stochastic roadmap simulation: an efficient representation and algorithm for analyzing molecular...
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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
Outline
Introduction Stochastic Roadmap Simulation (SRS) First-step Analysis and Roadmap Query SRS vs. Monte Carlo Transmission Coefficients Results Discussions
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
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:
(
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
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
First-Step Analysis
Macrostate (F) Nodes that share a
common property
Transitions (t) Steps from a node to a
macrostate
SRS vs. Monte Carlo
1
3
2
Associated limiting distribution
Stationary distributioni = jPji
i > 0
i = 1
SRS vs. Monte Carlo
Monte Carlo
SRS
SRS vs. Monte Carlo
S subset of C Relative volume (S) > 0 Absolute error > 0 Relative error > 0 Confidence level > 0 N uniformly sampled
nodes
High probability, can approximate
Given certain constants, number of node:
Transmission Coefficients
Kinetic distance between conformations Macrostates
F: folded state U: unfolded state q in U; = 0; q in F; = 1;
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
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
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)