Stochastic Roadmap Simulation: An Efficient Representation and Algorithm for Analyzing Molecular...
-
date post
22-Dec-2015 -
Category
Documents
-
view
214 -
download
0
Transcript of Stochastic Roadmap Simulation: An Efficient Representation and Algorithm for Analyzing Molecular...
![Page 1: Stochastic Roadmap Simulation: An Efficient Representation and Algorithm for Analyzing Molecular Motion Mehmet Serkan Apaydin, Douglas L. Brutlag, Carlos.](https://reader030.fdocuments.us/reader030/viewer/2022032523/56649d765503460f94a58166/html5/thumbnails/1.jpg)
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
![Page 2: Stochastic Roadmap Simulation: An Efficient Representation and Algorithm for Analyzing Molecular Motion Mehmet Serkan Apaydin, Douglas L. Brutlag, Carlos.](https://reader030.fdocuments.us/reader030/viewer/2022032523/56649d765503460f94a58166/html5/thumbnails/2.jpg)
Outline
Introduction Stochastic Roadmap Simulation (SRS) First-step Analysis and Roadmap Query SRS vs. Monte Carlo Transmission Coefficients Results Discussions
![Page 3: Stochastic Roadmap Simulation: An Efficient Representation and Algorithm for Analyzing Molecular Motion Mehmet Serkan Apaydin, Douglas L. Brutlag, Carlos.](https://reader030.fdocuments.us/reader030/viewer/2022032523/56649d765503460f94a58166/html5/thumbnails/3.jpg)
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
![Page 4: Stochastic Roadmap Simulation: An Efficient Representation and Algorithm for Analyzing Molecular Motion Mehmet Serkan Apaydin, Douglas L. Brutlag, Carlos.](https://reader030.fdocuments.us/reader030/viewer/2022032523/56649d765503460f94a58166/html5/thumbnails/4.jpg)
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:
(
![Page 5: Stochastic Roadmap Simulation: An Efficient Representation and Algorithm for Analyzing Molecular Motion Mehmet Serkan Apaydin, Douglas L. Brutlag, Carlos.](https://reader030.fdocuments.us/reader030/viewer/2022032523/56649d765503460f94a58166/html5/thumbnails/5.jpg)
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
![Page 6: Stochastic Roadmap Simulation: An Efficient Representation and Algorithm for Analyzing Molecular Motion Mehmet Serkan Apaydin, Douglas L. Brutlag, Carlos.](https://reader030.fdocuments.us/reader030/viewer/2022032523/56649d765503460f94a58166/html5/thumbnails/6.jpg)
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
![Page 7: Stochastic Roadmap Simulation: An Efficient Representation and Algorithm for Analyzing Molecular Motion Mehmet Serkan Apaydin, Douglas L. Brutlag, Carlos.](https://reader030.fdocuments.us/reader030/viewer/2022032523/56649d765503460f94a58166/html5/thumbnails/7.jpg)
First-Step Analysis
Macrostate (F) Nodes that share a
common property
Transitions (t) Steps from a node to a
macrostate
![Page 8: Stochastic Roadmap Simulation: An Efficient Representation and Algorithm for Analyzing Molecular Motion Mehmet Serkan Apaydin, Douglas L. Brutlag, Carlos.](https://reader030.fdocuments.us/reader030/viewer/2022032523/56649d765503460f94a58166/html5/thumbnails/8.jpg)
SRS vs. Monte Carlo
1
3
2
Associated limiting distribution
Stationary distributioni = jPji
i > 0
i = 1
![Page 9: Stochastic Roadmap Simulation: An Efficient Representation and Algorithm for Analyzing Molecular Motion Mehmet Serkan Apaydin, Douglas L. Brutlag, Carlos.](https://reader030.fdocuments.us/reader030/viewer/2022032523/56649d765503460f94a58166/html5/thumbnails/9.jpg)
SRS vs. Monte Carlo
Monte Carlo
SRS
![Page 10: Stochastic Roadmap Simulation: An Efficient Representation and Algorithm for Analyzing Molecular Motion Mehmet Serkan Apaydin, Douglas L. Brutlag, Carlos.](https://reader030.fdocuments.us/reader030/viewer/2022032523/56649d765503460f94a58166/html5/thumbnails/10.jpg)
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:
![Page 11: Stochastic Roadmap Simulation: An Efficient Representation and Algorithm for Analyzing Molecular Motion Mehmet Serkan Apaydin, Douglas L. Brutlag, Carlos.](https://reader030.fdocuments.us/reader030/viewer/2022032523/56649d765503460f94a58166/html5/thumbnails/11.jpg)
Transmission Coefficients
Kinetic distance between conformations Macrostates
F: folded state U: unfolded state q in U; = 0; q in F; = 1;
![Page 12: Stochastic Roadmap Simulation: An Efficient Representation and Algorithm for Analyzing Molecular Motion Mehmet Serkan Apaydin, Douglas L. Brutlag, Carlos.](https://reader030.fdocuments.us/reader030/viewer/2022032523/56649d765503460f94a58166/html5/thumbnails/12.jpg)
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
![Page 13: Stochastic Roadmap Simulation: An Efficient Representation and Algorithm for Analyzing Molecular Motion Mehmet Serkan Apaydin, Douglas L. Brutlag, Carlos.](https://reader030.fdocuments.us/reader030/viewer/2022032523/56649d765503460f94a58166/html5/thumbnails/13.jpg)
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
![Page 14: Stochastic Roadmap Simulation: An Efficient Representation and Algorithm for Analyzing Molecular Motion Mehmet Serkan Apaydin, Douglas L. Brutlag, Carlos.](https://reader030.fdocuments.us/reader030/viewer/2022032523/56649d765503460f94a58166/html5/thumbnails/14.jpg)
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)