due next
Wednesday, 3/10/10).
2. March 15th, 17th, night of 18th: Presentations
Reports due night of 18th.
Today’s take-home lessons
(i.e. what you should be able to answer at end of lecture)
1. Twisting– anharmonicity of DNA
2. Resolution (Limited by Heisenberg, l/2, or
recently very very good, 10-25 nm)
vs. Accuracy (Potentially infinitely good, 1 nm).
Torsionally stressed single DNA molecule
Playing with phone cord: can you explain graphs?
When the force is
increased above 0.5
pN, the curve becomes
asymmetric: supercoils
still form for positive
coiling while local
denaturation adsorbs
the torsional stress for
negative s.
Low F: symmetric
under s  - s
The shortening
corresponds to the
formation of
plectonemes upon
writhing.
At forces larger than 3
pN no plectonemes are
observed: the torsional
stress is adsorbed not
by writhe but in local
structural changes of
the molecule.
Extension vs. supercoiling at constant force
T. Strick et al., J. Stat. Phys., 93, 648-672, 1998
Three regimes
Today
Techniques for measuring distances
(where physicists have made a big impact on bio.)
X-ray diffraction (atomic resolution)
Electron (Imaging) Microscopy (nm-scale)
Visible (Imaging) Microscopy (nm - µm)
Bacteria on head of a pin
at different magnifications
Microscopes
Cells discovered with invention of microscope.
MBC, Fig. 4-
Or with CCD
1000x, 0.2um
106x, 2 nm
20,000, 10 nm (3-d)
Resolution: The Rayleigh criteria
How well can you resolve two point objects?
A single spot will be smeared out, no matter how small the
spot is, because of the wavelength of light to ~ l/2.
Point-Spread Function (PSF)
What determines (ultimate, i.e. best) resolution of
technique… microscope, eye, etc.?
[2 parts]
1. Primarily λ (wavelength).
Why? Uncertainty principle (Will show).
2. Collection Angle/focal length/ Numerical Aperture
Resolution ≈
# λ/N.A.
# = a factor = ½ (details not important)
Resolution ≈ λ/2N.A.
Why is resolution l/2 N.A. (N.A. = nsinq)
Resolution:
1) how small of a spot of excitation light can you make
(scanning microscope)
2) how big of a spot an infinitely small object makes
Point Spread Function (PSF)
Calculating optimal diffraction-limited
resolution.
What is uncertainty principle applied here?
Δpx Δx ≥ h/2π Δx = resolution; how small spot
Photon 2
Remember: Applies to each direction!
Photon 1
Photon 1: p = p ŷ
Photon 2: px = p sin θ
: py = p cos θ
Δpx = p sin θ – (- p sin θ)
= 2p sin θ
Calculating resolution (con’t)
DpDx = h/2p
2psinq Dx = h/2p
p = h/l
Wavelength at screen
… need n.
Where does n come in?
Calculating resolution (con’t) : “n”, index of refraction
Coverslip (glass)
(thin, n= 1.33)
object
Fill with oil (n ~ 1.5)
where air = 1
(Homework)
Wavelength & Resolution
lvisible=≈ 400-700 nm
l/2 N.A.: air= l/2: oil= l/(2)(1.4)
400 nm 488
633
750
red
gree
n
blue
purple
Short l
l = 500 nm: Best resolution 200-250 nm
514 532
Long l
Modern day optical microscopes are highly optimized– perfect diffraction limited.
(Electron microscopes are 1000’s of times worse.)
l of electrons
(Who was famous guy who got
Nobel prize in 1929 for the “wave
nature of electrons”?
What relationship between wavelength,
l, and energy, E, and momentum, p,
does this correspond to?
Debroglie
E= hn = hc/l; p = h/l
Where does Planck’s constant come from?
Relationship between
radiation of an object and
its temperature
The Planck constant came from law of black body radiation: that the
electromagnetic radiation emitted by a black body could be modeled as a set of
harmonic oscillators with quantized energy of the form: E = hn
http://en.wikipedia.org/wiki/Black-body
Resolution of Electron Microscope
Given electron 100 KeV,
(typical upper-value for electron microscope)
what is l?
h =6.63 × 10-34 J-sec = 4.1 × 10-15 eV-sec
E100kV = 0.004 nm (really short!)
In reality, because not perfect electron lenses,
resolution is ~1 nm.
E.M. are far from ideal.