Bioinformatics: Practical Application of Simulation and Data

Mining

Markov Modeling II

Prof. Corey O’HernDepartment of Mechanical Engineering

Department of PhysicsYale University

1

“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.

2

I. Alanine Dipeptide

6 backbone atoms; 3 dihedral angles (, , )

3

T=500K

Macrostate Definition

1

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

5

6

MS Lifetime DistributionsMS1 MS5

1/(1-Tii)

7

Transition Matrix Eigenvalues

−t

lnμ i

−t

lnμ i

F ~ 550ps

spurious

Markovian

Non-Markovian

F >> tkin= 100ps

8

II. -hairpin motif of protein G

G41EWTYDDATKTFTVTE56

1 2 3 4 5 6

Hydrogenbonding

9

•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

10

11

MS Lifetime Distributions

000000E 00111X

Non-Markovian Markovian > 50ps

12

Transition Matrix Eigenvalues

TimereversedNon-

Markovian

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

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.

16

Villin headpiece-HP-36

MLSDEDFKAVFGMTRSAFANLPLWKQQNLKKEKGLF: PDB 1 VII

17

50,000 trajectories *10ns/trajectory = 500 s

•Gromacs with explicit solvent (5000 water molecules)and eight counterions; Amber + bond constraints

Simulation Details

18

Native State Ensemble

19