Protein p Ka's from Adaptive Landscape Flattening Instead of Constant-pH Simulations.

Protein acid/base constants, or p Ka's are often computed from Monte Carlo or molecular dynamics simulations at a series of constant pH values. Instead, we propose to adaptively flatten the free energy landscape in the space of protonation states. The flattening is achieved by a Wang-Landau Monte Carlo, where a bias potential is constructed adaptively during an initial phase, such that all protonation states achieve comparable probabilities. Biased ensembles of states are then reweighted by subtracting out the bias and adding a pH-dependent free energy term. Titration curves constructed for three test proteins agreed, within the small numerical uncertainty, with those obtained earlier from the constant-pH approach.