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Bioinformatics: Practical Application of Simulation and Data Mining Markov Modeling II Prof. Corey O’Hern Department of Mechanical Engineering Department of Physics Yale University 1
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“Describing protein folding kinetics by Molecular Dynamics Simulations. 1. Theory” W. C. Swope, J. W. Pitera, and F. Suits, J. Phys. Chem. B 108 (2004) 6571. Markov Modeling of Proteins “Describing protein folding kinetics by Molecular Dynamics Simulations. 2. Example applications to Alanine Dipeptide and a -hairpin peptide” W. C. Swope, J. W. Pitera, et al., J. Phys. Chem. B 108 (2004) 6582. 2
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I. Alanine Dipeptide 6 backbone atoms; 3 dihedral angles ( , , ) 3
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T=500K Macrostate Definition 1 1 1 1 2 3 4 5 4
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Kinetics at T=500 K 10,000 separate trajectories sampled 200 times at 0.5ps intervals (100ps) using AMBER+Shake 5
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MS Lifetime Distributions MS1 MS5 1/(1-T ii ) 7
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Transition Matrix Eigenvalues F ~ 550ps spurious Markovian Non- Markovian F >> t kin = 100ps 8
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II. -hairpin motif of protein G G41EWTYDDATKTFTVTE56 12 3 45 6 Hydrogen bonding 9
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287 conformations run at NVE (310 K) for 0.5 ns using explicit water and Na + counterions Order parameters: R g, number and order of hydrogen bonds Macrostate Definition 000000 111111 000001 turntermini Hydrogen bonds Radius of gyration S,M,L,E 2 6 *4 22-35 macrostates 00011X 10
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MS Lifetime Distributions 000000E00111X Non-MarkovianMarkovian > 50ps 12
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Transition Matrix Eigenvalues Time reversed Non- Markovian 13
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Predicted Folding Time F ~ 20 ns << 6 s 1. Short 0.5 ns trajectories (4 orders of magnitude difference) 2. Long-lived conformations 14
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Long-lived Conformations Misregistered H-bonds Misregistered H-bonds splayed, ion association misformed turn tight turn 15
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“Using massively parallel simulation and Markovian Models to study protein folding: Examining the dynamics Of the villin headpiece,” J. Chem. Phys. 124 (2006) 164902. 16
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Villin headpiece-HP-36 MLSDEDFKAVFGMTRSAFANLPLWKQQNLKKEKGLF: PDB 1 VII 17
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50,000 trajectories *10ns/trajectory = 500 s Gromacs with explicit solvent (5000 water molecules) and eight counterions; Amber + bond constraints Simulation Details 18
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Native State Ensemble 19
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