Study On The Dynamic Mechanism Of The Kinesins Directed Motion

Kinesins are a class of linear molecular motors, which move along microtuble towards its plus end. In all eukaryotic cells, kinesin plays an important role in intracellular transport, mitosis, cellular morphogenesis and cellar functions. Study on directionality, processivity and higher efficency of kinesin, can not only help people to understand the two-headed cooperation, walking manner and influence of related factors, but also can help people to understan other biological molecular motors’ motility and can shed light on synthesizing nano-machines.In this paper, we focus on the physical mechanics of kinesin by using Brownin ratchet method, which identical heads attach to the microtuble alternatively and step unidirectionally along linear track. The research mainly includes the following two aspects:First, open-loop ratchet models of kinesin are presented. In which, the two heads coupled through an elastic spring, asymmetrical periodical potential flash between two states stochastically or perodically which is applied independently of the state of the systems to be controlled. There are three models, including:(1) A model of elastically coupled two-headed molecular motors in flashing potential. In the model, the potential swtiches on or off between two states stochastically. The current is sensitive to the transition rates, neck length and other parameters. The coupling of transition rates and neck length leads to variations both in the values and directions of current, which is very likely the case of different molecular motors with different neck length can move along cytoskeleton in different direction.(2) A model for inchworm motion of elastically-coupled molecular motors. Corresponding to ATP hydrolyzed circle, the motor has four states which each head submitted to a one-dimension flashing ratchet potential. It is concluded that the trajectory is inchworm manner, and the probability current changes with the neck’s initial length a and the elastic coefficient k.With the increase of k, the probability current reaches to some a certain value, and there is optimal values for initial length to achieve the maximal current. Efficiency decrease nonlinearly with the increase of the open time of potential ton, and a maximum value can be obtained for some certain noise strength.(3) Two-dimensional model of elastically coupled molecular motors. A flashing ratchet model of a two-headed molecular motor in a two-dimensional potential is proposed to simulate the hand-over-hand motion of kinesins. The directed motion is obtained along the x direction, although the probability finding the particle along the y direction is non zero. When the external load is present, the current reversion is observed. The efficiency varies with both the temperature and the load, and there is a maximum value for a certain temperature and a certain load, which accords with experimental obserbations.Secondly, feedback controls of Brownian ratchet models are studied.(1)In the former model, the positions of the two Brownian motors are monitored and the flashing ratchet potential can be switched on or off depending on the positions of the two particles. Without external load, the currents of Brownian motors show a periodic change in a certain temperatur range, and when the initial length of the spring reaches a value that approximately equals an integer times of the period of the potential, the average velocity reaches a minimum. Under external load, there is an optimal value of spring constant. And the dependence of the current on the opposing force is reversed. There are optimal values of temperature and the opposing force to obtain the better efficiency.(2)In the latter model, a feedback-controlled Brownian ratchet is operated by a temerature switch. The velocity induced by the feedback ratchet is a function of several parameters, including the ratio of the potential height and the noise strenghth α, the ratio of the two switching temperatures β and the asymmetry parameter of the potential field. The motor shows a current inversion when the gradient of β inverse, and there is no current when α=0or β=1. When the absolute values of difference between a and1, or β and1is big (ie. The intension of asymmetry actions is stronger), the mean velocity is big as well.