Analysis of the Equilibrium Distribution of Ligands in Heterogeneous Media-Approaches and Pitfalls

The equilibrium distribution of small molecules (ligands) between binding agents in heterogeneous media is an important property that determines their activity. Heterogeneous systems containing proteins and lipid membranes are particularly relevant due to their prevalence in biological systems, and their importance to ligand distribution, which, in turn, is crucial to ligand's availability and biological activity. In this work, we review several approaches and formalisms for the analysis of the equilibrium distribution of ligands in the presence of proteins, lipid membranes, or both. Special attention is given to common pitfalls in the analysis, with the establishment of the validity limits for the distinct approaches. Due to its widespread use, special attention is given to the characterization of ligand binding through the analysis of Stern-Volmer plots of protein fluorescence quenching. Systems of increasing complexity are considered, from proteins with single to multiple binding sites, from ligands interacting with proteins only to biomembranes containing lipid bilayers and membrane proteins. A new formalism is proposed, in which ligand binding is treated as a partition process, while considering the saturation of protein binding sites. This formalism is particularly useful for the characterization of interaction with membrane proteins.