Computing pKa Shifts Using Traditional Molecular Dynamics: Example of Acid-Base Indicator Dyes in Organized Solutions

Estimation of Nanoparticle's Surface Electrostatic Potential in Solution Using Acid-Base Molecular Probes I: In Silico Implementation for Surfactant Micelles

Surface electrostatic potential Ψ is a key characteristic of colloid particles. Since the surface of the particles adsorbs various compounds and facilitates chemical reactions between them, Ψ largely affects the properties of adsorbed reactants and governs the flow of chemical reactions occurring between them. One of the most popular methods for estimating Ψ in hydrophilic colloids, such as micellar surfactant solutions and related systems, is the application of molecular probes, predominantly acid-base indicator dyes. The Ψ value is calculated from the difference of the probe's indices of the apparent acidity constant between the examined colloid solution and, usually, some other colloid solution with noncharged particles. Here, we show how to implement this method in silico using alchemical free energy calculations within the framework of molecular dynamics simulations. The proposed implementation is tested on surfactant micelles and is shown to predict experimental Ψ values with quantitative accuracy depending on the kind of surfactant. The sources of errors in the method are discussed, and recommendations for its application are given.

Estimation of Nanoparticle's Surface Electrostatic Potential in Solution Using Acid-Base Molecular Probes II: Insight from Atomistic Simulations of Micelles

Exploiting acid-base indicators as molecular probes is one of the most popular methods for determining the surface electrostatic potential Ψ in hydrophilic colloids like micellar surfactant solutions and related systems. Specifically, the indicator's apparent acidity constant index is measured in the colloid solution of interest and, as a rule, in a nonionic surfactant solution; the difference between the two is proportional to Ψ. Despite the widespread use of this approach, a major problem remains unresolved, namely, the dissimilarity of Ψ values obtained with different indicators for the same system. The common point of view recognizes the effect of several factors (the choice of the nonionic surfactant, the probe's localization, and the degree of hydration of micellar pseudophase) but does not allow to quantitatively assess their impact and decide which indicator reports the most correct Ψ value. Here, based on the ability to predict the reported Ψ values in silico, we examined the role of these factors using molecular dynamics simulations for five probes and two surfactants. The probe's hydration in the Stern layer was found responsible for approximately half of the dissimilarity range. The probe's localization is found important but hard to quantify because of the irregular structure of the Stern layer. The most accurate indicators among the examined set were identified. Supplementing experiments on measuring Ψ with molecular dynamics simulation is proposed as a way of improving the efficacy of the indicator method: the simulations can guide the choice of the most suitable probe and nonionic surfactant for the given nanoparticles.

Correction Schemes for Absolute Binding Free Energies Involving Lipid Bilayers

Absolute binding free-energy (ABFE) calculations are playing an increasing role in drug design, especially as they can be performed on a range of disparate compounds and direct comparisons between them can be made. It is, however, especially important to ensure that they are as accurate as possible, as unlike relative binding free-energy (RBFE) calculations, one does not benefit as much from a cancellation of errors during the calculations. In most modern implementations of ABFE calculations, a particle mesh Ewald scheme is typically used to treat the electrostatic contribution to the free energy. A central requirement of such schemes is that the box preserves neutrality throughout the calculation. There are many ways to deal with this problem that have been discussed over the years ranging from a neutralizing plasma with a post hoc correction term through to a simple co-alchemical ion within the same box. The post hoc correction approach is the most widespread. However, the vast majority of these studies have been applied to a soluble protein in a homogeneous solvent (water or salt solution). In this work, we explore which of the more common approaches would be the most suitable for a simulation box with a lipid bilayer within it. We further develop the idea of the so-called Rocklin correction for lipid-bilayer systems and show how such a correction could work. However, we also show that it will be difficult to make this generalizable in a practical way and thus we conclude that the use of a “co-alchemical ion” is the most useful approach for simulations involving lipid membrane systems.

Morphology of Ionic Micelles as Studied by Numerical Solution of the Poisson Equation

The existing concepts of the ionic micelle structure were specified. It was noted that the composition of dispersed phase particles in a liquid dispersion medium should necessarily include adsorbed counterions rigidly bound to these particles. By numerical solution of the Poisson equation for the two most often used approximations, the Poisson-Boltzmann (PB) model and the Jellium-approximation (JA), the electric potential decay from the Stern potential of dispersed phase particles was defined. A new methodological approach to analyze the reaction of micelle potential decay based on small variability of the CMC value was proposed. It made possible to determine the dimension parameter, which in the presence of weak thermal effects approximately corresponds to the micelle hydrodynamic radius, and to calculate the electrokinetic potential of micelles. The results of theoretical calculations were compared with our previous experimental data on the thickness of the SDS micelle hydrophilic layer obtained by SAXS. A good agreement between the calculated and measured values was obtained, and it was noted that for low concentrations the experimental values are more correctly described by the PB model, but for concentrations greater than 100 mM the JA model is more preferable. It was found that the slipping plane is located near the outer Stern plane and is separated from it only by a few molecular layers of water. The influence stronger than the thermal one can shift the slipping plane closer to the micelle core. Accordingly, the smallest hydrodynamic micelle size is determined by the outer Stern plane. The results of our work allowed us to conclude that the micelle is not something soft and watery, but according to its specified structure, it is a more solid-like particle than was previously assumed. The proposed approach can be extended to investigate other effects of a physicochemical nature, in particular, those observed with the addition of an external electrolyte or nanoparticles.