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