Molecular simulations of rare events

Rare events are transitions between stable separated by a high free energy barrier. Conventional simulation techniques like Molecular dynamics and Monte Carlo simulations are generally insufficient to accurately study rare events. In this thesis, we have tried to outline how such events can be investigated. In particular we present ways to optimize replica exchange molecular dynamics simulations, a very common modification of molecular dynamics used to study biological systems. We also present a new density of states (DOS) based Monte-Carlo algorithm to precisely predict the free energy profiles associated with phase transitions. Currently, one of the most successful simulation technique to study the dynamics of rare events is transition path sampling (TPS), in this work we describe various improvement over the conventional TPS techniques.;Finally we apply the techniques developed in this thesis to the study of misfolding and aggregation of extended polyglutamine (PolyQ) sequences. Extended PolyQ sequences have been implicated in the pathogenesis of various neurodegenerative diseases. In this thesis we provide in unprecedented detail and accuracy the mechanism of the misfolding and aggregation of extended PolyQ chains, and suggest ways to avoid their aggregation. The PolyQ aggregation mechanism presented here can potentially be used to design therapeutic strategies to prevent the aggregation of Huntingtin protein and eventually the onset of Huntington's disease.