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Computational methods in molecular biophysics (examples of solving real biological problems) EXAMPLE I: THE PROTEIN FOLDING PROBLEM. Alexey Onufriev, Virginia Tech www.cs.vt.edu/~onufriev. OUTLINE: Folding proteins in ``virtual water”. Energy landscapes.

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Computational methods in molecular biophysics examples of solving real biological problems exa

Computational methods in molecular biophysics (examples of solving real biological problems)

EXAMPLE I: THE PROTEIN FOLDING PROBLEM

Alexey Onufriev,

Virginia Tech

www.cs.vt.edu/~onufriev


Computational methods in molecular biophysics examples of solving real biological problems exa

  • OUTLINE:

  • Folding proteins in ``virtual water”. Energy landscapes.

  • Insights into the function of bacteriorhodopsin – the smallest solar panel.

  • Understanding stability of proteins from bacteria living under extreme conditions (high salt).

Claims: 1. The use of detailed, atomic resolution models is often

critical.

2. Simple physics works on very complex biological systems.


Computational methods in molecular biophysics examples of solving real biological problems exa

Protein Structure in 3 steps.

Step 1. Two amino-acids together (di-peptide)

Peptide bond

Amino-acid #1

Amino-acid #2


Computational methods in molecular biophysics examples of solving real biological problems exa

Protein Structure in 3 steps.

Step 2: Most flexible degrees of freedom:


Computational methods in molecular biophysics examples of solving real biological problems exa

Protein Structure in 3 steps.

Sometimes, polypeptide chain forms helical structure:


Computational methods in molecular biophysics examples of solving real biological problems exa

THEME I.Protein folding using the GB

Amino-acid sequence – translated genetic code.

MET—ALA—ALA—ASP—GLU—GLU--….

How?

Experiment: amino acid sequence uniquely

determines protein’s 3D shape (ground state).

Nature does it all the time. Can we?


Computational methods in molecular biophysics examples of solving real biological problems exa

f4

f2

f3

f1

The magnitude of the protein folding challenge:

Enormous number of the possible conformations of the polypeptide chain

A small protein is a chain of ~ 50 mino acids (more for most ).

Assume that each amino acid has only 10 conformations (vast underestimation)

Total number of possible conformations: 1050

Say, you make one MC step per femtosecond.

Exhaustive search for the ground state will take 1027 years.

Why bother: protein’s shape determines its biological function.


Computational methods in molecular biophysics examples of solving real biological problems exa

2

3

Free energy

1

Finding a global minimum in a multidimensional case is easy only when the landscape is smooth. No matter where you start (1, 2 or 3), you quickly end up at the bottom -- the Native (N), functional state of the protein.

Folding coordinate

Adopted from Ken Dill’s web site at UCSF



Computational methods in molecular biophysics examples of solving real biological problems exa

Realistic landscapesare much more complex, with multiple local minima –folding traps.

Adopted from Ken Dill’s web site at UCSF



Computational methods in molecular biophysics examples of solving real biological problems exa

Principles of Molecular Dynamics (MD):

Y

F = dE/dr

System’s energy

Bond

spring

+ A/r12 – B/r6

+ Q1Q2/r

Kr2

VDW interaction

Electrostatic forces

Bond stretching

x

Each atom moves by Newton’s 2nd Law: F = ma

+

-

+ …

E =


Computational methods in molecular biophysics examples of solving real biological problems exa

Computational advantages of

representing

water implicitly, via a continuum

solvent model

Implicit water as dielectric continuum

Explicit water

Low computational cost. Fast dynamics.

  • Other advantages:

  • Instant dielectric response => no water equilibration necessary.

  • No viscosity => faster conformational transitions.

  • Solvation in an infinite volume => no boundary artifacts.

  • Solvent degrees of freedom taken into account implicitly => easy to

  • estimate total energy of solvated system.

Large computational cost. Slow dynamics.

Electrostatic Interactions are key!


Computational methods in molecular biophysics examples of solving real biological problems exa

+

Solvation energy of individual ion

+


Computational methods in molecular biophysics examples of solving real biological problems exa

+

+

rij

qi

-

-

qj

-

molecule

The generalized Born approximation (GB):

Total electrostaticenergy

Solvent polarization, DW

Vacuum part

Function to be determined.


Computational methods in molecular biophysics examples of solving real biological problems exa

 0

f  rij E ~ 1/r

f  (RiRj)1/2 E ~ 1/R

 0  1

rij

j

i

Interpolates between the case when

atoms are far from each otherand Coulomb’s law is recovered

i

j

And when they fuse into one, and Born’s formula is recovered

The “magic” formula:

f = [ rij2 + RiRjexp(-rij2/4RiRj) ]1/2 /Still et al. 1990 /

details: Onufriev et al. J. Phys. Chem. 104, 3712 (2000)

Onufriev et al. J. Comp. Chem. 23, 1297 (2002)

Onufriev et al. Proteins, 55, 383 (2004)


Computational methods in molecular biophysics examples of solving real biological problems exa

Simulated Refolding pathway

of the 46-residue protein. Molecular

dynamics based on AMBER-7

Movie available at: www.scripps.edu/~onufriev/RESEARCH/in_virtuo.html

1

3

0 1 2 3 4 5 6

5

NB: due to the absence of viscosity, folding occurs on much shorter time-scale than in an experiment.


Computational methods in molecular biophysics examples of solving real biological problems exa

Folding a protein in virtuo

using Molecular Dynamics based on the Generalized Born

(implicit solvation) model.

Simulation time: overnight on 16 processors.

Protein to fold: 46 -residue protein A (one of the guinea pigs in folding studies).

Protocol details: AMBER-7 package, parm-94 force-field.

New GB model.


Computational methods in molecular biophysics examples of solving real biological problems exa

Recent landmark attempt to fold a (36 residue) protein

in virtuo using Molecular Dynamics:

Duan Y, Kollman, P Science, 282 740 (1998).

Simulation time: 3 months on 256 processors

= 64 years on one processor.

Result: partially folded structure.

Problem: explicit water simulation are

too expensive computationally – can’t wait long enough.