Cellular Biophysics

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Cellular Biophysics
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The world you live in

• 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
• Fima

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The Viscous World

• In fluids, viscosity becomes important
• The force imparted by the fluid is dependent upon
  its viscosity

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Things get weird when viscosity increases

• 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

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Now consider density and viscosity
Fluid Density Viscosity
Air 1 2x10-5
Water 1000 .0009
Olive oil 900 .08
Glycerine 1300 1
Corn syrup 1000 5
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Reynolds Number-the ratio of inertal to viscous
forces
Inertial Force Fma (l3r)v2/l
Viscous Force hl3v/R2
Re Inertial Force rvR/h Viscous Force

• Reynolds numberinertial force/viscous force
• rdensity (of medium), llength, Sarea,
  v/tvelocity over timeacceleration µviscosity
  (of medium)
• Inertial is densityxvolumemass x accel (v/t)
• Viscous is Force/area viscosity x the velocity
  gradient.

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What does it mean?

• As size goes down, Re goes down
• As viscosity goes up, Re goes down
• At high Reynolds numbers- inertial forces
  dominate
• At low Reynolds numbers- viscous forces dominate
• Small objects in fluids are affected by the
  frictional drag of the media to a great extent

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Sample Reynolds numbers

• Bacterium swimming (organelle) 10-6
• Sperm swimming 10-2
• Fruit fly in flight 100
• Small bird flying 105
• Whale swimming 2x108

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What does it mean

• 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)
• 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

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What does it mean to Cell Biology?

• 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

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Diffusion

• What is diffusion?
• The random movement of molecules due to thermal
  energy
• The fundamental principle underlying all life
  processes!
• Determines the rate of enzyme reactions
• Determines the size and shape of cells
• Determines the speed of signal transduction

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History

• Until the early 1900s, the idea of molecules was
  controversial
• In 1828, Robert Brown observed movement of pollen
  particles in suspension (Brownian motion)
• What was driving the motion?
• Hypothesis 1- they were alive
• But they never stopped!
• Lifeless particles (soot) did the same

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• Hypothesis 2 (1860s)- movement was caused by
  collisions of water molecules with the pollen
• At higher temperatures, they moved faster!
• 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???

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Einstein strikes again

• 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

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The Diffusion Law

• mean square displacement x26Dt
• This is stochastic, not the behavior of a
  individual molecule
• Any molecule might not move at all
• Others may move a great distance
• There is no rate of diffusion
• x/tv6D/x or the rate gets slower the farther
  you are away
• 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

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Diffusion of Biological Molecules

• Substance M D (cm2/sec) time to diffuse 1µ
  diffuse 10µm
• bacterium 5x10-9 1 sec 100sec
• TMV 4x107 3x10-8 0.1 sec 10 sec
• albumin 7x104 6x10-7 10 msec 1 sec
• sucrose 3x102 5x10-6 1msec 100msec

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Diffusion and Signalling

• 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?

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Dif
fusion of Pulse vs. Continuous signal

Diffusion of Pulse vs. Continuous signal











































































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Signaling in large cells (multicellular organisms)

• 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

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What is cytoplasm like

• Cells are about 20mg/ml protein
• You cant 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

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FRAP of cytoplasm

• 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)

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Figure 2 JCB 138131
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Conclusions

• 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
• Immobile obstacles?
• Cytoskeletal mesh?