Protein Folding and Modeling

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Protein Folding and Modeling

• Carol K. Hall
• Chemical and Biomolecular Engineering
• North Carolina State University

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Computational Methods for Modeling Protein
Folding and Structure

• 1. Homology Modeling
• Assumes 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 approaches
• Deduce 3-d structure for given sequence by
  finding minimum energy based on force field

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Types of Computer Simulations

• Molecular Dynamics
• Decide on model intermolecular forces
• Distribute 500-100,000 molecules in simulation
  cell assigning random positions and velocities to
  each molecule
• Monitor molecules motion as a function of time
  by solving Newtons equation of motion (Fma) at
  each time step to predict new position and
  velocity
• Take time averages of properties of interest
• Monte Carlo
• Decide on model intermolecular forces
• Distribute 500-10,000 molecules at random
  locations in cell
• Generate configurations of these molecules
  randomly (in proportion to their probability of
  occurring)
• Take averages over all configurations generated
  to calculate properties of interest

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Types of Computer Simulations cont.

1. Periodic Boundary Conditions makes 1000
   molecules look like 1023 molecules
2. Computer simulation gives exact results for the
   molecular model studied

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Simulation of a System of Hard Spheres
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Folding Kinetics
New View Energy Bias
Dill Chan (1997)
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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

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All-Atom Simulations
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Folding of Villin Headpiece Subdomain

• Well-studied, fast-folding 36-residue protein
• Folding time is 10 microseconds
• Duan and Kollman (1998) conducted a 1-
  microsecond simulation of folding using 256
  dedicated CPU for 2 months
• Unfolded state? hydrophobic collapse ?helix
  formation ? conformational readjustment?
  partially-folded intermediate

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All-atom simulations
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Folding of Polyalanine 30-mer
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Villin Headpiece Folds at Home
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Intermolecular Potentials for Spherical
MoleculesOne Example Lennard Jones Potential

• Lennard-Jones potential in dimensionless form
• r r/ s where s is molecular diameter of system
  under study

taken from Dr. D. A. Kofkes lectures on
Molecular Simulation, SUNY Buffalo http//www.eng.
buffalo.edu/kofke/ce530/index.html
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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

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Lattice Models for Folding Monte
Carlo Simulations

• 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

(2)


(1)
(3)
(4)
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Lattice Models -The HP Model

• Energy function amino acids are either
  hydrophobic (H) or polar(P),
• Hydrophobic beads, H, attract each other with
  strength e when they are on neighboring lattice
  sites
• U e number H-H contacts

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Lattice model of folding
1016 possible starting configurations

Q0 of native contacts C total of
contacts F free energy 1016 possible starting
conformations rapidly fold to one of 1010
disordered globules and then slowly search for
one of 103 compact transition states that rapidly
fold to the unique native structure.

1010 disordered globules
F
Q0
C
103 transition states
1 native configuration