Constant pH Simulations with the Double Reservoir pH Replica Exchange

Abstract

We present the double reservoir pH replica exchange (DR-pH-Rex) method, which can improve convergence of constant pH simulations in situations where proper sampling is difficult. This method separates the sampling of protonation states from much of the sampling of protein conformations. The DR-pH-Rex method was inspired by the single reservoir temperature replica exchange method. The DR-pH-Rex method relies on pre-generation of two Boltzmann-weighted structural reservoirs of conformations that correspond to two end states at pH values where titratable groups are fully protonated and fully deprotonated. The end state conformations are coupled to simulations at intermediate pH values through the pH replica exchange (pH-Rex) methodology. We tested this method on three different systems: amino acid model compounds Lys and Glu, a small peptide, and a challenging case of V66K variant of Staphylococcal nuclease (SNase) which exhibits two distinctly different conformations of Lys-66 with slow transitions between the two conformations. We benchmarked the performance of the method through comparison with results of the pH-Rex method, which already provides better sampling than regular constant pH simulations. For the model compounds pH-Rex and DR-pH-Rex methods yield identical results. For the peptide, the pKa values are comparable between the two methods, but the DR-pH-Rex method exhibits faster convergence and less noise. For the V66K variant the pH-Rex method fails to properly sample conformational transitions of Lys-66 and results in two different pKa values when different conformations are used as starting structure. The DR-pH-Rex method, however, results in convergence of pKa values. Additionally we construct a four state model with two protonation states and only two conformations of Lys-66 and show that the pKa values calculated from DR-pH-Rex simulations are in excellent agreement with the pKa values determined from the four state model.