Protein Folding and Modeling

Carol K. HallChemical and Biomolecular

EngineeringNorth Carolina State University

Computational Methods for Modeling Protein Folding and Structure

1. Homology ModelingAssumes that proteins with similar sequences have

similar structures, alignments

2. Threading“Threads” sequence of unknown structure through

database of known structures and scores match based on contact potentials

3. Ab initio or de novo approachesDeduce 3-d structure for given sequence by finding

minimum energy based on force field

Types of Computer SimulationsTypes of Computer Simulations

1. Molecular Dynamics

a. Decide on model intermolecular forces

b. Distribute 500-100,000 molecules in simulation cell assigning random positions and velocities to each molecule

c. Monitor molecule’s motion as a function of time by solving Newton’s equation of motion (F=m*a) at each time step to predict new position and velocity

d. Take time averages of properties of interest

2. Monte Carlo

a. Decide on model intermolecular forces

b. Distribute 500-10,000 molecules at random locations in cell

c. Generate configurations of these molecules randomly (in proportion to their probability of occurring)

d. Take averages over all configurations generated to calculate properties of interest

Types of Computer Simulations – cont.Types of Computer Simulations – cont.

3. Periodic Boundary Conditions: makes 1000 molecules look like 1023 molecules

4. Computer simulation gives exact results for the molecular model studied

Simulation of a System of Hard Spheres

Folding Kinetics

New View: Energy Bias

Dill & Chan (1997)

Representing Protein Geometry• Atomic Resolution Models

Each atom on protein and on solvent molecules is represented as a sphere interacting via a realistic set of potentials based on the Lennard Jones potential and electrostatic Coulomb potential Includes correct bond lengths, bond angles, planar trans peptide bond, leads to faithful representation of protein geometry.

• Low resolution models ( Coarse-grained or Simplified Folding Models)Solvent molecules not included in the simulation.

Lattice Models: protein is chain of single-site amino acid residues arranged on the sites of a square or cubic lattice

Off-Lattice models: protein is a flexible chain of single-sphere amino acid residues interacting via Lennard Jones or other potentials

• Intermediate Resolution Models – in between

All-Atom Simulations

Folding of Villin Headpiece Subdomain

Well-studied, fast-folding 36-residue proteinFolding time is ~10 microsecondsDuan and Kollman (1998) conducted a 1-

microsecond simulation of “folding” using 256 dedicated CPU for 2 monthsUnfolded state hydrophobic collapse helix formation conformational readjustment partially-folded intermediate

All-atom simulations

Folding of Polyalanine 30-mer

Villin Headpiece Folds at Home

Intermolecular Potentials for Spherical MoleculesOne Example– Lennard Jones Potential

Lennard-Jones potential in dimensionless form

r*= r/ σ where σ is molecular diameter of system under study

612

*

1

*

14*)(*

rrru

taken from Dr. D. A. Kofke’s lectures on Molecular Simulation, SUNY Buffalohttp://www.eng.buffalo.edu/~kofke/ce530/index.html

Why use simplified ( coarse-grained) protein models?

• All atom simulations take too long, can depend sensitively on the details, and sample only very early folding events.

• Simplified models allow us to learn general physical principles of protein folding. contain few parameters ,implicit biases.

• Allow complete exploration of conformational and sequence space

Lattice Models for Folding: Monte Carlo

Simulations

(1) (2)

(3) (4)

• Amino acid residues are sites ( beads) on a cubic lattice•Generate random moves of “beads” on the lattice protein• Accept moves based on their probability of occurring= exp( Enew-E old)/kT

Lattice Models -The HP Model

• Energy function: amino acids are either hydrophobic (H) or polar(P),

• Hydrophobic beads, H, attract each other with strength ε when they are on neighboring lattice sites

U= ε [number H-H contacts]

Lattice model of folding

Q0 = # of native contactsC = total # of contactsF = free energy

1016 possible starting conformations rapidly fold to one of 1010 disordered globules and thenslowly search for one of 103

compact transition states thatrapidly fold to the unique native structure.

F

C

Q0

1016 possible starting configurations

1010 disordered globules

103 transition states

1 native configuration