Protonation of interacting residues in a protein by a Monte Carlo method: application to lysozyme and the photosynthetic reaction center of Rhodobacter sphaeroides.

We used Monte Carlo methods to treat 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.