Competitive sorption of mono- versus di-valent ions by highly charged globular macromolecules

TL;DR

This paper develops and compares theoretical models to predict the competitive binding of mono- and di-valent ions to highly charged macromolecules, validated by computer simulations of dendritic polyglycerol sulfate.

Contribution

It introduces combined electrostatic models to accurately predict ion sorption ratios for charged macromolecules, validated with simulation data.

Findings

Models accurately predict ion binding ratios.

Simulation data supports model validity.

Effective charge varies with divalent ion concentration.

Abstract

When a highly charged globular macromolecule, such as a dendritic polyelectrolyte or charged nanogel, is immersed into a physiological electrolyte solution, monovalent and divalent counterions from the solution bind to the macromolecule in a certain ratio and thereby almost completely electroneutralize it. For charged macromolecules in biological media, the number ratio of bound mono- versus di-valent ions is decisive for the desired function. A theoretical prediction of such a sorption ratio is challenging because of the competition of electrostatic (valency), ion-specific, and binding saturation effects. Here, we devise and discuss a few approximate models to predict such an equilibrium sorption ratio by extending and combining established electrostatic binding theories such as Donnan, Langmuir, Manning as well as Poisson-Boltzmann approaches, to systematically study the competitive uptake of mono- and di-valent counterions by the macromolecule. We compare and fit our models to coarse-grained (implicit-solvent) computer simulation data of the globular polyelectrolyte dendritic polyglycerol sulfate (dPGS) in salt solutions of mixed valencies. The dPGS has high potential to serve in macromolecular carrier applications in biological systems and at the same time constitutes a good model system for a highly charged macromolecule. We finally use the simulation-informed models to extrapolate and predict electrostatic features such as the effective charge as a function of the divalent ion concentration for a wide range of dPGS generations (sizes).