Arieh Warshel

▪ Abstract Understanding the action of enzymes on an atomistic level is one of the important aims of modern biophysics. This review describes the state of the art in addressing this challenge by simulating enzymatic reactions. It considers different modeling methods including the empirical valence bond (EVB) and more standard molecular orbital quantum mechanics/molecular mechanics (QM/MM) methods. The importance of proper configurational averaging of QM/MM energies is emphasized, pointing out that at present such averages are performed most effectively by the EVB method. It is clarified that all properly conducted simulation studies have identified electrostatic preorganization effects as the source of enzyme catalysis. It is argued that the ability to simulate enzymatic reactions also provides the chance to examine the importance of nonelectrostatic contributions and the validity of the corresponding proposals. In fact, simulation studies have indicated that prominent proposals such as desolvation, steric strain, near attack conformation, entropy traps, and coherent dynamics do not account for a major part of the catalytic power of enzymes. Finally, it is pointed out that although some of the issues are likely to remain controversial for some time, computer modeling approaches can provide a powerful tool for understanding enzyme catalysis.

Realistic studies of ion current in biologic channels present a major challenge for computer simulation approaches. All‐atom molecular dynamics simulations involve serious time limitations that prevent their use in direct evaluation of ion current in channels with significant barriers. The alternative use of Brownian dynamics (BD) simulations can provide the current for simplified macroscopic models. However, the time needed for accurate calculations of electrostatic energies can make BD simulations of ion current expensive. The present work develops an approach that overcomes some of the above challenges and allows one to simulate ion currents in models of biologic channels. Our method provides a fast and reliable estimate of the energetics of the system by combining semimacroscopic calculations of the self‐energy of each ion and an implicit treatment of the interactions between the ions, as well as the interactions between the ions and the protein‐ionizable groups. This treatment involves the use of the semimacroscopic version of the protein dipole Langevin dipole (PDLD/S) model in its linear response approximation (LRA) implementation, which reduces the uncertainties about the value of the protein “dielectric constant.” The resulting free energy surface is used to generate the forces for on‐the‐fly BD simulations of the corresponding ion currents. Our model is examined in a preliminary simulation of the ion current in the KcsA potassium channel. The complete free energy profile for a single ion transport reflects reasonable energetics and captures the effect of the protein‐ionized groups. This calculated profile indicates that we are dealing with the channel in its closed state. Reducing the barrier at the gate region allows us to simulate the ion current in a reasonable computational time. Several limiting cases are examined, including those that reproduce the observed current, and the nature of the productive trajectories is considered. The ability to simulate the current in realistic models of ion channels should provide a powerful tool for studies of the biologic function of such systems, including the analysis of the effect of mutations, pH, and electric potentials. Proteins 2002;47:265–280.

Implicit models for evaluation of electrostatic energies in proteins include dielectric constants that represent effect of the protein environment. Unfortunately, the results obtained by such models are very sensitive to the value used for the dielectric constant. Furthermore, the factors that determine the optimal value of these constants are far from being obvious. This review considers the meaning of the protein dielectric constants and the ways to determine their optimal values. It is pointed out that typical benchmarks for validation of electrostatic models cannot discriminate between consistent and inconsistent models. In particular, the observed pK_a values of surface groups can be reproduced correctly by models with entirely incorrect physical features. Thus, we introduce a discriminative benchmark that only includes residues whose pK_a values are shifted significantly from their values in water. We also use the semimacroscopic version of the protein dipole Langevin dipole (PDLD/S) formulation to generate a series of models that move gradually from microscopic to fully macroscopic models. These include the linear response version of the PDLD/S models, Poisson Boltzmann (PB)‐type models, and Tanford Kirkwwod (TK)‐type models. Using our different models and the discriminative benchmark, we show that the protein dielectric constant, ε_p, is not a universal constant but simply a parameter that depends on the model used. It is also shown in agreement with our previous works that ε_p represents the factors that are not considered explicitly. The use of a discriminative benchmark appears to help not only in identifying nonphysical models but also in analyzing effects that are not reproduced in an accurate way by consistent models. These include the effect of water penetration and the effect of the protein reorganization. Finally, we show that the optimal dielectric constant for self‐energies is not the optimal constant for charge‐charge interactions. Proteins 2001;44:400–417.

Consistent approaches for calculations of solvation free energies should provide results which are independent of the size of the simulation region. Simulations that use periodic boundary conditions and a standard Ewald treatment yield size dependent results. Corrections that can overcome this problem have been formulated, but have not yet been fully validated for solutes with general charge distributions. Furthermore, Ewald treatments of proteins may involve size dependent problems whose nature has not been explored by systematic studies. Here we demonstrate that our surface constraint all-atom solvent (SCAAS) model with its spherical boundary conditions (that include special polarization constraints) provides proper size independent results. It is also pointed out that this approach lends itself to an effective treatment of long-range interactions and offers a useful way of obtaining size independent free energies in studies of electrostatic effects in proteins.

The origin of the catalytic power of enzymes is discussed, paying attention to evolutionary constraints. It is pointed out that enzyme catalysis reflects energy contributions that cannot be determined uniquely by current experimental approaches without augmenting the analysis by computer simulation studies. The use of energy considerations and computer simulations allows one to exclude many of the popular proposals for the way enzymes work. It appears that the standard approaches used by organic chemists to catalyze reactions in solutions are not used by enzymes. This point is illustrated by considering the desolvation hypothesis and showing that it cannot account for a large increase in k_catrelative to the corresponding k_cagefor the reference reaction in a solvent cage. The problems associated with other frequently invoked mechanisms also are outlined. Furthermore, it is pointed out that mutation studies are inconsistent with ground state destabilization mechanisms. After considering factors that were not optimized by evolution, we review computer simulation studies that reproduced the overall catalytic effect of different enzymes. These studies pointed toward electrostatic effects as the most important catalytic contributions. The nature of this electrostatic stabilization mechanism is far from being obvious because the electrostatic interaction between the reacting system and the surrounding area is similar in enzymes and in solution. However, the difference is that enzymes have a preorganized dipolar environment that does not have to pay the reorganization energy for stabilizing the relevant transition states. Apparently, the catalytic power of enzymes is stored in their folding energy in the form of the preorganized polar environment.