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 defined 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 local-minima 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 efficiently 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.

An important step in NMR protein structure determination is the assignment of resonances and NOEs to corresponding nuclei. Structure-based assignment (SBA) uses a model structure ("template") for the target protein to expedite this process. Nuclear vector replacement (NVR) is an SBA framework that combines multiple sources of NMR data (chemical shifts, RDCs, sparse NOEs, amide exchange rates, TOCSY) and has high accuracy when the template is close to the target protein's structure (less than 2 A backbone RMSD). However, a close template may not always be available. We extend the circle of convergence of NVR for distant templates by using an ensemble of structures. This ensemble corresponds to the low-frequency perturbations of the given template and is obtained using normal mode analysis (NMA). Our algorithm assigns resonances and sparse NOEs using each of the structures in the ensemble separately, and aggregates the results using a voting scheme based on maximum bipartite matching. Experimental results on human ubiquitin, using four distant template structures show an increase in the assignment accuracy. Our algorithm also improves the robustness of NVR with respect to structural noise. We provide a confidence measure for each assignment using the percentage of the structures that agree on that assignment. We use this measure to assign a subset of the peaks with even higher accuracy. We further validate our algorithm on data for two additional proteins with NVR. We then show the general applicability of our approach by applying our NMA ensemble-based voting scheme to another SBA tool, MARS. For three test proteins with corresponding templates, including the 370-residue maltose binding protein, we increase the number of reliable assignments made by MARS. Finally, we show that our voting scheme is sound and optimal, by proving that it is a maximum likelihood estimator of the correct assignments.

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Understanding the dynamics of ligand-protein interactions is indispensable in the design of novel therapeutic agents. In this paper, we establish the use of Stochastic Roadmap Simulation (SRS) for the study of ligand-protein interactions through two studies. In our first study, we measure the effects of mutations on the catalytic site of a protein, a process called computational mutagenesis. In our second study, we focus on distinguishing the catalytic site from other putative binding sites. SRS compactly represents many Monte Carlo (MC) simulation paths in a compact graph structure, or roadmap. Furthermore, SRS allows us to analyze all the paths in this roadmap simultaneously. In our application of SRS to the domain of ligand-protein interactions, we consider a new parameter called escape time, the expected number of MC simulation steps required for the ligand to escape from the 'funnel of attraction' of the binding site, as a metric for analyzing such interactions. Although computing escape times would probably be infeasible with MC simulation, these computations can be performed very efficiently with SRS. Our results for six mutant complexes for the first study and seven ligand-protein complexes for the second study, are very promising: In particular, the first results agree well with the biological interpretation of the mutations, while the second results show that escape time is a good metric to distinguish the catalytic site for five out of seven complexes.