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Lecture 10

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.

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Lecture 10

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  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

  4. 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?

  5. Oscillatory muscles Stretch activation Synchronous Asynchronous

  6. Stretch- activated currents

  7. Sliding filamentds

  8. Myosin • 5.3 pN for each myosin molecule • 100 molecules per filament. • Each filament has c.s.a. of 1.8 X 10 –15 m2 in the relaxed muscle.

  9. Strain in solids and fluids A f d

  10. Sample fluid properties When f > fcrit- inertial forces dominate

  11. Swimming: is it worth it? • Cilium with velocity, v, length, d, time scale: • Diffusion time scale : • Swimming time, ts should be < tD

  12. A vo f d Viscous flow • Newtonian fluids are isotropic • What is a viscous fluid? • When f< fcrit Shear Planar geometry

  13. I.e., 1 mm cilium, D = 10-5 cm2/sec, • so v> 103mm /sec: • stirring and swimming is not energetically favorable for nutrition.

  14. Comparative motors

  15. ATP SYNTHASE — A MARVELLOUS ROTARY ENGINE OF THE CELL < previousnext >

  16. Rotary Cellular Motors • The rotary mechanism of ATP synthase , Stock D, Gibbons C, Arechaga I, Leslie AGW, Walker JECURRENT 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 TNATURE 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.

  17. ATP SYNTHASE — A MARVELLOUS ROTARY ENGINE OF THE CELL < previousnext >

  18. 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 * 2p/3) equivalent to free energy from ATP hydrolysis • Can see rotation by attaching an actin filament

  19. Nature Reviews Molecular Cell Biology2; 669-677 (2001)ATP SYNTHASE — A MARVELLOUS ROTARY ENGINE OF THE CELL < previousnext >

  20. 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?

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

  22. 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

  23. 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..

  24. 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

  25. Transition Probabilities Today’s Game Outcome Need a P for Today’s game Tomorrow’s Game Outcome

  26. Good Bad Good 3/4 1/2 Bad 1/4 1/2 Sum 1 1 Grades Transition Matrix This Semester Grade Tendencies To predict future: Start with now: What are the grade probabilities for this semester? Next Semester

  27. Markov Chain Intial Probability Set independently

  28. 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

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