Charge regulation and orientation dictate protein uptake into polyelectrolyte brushes

The phenomenon of charge regulation is of central importance in the interaction of many proteins with soft, electrically charged environments. Here, we used coarse-grained simulations to study the interaction of a globular protein-represented as a quadrupolar, charge-regulating nanoparticle-with a weak polyelectrolyte brush. Our simulations show that a quadrupolar nanoparticle interacting with a brush exhibits multistep complexation, producing double reionization jumps and distinct regimes of charge regulation as the nanoparticle penetrates the brush. In particular, strong local electrostatic fields induced by direct complexation with polymer strands yield nanoparticle charge states that decidedly differ from mean-field predictions based on the local pH alone. Moreover, we show that the nanoparticle orientation becomes a key degree of freedom governing the complexation: quadrupolar symmetry leads to angular locking near the brush surface, resulting in intricate orientational complexation pathways and characteristic kinks in the free-energy. All of these features represent beyond-mean-field coupling effects that arise from strongly localized charge clusters and cannot be described by simple multipole expansions or Poisson-Boltzmann approaches. Overall, our results highlight how higher-order charge asymmetries can profoundly influence the adsorption landscape and underscore the need to go beyond dipolar models when modeling realistic protein-brush interactions.