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

Abstract

Development of a pH stat to properly control solution pH in biomolecular simulations has been a long-standing goal in the community. Towards 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 pKa’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 pKa 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.

Constant-pH Molecular Dynamics Simulations for Large Biomolecular Systems

“…48 This was intended to reproduce as closely as possible the setup used by Huang et al 19 in their constant-pH simulations of the same system, except omitting their use of a hydroxide force field. All simulations of this system also utilized hydrogen mass repartitioning of the protein.…”

“…A similar argument can be made for continuous titration methods, which many research groups analyze by creating ad hoc bins for the fractional occupations observed near zero and one. 19 In this binning approach, the data outside of the bins is completely discarded in some cases. Clearly, the amount of time spent completely outside of the bins must be directly proportional to the number of fractional sites, thereby rendering less and less useable data as the system size increases.…”

Computational investigation of proton transfer, pKa shifts and pH-optimum of protein-DNA and protein-RNA complexes

“… for detailed discussion), others can be handled via continuum approach as explicit ion binding, but were not implemented in this study in order to reduce computational cost of modeling such large set of complexes. Further insights can be obtained via constant pH molecular dynamics simulations (MD) . Recent constant pH MD study proposed “trap‐and‐trigger” mechanism was proposed to accompany protein binding and to involve structural rearrangement and water penetration at the interface .…”

GPU-Accelerated Implementation of Continuous Constant pH Molecular Dynamics in Amber: pKa Predictions with Single-pH Simulations

“…By linking the protonation states of the titratable residues to the solute conformation, the effects of conformational flexibility on the pK a estimates are explicitly taken into account. Several CpHMD methods have been developed in the past, and they generally fall into two categories: The Monte-Carlo based methods, 15,16,18,20 which maintain a constant pH by periodically attempting Metropolis Monte Carlo moves to protonate or deprotonate titratable sites and continuous CpHMD, 17,[21][22][23][24][25][26] which is rooted in the λ-dynamics method for free energy calculations 27 and treats the protonation states of the titratable sites as continuous dynamic variables of the system. Continuous CpHMD lets systems escape local energy minima by allowing transient access to partially protonated states which are unphysical and must be discarded from the final pK a calculations.…”