Relative pKa values from first-principles molecular dynamics: the case of histidine deprotonation

Accurate calculation of pK(a) values and free energies for acid/base reactions in the condensed phase has been a long-standing goal of theoretical chemistry. We present a novel application of the Car-Parrinello molecular dynamics method to the problem of relative pK(a) determination. As a particular example, we focus on the second stage in the dissociation of histidine, a process that holds special importance for biology. Using constrained molecular dynamics, we have analyzed the structural, electronic, and dynamical transformations taking place along a preselected, intuitive reaction coordinate. By integrating the potentials of mean force for the deprotonation of histidine and for a reference reaction, autodissociation of water, we obtain a pK(a) value of 6.8, which appears to be in good agreement with the experimental estimate of 6.1. Detailed analysis was undertaken to determine the value of the constraint, which transformed the N*-H* from a covalent to a hydrogen bond. This helped to identify a number of properties that could be successfully used in monitoring the dissociation process. Additional analysis in terms of electron localization functions provided valuable insight into the nature of the deprotonation reaction.