Simulating proton translocations in proteins: Probing proton transfer pathways in the Rhodobacter sphaeroides reaction center

A general method for simulating proton translocations in proteins and for exploring the role of different proton transfer pathways is developed and examined. The method evaluates the rate constants for proton transfer processes using the energetics of the relevant proton configurations. The energies (ΔG((m))) of the different protonation states are evaluated in two steps. First, the semimicroscopic version of the protein dipole Langevin dipole (PDLD/S) method is used to evaluate the intrinsic energy of bringing the protons to their protein sites, when the charges of all protein ionized residues are set to zero. Second, the interactions between the charged groups are evaluated by using a Coulomb's Law with an effective dielectric constant. This approach, which was introduced in an earlier study by one of the authors of the current report, allows for a very fast determination of any ΔG((m)) and for practical evaluation of the time-dependent proton population: That is, the rate constants for proton transfer processes are evaluated by using the corresponding ΔG((m)) values and a Marcus type relationship. These rate constants are then used to construct a master equation, the integration of which by a fourth-order Runge-Kutta method yields the proton population as a function of time. The integration evaluates, 'on the fly,' the changes of the rate constants as a result of the time-dependent changes in charge-charge interaction, and this feature benefits from the fast determination of ΔG((m)). The method is demonstrated in a preliminary study of proton translocation processes in the reaction center of Rhodobacter sphaeroides. It is found that proton transfer across water chains involves significant activation barriers and that ionized protein residues probably are involved in the proton transfer pathways. The potential of the present method in analyzing mutation experiments is discussed briefly and illustrated. The present study also examines different views of the nature of proton translocations in proteins. It is shown that such processes are controlled mainly by the electrostatic interaction between the proton site and its surroundings rather than by the local bond rearrangements of water molecules that are involved in the proton pathways. Thus, the overall rate of proton transport frequently is controlled by the highest barrier along the conduction pathway.