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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
slide2

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
slide3

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.

slide4

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

slide5

and dynamics

different

mapping?

slide6

Molecular Dynamics: Equations of Motion

Coupled 2nd order

Diff. Eq.

How are they coupled?

for i=1,…Natoms

slide8

Pair Forces: Lennard-Jones Interactions

i

j

Parallelogram

rule

force on i

due to j

-dV/drij > 0; repulsive

-dV/drij < 0; attractive

slide9

‘Long-range interactions’

BB

LL, LB

NB, NL, NN

V(r)

hard-core

attractions

-dV/dr < 0

r*=21/6

r/

slide10

Bond Angle Potential

0=105

ijk

k

i

j

ijk=[0,]

slide11

Dihedral Angle Potential

Vd(ijkl)

Successive N’s

Vd(ijkl)

ijkl

slide12

Bond Stretch Potential

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

i

j

slide13

Equations of Motion

velocity

verlet

algorithm

Constant Energy vs. Constant Temperature

(velocity rescaling, Langevin/Nosé-Hoover thermostats)

slide14

Collapsed Structure

T0=5h; fast quench; (Rg/)2= 5.48

slide15

Native State

T0=h; slow quench; (Rg/)2= 7.78

slide19

Radius of Gyration

unfolded

Tf

native

state

slow quench

slide20

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.

slide22

Energy Landscape

E/C

E/C

end-to-end distance

end-to-end distance

5 contacts

4 contacts

3 contacts

slide23

Rate Dependence

2 contacts

3 contacts

4 contacts

5 contacts

slide28

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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