We used Monte Carlo methods to treat the statistical problem of electrostatic interactions among many titrating amino acids and applied these methods to lysozyme and the photosynthetic reaction center of Rhodobacter sphaeroides, including all titrating sites. We computed the average protonation of residues as a function of pH from an equilibrium distribution of states generated by random sampling. Electrostatic energies were calculated from a finite difference solution to the linearized Poisson-Boltzmann equation using the coordinates from solved protein structures. For most calculations we used the Metropolis algorithm to sample protonation states; for strongly coupled sites, we substantially reduced sampling errors by using a modifIed algorithm that allows multiple site transitions. The Monte Carlo method agreed with calculations for a small test system, lysozyme, for which the complete partition function was calculated. We also calculated the pH dependence of the free energy change associated with electron transfer from the primary to the secondary quinone in the photosynthetic reaction center. The shape of the resulting curve agreed fairly well with experiment, but the proton uptake from which the free energy was calculated agreed only to within a factor of two with the observed values. We believe that this discrepancy resulted from errors in the individual electrostatic energy calculations rather than from errors in the Monte Carlo sampling.Electrostatic interactions in proteins are important for protein structure and function. The largest contribution to the electrostatic potential within a protein arises from protonatable amino acids that can carry a net charge. The problem of determining the average charges on protonatable residues can be separated into two parts. (i) The energies of protonation of the individual amino acids and the interaction energies between pairs of charged residues must be calculated. Much progress along these lines has been made (1-4). (ii) The average protonation of each residue must be determined from the electrostatic energies. Since the protonation of a site depends on the protonation of all other sites (in a typical protein there may be hundreds of titrating sites), an exact statistical calculation becomes too time consuming for more than -25 titrating residues. In this paper we present a Monte Carlo method to solve the statistical problem of finding the protonation of many interacting protonatable residues.Previous methods used to solve this problem can handle only a small number of sites or are inaccurate. Exact values of average protonations calculated from a partition function work well when the number of sites is below -25, and the reduced-site approximation can treat twice as many sites for some systems (5). The Tanford-Roxby approximation (6) ignores fluctuations in the protonation of residues and has been shown to be inaccurate for strongly interacting titrating residues (5).We used a Monte Carlo technique for determining the protonation of many interacting sit...

The Poisson±Boltzmann (PB) continuum solvent model shows considerable promise in providing a description of electrostatic solvation eects in biomolecules, but it can be computationally expensive to obtain converged results for large systems. Here we examine the performance of a pairwise generalized Born approximation (GB) method on multiple conformations of a small peptide, three proteins (protein A, myoglobin, and rusticyanin) and four RNA and DNA duplexes and hairpins containing 20±24 nucleotides. Charge and dielectric radii models were adapted from the CHARMM and Amber force ®elds. Finite dierence PB calculations were carried out with the Delphi and PEP programs, and for several examples the matrix of all pairwise interaction energies was determined. In general, this parameterization of the GB model does an excellent job of reproducing the PB solvation energies for small molecules and for groups near the surface of larger molecules. There is a systematic tendency for this GB model to overestimate the eects of solvent screening (compared to PB) for pairs of buried atoms, but individual errors tend to cancel, and a good overall account of conformational energetics is obtained. A simple extension to the GB model to account for salt eects (in the linearized Debye±HuÈ ckel approximation) is proposed that does a good job of reproducing the salt dependence of the PB calculations. In many cases, it should be possible to replace PB calculations with much simpler GB models, but care needs to be taken for systems with extensive burial of charges or dipoles.

The titration of amino acids and the energetics of electron transfer from the primary electron acceptor (QA) to the secondary electron acceptor (QB) in the photosynthetic reaction center of Rhodobacter sphaeroides are calculated using a continuum electrostatic model. Strong electrostatic interactions between titrating sites give rise to complex titration curves. Glu L212 is calculated to have an anomalously broad titration curve, which explains the seemingly contradictory experimental results concerning its pKa. The electrostatic field following electron transfer shifts the average protonation of amino acids near the quinones. The pH dependence of the free energy between Q-AQB and QAQ-B calculated from these shifts is in good agreement with experiment. However, the calculated absolute free energy difference is in severe disagreement (by approximately 230 meV) with the observed experimental value, i.e., electron transfer from Q-A to QB is calculated to be unfavorable. The large stabilization energy of the Q-A state arises from the predominantly positively charged residues in the vicinity of QA in contrast to the predominantly negatively charged residues near QB. The discrepancy between calculated and experimental values for delta G(Q-AQB-->QAQ-B) points to limitations of the continuum electrostatic model. Inclusion of other contributions to the energetics (e.g., protein motion following quinone reduction) that may improve the agreement between theory and experiment are discussed.

Carboxylesterases (CE) are ubiquitous enzymes responsible for the metabolism of xenobiotics. Because the structural and amino acid homology among esterases of different classes, the identification of selective inhibitors of these proteins has proved problematic. Using Telik's target-related affinity profiling (TRAP) technology, we have identified a class of compounds based on benzil (1,2-diphenylethane-1,2-dione) that are potent CE inhibitors, with K(i) values in the low nanomolar range. Benzil and 30 analogues demonstrated selective inhibition of CEs, with no inhibitory activity toward human acetylcholinesterase or butyrylcholinesterase. Analysis of structurally related compounds indicated that the ethane-1,2-dione moiety was essential for enzyme inhibition and that potency was dependent on the presence of, and substitution within, the benzene ring. 3D-QSAR analyses of these benzil analogues for three different mammalian CEs demonstrated excellent correlations of observed versus predicted K(i) (r(2) > 0.91), with cross-validation coefficients (q(2)) of 0.9. Overall, these results suggest that selective inhibitors of CEs with potential for use in clinical applications can be designed.