1. Cellular Biophysics

2. 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 • Fi=ma

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

5. 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

6. Now consider density and viscosity

7. Reynolds Number-the ratio of inertal to viscous forces • 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. Inertial Force F=ma= (l3r)v2/l Viscous Force= hl3v/R2 Re= Inertial Force = rvR/h Viscous Force

8. What does it mean? • 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

9. Sample Reynolds’ numbers • Bacterium swimming (organelle) 10-6 • Sperm swimming 10-2 • Fruit fly in flight 100 • Small bird flying 105 • Whale swimming 2x108

10. 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

11. 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

12. 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

13. History • 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? • Hypothesis 1- they were alive • But they never stopped! • Lifeless particles (soot) did the same

14. Hypothesis 2 (1860’s)- 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???

15. 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

16. The Diffusion Law • mean square displacement x2=6Dt • 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/t=v=6D/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

17. 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

18. 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?

19. Dif fusion of Pulse vs. Continuous signal Diffusion of Pulse vs. Continuous signal * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

20. 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

22. What is cytoplasm like • 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

23. 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)

25. Figure 2 JCB 138:131

26. 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?