Polyelectrolyte Brush Interacting with Ampholytic Nanoparticles as Coarse-Grained Models of Globular Proteins: Poisson-Boltzmann Theory

The self-consistent field Poisson-Boltzmann frameworkisapplied to analyze equilibrium partitioning of ampholytic nanoparticles(NPs) between buffer solution and polyelectrolyte (PE) polyanionicbrush. We demonstrate that depending on pH and salt concentrationin the buffer solution, interactions between ionizable (acidic andbasic) groups on the NP surface and electrostatic field created byPE brush may either lead to the spontaneous uptake of NPs or createan electrostatic potential barrier, preventing the penetration ofNPs inside PE brush. The capability of PE brush to absorb or repelNPs is determined by the shape of the insertion free energy that iscalculated as a function of NP distance from the grafting surface.It is demonstrated that, at a pH value below or slightly above theisoelectric point (IEP), the electrostatic free energy of the particleis negative inside the brush and absorption is thermodynamically favorable.In the latter case, the insertion free energy exhibits a local maximum(potential barrier) at the entrance to the brush. An increase in pHleads to the shallowing of the free energy minimum inside the brushand a concomitant increase in the free energy maximum, which may resultin kinetic hindering of NP uptake. Upon further increase in pH theinsertion free energy becomes positive, making NP absorption thermodynamicallyunfavorable. An increase in salt concentration diminishes the depthof the free energy minimum inside the brush and eventually leads toits disappearance. Hence, in accordance with existing experimentaldata our theory predicts that an increase in salt concentration suppressesabsorption of NPs (protein globules) by PE brush in the vicinity ofIEP. The interplay between electrostatic driving force for NP absorptionand osmotic repelling force (proportional to NP volume) indicatesthat for large NPs with relatively small number of ionizable groupsosmotic repulsion overcomes electrostatic attraction preventing therebyabsorption of NPs by PE brush.