Charge Regulation Enables Uptake of Ampholytes to Polyelectrolyte Brushes

Uptake of proteins and ampholytic solutes into polyelectrolyte brushes underlies some biological processes and also applications in sensing or biomedicine. Especially uptake on the "wrong" side of the isoelectric point (pI) remains puzzling, with charge regulation and solute patchiness proposed as possible mechanisms. Using a hierarchy of approximations, coarse-grained molecular simulations, self-consistent mean-field, and a simple phenomenological model, we investigated the uptake of model ampholytic solutes into polyanionic brushes across varying pH, salt concentrations, pK_a values, and peptide sequences. In a narrow pH range on the wrong side of pI, charge regulation enables uptake of the ampholytes by inducing charge inversion so that they become positively charged in the brush despite being negatively charged in the bulk. This charge inversion can be calculated from the pH difference between the brush and the bulk, which is related to the Donnan potential. It is strongest for ampholytes with small differences between acidic and basic pK_a values and decreases with increasing salt. Our phenomenological model reproduces the universal effect of charge regulation promoting ampholyte uptake into brushes but fails to be quantitative. The mean field model is close to explicit simulations for alternating sequences, but fails to describe the effect of charge patchiness, which is only captured by explicit simulations. Thus, our phenomenological framework offers a practical rule of thumb for estimating uptake from experimentally accessible parameters without sophisticated calculations. Deviations from this rule of thumb for complex ampholytes, such as proteins or peptides with patterned charge sequences, are captured only by explicit simulations.