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

Bioinformatics: Practical Application of Simulation and Data MiningProtein Folding II

  • Prof. Corey O’Hern

  • Department of Mechanical Engineering

  • Department of Physics

  • Yale University


Bioinformatics practical application of simulation and data mining protein folding ii

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


Bioinformatics practical application of simulation and data mining protein folding ii

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.


Bioinformatics practical application of simulation and data mining protein folding ii

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


Bioinformatics practical application of simulation and data mining protein folding ii

and dynamics

different

mapping?


Bioinformatics practical application of simulation and data mining protein folding ii

Molecular Dynamics: Equations of Motion

Coupled 2nd order

Diff. Eq.

How are they coupled?

for i=1,…Natoms


Bioinformatics practical application of simulation and data mining protein folding ii

(iv) Bond length potential


Bioinformatics practical application of simulation and data mining protein folding ii

Pair Forces: Lennard-Jones Interactions

i

j

Parallelogram

rule

force on i

due to j

-dV/drij > 0; repulsive

-dV/drij < 0; attractive


Bioinformatics practical application of simulation and data mining protein folding ii

‘Long-range interactions’

BB

LL, LB

NB, NL, NN

V(r)

hard-core

attractions

-dV/dr < 0

r*=21/6

r/


Bioinformatics practical application of simulation and data mining protein folding ii

Bond Angle Potential

0=105

ijk

k

i

j

ijk=[0,]


Bioinformatics practical application of simulation and data mining protein folding ii

Dihedral Angle Potential

Vd(ijkl)

Successive N’s

Vd(ijkl)

ijkl


Bioinformatics practical application of simulation and data mining protein folding ii

Bond Stretch Potential

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

i

j


Bioinformatics practical application of simulation and data mining protein folding ii

Equations of Motion

velocity

verlet

algorithm

Constant Energy vs. Constant Temperature

(velocity rescaling, Langevin/Nosé-Hoover thermostats)


Bioinformatics practical application of simulation and data mining protein folding ii

Collapsed Structure

T0=5h; fast quench; (Rg/)2= 5.48


Bioinformatics practical application of simulation and data mining protein folding ii

Native State

T0=h; slow quench; (Rg/)2= 7.78


Bioinformatics practical application of simulation and data mining protein folding ii

start

end


Bioinformatics practical application of simulation and data mining protein folding ii

Total Potential Energy

native states


Bioinformatics practical application of simulation and data mining protein folding ii

Radius of Gyration

unfolded

Tf

native

state

slow quench


Bioinformatics practical application of simulation and data mining protein folding ii

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.


Bioinformatics practical application of simulation and data mining protein folding ii

Energy Landscape

E/C

E/C

end-to-end distance

end-to-end distance

5 contacts

4 contacts

3 contacts


Bioinformatics practical application of simulation and data mining protein folding ii

Rate Dependence

2 contacts

3 contacts

4 contacts

5 contacts


Bioinformatics practical application of simulation and data mining protein folding ii

Misfolding


Bioinformatics practical application of simulation and data mining protein folding ii

Reliable Folding at Low Rate


Bioinformatics practical application of simulation and data mining protein folding ii

Slow rate


Bioinformatics practical application of simulation and data mining protein folding ii

Fast rate


Bioinformatics practical application of simulation and data mining protein folding ii

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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