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Bioinformatics: Practical Application of Simulation and Data Mining Markov Modeling III

Bioinformatics: Practical Application of Simulation and Data Mining Markov Modeling III. Prof. Corey O’Hern Department of Mechanical Engineering & Materials Science Department of Physics Yale University. 1. “Using massively parallel simulation and Markovian

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Bioinformatics: Practical Application of Simulation and Data Mining Markov Modeling III

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  1. Bioinformatics: Practical Application of Simulation and Data MiningMarkov Modeling III • Prof. Corey O’Hern • Department of Mechanical Engineering & Materials Science • Department of Physics • Yale University 1

  2. “Using massively parallel simulation and Markovian models to study protein folding: Examining the dynamics of the villin headpiece,” J. Chem. Phys. 124 (2006) 164902. 2

  3. Villin headpiece-HP-36 MLSDEDFKAVFGMTRSAFANLPLWKQQNLKKEKGLF: PDB 1 VII 3

  4. Simulation Details 50,000 trajectories *10ns/trajectory = 500 s 50,000 trajectories*10 ns/trajectory*1 conformation/100 ps = 4,509,355 conformations • Gromacs with explicit solvent (5000 water molecules) and eight counterions; Amber + bond constraints; T=300K 4

  5. I. Native State Ensemble 5

  6. II. Unfolded State Ensemble • 10,000 trajectories equilibrated at T=1000K for 1 ns • Remove all structure • Random walk statistics chain crossing ideal excluded volume end-to-end distance N= # of amino acids • Each trajectory quenched from 1000K to 300K; run for 25 ns 6

  7. Estimation of Folding Time: Including Unfolded Events determined by dRMSD first passage time: tf F: folded Initially unfolded states tu U: unfolded 7

  8. Floppy Residues 8

  9. Maximum Likelihood Estimator (MLE) F  4.3-10 s from laser-jump and other experiments F  8 s from MLE F  24 s from MLE + correction of water diffusion coefficient

  10. Sensitivity of MLE Results “With these issues in mind, the calculated rate is well within an order of magnitude of expeirmental measurements.”

  11. III. Transition State Ensemble: Effect of Perturbations N(X)= # of trajectories that meet condition X before Y s: unperturbed state s’: perturbed state after 500 ps Water does not affect dynamics 11

  12. Markov States • 4,509,355 conformations  2454 Markov states based on clustering of C dRMSD s3 s1 sf s2 s4 • No dead ends 12

  13. CdRMSD k=sum over amino acids i,j=configurations 13

  14. Transition Probabilites and Mean First Passage Time MFPT=3 s stable MFPT 14

  15. Comparison of Short and Long Times MSM: single exponential 15

  16. First Passage Time in Random Processes unfolded folded P(x) Gaussian unfolded folded  partially unfolded x 16

  17. Survival Probability for Two Particles 17

  18. Protein Aggregation “Molecular simulation of protein aggregation,” Biotechnology & Bioengineering 96 (2007) 1. 18

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