Locating transition path region in the free energy landscape of protein folding

Abstract

Protein folding processes are generally described statistically with the help of multidimensional free energy landscape, typically reduced to a 1-D free energy profile along good reaction co-ordinate. There are many physical parameters which are responsible for protein molecule to hop between the native and unfolded states. The transition path region across the barrier is the region corresponding to the minimum fluctuation. The extent to which this transition region can extend beyond the obvious 1/2 kBT region has been a question of interest for a long time. We propose a new method to locate this transition path region and to study its dependence on the asymmetry of the transition state for a given free energy landscape. We have performed Brownian dynamics simulations with Gaussian white noise and Monte-Carlo simulation by sampling ten thousand successful transitions across the barrier for three different energy landscape having fixed barrier height with asymmetry in their curvatures. It was found that the transition path region increases with the increase in the asymmetry of the energy landscape in the transition region. The rate limiting parameter diffusion constant over the diffusive barrier, rate constant at particular force and transition path time for different potentials were estimated directly from the landscape profile using Kramers theory for diffusive barrier crossing. It was also found that the average diffusion in the native state increases with the increase in the asymmetry of the transition state towards the non-native state.