A new method for exact analytical calculation of the accessible surface areas and their gradients with respect to atomic coordinates is described. The new surface routine, GETAREA, finds solvent-exposed vertices of intersecting atoms, and thereby avoids calculating buried vertices which are not needed to determine the accessible surface area by the Gauss)Bonnet theorem. The surface routine was implemented in FANTOM, a program for energy minimization and Monte Carlo simulation, and tested for accuracy and efficiency in extensive energy minimizations of Met-enkephalin, the a-amylase inhibitor . tendamistat, and avian pancreatic polypeptide APP . The CPU time for the exact calculation of the accessible surface areas and their gradients has been . . reduced by factors of 2.2 Met-enkephalin and 3.2 tendamistat compared with our previous approach. The efficiency of our exact method is similar to the recently described approximate methods MSEED and SASAD. The performance of several atomic solvation parameter sets was tested in searches for low energy conformations of APP among conformations near the native X-ray crystal structure and highly distorted structures. The protein solvation parameters from w . x

Exact and efficient analytical calculation of the accessible surface areas and their gradients for macromolecules

Biased probability Monte Carlo conformational searches and electrostatic calculations for peptides and proteins.

The understanding of noncovalent interactions in protein–ligand complexes is essential in modern biochemistry and should contribute toward the discovery of new drugs. In the present review, we summarize recent work aimed at a better understanding of the physical nature of molecular recognition in protein–ligand complexes and also at the development and application of new computational tools that exploit our current knowledge on structural and energetic aspects of protein–ligand interactions in the design of novel ligands. These approaches are based on the exponentially growing amount of information about the geometry of protein structures and the properties of small organic molecules exposed to a structured molecular environment. The various contributions that determine the binding affinity of ligands toward a particular receptor are discussed. Their putative binding site conformations are analyzed, and some predictions are attempted. The similarity of ligands is examined with respect to their recognition properties. This information is used to understand and propose binding modes. In addition, an overview of the existing methods for the design and selection of novel protein ligands is given.

What Can We Learn from Molecular Recognition in Protein–Ligand Complexes for the Design of New Drugs?

Continuum Solvation Models: Classical and Quantum Mechanical Implementations

Recently a semiempirical method has been proposed by Aqvist et al. to calculate absolute and relative binding free energies. In this method, the absolute binding free energy of a ligand is estimated as deltaGbind = alpha + beta , where Vel(bound) and Vvdw(bound) are the electrostatic and van der Waals interaction energies between the ligand and the solvated protein from an molecular dynamics (MD) trajectory with ligand bound to protein and Vel(free) and Vel(free) and Vvdw(free) are the electrostatic and van der Waals interaction energies between the ligand and the water from an MD trajectory with the ligand in water. A set of values, alpha = 0.5 and beta = 0.16, was found to give results in good agreement with experimental data. Later, however, different optimal values of beta were found in studies of compounds binding to P450cam and avidin. The present work investigates how the optimal value of beta depends on the nature of binding sites for different protein-ligand interactions. By examining seven ligands interacting with five proteins, we have discovered a linear correlation between the value of beta and the weighted non-polar desolvation ratio (WNDR), with a correlation coefficient of 0.96. We have also examined the ability of this correlation to predict optimal values of beta for different ligands binding to a single protein. We studied twelve neutral compounds bound to avidin. In this case, the WNDR approach gave a better estimate of the absolute binding free energies than results obtained using the fixed value of beta found for biotin-avidin. In terms of reproducing the relative binding free energy to biotin, the fixed-beta value gave better results for compounds similar to biotin, but for compounds less similar to biotin, the WNDR approach led to better relative binding free energies.

What determines the van der Waals coefficient beta in the LIE (linear interaction energy) method to estimate binding free energies using molecular dynamics simulations

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.

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

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