1. Lecture 10 Background for cell propulsion Fluid dynamics Enzyme kinetics How do animals swim?: 1. pushing fluid backward by limb action; 2. pushing fluid forward by resistance of body. I.e fish starting from release will accelerate until the backward & forward momentum (of the fluid) balance. Viscosity is only significant at the boundary layer.

2. Cell Propulsion Small scale phenomenon: slow velocities driven by surface forces: pressure and viscous stress. Fluid resistance is significant, and balances propulsive force. Motion of a body depends on the ratio of viscous and inertial effects: Reynold’s number: Small for cells, large for almost all animals. Cellular world is ruled by friction.

3. Reynold’s number quantifies the relative magnitudes of frictional and inertial forces

5. Cellular Motors Molecular motors must move (swim) in fluids, where most of the work is dissipated What forces must they overcome? Where do the motors get their fuel? How do they exhaust spent fuel? What is the efficiency?

6. Creature R Bacteria10 -4 Spermatozoa10 -2 Flying Insects Birds 10 4 10 5

7. Oscillatory muscles Synchronous Asynchronous Stretch activation

8. Stretch- activated currents

9. Sliding filamentds

10. Myosin 5.3 pN for each myosin molecule 100 molecules per filament. Each filament has c.s.a. of 1.8 X 10 –15 m 2 in the relaxed muscle.

16. Strain in solids and fluids f A d

17. Sample fluid properties When f > f crit - inertial forces dominate

18. Swimming: is it worth it? Cilium with velocity, v, length, d, time scale: Diffusion time scale : Swimming time, t s should be < t D

19. Viscous flow Newtonian fluids are isotropic What is a viscous fluid? When f< f crit v o f A d Shear Planar geometry

20. I.e., 1  m cilium, D = 10 -5 cm 2 /sec, so v> 10 3  m /sec: stirring and swimming is not energetically favorable for nutrition.

23. Comparative motors

24. ATP SYNTHASE — A MARVELLOUS ROTARY ENGINE OF THE CELL< previous next >

25. Rotary Cellular Motors The rotary mechanism of ATP synthase, Stock D, Gibbons C, Arechaga I, Leslie AGW, Walker JE CURRENT OPINION IN STRUCTURAL BIOLOGY,10 (6): 672- 679 DEC 2000 2. ATP synthase - A marvellous rotary engine of the cell, Yoshida M, Muneyuki E, Hisabori T NATURE REVIEWS MOLECULAR CELL BIOLOGY 2 (9): 669-677 SEP 2001 3. The gamma subunit in chloroplast F-1-ATPase can rotate in a unidirectional and counter-clockwise manner Hisabori T, Kondoh A, Yoshida M FEBS LETTERS 463 (1-2): 35-38 DEC 10 1999 4. Constructing nanomechanical devices powered by biomolecular motors.C. Montemagno, G Bachand, Nanotechnology 10: 225-2312, 1999.

27. ATP SYNTHASE — A MARVELLOUS ROTARY ENGINE OF THE CELL< previous next >

28. F1 ATPase: A rotary motor Can either make or break ATP, hence is reversible Torque of 40 pN-nM; work in 1/3 rev. is 80 pn-nM (40 * 2  /3) equivalent to free energy from ATP hydrolysis Can see rotation by attaching an actin filament

30. Nature Reviews Molecular Cell Biology 2; 669-677 (2001) ATP SYNTHASE — A MARVELLOUS ROTARY ENGINE OF THE CELL < previous next >

34. Elasticity Nano versus macro elasticity Behaviour relative to kT: Stretch a rubber band and a string of paper clips. Significant for The nanometer-scale monomers of a macromolecule, but not for a string of paper clips. The retracting force exerted by a stretched rubber band is entropic. It increases disorder. Do most polymers have persistence lengths longer than their total (contour) length?

35. When L>>  the chain has many bends and is always crumpled in solution – the FJC model applies, with each link approximated as 2  and perfectly flexible joints. To count all possible curved states in a smooth-bending rod in solution- it’s a WLC- supercoiling is possible.

36. Promoters have different abilities to uncoil Twisting DNA torsional buckling instability Unwinding and causes local denaturation Many motors are needed: RNA plymerase, DNA polymerase: 100 nucleotides/sec. Forces (pN) can stop transcription

37. Mechano - regulation Growth, proliferation, protein synthesis, gene expression, homeostasis. Transduction process- how? Single cells do not provide enough material. MTC can perturb ~ 30,000 cells and is limited. MTS is more versatile- more cells, longer periods, varied waveforms..

43. Markov Chains A dynamic model describing random movement over time of some activity Future state can be predicted based on current probability and the transition matrix

45. Transition Probabilities WinLose Win3/41/2 Lose1/41/2 Sum11 Today’s Game Outcome Tomorrow’s Game Outcome Need a P for Today’s game

46. Grades Transition Matrix 11Sum 1/21/4Bad 1/23/4Good BadGood This Semester Next Semester Grade Tendencies To predict future: Start with now: What are the grade probabilities for this semester?

47. Markov Chain Intial Probability Set independently

48. Computing Markov Chains % A is the transition probability A= [.75.5.25.5] % P is starting Probability P=[.1.9] for i = 1:20 P(:,i+1)=A*P(:,i) end