The Study Of The Directional Movement Mechanism Of Molecule Motor With Gauss-Transition Rates

Molecular motors are multi-component molecular structures. They do mechanical work through the hydrolization of ATP: the energy source of the cell. During hydrolization of ATP, conformational changes occur within the motor protein (a mechanochemical process), and mechanical work is done. They are specialized molecules which convert chemical energy to mechanical work, thereby generating directional motion.The complex behavior of these systems consequently offers a formidable challenge for theoretical descriptions and numerical approaches that aim at a fundamental analysis of the underlying interaction mechanisms as well as interpretations. The methods of non-equilibrium statistical mechanics permit a general analysis of how to generate the movement of an individual motor. Up to now, some people represent certain-position transition model in which molecular motors transition are supposed to occur at some fixed positions. The molecular motors are described by M internal states and undergo transitions at K spatial locations within the period of the molecular force potentials. But their assumption is too narrow to be accepted. Other people advance equal- probability transition model in which molecular motors transition are supposed to occur at any positions. But this model is usually applied to discuss the case of the simplest indented sawtooth potential.So a nonuniform ratchet model with Gauss-transition rates is proposed to discuss the directed motion of Brownian particles in asymmetrical periodic potentials. It is assumed that the particles experience several internal states in a single mechanical-chemical circle. In this model, the transition rates between different states are position-dependent which have the form ofGaussian function. For any internal states, the probability distribution as a function of the time and position may be expanded near the transition points to any rank if necessary.The focus of our study is concentrated on a two-state model, in which we choose (M, K) = (2, 2) and calculate the average current as a function of the transition width, temperature and transition rates. The results are summarized as follows: for small temperature, as well as for very high temperature the current vanishes. For the appropriate temperature and each given transition rates, the current has a maximum. With the increasing of the amplitude of transition rates the maximal current appears at the position of higher temperature. So we known the maximal current appear at the appropriate temperature and the appropriate flashing frequency. Then we focus on the relationship between the current and the transition width. For small temperature, as well as for very high temperature the current does not inflect with the change of the transition width. At the appropriate temperature, the current increases with the transition width increasing. It is revealed that the transitions width influences the current greatly.