Studies of proton translocations in biological systems: simulating proton transport in carbonic anhydrase by EVB-based models

Proton transport (PTR) processes play a major role in bioenergetics and thus it is important to gain a molecular understanding of these processes. At present the detailed description of PTR in proteins is somewhat unclear and it is important to examine different models by using well-defined experimental systems. One of the best benchmarks is provided by carbonic anhydrase III (CA III), because this is one of the few systems where we have a clear molecular knowledge of the rate constant of the PTR process and its variation upon mutations. Furthermore, this system transfers a proton between several water molecules, thus making it highly relevant to a careful examination of the "proton wire" concept. Obtaining a correlation between the structure of this protein and the rate of the PTR process should help to discriminate between alternative models and to give useful clues about PTR processes in other systems. Obviously, obtaining such a correlation requires a correct representation of the "chemistry" of PTR between different donors and acceptors, as well as the ability to evaluate the free energy barriers of charge transfer in proteins, and to simulate long-time kinetic processes. The microscopic empirical valence bond (Warshel, A., and R. M. Weiss. 1980. J. Am. Chem. Soc. 102:6218-6226; and Aqvist, J., and A. Warshel. 1993. Chem. Rev. 93:2523-2544) provides a powerful way for representing the chemistry and evaluating the free energy barriers, but it cannot be used with the currently available computer times in direct simulation of PTR with significant activation barriers. Alternatively, one can reduce the empirical valence bond (EVB) to the modified Marcus' relationship and use semimacroscopic electrostatic calculations plus a master equation to determine the PTR kinetics (Sham, Y., I. Muegge, and A. Warshel. 1999. Proteins. 36:484-500). However, such an approximation does not provide a rigorous multisite kinetic treatment. Here we combine the useful ingredients of both approaches and develop a simplified EVB effective potential that treats explicitly the chain of donors and acceptors while considering implicitly the rest of the protein/solvent system. This approach can be used in Langevin dynamics simulations of long-time PTR processes. The validity of our new simplified approach is demonstrated first by comparing its Langevin dynamics results for a PTR along a chain of water molecules in water to the corresponding molecular dynamics simulations of the fully microscopic EVB model. This study examines dynamics of both models in cases of low activation barriers and the dependence of the rate on the energetics for cases with moderate barriers. The study of the dependence on the activation barrier is next extended to the range of higher barriers, demonstrating a clear correlation between the barrier height and the rate constant. The simplified EVB model is then examined in studies of the PTR in carbonic anhydrase III, where it reproduces the relevant experimental results without the use of any parameter that is specifically adjusted to fit the energetics or dynamics of the reaction in the protein. We also validate the conclusions obtained previously from the EVB-based modified Marcus' relationship. It is concluded that this approach and the EVB-based model provide a reliable, effective, and general tool for studies of PTR in proteins. Finally in view of the behavior of the simulated result, in both water and the CA III, we conclude that the rate of PTR in proteins is determined by the electrostatic energy of the transferred proton as long as this energy is higher than a few kcal/mol.