RF Fox FNAL 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 Nanobiology Biochemistry Molecular biology Can we learn mechanisms from nanobiology that are applicable to nanotechnology?

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

RF Fox FNAL 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)

RF Fox FNAL 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, (2001) (with Mee Choi) Kinesin’s Biased Stepping Mechanism: Amplification of Neck Linker Zippering Biophysical Journal, (2006 ) (with William Mather)

RF Fox FNAL Minnow m(gm)134 R(cm)2 v S (cm/s)100 v T (cm/s)3 x W S (W)3.8 x W T (W)3.4 x A Minnow

RF Fox FNAL A Minnow and an E. Coli MinnowE. Coli m (gm)1342 x R(cm)25 x v S (cm/s)1002 x v T (cm/s)3 x W S (W)3.8 x W T (W)3.4 x

RF Fox FNAL A Minnow, an E. Coli and Ubiquinone MinnowE. ColiUbiquinone m (gm)1342 x x R (cm)25 x x v S (cm/s)1002 x (0.8) v T (cm/s)3 x ,300 W S (W)3.8 x (2.3 x ) W T (W)3.4 x x 10 -6

RF Fox FNAL Reynolds Number MinnowE. ColiUbiquinone Secular2 x x (2.4 x ) Thermal4 x x x 10 -3

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

RF Fox FNAL 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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RF Fox FNAL diffusion for reduced ubiquinone boundary layer equation

RF Fox FNAL diffusive rate parameter reaction rate parameter

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

RF Fox FNAL Langevin equation Einstein’s Relation 1905

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

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

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

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

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RF Fox FNAL 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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RF Fox FNAL Load (pN)MFPT (s) x x x x

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