Download Cellular Biophysics

Cellular Biophysics
The world you live in
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An inertial world- objects that are
moving tend to keep moving even after
force is removed- inertia
This is the basis of motion in our world
Fi=ma
The Viscous World
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In fluids, viscosity becomes important
The force imparted by the fluid is
dependent upon its viscosity
Viscous Force
Force
Area, S
velocity, v
distance, l
Things get weird when
viscosity increases
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Consider a cylinder containing corn syrup
Add a dot of dye in corn syrup
Stir the syrup/dye in one direction
Reverse the direction of stirring
The dot reforms
Viscous fluids do not flow or mix
No turbulence, no inertia
Now consider density and viscosity
Fluid
Air
Density
1
Viscosity
2x10-5
Water
1000
.0009
Olive oil
900
.08
Glycerine
1300
1
Corn syrup
1000
5
Reynolds Number-the ratio of
inertal to viscous forces
Inertial Force F=ma= (l3r)v2/l
Viscous Force= hl3v/R2
Re= Inertial Force = rvR/h
Viscous Force
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Reynolds number=inertial force/viscous force
r=density (of medium), l=length, S=area,
v/t=velocity over time=acceleration
µ=viscosity (of medium)
Inertial is densityxvolume=mass x accel (v/t)
Viscous is Force/area= viscosity x the velocity
gradient.
What does it mean?
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As size goes down, Re goes down
As viscosity goes up, Re goes down
At high Reynold’s numbers- inertial forces
dominate
At low Reynold’s numbers- viscous forces
dominate
Small objects in fluids are affected by the
frictional drag of the media to a great extent
Sample Reynolds’ numbers
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Bacterium swimming (organelle)
Sperm swimming
Fruit fly in flight
Small bird flying
Whale swimming
10-6
10-2
100
105
2x108
What does it mean
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The forces associated with molecules of water interacting with each
other and solutes become relevant
To a small molecule (bacteria) moving through a fluid is like you trying to
move in a highly viscous liquid. Imagine yourself living in asphalt (Berg
experiment)
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Being small is equivalent to being in a very viscous environment
Water is highly ordered around you-you are the boundary layer
surfaces nearby create boundary effects that alter the properties of water
significant distances away
There is no inertia- if a bacteria stops swimming, it glides about the
distance of a hydrogen atom
drag is irrelevant (shape is irrelevant) so streamlining is irrelevant
What does it mean to Cell Biology?
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A small predator cannot catch a prey by
swimming at it, because it pushes the
prey away as it swims
A bacteria cannot swim by waving a
flagella or cilia- it would return to the
same place after a cycle of motion
Diffusion
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What is diffusion?
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The random movement of molecules due to
thermal energy
The fundamental principle underlying all life
processes!
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Determines the rate of enzyme reactions
Determines the size and shape of cells
Determines the speed of signal transduction
History
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Until the early 1900’s, the idea of molecules
was controversial
In 1828, Robert Brown observed movement
of pollen particles in suspension (Brownian
motion)
What was driving the motion?
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Hypothesis 1- they were alive
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But they never stopped!
Lifeless particles (soot) did the same
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Hypothesis 2 (1860’s)- movement was
caused by collisions of water molecules with
the pollen
At higher temperatures, they moved faster!
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But- particles are much larger than water
molecules- how can water move particles?
The speed of water molecules is 103m/s and there
would be about 1012 collisions/sec. Too fast for the
eye to see
How to resolve this???
Einstein strikes again
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Clarified the stochastic nature of molecular
motion- there are many events happening very
rapidly
If you take the look at the probabilities, then with
that many collisions with water molecules with a
range of velocities, then periodically you will get
a displacement of the particle by many more
collisions on one side than another
The process will lead to a 3D random walk of
the particle: Diffusion
The Diffusion Law
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mean square displacement x2=6Dt
This is stochastic, not the behavior of a individual molecule
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Any molecule might not move at all
Others may move a great distance
There is no “rate” of diffusion
x/t=v=6D/x or the rate gets slower the farther you are away
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So if you follow a certain concentration of molecules, that
concentration will move rapidly away from a source, and the farther
you get from the source, the slower that concentration will move
If the source only produces a limited number of molecules, then at
some distance, you will never reach that concentration
Diffusion of Biological Molecules
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Substance
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bacterium
5x10-9
TMV
4x107 3x10-8
albumin
7x104 6x10-7
sucrose
3x102 5x10-6
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M
D (cm2/sec)
time to diffuse 1µ
1 sec
0.1 sec
10 msec
1msec
diffuse 10µm
100sec
10 sec
1 sec
100msec
Diffusion and Signalling
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If you want to send a signal inside a cell, how
do you do it?
IP3 or Ca release at the membrane
You assume there is a threshold for the
effect- ie. you need above a certain
concentration of the signal molecule to
activate the effectors
Do you want the response to be local or
general?
Do you want it to continue or terminate?
Diffusion of Pulse vs. Continuous signal
Diffusion of Pulse vs. Continuous signal
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Signaling in large cells
(multicellular organisms)
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If you release a signal in a cell (Ca ions) and they
diffuse from the site of release, it will take time for
signal to reach other parts of the cell, and the
concentration will be lower, the farther you get from
the site of release
If there is a threshold for action, you might not
exceed it at distant sites- allows for local action
It would take about 10 minutes for a Ca wave to get
across a 1mm Xenopus egg and it would never reach
as hi a concentration because it would be diluted
Reaction diffusion waves- you relay the signal so that
the size of the signal remains constant
What is cytoplasm like
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Cells are about 20mg/ml protein
You can’t dissolve 20mg/ml of most proteins
How do you do it in a cell?
Based upon this, it was hypothesized that
most of the cellular water was tied up in
coating proteins, and thus the cytoplasm had
limited water
This would affect diffusion
FRAP of cytoplasm
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Introduce a fluorescent molecule into the
cytoplasm of the cell
Microinject fluorescein dextran
Shine a very bright light source as a small
spot onto a stained region to bleach the dye
Produces a dark spot on a light background
Now measure the fluorescence intensity of
the spot over time as fluorescence recovers
(Fluorescence Recovery After
Photobleaching)
FRAP analysis
Figure 2 JCB 138:131
Figure 2 JCB 138:131
Conclusions
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Dc/Dw is constant over a range of sizes and
locations in the cell
The ratio is about 0.25: diffusion in cytoplasm is
about 4x slower than in water for macromolecules
At these rates it would take a large
macromolecule about 7 seconds to diffuse across
a cell
For large macromolecules, there is little diffusion
Reason is controversial
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Immobile obstacles?
Cytoskeletal mesh?