Bioinformatics: Practical Application of Simulation and Data Mining Protein Folding II

1. Bioinformatics: Practical Application of Simulation and Data MiningProtein Folding II • Prof. Corey O’Hern • Department of Mechanical Engineering & Materials Science • Department of Physics • Yale University 1

2. What did we learn about proteins? • Many degrees of freedom; exponentially growing # of • energy minima/structures • Folding is process of exploring energy landscape to • find global energy minimum • Need to identify pathways in energy landscape; # of pathways grows exponentially with # of structures • Coarse-graining/clumping required energy minimum transition • Transitions are temperature dependent 2

3. Coarse-grained (continuum, implicit solvent, C) models for proteins J. D. Honeycutt and D. Thirumalai, “The nature of folded states of globular proteins,” Biopolymers 32 (1992) 695. T. Veitshans, D. Klimov, and D. Thirumalai, “Protein folding kinetics: timescales, pathways and energy landscapes in terms of sequence-dependent properties,” Folding & Design 2 (1996)1. 3

4. 3-letter C model: B9N3(LB)4N3B9N3(LB)5L B=hydrophobic N=neutral L=hydrophilic Number of sequences for Nm=46 Nsequences= 3~ 1022 Number of structures per sequence Np ~ exp(aNm)~1019 4

5. and dynamics different mapping? 5

6. Molecular Dynamics: Equations of Motion Coupled 2nd order Diff. Eq. How are they coupled? for i=1,…Natoms 6

7. (iv) Bond length potential 7

8. Pair Forces: Lennard-Jones Interactions i j Parallelogram rule force on i due to j -dV/drij > 0; repulsive -dV/drij < 0; attractive 8

9. ‘Long-range interactions’ BB LL, LB NB, NL, NN V(r) hard-core attractions -dV/dr < 0 r*=21/6 r/ 9

10. Bond Angle Potential 0=105 ijk k i j ijk=[0,] 10

11. Dihedral Angle Potential Vd(ijkl) Successive N’s Vd(ijkl) ijkl 11

12. Bond Stretch Potential for i, j=i+1, i-1 i j 12

13. Equations of Motion velocity verlet algorithm Constant Energy vs. Constant Temperature (velocity rescaling, Langevin/Nosé-Hoover thermostats) 13

14. Collapsed Structure T0=5h; fast quench; (Rg/)2= 5.48 14

15. Native State T0=h; slow quench; (Rg/)2= 7.78 15

16. 16

17. start end 17

18. Total Potential Energy native states 18

19. Radius of Gyration unfolded Tf native state slow quench 19

20. 2-letter C model: (BN3)3B (1) Construct the backbone in 2D N B (2) Assign sequence of hydrophobic (B) and neutral (N) residues, B residues experience an effective attraction. No bond bending potential. (3) Evolve system under Langevin dynamics at temperature T. (4) Collapse/folding induced by decreasing temperature at rate r. 20

22. Energy Landscape E/C E/C end-to-end distance end-to-end distance 5 contacts 4 contacts 3 contacts 22

23. Rate Dependence 2 contacts 3 contacts 4 contacts 5 contacts 23

24. Misfolding 24

25. Reliable Folding at Low Rate 25

26. Slow rate

27. Fast rate

28. So far… • Uh-oh, proteins do not fold reliably… • Quench rates and potentials Next… • Thermostats…Yuck! • More results on coarse-grained models • Results for atomistic models • Homework 28