1. RF Fox FNAL 20061 Rectified Brownian Motion in Subcellular Biology Ronald F. Fox Mee Choi William Mather School of Physics Georgia Institute of Technology

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3. 3 Nanobiology Biochemistry Molecular biology Can we learn mechanisms from nanobiology that are applicable to nanotechnology?

4. RF Fox FNAL 20064 One such lesson is the constructive use of thermal energy. Such a mechanism is called Rectified Brownian Motion.

5. RF Fox FNAL 20065 A Few Antecedents A. F. Huxley Prog. Biophys. Chem. 7, 255 (1957) M. Meister, S. R. Caplan and H. C. Berg Biophys. J. 55, 905 (1989) R. D. Vale and F. Oosawa Adv. Biophys. 26, 97 (1990)

6. RF Fox FNAL 20066 Rectified Brownian Movement in Molecular and Cell Biology Phys. Rev. E 57, 2177 (1998) Rectified Brownian Motion and Kinesin Motion Along Microtubules Phys. Rev. E 63, 051901 (2001) (with Mee Choi) Kinesin’s Biased Stepping Mechanism: Amplification of Neck Linker Zippering Biophysical Journal, 91 2416-2426 (2006 ) (with William Mather)

7. RF Fox FNAL 20067 Minnow m(gm)134 R(cm)2 v S (cm/s)100 v T (cm/s)3 x 10 -8 W S (W)3.8 x 10 -4 W T (W)3.4 x 10 -23 A Minnow

8. RF Fox FNAL 20068 A Minnow and an E. Coli MinnowE. Coli m (gm)1342 x 10 -12 R(cm)25 x 10 -5 v S (cm/s)1002 x 10 -3 v T (cm/s)3 x 10 -8 0.20 W S (W)3.8 x 10 -4 10 -17 W T (W)3.4 x 10 -23 10 -13

9. RF Fox FNAL 20069 A Minnow, an E. Coli and Ubiquinone MinnowE. ColiUbiquinone m (gm)1342 x 10 -12 1.4 x 10 -21 R (cm)25 x 10 -5 7.5 x 10 -8 v S (cm/s)1002 x 10 -3 (0.8) v T (cm/s)3 x 10 -8 0.209,300 W S (W)3.8 x 10 -4 10 -17 (2.3 x 10 -14 ) W T (W)3.4 x 10 -23 10 -13 3 x 10 -6

10. RF Fox FNAL 200610 Reynolds Number MinnowE. ColiUbiquinone Secular2 x 10 4 4 x 10 -5 (2.4 x 10 -6 ) Thermal4 x 10 -6 3 x 10 -4 1.6 x 10 -3

11. RF Fox FNAL 200611 Biological Energy Couplings Photon energy (electron excitation) Electron energy (redox reaction) Proton energy (pH gradient) Phosphate energy (monomer activation)

12. RF Fox FNAL 200612 Redox reaction variety Pure, 1 electron transfer Iron, copper, zinc… 1 electron and 1 proton transfer FADH 2, UQH 2,.. 2 electrons and 1 proton transfer NAD +, NADH,..

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15. RF Fox FNAL 200615 diffusion for reduced ubiquinone boundary layer equation

16. RF Fox FNAL 200616 diffusive rate parameter reaction rate parameter

17. RF Fox FNAL 200617 implications Weak linear steady state gradients Negligible energy dissipation associated with the gradients according to non-equilibrium steady state thermodynamics

18. RF Fox FNAL 200618 Langevin equation Einstein’s Relation 1905

19. RF Fox FNAL 200619 Brownian Work Theorem Secular power from secular force Stochastic power from Brownian force Power expended by drag force

20. RF Fox FNAL 200620 Rotary Enzymes Lipoamide 1.4 nm long acetyl or succinyl carrier pyruvate and  -ketoglutarate dehydrogenases Biocytin 1.4 nm long CO 2 carrier pyruvate carboxylase and fatty acid synthetase Phosphopantetheine 2.0 nm long thioester carrier gramicidin and tyrocidine synthetases fatty acid synthetase, polyketide synthetase

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23. RF Fox FNAL 200623 Kinesin Processivity Bias Coordination A two “headed” motor protein that “walks” on microtubules

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25. RF Fox FNAL 200625 Mechanisms Direct Chemo-Mechanical Energy Conversion “Power Stroke” ATP Powered Conformation Change Rectified Brownian Motion ATPase Switch Heat Powered Conformation Change

26. RF Fox FNAL 200626 The trailing head is “thrown forward” in a way that is “akin to a judo expert throwing an opponent with a rearward-to-forward swing of the arm.” [Vale and Milligan, Science 288, 88 (2000)] POWER STROKE  -sheet boundary hydrogen bonds ATP powered  -sheet closure

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28. RF Fox FNAL 200628 Forces Covalent C-C, C-N and C-O bonds 4.0 - 4.3 nano-Newtons Hydrogen bonds ~0.1 - ~50(?) pico-Newtons Unbound kinesin head neck linker tensions 100 - 200 pico-Newtons

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31. RF Fox FNAL 200631 Measured neck linker free energy of binding to the edge of the  -sheet is only a few kT. This is enough energy to cause a significant bias for attachment in the forward direction, or plus end of the microtubule. Rectified Brownian Motion

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38. RF Fox FNAL 200638 Load (pN)MFPT (s) 01.7727 x 10 -6 11.0991 x 10 -5 21.6465 x 10 -4 34.0071 x 10 -3 40.1231 54.3005 6163.1 76541

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