bioinformatics: practical application of simulation and data mining markov modeling ii prof. corey...
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Bioinformatics: Practical Application of Simulation and Data
Mining
Markov Modeling II
Prof. Corey O’HernDepartment of Mechanical Engineering
Department of PhysicsYale University
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“Describing protein folding kinetics by Molecular DynamicsSimulations. 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 DynamicsSimulations. 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.
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I. Alanine Dipeptide
6 backbone atoms; 3 dihedral angles (, , )
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T=500K
Macrostate Definition
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1
1
1 2
3 4
5
4
Kinetics at T=500 K
•10,000 separate trajectories sampled 200 times at0.5ps intervals (100ps) using AMBER+Shake
K , 4, 4,5, 4,5, 3,3,K
Ω3( ) t( ) = K ,0,0,0,0,0,1,1,K
Ω4( ) t( ) = K ,1,1,0,1,0,0,0,K
Ω5( ) t( ) = K ,0,0,1,0,1,0,0,K
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MS Lifetime DistributionsMS1 MS5
1/(1-Tii)
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Transition Matrix Eigenvalues
−t
lnμ i
−t
lnμ i
F ~ 550ps
spurious
Markovian
Non-Markovian
F >> tkin= 100ps
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II. -hairpin motif of protein G
G41EWTYDDATKTFTVTE56
1 2 3 4 5 6
Hydrogenbonding
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•287 conformations run at NVE (310 K) for 0.5 ns using explicit water and Na+ counterions•Order parameters: Rg, number and order of hydrogen bonds
Macrostate Definition
000000111111
000001
turntermini
Hydrogen bonds
5.25A ≤Rg ≤9.5ARadius of gyration
S,M,L,E
26*422-35 macrostates00011X
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MS Lifetime Distributions
000000E 00111X
Non-Markovian Markovian > 50ps
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Transition Matrix Eigenvalues
TimereversedNon-
Markovian
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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
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Long-lived Conformations
Misregistered H-bonds
Misregistered H-bonds
splayed, ionassociation
misformedturn
tightturn15
“Using massively parallel simulation and MarkovianModels to study protein folding: Examining the dynamics
Of the villin headpiece,” J. Chem. Phys. 124 (2006) 164902.
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Villin headpiece-HP-36
MLSDEDFKAVFGMTRSAFANLPLWKQQNLKKEKGLF: PDB 1 VII
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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
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Native State Ensemble
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