J. D. Honeycutt and D. Thirumalai, “The nature of foldedstates 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

3-letter C model: B9N3(LB)4N3B9N3(LB)5L

B=hydrophobic

N=neutral

L=hydrophilic

Nsequences= 3 ~ 1022

Np ~ exp(aNm)~1019 Number of structuresper sequence

Number of sequences forNm=46

2

different mapping?

and dynamics

3

Molecular Dynamics: Equations of Motion

for i=1,…Natoms

Coupled 2nd order Diff. Eq.

How are they coupled?

4

(iv) Bond length potential

5

Pair Forces: Lennard-Jones Interactions

ij

Parallelogramrule

-dV/drij > 0; repulsive-dV/drij < 0; attractive

force on i due to j

6

‘Long-range interactions’

BB

V(r)

r/

NB, NL, NN

LL, LB

r*=21/6

hard-core

attractions-dV/dr < 0

7

Bond Angle Potential

0=105

i jkijk

ijk=[0,]

8

Dihedral Angle Potential

Vd(ijkl)

Vd(ijkl)

ijkl

Successive N’s

9

Bond Stretch Potential

i j

for i, j=i+1, i-1

10

Equations of Motion

velocityverletalgorithm

Constant Energy vs. Constant Temperature (velocity rescaling, Langevin/Nosé-Hoover thermostats)

11

Collapsed Structure

T0=5h; fast quench; (Rg/)2= 5.48

12

Native State

T0=h; slow quench; (Rg/)2= 7.78

13

start end

16

native states

Total Potential Energy

17

slow quench

unfolded

native state

Radius of Gyration

Tf

18

Reliable Folding at Low Rate

19