The Study On The Directional Motion Of Kinesin Under Coupled Conformational Model

In the human cells, hundreds of molecular motors carry out various functions in the process of the contraction of muscles, cellular transportation, DNA duplication and mitosis. These motors can efficiently convert chemical energy in ATP into mechanical energy and move directionally. Of all these motors, kinesin received extensive interests for its special dynamical mechanics. The movements of kinesin have two features, the directionality and the stepping motion, on which the dynamical study are focused.In the scale of molecule, we cannot ignore the random collision between liquid molecules and motor. So the movement of motor has the features of Brownian movement. We can take molecular motor as a Brownian particle in the case of ignoring the conformational changes. The interaction between motor and microtubule can be described by a special potential function and the effect of the environment can be simplified as a noise.In kinesin's actual movement, it continuously changes its conformation to catalyze ATP's hydrolysis. The role of microtubule is not a simple periodic potential. In this paper, we consider more of the conformational changes in the process of ATP's hydrolysis and the complex structure of microtubule. We use a uniformly rotating dipole, which represent the inner freedom, to describe conformational changes. The microtubule is treated as assemble of dipoles and the actual potential is calculated. So we have the coupled conformational model, which is more similar to actual biological process. We respectively calculated the directional movement of kinesin under white noise and colored noise and the results are as follows: the coupled effect result in a directional particle current, and the current velocity is selective to the angular velocity 0) and noise intensity D, which reflect the effects of the rate of ATP's hydrolysis and the temperature of cell on the movement of molecular motors. The averagedisplacement can qualitatively explain the stepping movement of kinesin in experiment. When colored noise is applied, the velocity of kinesin is modulated by correlation time T . The selection and coordination among these parameters reflect the high degree of complexion, coordination and order of vital mechanics.