Charge-Neutral Constant pH Molecular Dynamics Simulations Using a Parsimonious Proton Buffer
In constant pH molecular dynamics simulations, the protonation states of titratable sites can respond to changes of the pH and of their electrostatic environment. Consequently, the number of protons bound to the biomolecule, and therefore the overall charge of the system, fluctuates during the simulation. To avoid artifacts associated with a non-neutral simulation system, we introduce an approach to maintain neutrality of the simulation box in constant pH molecular dynamics simulations, while maintaining an accurate description of all protonation fluctuations. Specifically, we introduce a proton buffer that, like a buffer in experiment, can exchange protons with the biomolecule enabling its charge to fluctuate. To keep the total charge of the system constant, the uptake and release of protons by the buffer are coupled to the titration of the biomolecule with a constraint. We find that, because the fluctuation of the total charge (number of protons) of a typical biomolecule is much smaller than the number of titratable sites of the biomolecule, the number of buffer sites required to maintain overall charge neutrality without compromising the charge fluctuations of the biomolecule, is typically much smaller than the number of titratable sites, implying markedly enhanced simulation and sampling efficiency.
Force field parameters for the hydronium ions, the parameters of the biasing potential Udwp, the coefficients of the polynomial fits to ΔGFF, dynamics of deprotonation of a single titratable site with different heights of the outer walls of the potential Udwp, charge conservation of the constraint approach, and the convergence of the protonation macrostate free energies in our simulations at pH = pKa (PDF)