Computing the pH-Dependent Thermodynamics of the Allostery between Dimerization and Palmitate Binding in β-Lactoglobulin

The study of pH-dependent allosteric processes presents a significant challenge, both experimentally and computationally. In this work, we apply the constant-pH molecular dynamics method to explore an interesting case of allostery involving protein-ligand binding and dimerization. As a model system, we use β-lactoglobulin (BLG), a small protein from bovine milk known to dimerize and bind palmitic acid in a hydrophobic pocket─both processes sensitive to pH. This study focuses on the holo form of BLG, and, when combined with our previous study of the apo form (da Rocha et al. <i>J. Chem. Theory Comput.</i> <b>2022</b> 18, 1982), completes the thermodynamic cycle of the allosteric process. The corresponding pH-dependent free energy profiles are obtained through the use of a thermodynamic linkage relation, avoiding the need of performing heavy computational calculations. Dimerization is found to be more favorable near the isoionic point, as observed in the apo form. Palmitate binding is found to be more favorable around pH 6-7, a biologically relevant pH range at which the gate covering the binding site is known to open. A pH-dependent measure of allosteric coupling is computed, showing that ligand binding and dimerization exhibit an antagonist relationship within the studied pH range of 3-8, with binding destabilizing dimerization and vice versa.