We present a set of Langmuir binding models in which electrostatic cooperativity effects to protein sorption is incorporated in the spirit of Guoy-Chapman-Stern models, where the global substrate (microgel) charge state is modified by bound reactants (charged proteins). Application of this approach to lysozyme sorption to oppositely charged core-shell microgels allows us to extract the intrinsic, binding affinity of the protein to the gel, which is salt concentration independent and mostly hydrophobic in nature. The total binding affinity is found to be mainly electrostatic in nature, changes many orders of magnitude during the sorption process, and is significantly influenced by osmotic deswelling effects. The intrinsic binding affinity is determined to be about 7 k(B)T for our system. We additionally show that Langmuir binding models and those based on excluded-volume interactions are formally equivalent for low to moderate protein packing, if the nature of the bound state is consistently defined. Having appreciated this, a more quantitative interpretation of binding isotherms in terms of separate physical interactions is possible in the future for a wide variety of experimental approaches.

We present a comprehensive study of the interaction of human serum albumin (HSA) with poly(acrylic acid) (PAA; number average degree of polymerization: 25) in aqueous solution. The interaction of HSA with PAA is studied in dilute solution as a function of the concentration of added salt (20-100 mM) and temperature (25-37 °C). Isothermal titration calorimetry (ITC) is used to analyze the interaction and to determine the binding constant and related thermodynamic data. It is found that only one PAA chain is bound per HSA molecule. The free energy of binding ΔGb increases with temperature significantly. ΔGb decreases with increasing salt concentration and is dominated by entropic contributions due to the release of bound counterions. Coarse-grained Langevin computer simulations treating the counterions in an explicit manner are used to study the process of binding in detail. These simulations demonstrate that the PAA chains are bound in the Sudlow II site of HSA. Moreover, ΔGb is calculated from the simulations and found to be in very good agreement with the measured data. The simulations demonstrate clearly that the driving force of binding is the release of counterions in full agreement with the ITC-data.

We study the pair complexation of a single, highly charged polyelectrolyte (PE) chain (of 25 or 50 monomers) with like-charged patchy protein models (CPPMs) by means of implicit-solvent, explicit-salt Langevin dynamics computer simulations. Our previously introduced set of CPPMs embraces well-defined zero-, one-, and two-patched spherical globules each of the same net charge and (nanometer) size with mono- and multipole moments comparable to those of globular proteins with similar size. We observe large binding affinities between the CPPM and the like-charged PE in the tens of the thermal energy, kBT, that are favored by decreasing salt concentration and increasing charge of the patch(es). Our systematic analysis shows a clear correlation between the distance-resolved potentials of mean force, the number of ions released from the PE, and CPPM orientation effects. In particular, we find a novel two-site binding behavior for PEs in the case of two-patched CPPMs, where intermediate metastable complex structures are formed. In order to describe the salt-dependence of the binding affinity for mainly dipolar (one-patched) CPPMs, we introduce a combined counterion-release/Debye-Hückel model that quantitatively captures the essential physics of electrostatic complexation in our systems.