摘要
研究了在一维三态周期跳跃模型下分子马达的定向运动 .对于给定的任意初始分布 ,得出了与时间有关的几率分布的解析表达式 ,包括到达稳态之前的所有的瞬态过程 ,由此可获得马达在各个时刻的漂移速度v、扩散系数D以及描述马达随机性质的随机参数r(randomnessparameter ) .同时还计算了马达到达稳态所需要的特征时间 .并把计算结果同实验进行了比较 .
Motivated by recent applications to experiments on molecular motors, the directed motion of molecular motors based on a periodic one-dimensional three-states hopping model is studied. The model combines the biochemical cycle of nucleotide hydrolysis with the motor's translation. An explicit solution is obtained for the probability distribution as a function of the time for any initial distribution with all the transients included, and the drift velocity v, the diffusion constant D and the randomness parameter r can also be obtained at any time from the probability distribution. Meanwhile, the characteristic time for the motor to reach steady state has been calculated. Lastly, several possible applications are proposed: the pure asymmetric case, the random symmetric case and the random asymmetric case. In the long-time limit, the drift velocity v and the diffusion constant D are obtained in terms of microscopic transition rates that are parameters in the three-state stochastic model for the pure asymmetric case. By comparison with experiments ( drift velocity v and randomness parameter r versus [ATP]), it is shown that the model presented here can rather satisfactorily explain the available data. The theoretical model provides a conceptual framework for realistic studies of molecular motor.
