A Stochastic Analysis of a Brownian Ratchet Model for Actin-Based Motility
Hong Qian

Source MCB: Molecular & Cellular Biomechanics, Vol. 1, No. 4, pp. 267-278, 2004
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Keywords Actin polymerization, exit problem, mean first passage time, nano-biochemistry, single-particle tracking, stochastic processes.
Abstract In recent single-particle tracking (SPT) measurements on {\it Listeria monocytogenes} motility in cells [\relax \begingroup \catcode `\ 12\relax \catcode `\\12\relax \catcode `\$12\relax \catcode `\&12\relax \catcode `\#12\relax \catcode `\^12\relax \catcode `\_12\relax \catcode `\%12\relax \catcode `\~12\relax \endgroup \relax \cite *{KMc:2000}], the actin-based stochastic dynamics of the bacterium movement has been analyzed statistically in terms of the mean-square displacement (MSD) of the trajectory. We present a stochastic analysis of a simplified polymerization Brownian ratchet (BR) model in which motions are limited by the bacterium movement. Analytical results are obtained and statistical data analyses are investigated. It is shown that the MSD of the stochastic bacterium movement is a monotonic quadratic function while the MSD for detrended trajectories is linear. Both the short-time relaxation and the long-time kinetics in terms the mean velocity and effective diffusion constant of the propelled bacterium are obtained from the MSD analysis. The MSD of the gap between actin tip and the bacterium exhibits an oscillatory behavior when there is a large resistant force from the bacterium. For comparison, a continuous diffusion formalism of the BR model with great analytical simplicity is also studied.
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