Dendritic polyelectrolytes with monovalent and divalent counterions: the charge regulation effect and counterion...

The charge regulation and the release of counterions are extremely important and substantial in determining the charge state of polyelectrolytes and the interaction between polyelectrolytes and proteins. Going beyond monovalent to multivalent cations, it is well-known that the effects of ions are qualitatively different. Therefore, the well-accepted descriptions of the charge regulation and the counterion release based on monovalent ions do not immediately apply to systems with multivalent ions. Here, we study the key structural and electrostatic features of charged dendrimers at hand of the pharmaceutically important dendritic polyglycerol sulfate (dPGS) macromolecule equilibrated with monovalent and divalent salts by molecular dynamics (MD) simulations. Following a simple but accurate scheme to determine its effective radius, the counterion condensed layer of the dPGS is determined with high accuracy and we observe the sequential replacement of condensed monovalent cations (MCs) to divalent cations (DCs) rendering a smaller dPGS effective charge versus the DC concentration. We resolve and track the release of counterions on the dPGS along its binding pathway with the plasma protein Human Serum Albumin (HSA). We find that the release of MCs remains favorable for the complexation leading to a considerable amount of release entropy as the driving force for complexation. The release of DCs only occurs above a certain DC concentration with a comparably smaller number of released ions than MCs. Its contribution to the binding free energy is small indicating a subtle cancellation between the entropy gain in releasing DCs and the enthalpy penalty from dissociating DCs from the dendrimer.