The Study On The Directed Motionof A Molecular Motor Based On The Two-State Model

Molecular motors are a kind of enzyme proteins which exist in the cell and play an important role in the process of the muscle contraction, intracellular transport, DNA duplication, mitosis and so on. The energy for the motion of the motors comes from the chemical energy of ATP hydrolyzation. The motors can transduce the chemical energy into mechanical work. So the motors act as a function of the energy transducer. When the motion of the motors is coordinated, the macroscopic directed motion is brought. Especially, kinesin, which has the feature of the directivity and stepping motion, has been focused on its particular dynamical mechanism.The paper is composed of three parts mainly. In the first part, the biology study evolvement of molecular motor are introduced, including their categories, structure features and motion properties. In the second parts, a method on studying stochastic transition of the Fokker-Planck equation is introduced, how to use the method of the latent root to on the Fokker-Planck equation is mainly deduced. In the third part, according to the motion characteristic of the motor a simple transition model (two-state model) is established. The current, the effective potential and the slope of the effective potential of the motor are calculated. First, it is shown that the slope of the effective potential increase or decrease faster than the current. All of these facts indicate that the current and the slope are not simply linear relevant. Second, the results show that the current and the slope of the effective potential change simultaneously when the temperature is in a certain range. Third, the slope of the effective potential corresponds to an average force. Because of the existence of the average force, the motor protein can have a directed motion against the loadforce. If the load force is zero, the directed motion is mainly dependent on the average force without the effect of the load force. When the temperature T is smaller, even if there is the slope of the effective potential, most Brownian particles (motor proteins) can not span the potential. Therefore the current is small, the ratio of the slope of the effective potential to the current is not linear relevant simply. When the temperature T is larger, the particles can span the potential at the effect of the average force, so the ratio of them is near linear relevant. Besides, the interaction between particles is not considered. This interaction also has an effect on the current.Our purpose is to discuss the force and the motion of the motor. So we can understand the motion mechanism of the motor deeply. At the same time, we compare the force-velocity theoretical curve with the experiment, the result shows that they are identical basically.