Event Description
Title: Computing Kinetics of the Potts Protein Model
Physics Major: Brian Cohen
Abstract: Statistical mechanical models are intended to provide a means of characterizing the configurations of systems without needing to consider the spatial evolution such that the configurations behave as they would in nature. In this project, we use the Helix-Coil-Sheet Potts protein model to study the transformations between an alpha-helical structure and a beta-sheet structures, the so-called alpha-beta transition. The model describes one-dimensional chain of residue states (either in alpha helix, beta sheet, or random coil) representing the conformational states of the protein. The three-states of individual residues are determined by the ranges of their dihedral angles. This is a generalization of the two-state Ising spin model, which uses a regular array of spin-up and spin-down elements.
This model qualifies as a Markov Chain model, in which, at any given moment only the current state of a process in governing future dynamics, the prior history has no relevance. These can be solved with a class of algorithms called Monte-Carlo Markov Chain algorithms. The Metropolis-Hastings algorithm is one of the most straightforward ways of sampling the probability distribution of the next state, in which one picks a random site along the chain, proposes a new "spin", and roll dice to determine whether to accept or reject the conformational change based on the conditional probability of the transition. However, this approach was found to lead to trapping at local minima. This motivated the implementation of more advanced algorithms, in particular, the Replica exchange method and the Wolff cluster flip, the former in which parallel systems at different temperatures are swapped based off a roll of the dice and a metropolis step, the latter involves proposing flipping contiguous clusters all at once.
Advisor: Dr. Jian-Min Yuan |
