1. 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

2. “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

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

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

5. Kinetics at T=500 K 10,000 separate trajectories sampled 200 times at 0.5ps intervals (100ps) using AMBER+Shake 5

6. 6

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

8. Transition Matrix Eigenvalues  F ~ 550ps spurious Markovian Non- Markovian  F >> t kin = 100ps 8

9. II.  -hairpin motif of protein G G41EWTYDDATKTFTVTE56 12 3 45 6 Hydrogen bonding 9

10. 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

11. 11

12. MS Lifetime Distributions 000000E00111X Non-MarkovianMarkovian > 50ps 12

13. Transition Matrix Eigenvalues Time reversed Non- Markovian 13

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

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

16. “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

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

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

19. Native State Ensemble 19