1. Collective Brownian Motors - Experiments and Models Erin Craig, Heiner Linke University of Oregon Ann Arbor, June 12 2007 Load force

2. - + J. Bader et al, PNAS 96, 13165 (1999) Ajdari and Prost, C.R. Acad. Sci. Paris II 315, 1635 (1992) Non-equilibrium + Asymmetry + Thermal fluctuations = Transport Brownian motors example: flashing ratchet ON OFF ON

3. Brownian motors: overview of projects Experimental ratchets: Collective Brownian motors: modeling and experimental planning Computational models of biological molecular motors: Information feedbackCoupled particle ratchetPolymer motor Self-propelled droplets Quantum ratchets 1D kinesin model3D myosin V model Efficient thermoelectrics

4. Self-propelled fluids

5. Droplet of liquid nitrogen (77 K) on machined brass surface (300 K). Filmed at 500 frames per second 15 mm Slow motion

6. Film boiling (Leidenfrost effect) Vapor layer separates solid and liquid (≈ 10 - 100 µm). Film boiling point: Water ≈ 200 - 300 °C Ethanol ≈ 120 °C R134a ≈ 22 °C 0.3 mm 1.5 mm

7. Film boiling (Leidenfrost effect) 0.3 mm 1.5 mm H. Linke et. al., PRL 96, 154502 (2006). More movies: darkwing.uoregon.edu/~linke/dropletmovies

8. Brownian motors: overview of projects Experimental ratchets: Collective Brownian motors: modeling and experimental planning Computational models of biological molecular motors: Information feedbackCoupled particle ratchetPolymer motor Self-propelled droplets Quantum ratchets 1D kinesin model3D myosin V model Efficient thermoelectrics

9. How to get flux or work out of a thermal system? Open-loop strategy: ex: Brownian ratchet Closed-loop (feedback) strategy: ex: Maxwell’s demon Directionality: spatial asymmetry Energy input: turning potential on/off Directionality: information feedback Energy input: collecting information open/closing door

10. How to get flux or work out of a thermal system? Open-loop strategy: ex: Brownian ratchet Closed-loop (feedback) strategy: ex: Maxwell’s demon Directionality: spatial asymmetry Energy input: turning potential on/off Directionality: information feedback Energy input: collecting information open/closing door Both systems produce net flux w/o applying macroscopic forces directly to particles and w/o violating the 2nd Law of Thermodynamics.

11. How to get flux or work out of a thermal system? Open-loop strategy: ex: Brownian ratchet Closed-loop (feedback) strategy: ex: Maxwell’s demon Directionality: spatial asymmetry Energy input: turning potential on/off Directionality: information feedback Energy input: collecting information open/closing door Do closed-loop strategies always out perform open-loop strategies? Fundamental limitations on output of information feedback strategy? Experimental realization?

12. Information feedback in thermal ratchets: F. J. Cao et. al., PRL 93, 040603 (2004). V(x) x aL L

13. Information feedback in thermal ratchets: F. J. Cao et. al., PRL 93, 040603 (2004). optimal periodic switching

14. Time delay in feedback implementation: t1 = delay due to computational time (If a measurement is taken at time t, the feedback based on this measurement will occur at time t + t1.) t2 = delay due to measurement time (If a measurement is taken at time t, the next measurement will be taken at time t + t2.)

15. Time delay in feedback implementation: Original scheme: higher current than optimal periodic switching Delay t1 reduces current because high fluctuations reduce relevance of delayed information Original scheme worse than periodic switching For some values of t1, system settles into steady state that reproduces optimal periodic flashing. Large N (more deterministic): Small N (high fluctuations): E. Craig et. al., to submit (2007).

16. Time delay in feedback, N=10 6 : b) a) t 1 = 0.02 L 2 /D; t 2 = 0t 1 = 0.09 L 2 /D; t 2 = 0 E. Craig et. al., to submit (2007).

