Empirical solvation models in the context of conformational energy searches: Application to bovine pancreatic trypsin inhibitor

Abstract

Continuum solvation models that estimate free energies of solvation as a function of solvent accessible surface area are computationally simple enough to be useful for predicting protein conformation. The behavior of three such solvation models has been examined by applying them to the minimization of the conformational energy of bovine pancreatic trypsin inhibitor. The models differ only with regard to how the constants of proportionality between free energy and surface area were derived. Each model was derived by fitting to experimentally measured equilibrium solution properties. For two models, the solution property was free energy of hydration. For the third, the property was NMR coupling constants. The purpose of this study is to determine the effect of applying these solvation models to the nonequilibrium conformations of a protein arising in the course of global searches for conformational energy minima. Two approaches were used: (1) local energy minimization of an ensemble of conformations similar to the equilibrium conformation and (2) global search trajectories using Monte Carlo plus minimization starting from a single conformation similar to the equilibrium conformation. For the two models derived from free energy measurements, it was found that both the global searches and local minimizations yielded conformations more similar to the X-ray crystallographic structures than did searches or local minimizations carried out in the absence of a solvation component of the conformational energy. The model derived from NMR coupling constants behaved similarly to the other models in the context of a global search trajectory. For one of the models derived from measured free energies of hydration, it was found that minimization of an ensemble of near-equilibrium conformations yielded a new ensemble in which the conformation most similar to the X-ray determined structure PTI4 had the lowest total free energy. Despite the simplicity of the continuum solvation models, the final conformation generated in the trajectories for each of the models exhibited some of the characteristics that have been reported for conformations obtained from molecular dynamics simulations in the presence of a bath of explicit water molecules. They have smaller root mean square (rms) deviations from the experimentally determined conformation, fewer incorrect hydrogen bonds, and slightly larger radii of gyration than do conformations derived from search trajectories carried out in the absence of solvent.

Prediction of protein conformation on the basis of a search for compact structures: Test on avian pancreatic polypeptide

“…This conversion was carried out with our recently developed dipole-path method, discussed in the accompanying paper (Liwo et al, 1993). Generation of the backbone is completed by carrying out EDMC (electrostatically driven Monte Carlo) simulations (Ripoll & Scheraga, 1988,1989Williams et al, 1992) in a "hybrid" representation of the polypeptide chain, Le., with an all-atom backbone and united side chains, still subject to the C"-distance constraints following from the united-residue simulations. The latter means that some or even all the distances of the virtual-bond chain obtained in the united-residue simulation are substantially preserved.…”

“…Because we have developed a new potential function, the version of the MCM algorithm is slightly different from its original formulation by Scheraga (1987, 1988) or from its more recent development (Ripoll & Scheraga, 1988, 1989Williams et al, 1992).…”

“…Each of the structures obtained in the preceding stages is subjected to Monte Carlo perturbation using the EDMC method (Ripoll & Scheraga, 1988, 1989Williams et al, 1992). At this stage of the calculations the all-atom representation of the polypeptide backbone is maintained, while the side chains are stilI represented by single interaction sites.…”

Towards protein folding by global energy optimization

“…These kinds of terms can be calculated efficiently [56-581, differentiated analytically [56,59] and used in molecular simulations [32,60,61]. The solvation free energy consists of two major components.…”

“…Since introduction of explicit water molecules is far too demanding computationally, semi-em-pirical approaches, in which solvent is treated as a continuous medium [ 18,21,3 1,32,54,55], are preferred. These kinds of terms can be calculated efficiently [56-581, differentiated analytically [56,59] and used in molecular simulations [32,60,61].…”