1. 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. Coarse-grained (continuum, implicit solvent, C  ) models for proteins 1

2. 3-letter C  model: B 9 N 3 (LB) 4 N 3 B 9 N 3 (LB) 5 L B=hydrophobic N=neutral L=hydrophilic N sequences = 3 ~ 10 22 N p ~ exp(aN m )~10 19 Number of structures per sequence Number of sequences for N m =46 2

3. different mapping? and dynamics 3

4. Molecular Dynamics: Equations of Motion for i=1,…N atoms Coupled 2nd order Diff. Eq. How are they coupled? 4

5. (iv) Bond length potential 5

6. Pair Forces: Lennard-Jones Interactions i j Parallelogram rule -dV/dr ij > 0; repulsive -dV/dr ij < 0; attractive force on i due to j 6

7. ‘Long-range interactions’ BB V(r) r/  NB, NL, NN LL, LB r*=2 1/6  hard-core attractions -dV/dr < 0 7

8. Bond Angle Potential  0 =105  ij k  ijk  ijk =[0,  ] 8

9. Dihedral Angle Potential V d (  ijkl )  ijkl Successive N’s 9

10. Bond Stretch Potential ij for i, j=i+1, i-1 10

11. Equations of Motion velocity verlet algorithm Constant Energy vs. Constant Temperature (velocity rescaling, Langevin/Nosé-Hoover thermostats) 11

12. Collapsed Structure T 0 =5  h ; fast quench; (R g /  ) 2 = 5.48 12

13. Native State T 0 =  h ; slow quench; (R g /  ) 2 = 7.78 13

16. startend 16

17. native states Total Potential Energy 17

18. slow quench unfolded native state Radius of Gyration TfTf 18

19. Reliable Folding at Low Rate 19