Stochastic Roadmap Simulation: An Ef cient Representation and Algorithm for Analyzing Molecular Motion

Classic molecular motion simulation techniques, such as Monte Carlo (MC) simulation, generate motion pathways one at a time and spend most of their time in the local minima of the energy landscape deŽ ned over a molecular conformation space. Their high computational cost prevents them from being used to compute ensemble properties (properties requiring the analysis of many pathways). This paper introduces stochastic roadmap simulation (SRS) as a new computational approach for exploring the kinetics of molecular motion by simultaneously examining multiple pathways. These pathways are compactly encoded in a graph, which is constructed by sampling a molecular conformation space at random. This computation, which does not trace any particular pathway explicitly, circumvents the localminima problem. Each edge in the graph represents a potential transition of the molecule and is associated with a probability indicating the likelihood of this transition. By viewing the graph as a Markov chain, ensemble properties can be efŽ ciently computed over the entire molecular energy landscape. Furthermore, SRS converges to the same distribution as MC simulation. SRS is applied to two biological problems: computing the probability of folding, an important order parameter that measures the “kinetic distance” of a protein’s conformation from its native state; and estimating the expected time to escape from a ligand–protein binding site. Comparison with MC simulations on protein folding shows that SRS produces arguably more accurate results, while reducing computation time by several orders of magnitude. Computational studies on ligand–protein binding also demonstrate SRS as a promising approach to study ligand–protein interactions.