Modelling the Stochastic Dynamics of Biological Nano-Motors: An Overview of Recent Results

We review our recent results on modelling the dynamics of two types of intracellular nano-biomolecular motor proteins; the kinesin nano-motor moving in a stepping fashion on microtubule tracks within cells and delivering cargoes to the nuclei, and the rotary ATPase nano-motor that synthesises the ATP molecule used as a biological fuel for the operation of nano-motors such as kinesin. These nano-scale motors operate in a stochastically-fluctuating environment, and hence stochastic dynamics are used to model their motion. Our modelling of the kinesin motion is based on an asymmetric so-called hand-over-hand mechanism, within the framework of Langevin dynamics. The two kinesin's heads that move on the track experience a flashing ratchet potential as well as a bistable potential. Our simulation results agree well with the experimental data concerning the number of ATP molecules consumed per one step of kinesin motion, the space-time trajectories of the heads, and the variation of the kinesin's velocity with the applied external force. A similar type of dynamics is also employed to model the rotary part of the F₀F₁ ATPase nano-motor. We have investigated the operation of this motor in the absence and presence of an externally applied electric field and current, and have shown how these external influences affect the production rate of the ATP molecules. The results obtained from this part of our work also agree well with the experimental findings. The investigation into the dynamics of these nano-motors opens the real prospect of designing man-made nano-scale functional motors, mimicking as far as possible the corresponding machines in biological systems.