Charge regulation in ionic solutions: thermal fluctuations and Kirkwood-Schumaker interaction

TL;DR

This paper investigates how charge regulation and thermal fluctuations influence interactions between macroions in ionic solutions, revealing conditions for attraction between like-charged macroions and extending the Kirkwood-Schumaker theory.

Contribution

It provides an analytical and numerical framework for charge correlation functions and fluctuation forces in macroions with dissociable charges, generalizing the Kirkwood-Schumaker interaction.

Findings

Strong attraction occurs near zero charge due to anticorrelated fluctuations.

Charge fluctuations can lead to attraction between like-charged macroions.

The theory is applied to protein-like macroions, extending existing models.

Abstract

We study the behavior of two macroions with dissociable charge groups, regulated by local variables such as pH and electrostatic potential, immersed in a mono-valent salt solution, considering cases where the net charge can either change sign or remain of the same sign depending on these local parameters. The charge regulation, in both cases, is described with the proper free energy function for each of the macroions, while the coupling between the charges is evaluated on the approximate Debye-H\"uckel level. The charge correlation functions and the ensuing charge fluctuation forces are calculated analytically and numerically. Strong attraction between like-charged macroions is found close to the point of zero charge, specifically due to asymmetric, anticorrelated charge fluctuations of the macroion charges. The general theory is then implemented for a system of two protein-like macroions, generalizing the form and magnitude of the Kirkwood-Schumaker interaction.