# Charge Regulation Enables Uptake of Ampholytes to Polyelectrolyte Brushes

## TL;DR

The paper explains how ampholytes can be taken up into polyelectrolyte brushes even when they are negatively charged in the bulk, due to charge regulation and pH differences.

## Contribution

The study introduces a phenomenological model to estimate ampholyte uptake based on experimentally accessible parameters.

## Key findings

- Charge regulation enables uptake of ampholytes on the 'wrong' side of the isoelectric point via charge inversion.
- The effect is strongest for ampholytes with small pKa differences and decreases with increasing salt concentration.
- Explicit simulations are needed to capture deviations from the model for complex ampholytes like patterned peptides.

## Abstract

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.