Grand-Reaction Method for Simulations of Ionization Equilibria Coupled to Ion Partitioning

Abstract

We developed a new method for coarse-grained simulations of acid-base equilibria in a system coupled to a reservoir at a given pH and concentration of added salt, that we term the Grand-reaction method. More generally, it can be used for simulations of any reactive system coupled to a reservoir of a known composition. Conceptually, it can be regarded as an extension of the reaction ensemble, combining explicit simulations we showed that neglecting one or the other eect may lead to erroneous predictions or misinterpretations of results. In contrast, the Grand-reaction method accounts for both eects on the results and allows us to quantify them. Finally, we outline possible extensions and generalizations of the method and provide a set of guidelines for its safe application by a broad community of users.

Curvature effects in charge-regulated lipid bilayers

“…Even in the most accurate parametrization of the lipid molecular force fields that take into account the dissociation state of the lipid headgroup through the partial charges, the charge regulation, i.e., the dependence of the dissociation state on the local bathing solution conditions, is usually not considered [64]. To include the effects discussed in our paper one would need to implement the charge dissociation reactions explicitly into the simulation scheme along the lines of recent advances in the simulation techniques for reaction ensembles [65,66]. Inclusion of the explicit charge regulation model into the detailed mean-field electrostatic theory applied to a curved phospholipid bilayer membrane allowed us to uncover and analyse several effects that have heretofore remained outside the electrostatic renormalization of the membrane mechanical properties [37].…”

Curvature effects in charge-regulated lipid bilayers

“…Even in the most accurate parametrization of the lipid molecular force fields that take into account the dissociation state of the lipid headgroup through the partial charges, the charge regulation, i.e., the dependence of the dissociation state on the local bathing solution conditions, is usually not considered 66 . To include the effects discussed in our paper one would need to implement the charge dissociation reactions explicitly into the simulation scheme along the lines of recent advances in the simulation techniques for reaction ensembles 44,67 . Inclusion of the explicit charge regulation into the detailed mean-field electrostatic theory applied to a curved phospholipid bilayer membrane allowed us to uncover and analyse several effects that have heretofore remained outside the paradigm of electrostatic renormalization of the membrane mechanical properties 37 .…”

“…, p = protons, ions) is model specific, 14 but can be written as a sum of α = Δ g + μ = Δ g + k B T ln a p where Δ g is the dissociation free energy difference, while the chemical potential μ = k B T ln a p of the dissociation product is expressed through the absolute activity, a p , that contains also the excess part dependent on the contribution of electrostatic interactions, see ref. 44. On the mean-field PB level the chemical potential is given by the ideal gas form, which does not take into account the electrostatic interactions, with the activity proportional to the concentration.…”

Charge symmetry broken complex coacervation

“…Finally, recent advances in the simulations of acid-base equilibria in systems coupled to a reservoir with a fixed pH, based either on a hybrid Monte Carlo method to resolve the charges of individual surface groups [40], on the grand-reaction method for coarse-grained simulations of acid-base equilibria with a fixed pH reservoir and salt concentration [41], or simulating the pH effects with classical coarse-grained molecular dynamics simulations [42], could in principle provide a proper background to different analytical approaches and hopefully elucidate the reality of the predicted phenomena. The comparison with experiments, in which other types of interactions and the notoriously difficult solvent effects come into play, poses another challenge that will have to be faced in the future.…”