Stochastic roadmap simulation

For robot control, Stochastic roadmap simulation is inspired by probabilistic roadmap methods (PRM) developed for robot motion planning. The main idea of these methods is to capture the connectivity of a geometrically complex high-dimensional space by constructing a graph of local paths connecting points randomly sampled from that space. A roadmap G = (V,E) is a directed graph. Each vertex v is a randomly sampled conformation in C. Each (directed) edge from vertex vi to vertex vj carries a weight Pij , which represents the probability that the molecule will move to conformation vj , given that it is currently at vi. The probability Pij is 0 if there is no edge from vi to vj. Otherwise, it depends on the energy difference between conformations. Stochastic roadmap simulation is used to explore the kinetics of molecular motion by simultaneously examining multiple pathways in the roadmap. Ensemble properties of molecular motion (e.g., probability of folding (PFold), escape time in ligand-protein binding) is computed efficiently and accurately with stochastic roadmap simulation. PFold values are computed using the first step analysis of Markov chain theory.

For robot control, Stochastic roadmap simulation^[1] is inspired by probabilistic roadmap^[2] methods (PRM) developed for robot motion planning.

The main idea of these methods is to capture the connectivity of a geometrically complex high-dimensional space by constructing a graph of local paths connecting points randomly sampled from that space. A roadmap G = (V,E) is a directed graph. Each vertex v is a randomly sampled conformation in C. Each (directed) edge from vertex v_i to vertex v_j carries a weight P_ij , which represents the probability that the molecule will move to conformation v_j , given that it is currently at v_i. The probability P_ij is 0 if there is no edge from v_i to v_j. Otherwise, it depends on the energy difference between conformations.

Stochastic roadmap simulation is used to explore the kinetics of molecular motion by simultaneously examining multiple pathways in the roadmap. Ensemble properties of molecular motion (e.g., probability of folding (P_Fold), escape time in ligand-protein binding) is computed efficiently and accurately with stochastic roadmap simulation. P_Fold values are computed using the first step analysis of Markov chain theory.

See also

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• Jean-Claude Latombe
• Mark Overmars

References

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1. ^ Apaydin, Mehmet Serkan; Brutlag, Douglas L.; Guestrin, Carlos; Hsu, David; Latombe, Jean-Claude (2002), "Stochastic roadmap simulation: An efficient representation and algorithm for analyzing molecular motion", Proceedings of the sixth annual international conference on Computational biology, pp. 12–21, doi:10.1145/565196.565199, ISBN 1-58113-498-3
   • See also Apaydin, Mehmet Serkan; Brutlag, Douglas L.; Guestrin, Carlos; Hsu, David; Latombe, Jean-Claude; Varma, Chris (2003), "Stochastic Roadmap Simulation: An Efficient Representation and Algorithm for Analyzing Molecular Motion", Journal of Computational Biology, 10 (3–4): 257–281, doi:10.1089/10665270360688011, PMID 12935328
2. ^ Kavraki, L. E.; Svestka, P.; Latombe, J.-C.; Overmars, M. H. (1996), "Probabilistic roadmaps for path planning in high-dimensional configuration spaces", IEEE Transactions on Robotics and Automation, 12 (4): 566–580, CiteSeerX 10.1.1.19.6316, doi:10.1109/70.508439.

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