We use coarse-grained simulations to study the impact of charge regulation on the complexation of a weak polyacid and a strong polycation. Comparing an isolated polyacid with the polyelectrolyte pair, we demonstrate that charge regulation leads to a significant enhancement of the ionization. Furthermore, our simulations unveil that the condensation of isolated chains into a tightly bound complex happens in a discontinuous, first-order like transition as the pH value is varied. These results are corroborated using enhanced sampling calculations, which reveal the presence of a free energy barrier at the transition pH. To quantify the observed charge regulation effects, we compare binding constants of the complex, calculated under charge-regulating and constant charge conditions. We find that charge regulation significantly alters the binding affinity of the complex, emphasizing the importance of including the proper acid-base equilibria in a theoretical description of weak polyelectrolyte complexation.
Beyer et al. (Tue,) studied this question.