Stokes efficiency of molecular motor-cargo systems
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A molecular motor utilizes chemical free energy to generate a unidirectional motion through the viscous ﬂuid. In many experimental settings and biological settings, a molecular motor is elastically linked to a cargo. The stochastic motion of a molecular motor-cargo system is governed by a set of Langevin equations, each corresponding to an individual chemical occupancy state. The change of chemical occupancy state is modeled by a continuous time discrete space Markov process. The probability density of a motor-cargo system is governed by a two-dimensional Fokker-Planck equation. The operation of a molecular motor is dominated by high viscous friction and large thermal ﬂuctuations from surrounding ﬂuid. The instantaneous velocity of a molecular motor is highly stochastic: the past velocity is quickly damped by the viscous friction and the new velocity is quickly excited by bombardments of surrounding ﬂuid molecules. Thus, the theory for macroscopic motors should not be applied directly to molecular motors without close examination. In particular, a molecular motor behaves diﬀerently working against a viscous drag than working against a conservative force. The Stokes eﬃciency was introduced to measure how eﬃciently a motor uses chemical free energy to drive against viscous drag. For a motor without cargo, it was proved that the Stokes eﬃciency is bounded by 100% H. Wang and G. Oster, 2002 . Here, we present a proof for the general motor-cargo system.
Abstract and Applied Analysis ,Vol. 2008, Article ID 241738, 2008The article of record as published may be found at http://dx.doi.org/10.1155/2008/241736
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