1. Biophysics Master Course, Fall 2002 Some of the physics cells have to deal with: Random walks, diffusion and Brownian motion

2. Background reading: — Frederick Reif: Statistical and Thermal Physics, Chpt. 1 (random walks), Chpt. 15 (fluctuations, Brownian motion) — Howard Berg: Random Walks in Biology, Chpts. 1, 2 (diffusion), Appendix A (distributions) — Jonathon Howard, Mechanics of Motor Proteins and the Cytoskeleton, Chpt. 4 (diffusion), Chpt. 16 (motor models) — Richard Feynman, Feynman Lectures I, Chpt 41 (Brownian motion), Chpt. 46 (thermal ratchet) — Landau, Lifschitz, Volume V, Statistical Physics, Chpt. 12 (fluctuations, pretty advanced) — Frederick Gittes, Christoph Schmidt, Signals and noise in micromechanical measurements. In Laser Tweezers in Cell Biology. Methods in Cell Biology, 55: 129-156, Academic Press, San Diego, CA, 1998 (power spectral analysis). — Gittes, F., Schmidt, C.F. (1998), Thermal Noise Limitations on Micromechanical Experiments, Eur. Biophys. J., 27: 75-81 (spectral analysis, other noise)

3. Optical trapping of 0.2 µm silica beads in water

4. Bacterial motility, E. coli from Howard Berg lab, courtesy Linda Turner

5. Intracellular transport in Reticulomyxa, video: M. Schliwa, M. Koonce

7. 2D random walk, 18050 steps

8. Intracellular Transport on Cytoskeletal Tracks 1 m Cell Body Synapse Axon Vesicles with motors Active transport: v ≈ 1µm/s, T ≈ 10 days Diffusion: T = x 2 /6D ≈ 26,000 years Microtubules

9. The Main Motor Protein Families (asymmetric) track: actin filaments, microtubules Cargo: Vesicles, Organelles Motors: myosins, kinesins, dyneins Fuel: ATP

10. The Feynman Thermal Ratchet P forward ~exp(-  /kT 1 ) P backward ~exp(-  /kT 2 ) works only if T 1 >T 2 !! motor protein conformational change: µs decay of temperature gradient over 10 nm: ns wrong model  rel ≈ Cl 2 /(4  2  )

11. Brownian Ratchet (A.F. Huxley ‘57) Cargo Thermal motion Track Net transport perpetuum mobile? Not if ATP is used to switch the off-rate. Motor

12. Three-bead assay with ncd

13. Myosin: averaged power strokes (Veigel et al. Nature ‘99, 398, 530)

14. Myosin Power Stroke Mechano-chemical cycle: M*ATP M*ADP*Pi M attach working stroke detach recovery stroke ADP +P i ADP PiPi actin myosin

15. Conformational Change of Single ncd Molecule release DeCastro, Fondecave, Clarke, Schmidt, Stewart, Nature Cell Biology (2000), 2:724 ADP ADP*P i ~ 7 nm

17. Stepping and Stalling of a Single Kinesin Molecule ~ 6 pN stall force ~ 8 nm steps Svoboda, Schmidt, Schnapp, Block, Nature (1993), 365: 721

18. - 2 Randomness parameter r:= lim t -> ∞ d 1 -> 2 -> 3 -> 4 -> 5 -> 6 kkkkk r = 0 r = 1 1 -> 2 k  t=const. “clockwork”  t exponentially distributed Poisson process

19. Randomness parameter for single kinesin (Visscher,Schnitzer, Block (‘99), Nature 400, 184)

20. Time series: Spectrum:

21. Efficiency, Invertability and Processivity of Molecular Motors F. Jülicher, Institut Curie, Paris http://www.curie.fr/~julicher A. Parmeggiani L. Peliti (Naples) A. Ajdari (Paris) J. Prost (Paris)

22. Mechano-chemical coupling M M-ADP M-ADP-P M-ATP mean velocity 1 2 3 4 x

23. Example: weakly bound state ATP ADP-P ADP strongly bound weakly bound

24. Example: identical shifted states l a U chemical free energy of hydrolysis:

25. Dissipation rates motion within a state: chemical transitions: total internal dissipation of the motor:

26. Efficiency of energy transduction force chemical energy velocity chemical rate A. Parmeggiani, F. Jülicher, A. Ajdari and J. Prost, PRE 60, 2127 (1999) Energy conservation: chemical work mechanical work total internal dissipation