On The Model About The Motion Of Kinesin's Legs

In this paper, we study coupled diffusion processes with smooth coefficients, which model the system of the molecular motor. In recent years, unidirectionalparticle flows (ratchet effects) are found in some systems of chemical reactions. Freeenergy of the chemical reaction can be converted to mechanical energy through theratchet, which becomes an engine in the level of nanometer and is called a molecularmotor. The microcosmic motor has very wide applications, and becomes one of themost prevail problems in physics, chemistry and biology now. We refer to the paperby Reimann as a comprehensive reference, which is more than 200 pages and ispublished in the famous journal Physics Reports (2002). According to Reimann'sidea, a microcosmic particle moves as a Brownian motion in small scales in the levelof nanometer, and the essential reason of the ratchet effect is the chemical reactioncan change the inner state of a particle and its moving rule as a result. In thissense, the molecular motor is called a Brownian particle coupled with a chemicalreaction. The two entries of a particle's state-the inner state and the position, evolve as a Markov process, which we call a coupled diffusion process. It nowbecomes a significant theoretical model of the molecular motor. However, very fewmathematical tools and theories are available in review and research articles. Thatzhangfuxi's doctor paper is to present a rather tractable and organized mathematicaltreatment of this subject. Base on this mathematical treatment, we proposed a newmathematical model about the motion of Kinesin's legsThe paper separates mainly into four parts. In the first part, the biophysicssettling and the studing of current situation of molecular motor is introduced, atmean time, we have introduced the significance of the studies about this problem andthe main results of this paper. In the second part, we introduce the biology settlingsof Kinesin which is the motor mainly studied by our paper, and propose a model which could describe Kinesin's moving mechanism clearly. By numerical simulationabout the orbit of Knesin's legs moving, it is indicate the feasibility and validity ofour model. In the third part, we proposed some mathematical treatment about theprocess of our model, which is mainly about the existence of process, stationarity andreversibility. In the fourth part, by changing coordinate system, we make theroticalanalysis of directional movement of center of Kinesin, and we give two necessaryconditions for directional motion of Kinesin. At mean time we proposed a new modelbased on the model we put forward first. And we discussed the mean velocity of thedirectional movement by numerical simulation. The last three parts are main contentin our paper.