Master Equation Approach to Molecular Motor’s Directed Motion
FENG Juan1, ZHUO Yi-Zhong2,3,4
1College of Materials Science and Technology, China University of Geosciences, Beijing 100083
2China Institute of Atomic Energy, Beijing 102413
3Institute of Theoretical Physical, Chinese Academy Sciences, Beijing 100080
4Nuclear Theory Centre, Lanzhou Heavy Ion Accelerator State Laboratory, Lanzhou 730000
Master Equation Approach to Molecular Motor’s Directed Motion
FENG Juan1;ZHUO Yi-Zhong2,3,4
1College of Materials Science and Technology, China University of Geosciences, Beijing 100083
2China Institute of Atomic Energy, Beijing 102413
3Institute of Theoretical Physical, Chinese Academy Sciences, Beijing 100080
4Nuclear Theory Centre, Lanzhou Heavy Ion Accelerator State Laboratory, Lanzhou 730000
Abstract： The master equation approach based on the periodic one-dimensional three-state hopping model is developed to study the molecular motor’s directed motion. An explicit solution Px(t) is obtained for the probability distribution as a function of the time for any initial distribution Px(0) with all the transients included. We introduce dj to represent the sub-step lengths, which can reflect how the external load affects the individual rate via load distribution factors θj+ and θj-. A wide variety of molecular motor behaviour under external load f can readily be obtained by the unequal-distance transition model with load-dependent transition rates. By comparison with the experiments, namely of the drift velocity v and the randomness parameter r versus adenosine triphosphate concentration and external load f, it is shown that the model presented here can rather satisfactorily explain the available data.
2005, Vol. 22 
