Ion-Specific Potential of Mean Force Between two Aqueous Proteins

There is a considerable effort in the literature trying to calculate the mean force between globular proteins (and colloidal particles). To this purpose, we used here the ion-specific Poisson-Boltzmann (PB) equation that presents good results of ionic concentration profiles around a macroion, especially for salt solutions containing monovalent ions. The ion-specific PB equation includes not only electrostatic interactions but also dispersion potentials, originated from polarizabilities of ions and proteins. This enables us to predict ion-specific properties of colloidal systems. Results are in agreement with the experimental observed Hofmeister series. The main contribution of this paper is the use of a differential approach to calculate the mean force between aqueous proteins and colloidal particles instead of the classical quadrature approach. The integral expressions needed to calculate the mean force, potential of mean force and second virial coefficients have been avoided using this new numerical procedure. These integrals were transformed in a set of first order partial differential equations solved simultaneously with the ion-specific PB equation. Resulted expressions were written in bispherical coordinates, and then numerically solved through finite volume method. This simultaneous approach presents more accuracy in the calculation of the mean force in comparison with the classical approach, where the potential profile is obtained by solving the PB equation, and mean force is calculated afterwards. Important thermodynamic properties are obtained from the mean force (and consequently, from the potential of mean force), e. g., osmotic second virial coefficients and phase diagrams. These thermodynamic properties are related to protein aggregation, essential in biotechnology and pharmaceutical industries.