All-Atom Continuous Constant pH Molecular Dynamics With Particle Mesh Ewald and Titratable Water

Development of a pH stat to properly control solution pH in biomolecular simulations has been a long-standing goal in the community. Toward this goal recent years have witnessed the emergence of the so-called constant pH molecular dynamics methods. However, the accuracy and generality of these methods have been hampered by the use of implicit-solvent models or truncation-based electrostatic schemes. Here we report the implementation of the particle mesh Ewald (PME) scheme into the all-atom continuous constant pH molecular dynamics (CpHMD) method, enabling CpHMD to be performed with a standard MD engine at a fractional added computational cost. We demonstrate the performance using pH replica-exchange CpHMD simulations with titratable water for a stringent test set of proteins, HP36, BBL, HEWL, and SNase. With the sampling time of 10 ns per replica, most pK_a's are converged, yielding the average absolute and root-mean-square deviations of 0.61 and 0.77, respectively, from experiment. Linear regression of the calculated vs experimental pK_a shifts gives a correlation coefficient of 0.79, a slope of 1, and an intercept near 0. Analysis reveals inadequate sampling of structure relaxation accompanying a protonation-state switch as a major source of the remaining errors, which are reduced as simulation prolongs. These data suggest PME-based CpHMD can be used as a general tool for pH-controlled simulations of macromolecular systems in various environments, enabling atomic insights into pH-dependent phenomena involving not only soluble proteins but also transmembrane proteins, nucleic acids, surfactants, and polysaccharides.