17. Time delay in feedback, N=10 6 : b) a) t 1 = 0.02 L 2 /D; t 2 = 0t 1 = 0.09 L 2 /D; t 2 = 0 E. Craig et. al., to submit (2007). a) b)  = t 1  = t 1 /2 a b

18. Time delay in electrostatic experiment: Simulated time delay:Experimental time delay:

19. Brownian motors: overview of projects Experimental ratchets: Collective Brownian motors: modeling and experimental planning Computational models of biological molecular motors: Information feedbackCoupled particle ratchetPolymer motor Self-propelled droplets Quantum ratchets 1D kinesin model3D myosin V model Efficient thermoelectrics E. Craig et. al., PRE, 2006

20. Artificial single-molecule motor M. Downton

21. Average velocity peaks at L ≈ 5 , independent of polymer length N. Ratchet period L (  ) Velocity (L/   L t on = t off = 20  M. Downton et. al., Phys. Rev. E 73, 011909 (2006)

22. Stall force is proportional to polymer length F stall ≈ 1kT/  = 0.04 pN for  100 nm ≈ pN for  5 nm L = 5  Stall force (kT/  M. Downton et. al., Phys. Rev. E 73, 011909 (2006)

23. Experiment in progress 1 µm Brian Long, UO Jonas Tegenfeldt, Lund cycle time ≈ 20 ms ≈ 50 Hz expected speed ≈ 1 µ m/s

24. 10 µm High resolution images of DNA Response to voltage, background drift Future: analysis of conformations, fluctuations, trajectories Brian Long, UO Jonas Tegenfeldt, Lund Experiment in progress

25. Brownian motors: overview of projects Experimental ratchets: Collective Brownian motors: modeling and experimental planning Computational models of biological molecular motors: Information feedbackCoupled particle ratchetPolymer motor Self-propelled droplets Quantum ratchets 1D kinesin model3D myosin V model Efficient thermoelectrics

26. Myosin V: hand-over-hand walking molecular motor A. R. Dunn, J. A. Spudich, Nature SMB 14, 246 (2007). Processive motor involved in vesicle and organelle transport Two part step: lever arm rotation followed by diffusive search? A. Yildiz,..., P. Selvin, Science 300, 2061 (2003).

27. Myosin V mechanochemical cycle K.I. Skau, R.B. Hoyle, M.S. Turner, BPJ 91, 2475 (2006). M. Rief.,...,J. Spudich, PNAS 97, 9482 (2000). Conformational change Internal coordination Brownian diffusion ATP ADP ATP ADP·Pi ADP 4. 5. 1. 2. 3. ATP Pi ADP

28. Myosin V mechanochemical cycle ATP ADP ATP ADP·Pi ADP 4. 5. 1. 2. 3. ATP Pi ADP Conformational change creates strain K.I. Skau, R.B. Hoyle, M.S. Turner, BPJ 91, 2475 (2006). M. Rief.,...,J. Spudich, PNAS 97, 9482 (2000). Conformational change Internal coordination Brownian diffusion

29. Myosin V mechanochemical cycle ATP ADP ATP ADP·Pi ADP 4. 5. 1. 2. 3. ATP Pi ADP Conformational change creates strain Strain-dependent coordination of chemical cycle K.I. Skau, R.B. Hoyle, M.S. Turner, BPJ 91, 2475 (2006). M. Rief.,...,J. Spudich, PNAS 97, 9482 (2000). Conformational change Internal coordination Brownian diffusion

30. Myosin V mechanochemical cycle ATP ADP ATP ADP·Pi ADP 4. 5. 1. 2. 3. ATP Pi ADP Conformational change creates strain Release of strain K.I. Skau, R.B. Hoyle, M.S. Turner, BPJ 91, 2475 (2006). M. Rief.,...,J. Spudich, PNAS 97, 9482 (2000). Conformational change Internal coordination Brownian diffusion Strain-dependent coordination of chemical cycle

31. ATP ADP ATP ADP·Pi ADP 4. 5. 1. 2. 3. ATP Pi ADP Diffusion Myosin V mechanochemical cycle Conformational change creates strain Release of strain K.I. Skau, R.B. Hoyle, M.S. Turner, BPJ 91, 2475 (2006). M. Rief.,...,J. Spudich, PNAS 97, 9482 (2000). Conformational change Internal coordination Brownian diffusion Strain-dependent coordination of chemical cycle

