SUNY at Albany
June 19-23, 2001
Robbust calculation of conformational free energy in molecular modeling
We recently developed the force field consistent ES/IS method for calculating the conformational free energy of a macromolecule in water solvent 1,2. The implicit solvent (IS) model is used to calculate the average solvation free energy for snapshots from explicit simulations (ES). The solute's internal energy is taken from the explicit simulations and its entropy is estimated in the quasi-harmonic model by analysis of the covariance positional fluctuation matrix. A consistent set of atomic Born radii and the cavity-surface free energy coefficient have been optimized for the all-atom force field used in the explicit simulations (Cedar/Gromos with SPC water). The optimized continuum dielectric method reproduces a set of 40 microscopic solvent polarization free energies for charged and polar groups of dipeptides with accuracy within 3%, and the same was found to be true for a small protein, eglin. The optimized IS model is consistent with ES MD simulation in the tendency to decrease the protein free energy in solvent. The ES/IS model is applied for calculation of a stability of a hundreds of protein decoys of CASP3 models and the decoy set of Park and Levitt. It is found that the protein decoys have consistently higher free energy in water solvent relative of that of the native structure. The rmsd and free energy of the decoys relative to the native structure show little or no correlation in the range rmsd < 3 ? and a correlation in the large range of the rmsd. Average potential energy of protein packing (van der Waals+torsion+deformation energies), area of protein molecular surface (solvent excluded cavity) are consistently low for the native structures.
The robustness of the optimized ES/IS method of the free energy estimation suggest that the method is a practical one at the final stage of an abinitio protein folding prediction method to choose a several lowest energy decoys from hundreds decoys selected at a preceding coarse grain stage. The low energy decoys forms an initial set for the multi-copy temperature-exchange MD/MC simulation to find a final ÔnativeÕ structure. Application of the ES/IS method to estimate the free energy of binding of a ligand (benzamidine) to a protein (trypsin) has given results in very reasonable agreement with results of all-atom perturbation free energy simulations and with experiment. In order to obtain good results, internal water molecules had to be represented explicitly as part of protein molecule. Furthermore, in order to obtain the standard free energy of binding relative to a defined standard state, four water molecules exchanging for the benzamidine ligand had to be represented explicitly in the calculation of all contributions, including that of the internal entropy.
Yury N. Vorobjev, Jan Hermans
Department of Biochemistry and Biophysics, School of Medicine, University of North Carolina, Chapel Hill, NC 27599-7260, USA ;