1 / C\% Cellular Motions and Thermal Fluctuations: the Brownian Ratchet
1 / C\% 316 Biophysical Journal Volume 65 July 1993 316-324 ” Cellular Motions and Thermal Fluctuations: The Brownian Ratchet Charles S. Peskin,* Garrett M. Odell,* and George F. Osters l Courant Institute of Mathematical Sciences, New York, New York 10012; *Department of Zoology, University of Washington, Seattle, Washington 98195; SDepartments of Molecular and Cellular Biology, and Entomology, University of California, Berkeley, California 94720 USA ABSTRACT We present here a model for how chemical reactions generate protrusive forces by rectifying Brownian motion. This sort of energy transduction drives a number of intracellular processes, including filopodial protrusion, propulsion of the bacterium Wisteria, and protein translocation. INTRODUCTION Many types of cellular protrusions, including filopodia, This is the speed of a perfect BR. Note that as the ratchet lamellipodia, and acrosomal extension do not appear to in- interval, 8, decreases, the ratchet velocity increases. This is volve molecular motors. These processes transduce chemical because the frequency of smaller Brownian steps grows more bond energy into directed motion, but they do not operate in rapidly than the step size shrinks (when 6 is of the order of a mechanochemical cycle and need not depend directly upon a mean free path, then this formula obviously breaks down). nucleotide hydrolysis. In this paper we describe several such Several ingredients must be added to this simple expres- processes and present simple formulas for the velocity and sion to make it useful in real situations. First, the ratchet force they generate. We shall call these machines “Brownian cannot be perfect: a particle crossing a ratchet boundary may ratchets” (BR) because rectified Brownian motion is funda- occasionally cross back.
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