J. D. Honeycutt and D. Thirumalai, “The nature of folded states of globular proteins,”...

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