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# Approximate first passage time distribution for barrier crossing in a double well under fractional Gaussian noise

Chaudhury, Srabanti and Cherayil, Binny J (2006) Approximate first passage time distribution for barrier crossing in a double well under fractional Gaussian noise. In: Journal of Chemical Physics, 125 (11). 114106 (8 pages).

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## Abstract

The distribution of waiting times, f(t), between successive turnovers in the catalytic action of single molecules of the enzyme ${\beta}$-galactosidase has recently been determined in closed form by Chaudhury and Cherayil [J. Chem. Phys. 125, 024904 2006] using a one-dimensional generalized Langevin equation GLE formalism in combination with Kramers’ flux-over-population approach to barrier crossing dynamics. The present paper provides an alternative derivation of f(t) that eschews this approach, which is strictly applicable only under conditions of local equilibrium. In this alternative derivation, a double well potential is incorporated into the GLE, along with a colored noise term representing protein conformational fluctuations, and the resulting equation transformed approximately to a Smoluchowski-type equation. f(t) is identified with the first passage time distribution for a particle to reach the barrier top starting from an equilibrium distribution of initial points, and is determined from the solution of the above equation using local boundary conditions. The use of such boundary conditions is necessitated by the absence of definite information about the precise nature of the boundary conditions applicable to stochastic processes governed by non-Markovian dynamics. f(t) calculated in this way is found to have the same analytic structure as the distribution calculated by the flux-over-population method.

Item Type: Journal Article Copyright of this article belongs to American institute of Physics. Division of Chemical Sciences > Inorganic & Physical Chemistry 11 Jan 2007 19 Sep 2010 04:32 http://eprints.iisc.ernet.in/id/eprint/8870

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