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Collective Brownian Motors - Experiments and Models

Load force. Collective Brownian Motors - Experiments and Models. Erin Craig, Heiner Linke University of Oregon. Ann Arbor, June 12 2007. +. -. Brownian motors example: flashing ratchet. ON. OFF. ON. Ajdari and Prost, C.R. Acad. Sci. Paris II 315 , 1635 (1992). J. Bader et al,

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Collective Brownian Motors - Experiments and Models

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

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

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

  4. Self-propelled fluids

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

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

  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: Quantum ratchets Efficient thermoelectrics Self-propelled droplets Collective Brownian motors: modeling and experimental planning Information feedback Coupled particle ratchet Polymer motor Computational models of biological molecular motors: 1D kinesin model 3D myosin V model

  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: information feedback • Energy input: • collecting information • open/closing door • Directionality: spatial asymmetry • Energy input: turning potential on/off

  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: information feedback • Energy input: • collecting information • open/closing door • Directionality: spatial asymmetry • Energy input: turning potential on/off 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: information feedback • Energy input: • collecting information • open/closing door • Directionality: spatial asymmetry • Energy input: turning potential on/off • Do closed-loop strategies always out perform open-loop strategies? • Fundamental limitations on output of information feedback strategy? • Experimental realization?

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

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

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

  16. t1 = 0.02 L2/D; t2 = 0 t1 = 0.09 L2/D; t2 = 0 b) a) Time delay in feedback, N=106: E. Craig et. al., to submit (2007).

  17. a) t1 = 0.02 L2/D; t2 = 0 t1 = 0.09 L2/D; t2 = 0 b) a) b a b) t = t1 t = t1/2 Time delay in feedback, N=106: E. Craig et. al., to submit (2007).

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

  19. Brownian motors: overview of projects Experimental ratchets: Quantum ratchets Efficient thermoelectrics Self-propelled droplets Collective Brownian motors: modeling and experimental planning Information feedback Coupled particle ratchet Polymer motor E. Craig et. al., PRE, 2006 Computational models of biological molecular motors: 1D kinesin model 3D myosin V model

  20. Artificial single-molecule motor M. Downton

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

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

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

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

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

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

  27. 5. 4. ATP ATP ADP ADP ATP 3. 1. ADP·Pi ADP ADP Pi 2. ADP ADP ADP • Conformational change • Internal coordination • Brownian diffusion 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).

  28. 5. 4. ATP ATP ADP ADP ATP 3. 1. ADP·Pi ADP ADP Pi 2. ADP ADP ADP • Conformational change • Internal coordination • Brownian diffusion 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 creates strain

  29. 5. 4. ATP ATP ADP ADP ATP 3. 1. ADP·Pi ADP ADP Pi 2. ADP ADP ADP • Conformational change • Internal coordination • Brownian diffusion 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). Strain-dependent coordination of chemical cycle Conformational change creates strain

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

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

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

  33. r´3 r3 r´2 r2 A r1 r´1 r0 r´0 k r0 j Q i Myosin V 3D model: elasticity of neck domains • Neck domain: • 3 rigid segments • flexibility at joints Bending energy of semiflexible filaments: M. Terrak et. el., PNAS 102, 12718 (2005). M. Doi and S. F. Edwards, “The Theory of Polymer dynamics”, (1986).

  34. x z QA f = 0 r1 r1 x y y ADP.Pi-bound Myosin V 3D model: rotational states “Bird’s eye” view: Pre-stroke: Post-stroke: QB r1 x z y ADP-bound Empty ATP-bound

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

  36. 5. 4. ATP ADP ADP ATP ATP 3. 1. ADP·Pi ADP ADP Pi 2. ADP ADP ADP Myosin V 3D model: mechanical cycle I QA QB r1 r´1

  37. 5. 4. ATP ADP ADP ATP ATP 3. 1. ADP·Pi ADP ADP Pi 2. ADP ADP ADP Myosin V 3D model: mechanical cycle II I QA QA QA QB r´1 r1 r´1 r1

  38. 5. 4. ATP ADP ADP ATP ATP 3. 1. ADP·Pi ADP ADP Pi 2. ADP ADP ADP Myosin V 3D model: mechanical cycle III QA r´1 II I QA QA QA QB r´1 r1 r´1 r1

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

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

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

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

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

  44. fext Mechanistic model can demonstrate which physical assumptions are consistent with known data. This can help address... • 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?

  45. 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) Funding: NSF CAREER, NSF-GK12, NSF IGERT, ONR, Army, Australian Research Council, ONR-Global.

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