Allosteric Modulation of Membrane Proteins by Small Low-Affinity Ligands

Membrane proteins may respond to a variety of ligands under an applied external stimulus. These ligands include small low-affinity molecules that account for functional effects in the mM range. Understanding the modulation of protein function by low-affinity ligands requires characterizing their atomic-level interactions under dilution, challenging the current resolution of theoretical and experimental routines. Part of the problem derives from the fact that small low-affinity ligands may interact with multiple sites of a membrane protein in a highly degenerate manner to a degree that it is better conceived as a partition phenomenon, hard to track at the molecular interface of the protein. Looking for new developments in the field, we rely on the classic two-state Boltzmann model to devise a novel theoretical description of the allosteric modulation mechanism of membrane proteins in the presence of small low-affinity ligands and external stimuli. Free energy stability of the partition process and its energetic influence on the protein coupling with the external stimulus are quantified. The outcome is a simple formulation that allows the description of the equilibrium shifts of the protein in terms of the grand-canonical partition function of the ligand at dilute concentrations. The model's predictions of the spatial distribution and response probability shift across a variety of ligand concentrations, and thermodynamic conjugates can be directly compared to macroscopic measurements, making it especially useful to interpret experimental data at the atomic level. Illustration and discussion of the theory is shown in the context of general anesthetics and voltage-gated channels for which structural data are available.