Study On The Dynamics Of Molecular Motor Based On Polymer Model

Molecular motor is a kind of protein enzyme which converts chemical energy derived from adenosine tri-phosphate(ATP) hydrolysis into mechanical energy. The kernel problem about the locomotory mechanism of molecular motor is how to transfer chemical energy into mechanical energy and generate a unidirectional mechanical movement. This problem has attracted a lot of attention in the fields of biology and physics, since it involves in a wider physical problem: how to make a perpetual machine which can convert random thermal motion into directed movement without external work, a problem that rebels the second law of thermodynamics.Biochemists pay attention on the microscopic scale and focus on the study of the biological structure and conformation change of molecular motor; however, physicists have much more interest in macroscopic scale. They always ignore the detailed structural information of molecular motor and just simplify it as a particle and study how a thermal Brownian motion causes a unidirectional movement. In this paper, we choose kinesin, a kind of molecular motor, as the prototype. By combining the biological structure information and physical ideas, we establish three polymer models to study the mechanism of molecular motor, which are branched polymer model, polymer under linear potential field and polymer under asymmetrical saw tooth potential.1. A three arms branched polymer model is established by short chains to simulate the conformation distribution and energy transformation when kinesin walks on the microtubule. From this model, we find the position change of the branched point determine the whole conformation of kinesin, which is confirmed by the experiment. In order to describe short chain, a propagator function in quantum mechanics with boundary condition is developed to depict the distribution of the end-to-end vector of polymer. It is well tested that this new distribution function is much more precious than Gaussian distribution function when describing short chain. Using the composition law of propagator function, this function can be generalized to any two arms of the branched polymer.2.The distribution function of the end-to-end vector of polymer under linear potential field is deduced to study the effect of linear potential on the polymer size; Monte Carlo simulations of ideal polymer and real polymer both show that the mean square end-to-end distance of polymer( < R² >)under linear potential still satisfy the scaling law: 2 >～N^2v; The relationship between the movement which is similar to the experiment result of kinesin.In conclusion, To establish a polymer model which is similar to molecular motor, two main conditions are necessary l)the existence of asymmetrical potential; 2)the size of polymer should be close to the size of potential.