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

Markov Modeling of Proteins “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. “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

I. Alanine Dipeptide 6 backbone atoms; 3 dihedral angles (  ,  ,  ) 3

1 Macrostate Definition T=500K 1 2 5 3 1 4 1 4

Kinetics at T=500 K • 10,000 separate trajectories sampled 200 times at 0.5ps intervals (100ps) using AMBER+Shake   

, 4, 4, 5, 4, 5, 3, 3,

        

,0,0,0,0,0,1,1, ,1,1,0,1,0,0,0, ,0,0,1,0,1,0,0,

5

6

MS Lifetime Distributions MS1 MS5 1/(1-T ii ) 7

Transition Matrix Eigenvalues  F ~ 550ps  ln

t



i

Markovian  ln

t



i

Non Markovian spurious  F >> t kin = 100ps 8

II.  -hairpin motif of protein G G41EWTYDDATKTFTVTE56 1 2 3 4 5 6 Hydrogen bonding 9

Macrostate Definition • 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 termini Hydrogen bonds 000000 111111 turn Radius of gyration 5.25

A



R g

 9.5

A

S,M,L,E 000001 00011X 2 6 *4  22-35 macrostates 10

11

MS Lifetime Distributions Non-Markovian 000000E Markovian > 50ps 00111X 12

Non Markovian Transition Matrix Eigenvalues Time reversed 13

Predicted Folding Time  F ~ 20 ns << 6  s 1. Short 0.5 ns trajectories (4 orders of magnitude difference) 2. Long-lived conformations 14

Long-lived Conformations Misregistered H-bonds Misregistered H-bonds 15 splayed, ion association misformed turn tight turn

“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

Villin headpiece-HP-36 MLSDEDFKAVFGMTRSAFANLPLWKQQNLKKEKGLF: PDB 1 VII 17

Simulation Details 50,000 trajectories *10ns/trajectory = 500  s • Gromacs with explicit solvent (5000 water molecules) and eight counterions; Amber + bond constraints 18

Native State Ensemble 19