1. Department of Mechanical Engineering
Bioinformatics: Practical Application of Simulation and Data Mining Protein Folding II
Prof. Corey O’Hern
Department of Mechanical Engineering
Department of Physics
Yale University

2. What did we learn about proteins?
Many degrees of freedom; exponentially growing # of
energy minima/structures
Folding is process of exploring energy landscape to
find global energy minimum
Need to identify pathways in energy landscape; # of
pathways grows exponentially with # of structures
Coarse-graining/clumping required
energy minimum
transition
Transitions are temperature dependent

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

4. 3-letter C model: B9N3(LB)4N3B9N3(LB)5L
B=hydrophobic
N=neutral
L=hydrophilic
Number of sequences for
Nm=46
Nsequences= ~ 1022
Number of structures
per sequence
Np ~ exp(aNm)~1019

5. and dynamics
different
mapping?

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

7. (iv) Bond length potential

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

9. ‘Long-range interactions’BB
LL, LB
NB, NL, NN
V(r)
hard-core
attractions
-dV/dr < 0
r*=21/6
r/

10. Bond Angle Potential
0=105
ijk k i j
ijk=[0,]

11. Dihedral Angle Potential
Vd(ijkl)
Successive N’s
Vd(ijkl)
ijkl

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

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

14. T0=5h; fast quench; (Rg/)2= 5.48
Collapsed Structure
T0=5h; fast quench; (Rg/)2= 5.48

15. T0=h; slow quench; (Rg/)2= 7.78
Native State
T0=h; slow quench; (Rg/)2= 7.78

17. start
end

18. Total Potential Energy
native states

19. Radius of Gyration
unfolded Tf
native
state
slow quench

20. 2-letter C model: (BN3)3B
(1) Construct the backbone in 2D N B
(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.

22. Energy Landscape E/C E/C end-to-end distance end-to-end distance
5 contacts
4 contacts
3 contacts

23. Rate Dependence
2 contacts
3 contacts
4 contacts
5 contacts

24. Misfolding

25. Reliable Folding at Low Rate

26. Slow rate

27. Fast rate

28. So far…
Uh-oh, proteins do not fold reliably…
Quench rates and potentials
Next…
Thermostats…Yuck!
More results on coarse-grained models
Results for atomistic models
Homework
Next Lecture: Protein Folding III (2/15/10)