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

We study the behavior of two macroions with dissociable charge groups, regulated by local variables such as pH and electrostatic potential, immersed in a monovalent 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 by the proper free-energy function for each of the macroions, while the coupling between the charges is evaluated on the approximate Debye-Hückel 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 proteinlike macroions, generalizing the form and magnitude of the Kirkwood-Schumaker interaction.