Coarse Grained Simulations

  Why Coarse-Grained Simulations?

To characterize protein conformational characteristics at time and length scales that can not be reached by conventional fully atomistic MD simulations.

  The motions of nanoseconds to milliseconds time scale include:

1. the correlated fluctuations between residues
2. the structural changes and/or spatial reorganization of secondary structure units
3. the cooperative changes in tertiary contacts
4. the larger scale motions like domain movements

The coarse-grained simulations enable exploring such collective motions at the expense of accuracy. However, such simulations can become efficient and physically sensible with the use of semi-empirical potentials derived from Protein Databank Structures.

Figure I.4.6. Virtual bond model representation of the protein backbone. Dotted lines are the virtual bonds connecting successive a-carbons. This representation takes advantage of the planarity of the three successive backbone bonds, Cai-1-Ci, Ci-Ni and Ni-Cai corresponding to each amino acid. 

DATA File for Long Range and Short Range Interactions

Low-resolution Model

The atomic representation is reduced to a low-resolution model where each residue is represented by two interaction sites; one at the alpha carbon atom and the other at the side chain centroid.

The backbone is represented by the virtual bond model originally proposed by Flory and collaborators.The backbone of a protein of n residues consists of n-1 virtual bonds connecting the successive alpha carbon atoms. The amino acid side chains are represented by a single interaction site each, selected on the basis of specific properties.of the amino acid.

The virtual bond model where two points per residue are considered:
the alpha carbon (C^a) as the backbone site C_i, and the interaction site of the side chain, S_i.l_i is the virtual bond connecting C_i and Ci-1, phi (f) is the torsion angle of bond l and theta (q) is the bond angle between bonds i and i+1.

A fortran code to calculate bond lengths, bond angles and dihedral angles

  The energy of the conformation can be found from the additive contributions of two interaction potentials:

1. Short-range: between covalently bonded first or second neighboring units along the chain sequence

2. Long-range: between non-bonded residues that are close in space but distant along the sequence

  DATA File for Long Range and Short Range Interactions

  Dynamic Monte Carlo Method

  The low-resolution model of the protein structure can be allowed to move by a dynamic Monte Carlo method.

  The simple algorithm is as follows:

  - calculate the energy of the conformation
  - choose randomly a backbone or sidechain interaction site
  - perturb the coordinates of the chosen site
  - calculate the energy of the new conformation
  - accept or reject the move according to Metropolis criterion
  - repeat the procedure to obtain a trajectory for analysis

  What can be obtained from the analysis of the simulations?

  - prediction of crystallographic temperature factors
  - correlation between fluctuations of units
  - correlation between rotations of virtual backbone bonds
  - local flexibility from conformational autocorrelations
  - prediction of H/D exchange behavior
  - prediction of order parameters obtained from NMR relaxation data

  Related References

  "Efficient Characterization of Collective Motions and Interresidue Correlations in Proteins by Low-Resolution Simulations (.pdf)"
  I. Bahar, B. Erman, T. Haliloglu & R. L. Jernigan, Biochemistry, 36, 13512-13523 (1997)

  "Coarse-grained Simulations of Conformational Dynamics of Proteins: Application to Apomyoglobin (.pdf)"
  T. Haliloglu & I. Bahar, Proteins, 31, 271-281 (1998)

  "Coarse-Grained Simulations of Conformational Dynamics of Proteins"
  T. Haliloglu, Theoretical and Computational Polymer Science, 9/3-4, 255-260 (1999)

  "Characterization of Internal Motions of Escherichia coli Ribonuclease H by Monte Carlo Simulation"
  T. Haliloglu, Proteins, 34, 533-539 (1999)

  "Conformational Dynamics of Chymotrypsin Inhibitor 2 by Coarse-Grained Simulations"
  N. Kurt & T. Haliloglu, Proteins, 37, 454-464 (1999)

  "Conformational Dynamics of Cytochrome c by Coarse-Grained Simulations"
  T. Haliloglu, Polymer Preprints, 81, 155 (1999).

  Semi-empirical Potentials

  "Structure-Derived Potentials and Protein Simulations (.pdf)"
  R. L. Jernigan & I. Bahar Current Opinion in Structural Biology 6,195-209, 1996.

  "Inter-residue Potentials in Globular Proteins and the Dominance of Highly Specific Hydrophilic Interactions at Close; Separation"
  I. Bahar & R. L. Jernigan, J. Mol. Biol., 266, 195-214 (1997)

  "Short-range Conformational Energies, Secondary Structure Propensities, and Recognition of Correct Sequence-Structure Matches (.pdf)"
  I. Bahar, M. Kaplan & R. L. Jernigan, Proteins, 29, 292-308 (1997)

  "Coordination Geometry of Non-bonded Residues in Globular Proteins"
  I. Bahar & R. L. Jernigan, Folding & Design, 1 357-370 (1996)

  "Empirical solvent-mediated potentials hold for both intramolecular and inter-molecular inter-residue interactions"
  O. Keskin, I. Bahar, A. Badredtinov, O. Ptitsyn & R. L. Jernigan Protein Science 7, 2578-2586, 1998.