A Microscopic model for Microtubules

Abstract

The controlled polymerization and depolymerization of biological macromolecules, such as Microtubules plays an important role in the process of force generating mechanisms in living cells. There has been much activity in trying to understand the mechanism by which a microtubule alternates between polymerization and depolymerization. This thesis attempts to construct a microscopic model for the microtubule which can reproduce the experimentally observed structures. The basic subunit of the model in the present study is the Tubulin Heterodimer, and the microtubule is constructed by arranging 13 protofilaments in a cylindrical lattice. Each sub unit of the micro tubule lattice is connected to its four nearest neighbours by springs, and the energetics penalises deviations from the equilibrium bond length or the equilibrium bond angle both in the horizontal and vertical directions. There is also an energy cost for deviations from the perfect square topology between the bonds. In addition a self-avoiding energy term for the lateral and longitudinal bonds is incorporated. The model is defined and its elastic response is studied to small deformations. In particular the torsional and tilt moduli of the model microtubule is determined. The equilibrium structures generated by the Monte carlo and Brownian dynamics simulations are studied in different regimes of the parameters of the present model both at zero and at finite temperatures. It also attempts to provide a future direction for further work that needs to be done within the scope of the model.