Bioinformatics: Practical Application of Simulation and Data Mining Protein Folding II. Prof. Corey O’Hern Department of Mechanical Engineering Department of Physics Yale University. What did we learn about proteins?. Many degrees of freedom; exponentially growing # of
What did we learn about proteins?
pathways grows exponentially with # of structures
Coarse-grained (continuum, implicit solvent, C) models
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-letter C model: B9N3(LB)4N3B9N3(LB)5L
Number of sequences for
Nsequences= 3~ 1022
Number of structures
Np ~ exp(aNm)~1019
Molecular Dynamics: Equations of Motion
Coupled 2nd order
How are they coupled?
(iv) Bond length potential
Pair Forces: Lennard-Jones Interactions
force on i
due to j
-dV/drij > 0; repulsive
-dV/drij < 0; attractive
NB, NL, NN
-dV/dr < 0
Bond Angle Potential
Dihedral Angle Potential
Bond Stretch Potential
for i, j=i+1, i-1
Equations of Motion
Constant Energy vs. Constant Temperature
(velocity rescaling, Langevin/Nosé-Hoover thermostats)
T0=5h; fast quench; (Rg/)2= 5.48
T0=h; slow quench; (Rg/)2= 7.78
Total Potential Energy
Radius of Gyration
2-letter C model: (BN3)3B
(1) Construct the backbone in 2D
(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.
Reliable Folding at Low Rate