  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).
