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Stochastic Roadmap Simulation: Efficient Analysis of Molecular Motion

Learn about Stochastic Roadmap Simulation (SRS) and how it compares to Monte Carlo simulation in analyzing molecular motion. Explore its applications in protein modeling and overcoming energy barriers.

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Stochastic Roadmap Simulation: Efficient Analysis of Molecular Motion

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  1. Stochastic Roadmap Simulation: An Efficient Representation and Algorithm for Analyzing Molecular Motion Mehmet Serkan Apaydin, Douglas L. Brutlag, Carlos Guestrin, David Hsu, Jean-Claude Latombe Presented by: Alan Chen

  2. Outline • Introduction • Stochastic Roadmap Simulation (SRS) • First-step Analysis and Roadmap Query • SRS vs. Monte Carlo • Transmission Coefficients • Results • Discussions

  3. Introduction: Protein Modeling • Pathways Native Structure • Monte Carlo & Molecular Dynamics • Local minima • Single pathways • Stochastic Roadmap Simulation (SRS) • Random • Multiple pathways • Probabilistic Conformational Roadmap • Markov Chain Theory

  4. SRS: Conformation Space (C) • Configuration Space • Set of all conformations: (q) • Parameters of protein folding  interactions between atoms • van der Wall forces • electrostatic forces • Energy function: (E(q)) • Backbone torsional angles: (f, y)

  5. SRS: Roadmap Construction • Pathways in C roadmap (G) • Pij = probability of going from conformation i to conformation j • Protein • dE: Energy difference • T: Temperature • kB: Boltzmann Constant

  6. C SRS: Study Molecular Motion • Monte Carlo • Random path through C  global E minimum • Underlying continuous conformation space • Local minima problem • SRS • Sampled conformations • Discretized Monte Carlo • No local minima problem

  7. First-Step Analysis • Macrostate (F) • Nodes that share a common property • Transitions (t) • Steps from a node to a macrostate

  8. p2 p1 p3 SRS vs. Monte Carlo • Associated limiting distribution p • Stationary distribution • pi = SpjPji • pi > 0 • Spi = 1

  9. SRS vs. Monte Carlo • Monte Carlo • SRS

  10. SRS vs. Monte Carlo • S subset of C • Relative volume m(S) > 0 • Absolute error e > 0 • Relative error d > 0 • Confidence level g > 0 • N uniformly sampled nodes • High probability, p can approximate b • Given certain constants, number of node:

  11. Transmission Coefficients • Kinetic distance between conformations • Macrostates • F: folded state • U: unfolded state • q in U; t = 0; • q in F; t = 1;

  12. Results: Synthetic energy landscape 2-D Conformation Space Radially Symmetric Gaussians Paraboloid Centered at Origin Two global minima • SRS • Evaluating energy of nodes • 8 sec, 10,000 nodes • Solving linear equations • 750 sec, solve linear system • Monte Carlo • Est. 800,000 sec, 10,000 nodes

  13. Results: Repressor of Primer • Energy function • Hydrophobic interactions • Excluded volume • Folded macrostate • + 3 angstroms • Unfolded macrostate • +10 angstroms • Time • Monte Carlo: 3 days  trasmission coefficient of 1 conformation • SRS: 1 hour  transmission coefficients of all nodes 5000 nodes

  14. Discussions • SRS vs Monte Carlo • multiple paths vs. single path • In the limit, SRS converges to Monte Carlo • One hour vs. three days • Improvements • Better roadmaps • Reduce the dimension of C • Better sampling strategy • Faster linear system solver • Uses • Order of protein folding • Overcoming energy barriers (catalytic sites)

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