Statistical view of Biological dynamics.
- Polymer looping problem: Understanding the kinetics of loop formation of long chain polymer molecules has been an interesting research field both, to experimentalists and theoreticians. Loop formation is believed to be an initial step in understanding several protein events. The theories of loop formation dynamics are in general approximate. The looping dynamics of a single polymer chain having reactive end-groups have been modeled by simplest possible option. In our model, dynamics of end-to end distance is mathematically represented by an equation for a random walking under harmonic potential. Looping process is ensured by adding a sink of arbitrary strength in that equation. We have also incorporated the effect of all other chemical reactions involving either one or both of the end-group on rate of end-to-end loop formation - to the best of our knowledge this is the first time this has been done in any analytical model. We will also perform Brownian dynamics simulation studies of looping of a single polymer chains to see how the 'shape of sink function' decides the looping dynamics. The area focuses on providing statistical descriptions of random walk models of biopolymers such as proteins and view them as individual monomers. We use few mathematical tools to give an exact analytical result for rate constants for end-to-end polymer looping problem.
- Molecular Ratchets: It was mentioned by R. P. Feynman that a microscopic ratchet in equilibrium with an isothermal heat bath can not have any preference in rotational direction - otherwsie the ratchet can be used to extract work from an isothermal system, which violates the second law of thermodynamics. Here we plan to vary temperature with time and use symmetric and assymetric ratchet for computer simulation.