Stochastic modeling of the kinesin motor protein

In this thesis we discuss the Kinesin motor protein, related biological background, and experiments performed on the motor. In the first chapter we propose a one dimensional model for the motor protein following the work of (Peskin and Oster 1995). We give a formal mathematical specification of the model in terms of a system of stochastic differential equations and partial differential equations. It is then shown how approximations in the model can be used to compute force-velocity and force-variance statistics.; In the second chapter we show how the elasticity of the tether that attaches cargo to the motor protein can be derived from data obtained in the optical trap experiments of (Svoboda and Block 1994). From the experimental data we formulate a model of the restoring force of the tether as it is extended. the elasticity of macromolecules from optical trap experiments and propose some numerical methods.; In the third chapter we formulate a model of the Kinesin motor protein in three spatial dimensions incorporating the elasticity of the tether derived in the previous chapter. We then show approximations that can be made in the model and use a Monte-Carlo method to efficiently compute the force-velocity and force-variance statistics. In conclusion, the statistics of the three dimensional and one dimensional model are compared with the experimental data.