Polyelectrolyte–protein complexation driven by charge regulation Fernando Luı ´s Barroso da Silva * ab and Bo J€ onsson b Received 30th January 2009, Accepted 13th May 2009 First published as an Advance Article on the web 15th June 2009 DOI: 10.1039/b902039j The interplay between the biocolloidal characteristics (especially size and charge), pH, salt concentration and the thermal energy results in a unique collection of mesoscopic forces of importance to the molecular organization and function in biological systems. By means of Monte Carlo simulations and semi-quantitative analysis in terms of perturbation theory, we describe a general electrostatic mechanism that gives attraction at low electrolyte concentrations. This charge regulation mechanism due to titrating amino acid residues is discussed in a purely electrostatic framework. The complexation data reported here for interaction between a polyelectrolyte chain and the proteins albumin, goat and bovine a-lactalbumin, b-lactoglobulin, insulin, k-casein, lysozyme and pectin methylesterase illustrate the importance of the charge regulation mechanism. Special attention is given to pH y pI where ion– dipole and charge regulation interactions could overcome the repulsive ion–ion interaction. By means of protein mutations, we confirm the importance of the charge regulation mechanism, and quantify when the complexation is dominated either by charge regulation or by the ion–dipole term. I. Introduction Although the Coulomb’s law is an old and clear physical concept known since 1785, when it is applied to (bio)colloidal systems a rich diversity of peculiar mechanisms come into play. The combination of its characteristics with the chemical properties of the colloidal constituents, pH and salt concentration results in a unique collection of interparticle forces of importance for molecular organization and function. 1–9 Despite different system geometries, electrostatic phenomena in macromolecular solutions are usually classified according to the coupling regime: 10–12 (a) weak coupling regime (wcr), where the counter-ions and added salt are monovalent particles screening the electrostatic interactions, and the system is char- acterized by repulsive forces between the charged macromole- cules (as given by the DLVO theory 13 ), and (b) strong coupling regime (scr), where multivalent ions give rise to attractive forces due to ion–ion correlation. 14–16 This is a somewhat simplified picture, since even in the wcr, anomalous behaviour, i.e. attrac- tion between like charged objects can be observed. We will focus here on biological systems in the weak coupling regime where attraction can be seen instead of the expected repulsive behaviour. The idea of such a phenomenon goes back to Kirkwood’s structure sensitive electrostatic forces, 17 where attractive forces between biomolecules arise from fluctuations in proton charge due to the acid–base equilibrium. The attraction is pH-dependent and a result of an intrinsic physical property of the macromolecule, the capacitance, determining its ability for charge regulation. 9,18–21 Employing different model systems and experimental conditions, we aim here to illustrate the charge regulation mechanism in some biomolecular systems in the weak coupling regime. The purpose of this work is twofold: (i) to demonstrate that the complexation between polyelectrolytes and protein molecules at their isoelectric point (pI) can occur by a purely electrostatic mechanism, and (ii) to quantify when the picture is dominated either by the charge regulation or by the ion– dipole term. II. Theoretical modelling Invoking a minimum set of parameters, a coarse-grained model within the continuum solvent framework has been devised and solved by Monte Carlo (MC) simulations. 22,23 In all the MC simulations, the charged species are confined inside an electro- neutral spherical cell as shown in Fig. 1, whose radius, R cell , is determined by the protein concentration c P . This corresponds to the so-called cell model. 24–26 The physical assumption behind the model is that the solution can be divided into cells, each con- taining one macromolecule [as seen in Fig. 1a (or one macro- molecule and a polyelectrolyte as seen in Fig. 1b)] and the accompanying electrolytes (counter-ions and added salt). There is no explicit interaction between different electroneutral cells. The only manner macromolecule–macromolecule interactions are taken into account is by the definition of R cell . Each mobile ion k with valency z k is treated explicitly as a hard sphere of radius R k , while the solvent is treated as a structureless dielectric medium characterized by a relative dielectric permittivity 3 s . The same uniform static dielectric permittivity 3 s is assigned to all charged species interior, including the macromolecule and the polyelectrolyte. 27–29 The macromolecule is a rigid body kept fixed at the center of the cell. The interaction potential energy between any two particles (or interaction sites) i and j (either a protein fixed charge, a mobile ion or a polyelectrolyte monomer) is given by, a Department of Physics and Chemistry, Faculty of Pharmaceutical Sciences at Ribeira˜o Preto – University of Sa˜o Paulo, Av. do caf e, s/no., 14040–903 Ribeira˜o Preto, SP, Brazil. E-mail: fernando@fcfrp.usp.br; Fax: +55 (16)3602 48 80; Tel: +55 (16)3602 42 19 b Department of Theoretical Chemistry, Chemical Center – University of Lund, POB 124, S-221 00 Lund, Sweden. E-mail: Bo.Jonsson@teokem. lu.se 2862 | Soft Matter , 2009, 5, 2862–2868 This journal is ª The Royal Society of Chemistry 2009 PAPER www.rsc.org/softmatter | Soft Matter