The Study On The Directed Motion Of A Molecular Motor Based On The Four-State Model With Unequal Substeps

Molecular motors in biological cells play important role, which carry out various life functions in the process of muscle contraction, intracellular transport, DNA duplication, mitosis, and so on. Molecular motors with ATP as their 'fuel', which effectively and directly convert chemical energy into mechanical energy and move directionally. Particularly, kinesin, which has the feature of directivity and stepping motion, has been focused on its particular dynamical mechanism.Based on the actual biology settling, kinesin moves along microtubule which is constructed from asymmetrical o and P protein subunits which array periodically, so the microtubule's structure is also asymmetrical and periodical. During the motion, kinesin's configuration changes in a dynamic-chemical period in which there are several dynamic-chemical states for the motor, and the transitions are random between state and state to a certain extent. Based on this situation, in this paper, a more actual dynamic-chemical coupling model than two-state model, a periodic four-state kinetic hopping model, is established, and analyzed by the master equation method.The paper separates mainly into three parts. In the first part, the biology settling of molecular motors are introduced, including their categories, structure and properties of kinetics of molecular motors. In the second part, a method studying stochastic transition which is the master equation method is introduced, and explicit solutions of velocity V and diffusion constant D of the steady state are obtained when a particle hops among a dimensional and periodic N states. In the third part, a more actual dynamic-chemical coupling model than two-state model, a dimensionalV"J:)t Tperiodic four-state kinetic hopping model, is established. The results are summarized as follows.1. An explicit solution for the probability distribution as a function of the time and position in the master equation is obtained when the substeps between arbitrary adjacent states in a single period are equal for the molecular motor.2. The transient behav;ors in the initial period of time and the characteristic time to reach the steady state for the molecular motor are discussed. The results are as follows: the transient behaviors relate to the transition rates and the initial condition, and the characteristic time is only determined by the transition rates.3. An explicit solution for the probability distribution as a function of the time and position is obtained when the substeps between arbitrary adjacent states in a single period are unequal for the molecular motor.4. The theoretical curves V (F, [ATP]) and r (F, [ATP]) under the steady state are compared to experiments when a load acts on the molecular motor, the result is that these theoretical curves accord basically with experiments, which illustrates better the kinetic behaviors of a molecular motor.