Constant-pH molecular dynamics using continuous titration coordinates

In this work, we explore the question of whether pK(a) calculations based on a microscopic description of the protein and a macroscopic description of the solvent can be implemented to examine conformationally dependent proton shifts in proteins. To this end, we introduce a new method for performing constant-pH molecular dynamics (PHMD) simulations utilizing the generalized Born implicit solvent model. This approach employs an extended Hamiltonian in which continuous titration coordinates propagate simultaneously with the atomic motions of the system. The values adopted by these coordinates are modulated by potentials of mean force of isolated titratable model groups and the pH to control the proton occupation at particular sites in the polypeptide. Our results for four different proteins yield an absolute average error of approximately 1.6 pK units, and point to the role that thermally driven relaxation of the protein environment in the vicinity of titrating groups plays in modulating the local pK(a), thereby influencing the observed pK1/2 values. While the accuracy of our method is not yet equivalent to methods that obtain pK1/2 values through the ad hoc scaling of electrostatics, the present approach and constant pH methods in general provide a useful framework for studying pH-dependent phenomena. Further work to improve our model to approach quantitative agreement with experiment is outlined.