bindingcurves

Binding curves describe how the fraction of binding sites occupied by a ligand, or the observed biological response, changes with ligand concentration. They are used to characterize interactions between receptors, enzymes, and ligands in biochemistry, pharmacology, and biophysics.

A simple model is the Langmuir isotherm: fraction bound equals [L]/(Kd + [L]), where Kd is the dissociation constant. Kd reflects affinity; smaller values indicate tighter binding. In pharmacology, potency is often summarized by EC50, the concentration producing half-maximal effect. For cooperative binding, the Hill equation is employed: Y = [L]^n / (Kd^n + [L]^n), with n the Hill coefficient corresponding to cooperativity. Bmax denotes the maximum binding capacity or total number of binding sites.

Binding curves are generated by titrating the ligand and measuring bound ligand or functional response, using techniques such as radioligand assays, fluorescence polarization, surface plasmon resonance, isothermal titration calorimetry, or thermal shift assays. Data are analyzed by nonlinear regression to estimate parameters (Kd, Bmax, EC50, Hill n). The choice of model depends on system complexity; multi-site or allosteric interactions may require more elaborate fits.

Binding curves provide estimates of affinity, capacity, and cooperativity, informing drug discovery, receptor characterization, and enzymology. They assume equilibrium and known stoichiometry; deviations due to competition, allostery, or experimental artifacts can affect interpretation. Kinetic binding curves, showing association and dissociation over time, and thermodynamic analyses complement equilibrium curves.