Bioinformatics practical application of simulation and data mining protein folding ii
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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

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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 O’Hern

  • Department of Mechanical Engineering

  • Department of Physics

  • Yale University


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


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.


3-letter C model: B9N3(LB)4N3B9N3(LB)5L

B=hydrophobic

N=neutral

L=hydrophilic

Number of sequences for

Nm=46

Nsequences= 3~ 1022

Number of structures

per sequence

Np ~ exp(aNm)~1019


and dynamics

different

mapping?


Molecular Dynamics: Equations of Motion

Coupled 2nd order

Diff. Eq.

How are they coupled?

for i=1,…Natoms


(iv) Bond length potential


Pair Forces: Lennard-Jones Interactions

i

j

Parallelogram

rule

force on i

due to j

-dV/drij > 0; repulsive

-dV/drij < 0; attractive


‘Long-range interactions’

BB

LL, LB

NB, NL, NN

V(r)

hard-core

attractions

-dV/dr < 0

r*=21/6

r/


Bond Angle Potential

0=105

ijk

k

i

j

ijk=[0,]


Dihedral Angle Potential

Vd(ijkl)

Successive N’s

Vd(ijkl)

ijkl


Bond Stretch Potential

for i, j=i+1, i-1

i

j


Equations of Motion

velocity

verlet

algorithm

Constant Energy vs. Constant Temperature

(velocity rescaling, Langevin/Nosé-Hoover thermostats)


Collapsed Structure

T0=5h; fast quench; (Rg/)2= 5.48


Native State

T0=h; slow quench; (Rg/)2= 7.78


start

end


Total Potential Energy

native states


Radius of Gyration

unfolded

Tf

native

state

slow quench


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.


Energy Landscape

E/C

E/C

end-to-end distance

end-to-end distance

5 contacts

4 contacts

3 contacts


Rate Dependence

2 contacts

3 contacts

4 contacts

5 contacts


Misfolding


Reliable Folding at Low Rate


Slow rate


Fast rate


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)


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