MC-PHS: Monte Carlo implementation of the primary hydration shell for protein folding and design

A. Kentsis, M. Mezei, and R. Osman
Biophys. J., 84, 1-11 (2003).
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Theory

The primary hydration shell model (D. Beglov, and B. Roux, Biopolymers, 35, 171-188 (1995)) maintained a solvation layer by applying a tunable force on solvents that escaped this layer during a molecular dynamics simulation. Here we add a restoring potential to these solvents during a Monte Carlo simulation:

  Kshell(rij- RjvdW- rshell)2    rij- RjvdW> rshell
Ushell(rij,R)= SUMi=1,N    
 0     rij- RjvdW< rshell
N: the number of solvent molecules;
Kshell: restraining force constant (3.0 kcal/mol/2 ( see A. Rosenhouse-Dantsker, R. Osman, Biophys. J., 79, 66-79 (2000)) ;
rshell: solvent shell thicknes (fluctuates during the simulation);
RjvdW: van del Waals radius of solute atom j.

The average of the shell energy Ushell is periodically compared with Uref. If <Ushell> < Uref then the shell radius rshell is decresead, otherwise incresased. The amount of change is tuned to result in Ushell fluctuating around Uref.

Water droplet with the restraining potential:

Calibration

The target shell energy, Uref, is determined by comparing PHS and full PBC simulations of water. The right reference energy should reproduce the running coordination number function k(r) of the PBC run.

Running coordination numberk(r) for neat water simulated with different reference shell energy values and with PBC:

Mean number of waters in the solvent shell as a function of Uref:

The result show that different shell thickness required different reference energy. This suggested the use of the specific reference energy, Uref/Nout:

Calibration of the specific reference energy:

Note that all three lines cross the zero line (the structure representing neat water under PBC) at 0.15 kcal/mol/molecule

Tests of the correctness of sampling

The specific reference energy was found to be independent of the shell radius. Simulations with the optimal value (0.15 kcal/mol/molecule) were run on neat water and solutions of lysine, glutamic acid, threonine and phenylalanine. The results below compare the binding energy distributions, and some of the solute-solvent and solvent-solvent radial distributions and orientational correlation functions as calculated with the proximity analysis (see P.K. Mehrotra and D.L. Beveridge, J. Am. Chem. Soc., 102, 4287 (1980) and M. Mezei, Molecular Simulation, 1, 327 (1988)).

Comparison of neat water binding energy distributions from simulations with PHS and PBC:

Comparison of solute-water binding energy distributions from simulations with PHS and PBC of amino acids in water:

Comparison of solute-water radial distributions and orientational correlation fonctions from the proximity analysis of the simulations with PHS and PBC of amino acids in water:

Comparison of solute-water radial distributions and orientational correlation fonctions from the proximity analysis of the simulations with PHS and PBC of amino acids in water:

Comparison of water-water radial distributions from the proximity analysis of the simulations with PHS and PBC of amino acids in water:

Tests of the extent of sampling

The YPGDV pentapeptide was simulated with a 6  shell to see if the experimentally observed conformational equilibrium between folded and unfolded structures is reproduced by the simulation.

Distribution of the parameters distinguishing folded and unfolded states from three simulations (starting from extended, helix and hairpin conformations):

The three runs gave the consensus 50-50 distribution of folded and unfolded states, in agreement with NMR studies.

Conclusions

The comparisons of various distributions show that the structure of the solvent layer is preserved to a good extent with our MC-PHS simulations.

The test on the conformational equilibrium of the pentapeptide shows that MC-PHS is an efficient technique for sampling the conformation space of polypeptides.

Software

The calculations were performed with the MMC Monte Carlo program, available at the URL http://inka.mssm.edu/~mezei/mmc


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Last modified: 12/22/02 (MM)