32. Myosin V: 3D model pair of IQ motifs treated as rigid element flexibility at joints hinge between neck domains myosin head harmonic rotation about state- dependent equilibrium angle neck domain

33. Myosin V 3D model: elasticity of neck domains Neck domain: 3 rigid segments flexibility at joints M. Terrak et. el., PNAS 102, 12718 (2005). M. Doi and S. F. Edwards, “The Theory of Polymer dynamics”, (1986). Bending energy of semiflexible filaments: r´ 3 r1r1 r´ 1 r´ 2 r2r2 r3r3 r0r0 r´ 0 A  i j k r0r0

34. Myosin V 3D model: rotational states Post-stroke:Pre-stroke: ADP-bound Empty ATP-bound BB x z y r1r1 ADP.Pi-bound AA y x z r1r1 y x r1r1  “Bird’s eye” view:

35. Myosin V 3D model: mechanical cycle ATP ADP ATP ADP·Pi ADP 4. 5. 1. 2. 3. ATP Pi ADP

36. Myosin V 3D model: mechanical cycle ATP ADP ATP ADP·Pi ADP 4. 5. 1. 2. 3. ATP Pi ADP r1r1 r´ 1 AA BB I

37. Myosin V 3D model: mechanical cycle ATP ADP ATP ADP·Pi ADP 4. 5. 1. 2. 3. ATP Pi ADP r1r1 r´ 1 AA BB I r1r1 AA AA II

38. Myosin V 3D model: mechanical cycle ATP ADP ATP ADP·Pi ADP 4. 5. 1. 2. 3. ATP Pi ADP r1r1 r´ 1 AA BB I r1r1 AA AA II r´ 1 AA III

39. ATP ADP ATP ADP·Pi ADP 4. 5. 1. 2. 3. ATP Pi ADP Myosin V 3D model: mechanical cycle

40. ATP ADP ATP ADP·Pi ADP 4. 5. 1. 2. 3. ATP Pi ADP Myosin V 3D model: mechanical cycle

41. ATP ADP ATP ADP·Pi ADP 4. 5. 1. 2. 3. ATP Pi ADP Myosin V 3D model: mechanical cycle

42. Myosin V 3D model: inputs and outputs f ext Model Parameters: Binding sites Neck domain length Drag coefficients Transition rates Neck domain persistence length Equilibrium angles Rotational stiffness Neck domains: free swivel?

43. Myosin V 3D model: inputs and outputs f ext Model Parameters: Binding sites Neck domain length Drag coefficients Transition rates Neck domain persistence length Equilibrium angles Rotational stiffness Neck domains: free swivel? Experimentally measured behavior: Average step size Substep (“prestroke”) size, ATP dependence Step trajectories, cargo Step trajectories, individual heads Profile of step average, cargo Profile of step average, heads correlation of z-position with steps correlation of x and z variance with steps non-Gaussian fluctuations (failed steps?) positional distribution of detached head load dependence of velocity and dwell times Mechanical processivity (steps per contact) Kinetic processivity (1 step per ATP) Stepping vs. neck length Characteristics of backsteps under load

44. f ext Mechanics of stepping: what happens during one-head-bound state? Role of strain in coordinated walking? Backwards steps under load: processive walking? Mechanism behind distribution of step sizes for different neck lengths? Mechanistic model can demonstrate which physical assumptions are consistent with known data. This can help address...

45. Funding: NSF CAREER, NSF-GK12, NSF IGERT, ONR, Army, Australian Research Council, ONR- Global. UO Linke lab: PhD students: Erin Craig Eric Hoffman Ben Lopez Brian Long Nate Kuwada Preeti Mani Jason Matthews Postdoc Ann Persson Ugrads Adam Caccavano Mike Taormina Tyler Hennon Steve Battazzo Benji Aleman (Berkeley) Laura Melling (UCSB) Corey Dow (UCSC) Collaborations: Lars Samuelson, Henrik Nilsson, Linus Fröberg (Lund, Sweden) Martin Zuckermann, Mike Plischke, Matthew Downton, Nancy Forde (Simon Fraser University, B.C.) Dek Woolfson (Bristol, U.K.) Tammy Humphrey, Paul Curmi (Sydney)