Rectified Brownian Motion in Subcellular Biology

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Rectified Brownian Motion in Subcellular Biology
Ronald F. Fox Mee Choi William Mather School of
Physics Georgia Institute of Technology
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Nanobiology Biochemistry Molecular biology
Can we learn mechanisms from nanobiology that are
applicable to nanotechnology?
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One such lesson is the constructive use of
thermal energy. Such a mechanism is called
Rectified Brownian Motion.
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A Few Antecedents
A. F. HuxleyProg. Biophys. Chem. 7, 255
(1957)M. Meister, S. R. Caplan and H. C.
BergBiophys. J. 55, 905 (1989)R. D. Vale and
F. OosawaAdv. Biophys. 26, 97 (1990)
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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) Kinesins Biased Stepping Mechanism
Amplification of Neck Linker Zippering Biophysical
Journal, 91 2416-2426 (2006) (with William
Mather)
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A Minnow
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A Minnow and an E. Coli
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A Minnow, an E. Coli and Ubiquinone
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Reynolds Number
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Biological Energy Couplings
Photon energy (electron excitation) Electron
energy (redox reaction) Proton energy (pH
gradient) Phosphate energy (monomer activation)
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Redox reaction variety
Pure, 1 electron transfer Iron, copper, zinc 1
electron and 1 proton transfer FADH2, UQH2,.. 2
electrons and 1 proton transfer NAD, NADH,..
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diffusion for reduced ubiquinone
boundary layer equation
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diffusive rate parameter
reaction rate parameter
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implications
Weak linear steady state gradients
Negligible energy dissipation associated with
the gradients according to non-equilibrium
steady state thermodynamics
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Langevin equation
Einsteins Relation 1905
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Brownian Work Theorem
Secular power from secular force
Stochastic power from Brownian force
Power expended by drag force
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Rotary Enzymes
Lipoamide 1.4 nm long acetyl or succinyl
carrier pyruvate and a-ketoglutarate
dehydrogenases Biocytin 1.4 nm long CO2
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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Kinesin
A two headed motor protein that walks on
microtubules
Processivity Bias Coordination
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Mechanisms
Direct Chemo-Mechanical Energy Conversion Power
Stroke ATP Powered Conformation
Change Rectified Brownian Motion ATPase
Switch Heat Powered Conformation Change
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POWER STROKE
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.
b-sheet boundary hydrogen bonds
ATP powered b-sheet closure
Vale and Milligan, Science 288, 88 (2000)
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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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Measured neck linker free energy of binding to
the edge of the b-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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