Interaction of Polyanionic and Polycationic Brushes with Globular Proteins and Protein-like Nanocolloids

Abstract

A large number of experimental studies have demonstrated that globular proteins can be absorbed from the solution by both polycationic and polyanionic brushes when the net charge of protein globules is of the same or of the opposite sign with respect to that of brush-forming polyelectrolyte chains. Here, we overview the results of experimental studies on interactions between globular proteins and polycationic or polyanionic brushes, and present a self-consistent field theoretical model that allows us to account for the asymmetry of interactions of protein-like nanocolloid particles comprising weak (pH-sensitive) cationic and anionic groups with a positively or negatively charged polyelectrolyte brush. The position-dependent insertion free energy and the net charge of the particle are calculated. The theoretical model predicts that if the numbers of cationic and anionic ionizable groups of the protein are approximately equal, then the interaction patterns for both cationic and anionic brushes at equal offset on the "wrong side" from the isoelectric point (IEP), i.e., when the particle and the brush charge are of the same sign, are similar. An essential asymmetry in interactions of particles with polycationic and polyanionic brushes is predicted when fractions of cationic and anionic groups differ significantly. That is, at a pH above IEP, the anionic brush better absorbs negatively charged particles with a larger fraction of ionizable cationic groups and vice versa.

Keywords: Poisson-Boltzmann theory; electrostatic interactions; ionic strength; polyelectrolyte brushes; protein absorption.

Figure 1

Cross-sections of the 2D profiles of the insertion free energy $\Delta F_{ion}(z,|\delta p{H}_b\left|\right)$ (a) and net charge $Q(z,|\delta p{H}_b\left|\right)$ (b) for polycationic/polyanionic brush at $f=0.5$; $\Delta =(p{K}_{+}-p{K}_{-})/2=0$ and three different salt concentrations $C_s=c_s{a}^3$, where $c_s$ is the number concentration of cations and anions of low molecular weight salt, and a is the monomer unit length for the brush-forming chains. The brush parameters are polymerization degree of the brush-forming chains $N=300$, reduced surface area per chain $S=s/a^2=100$, and fraction of permanently (positively or negatively) charged monomer units $\alpha =0.5$. Black circles in panel (a) correspond to the coordinate of vanishing of the free energy, while black circles in panel (b) correspond to the charge inversion points. The red plane is a cross-section along the vertical axis at zero.

Figure 2

Cross-sections of the 2D profiles of the insertion free energy $\Delta F_{ion}(z,|\delta p{H}_b\left|\right)$ (a) and net charge $Q(z,|\delta p{H}_b\left|\right)$ (b) for polycationic/polyanionic brush at $f=0.5$ and salt concentration $C_s=0.001$ and two different values of $|\Delta =(p{K}_{+}-p{K}_{-})/2|=$ (0; 1) The brush parameters are as in Figure 1. Black circle in panel (a) corresponds to the coordinate of vanishing of the free energy, and black circles in the panel (b) correspond to the charge inversion points. The red plane is a cross-section along the vertical axis at zero.

Figure 3

Cross-sections of the 2D profiles of the insertion free energy $\Delta F_{ion}(z,|\delta p{H}_b\left|\right)$ (a) and net charge $Q(z,|\delta p{H}_b\left|\right)$ (b) for polyanionic (solid lines) and polycationic (dashed lines) brush at $f=0.8$, and three different salt concentrations. $p{K}_{+}=p{K}_{-}=7$. The brush parameters are the same as in Figure 1. Colored circles in the panel (b) correspond to the charge inversion points. The yellow plane is a cross-section along the vertical axis at zero.

Figure 4

Cross-sections of the 2D profiles of the insertion free energy $\Delta F_{ion}(z,|\delta p{H}_b\left|\right)$ (a) and net charge $Q(z,|\delta p{H}_b\left|\right)$ (b) for polyanionic (solid lines) and polycationic (dashed lines) brush at $f=0.8$, and three different salt concentrations. $p{K}_{+}=9, p{K}_{-}=5$. The brush parameters are the same as in Figure 1. Colored circles in the panel (b) correspond to the charge inversion points. The yellow plane is a cross-section along the vertical axis at zero.

Figure 5

Cross-sections of the 2D profiles of the insertion free energy $\Delta F_{ion}(z,|\delta p{H}_b\left|\right)$ (a) and net charge $Q(z,|\delta p{H}_b\left|\right)$ (b) for polyanionic (solid lines) and polycationic (dashed lines) brush at $f=0.8$, and three different salt concentrations. $p{K}_{+}=5, p{K}_{-}=9$. The brush parameters are the same as in Figure 1. Black circles in the panel (b) correspond to the charge inversion points. The red plane is a cross-section along the vertical axis at zero.