Bioinformatics: Practical Application of Simulation and Data Mining Protein Folding II

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Bioinformatics Practical Application of
Simulation and Data MiningProtein Folding II

• Prof. Corey OHern
• Department of Mechanical Engineering
• Department of Physics
• Yale University

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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

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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.
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3-letter C? model B9N3(LB)4N3B9N3(LB)5L
Bhydrophobic
Nneutral
Lhydrophilic
Number of sequences for Nm46
Nsequences 3 1022
Number of structures per sequence
Np exp(aNm)1019
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and dynamics
different mapping?
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Molecular Dynamics Equations of Motion
Coupled 2nd order Diff. Eq.
How are they coupled?
for i1,Natoms
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(iv) Bond length potential
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Pair Forces Lennard-Jones Interactions
i
j
Parallelogram rule
-dV/drij gt 0 repulsive -dV/drij lt 0 attractive
force on i due to j
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Long-range interactions
BB
LL, LB
NB, NL, NN
V(r)
hard-core
attractions -dV/dr lt 0
r21/6?
r/?
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Bond Angle Potential
?0105?
?ijk
k
i
j
?ijk0,?
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Dihedral Angle Potential
Vd(?ijkl)
Successive Ns
Vd(?ijkl)
?ijkl
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Bond Stretch Potential
for i, ji1, i-1
i
j
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Equations of Motion
velocity verlet algorithm
Constant Energy vs. Constant Temperature
(velocity rescaling, Langevin/Nosé-Hoover
thermostats)
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Collapsed Structure
T05?h fast quench (Rg/?)2 5.48
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Native State
T0?h slow quench (Rg/?)2 7.78
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start
end
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Total Potential Energy
native states
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Radius of Gyration
unfolded
Tf
native state
slow quench
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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.
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Energy Landscape
E/?C
E/?C
end-to-end distance
end-to-end distance
5 contacts
4 contacts
3 contacts
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Rate Dependence
2 contacts
3 contacts
4 contacts
5 contacts
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Misfolding
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Reliable Folding at Low Rate
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Slow rate
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Fast rate
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So far

• Uh-oh, proteins do not fold reliably
• Quench rates and potentials

Next

• ThermostatsYuck!
• More results on coarse-grained models
• Results for atomistic models
• Homework
• Next Lecture Protein Folding III (2/15/10)