1. Rotary motors – F 0 F 1 ATPase, helicase Goals – learn about rotary motor basic to biology landmark paper directly observing rotation in F1 ATPase some data from follow-up papers showing more detail over-view of more complex F 0 F 1 “double” rotator coupling proton gradient to ATP synthesis flagellar motors and magnetically-driven  m screws

2. F 1 ATPase Ancient, membrane-associated structure, found in all organisms from bacteria to man, synthesizes or degrades ATP ADP + P Crystal structure shows a central shaft protein (  ) surrounded by a hexamer consisting of 3  and 3   monomers  Many hypotheses that it might act as a rotary motor  coupling rotation to synthesis (degradation) of ATP

3. Crystal structure of mitochondrial F 1 ATPase What is diagram showing? What do you make of the fact that 1 of the  units has ATP, 1 has ADP, and 1 has no nucleotide? (ATP analogue)

4. Experimental set-up – purify component proteins from E Coli How was SA attached to actin and  ? Do either have to be attached at specific sites? How were  units attached to glass? How was actin visualized?

5. What do the pictures show? Is the motion generally unidirectional? Are you sure? What would you expect if the actin were tethered but free to rotate?  t = 33ms

6. Do you expect the slopes to decrease with actin length? How would you expect the slope to vary w/L?  1/L, 1/L 2 ?) Why might slopes differ for filaments of the same length? Why do some traces suddenly flatten out?

7. Brownian equivalents for linear & rotational motion F =  v N =   sphere  = 6  r  sphere = 8  r 3  rod = (  /3)  L 3 /[ln(L/r) – 0.477]  likely underestimate due to  surface proximity and “bumping” on glass  D = k B T/  D r = k B T/   = 6Dt  D r t L = 2000nm, r = 10nm,  = 10 -3 Ns/m 2,  rod  10 -21 Nms D r  4rad 2 /s, t(1rev=6rad)  1s, t(50rev)  2500s

8. Their conclusions: Rotation in 1 direction when hydrolyzing ATP Torque estimated from velocity and drag coeff (N=  )  30pNnm => more powerful than kinesin, myosin Power (  )   G from ATP hydrolysis with 3 ATP/cycle c/w high efficiency

9. Yasuda et al Nature 410:898 (2001) follow-up paper Why might it be helpful to replace actin with 40nm gold bead? Are you sur- prised bead rotates eccen- trically?  t = 0.5ms

10. Main result: bead pauses (moves) in 120 0 steps at low [ATP], begin to see 30 0, 90 0 substeps pause before 90 0 step  [ATP] -1 rotations time

11. Goal – relate step-wise motion to binding ATP, hydrolysis of ATP, release of ADP, P i, subunit conformational changes

12. Itoh et al, Nature 427:465 (2004) – magnetically rotating beads in opposite direction -> ATP synthesis Luciferin-luciferase, ADP, P i in buffer; ATP synthesis -> light Compare # photons/5min when rotation clockwise (Syn- thesis), counter-clockwise (Hydrolysis) or no rotation (N)

13. sum Indiv. expts. Main conclusion – Motor is reversible clockwise – synthesize ATP counter-clockwise – hydrolyze ATP Why slt. more light with H than N – a few motors are upside down on top surface of glass! Going cc’wise: think alter subunit affinity for ADP, P i, ATP, etc.

14. Englebrecht Review Nature 459:364 (2009)   Proposed mech. of torque generation compliance coupling stores energy good source of refs to potential presentation papers!

15. But wait, there’s more …. F 1 is part of F 0 F 1 complex F 0 is second rotary motor, embedded in membrane; H + transport thru F 0 drives rotation of  to make ATP

16. Proposed mechanism of ion driven rotation of F 0 - charge aa neut. in membrane

17. Flagellar motor similar to F 0 in that it is membrane- assoc. and driven by ion flow, but many proteins & connected to large, rigid, helical polymer = flagellum Pallen et al, Nature Reviews Microbiology 4:784 (2006) Mechanics of locomotion at low Reynolds # - reciprocal motion doesn’t work, need propellor (Purcell, Am. J. Phys. 45, 3 (1977), PNAS 94:11307 (1997)) Intermittant rotation -> altering flagellar on/off rate allows bacterium to move in direction of food gradient (Berg, Random Walks in Biology, 1993)

18. Man-made version - Magnetically controlled nano-propellors Ghosh et al Nano Letters 9:2243 (2009) SiO 2 propellor w/30nm cobalt evaporated on half of surface random motion without magnet

19. Propell via 3-d orientation-controllable electro magnet generating  50G field at up to 170Hz Propellor advances  210nm/rotation,  40  m/s at 170Hz controlled trajectories; dots = position at different frames

21. Summary Rotary motors form some of most fundamental bio-nano machines involved in metabolism and locomotion Rotation driven by ion gradients across membranes (F 0 ) Rotation coupled to ATP synthesis from ADP and P (F 1 ) Torques up to 50pNnm Flagellar screw one of few of modes of locomotion at low Reynolds number