Charge Regulation Triggers Condensation of Short Oligopeptides to Polyelectrolytes

Abstract

Electrostatic interactions between charged macromolecules are ubiquitous in biological systems, and they are important also in materials design. Attraction between oppositely charged molecules is often interpreted as if the molecules had a fixed charge, which is not affected by their interaction. Less commonly, charge regulation is invoked to interpret such interactions, i.e., a change of the charge state in response to a change of the local environment. Although some theoretical and simulation studies suggest that charge regulation plays an important role in intermolecular interactions, experimental evidence supporting such a view is very scarce. In the current study, we used a model system, composed of a long polyanion interacting with cationic oligolysines, containing up to 8 lysine residues. We showed using both simulations and experiments that while these lysines are only weakly charged in the absence of the polyanion, they charge up and condense on the polycations if the pH is close to the pK_a of the lysine side chains. We show that the lysines coexist in two distinct populations within the same solution: (1) practically nonionized and free in solution; (2) highly ionized and condensed on the polyanion. Using this model system, we demonstrate under what conditions charge regulation plays a significant role in the interactions of oppositely charged macromolecules and generalize our findings beyond the specific system used here.

Figure 1

Overview of the investigated system: long anionic poly(methacrylic acid) (PMAA) and short cationic oligolysines (Lys_n). The chemical structures on the left show the different ionization states. The schematic next to each chemical structure represents the coarse-grained model that we used for the corresponding chain. Color code: gray and black = backbone groups; orange = nonionized acidic groups; red = ionized acidic groups; cyan = nonionized basic groups; blue = ionized basic groups; green = small anion; yellow = small cation.

Figure 2

Degree of ionization of Lys_n with n ∈{2, 4, 8} as a function of pH. (a) Simulation results for Lys_n in the absence of PMAA (empty symbols) and Lys_n in the presence of PMAA (filled symbols). (b) Simulations (circles) and NMR results (crosses) for Lys₈ in the absence of PMAA (empty symbols) and Lys₈ in presence of PMAA (filled symbols).

Figure 3

Simulation results for the ionization degree of Lys_n (top row) and the relative population of lysines (bottom row) as a function of their distance to the nearest bead of the PMAA. Each point in the bottom panel corresponds to the distance between the center of mass of one oligolysine molecule and the closest PMAA bead in each of the simulation frames.

Figure 4

Simulation snapshots of the Lys₈ interacting with PMAA. At pH = 10.0 (≲ pK_A^eff) the lysines are highly ionized and condensed on the PMAA chain, and at pH = 12.5 (≳ pK_A^eff) the lysines are weakly ionized and free in solution. However, at pH = 11.5 (≈ pK_A^eff), the two different ionization states coexist in the solution. Color code is the same as that in Figure 1.

Figure 5

Condensation, swelling of the PMAA for Lys_n with n ∈{2, 4, 8} and diffusion of Lys₈ in the presence and absence of PMAA as a function of pH. (a) Fraction of Lys_n condensed on the PMAA, obtained from simulations. (b) End-to-end distance of PMAA in the presence of Lys_n, obtained from simulations. (c) Diffusion coefficient of Lys₈ and PMAA in a common solution (labeled as Lys₈ + PMAA), compared to Lys₈ in the absence of PMAA, determined from DOSY NMR experiments.