Browse Theses

Classic techniques to simulate molecular motion, such as Monte Carlo simulation (MCS), generate individual pathways and spend most of their time in the local minima of the energy landscape defined over a molecular conformation space. Due to their high computational cost, it is impractical to compute “ensemble properties”, properties requiring the analysis of many molecular pathways, using such techniques. In this thesis, we introduce Stochastic Roadmap Simulation (SRS) as a new computational framework for exploring the kinetics of molecular motion by simultaneously examining many pathways. These pathways are compactly encoded in a graph, which is constructed by sampling a molecular conformation space at random. By viewing the graph as a Markov chain, we compute ensemble properties efficiently. This computation does not trace any particular pathway explicitly and circumvents the local minima problem. Furthermore, we formally show that SRS converges to the same stationary distribution as MCS.

We use SRS to study both protein folding and ligand-protein binding. In the former application, we measure the “kinetic distance” of a protein's conformation from its native state with respect to its unfolded state, using a parameter, called probability of folding (pfold). We compare our pfold computations to those from MCS for three proteins. We find that SRS produces accurate results, while reducing the computation time by several orders of magnitude. We then use pfold to predict folding rates and Phi values for five small proteins and obtain a generally high correlation with experiment. In the latter application of SRS, we estimate the expected time to escape of a ligand from a protein binding site. We use escape time to qualitatively analyze the role of amino acids in the catalytic site of an enzyme by computational mutagenesis, and to distinguish the catalytic site from other potential binding sites for seven ligand-protein complexes. These applications establish SRS as a new approach to efficiently and accurately compute ensemble properties of molecular motion.

In these applications, we sample the conformation space uniformly. We investigate non-uniform sampling techniques to facilitate future application of SRS to more complex biological systems. We present some promising sampling schemes.