Equilibrium binding
Equilibrium binding refers to a state where, at any given concentration of ligand in the presence of a population of target proteins, and assuming that the concentration of ligand is not changing significantly over time as a result of clearance, a constant fraction of the target proteins are occupied by the ligand. A ligand binding curve – a plot of targets occupied versus ligand concentration – typically shows the concentration or fraction of targets occupied under equilibrium binding conditions, measured in a pharmacological assay in vitro where there is no clearance of ligand from the system.
When a ligand is added to a population of targets, the rate of formation of the complex between target proteins and ligand molecules is initially at its most rapid, with the rate of association of ligand with target protein (i.e. the rate of complex formation) determined by the concentrations of the unoccupied target protein and the ligand, and by the value for the association rate constant. As the concentration of complex continues to increase, the rate of complex formation slows because the concentration of unoccupied target protein becomes progressively smaller. At the same time, the rate of dissociation of the complex (i.e. the rate at which the complex breaks apart to yield free ligand and unoccupied protein target) increases, because the dissociation rate increases linearly with increasing concentration of complex, the rate depending upon the value of the dissociation rate constant. At some time point after adding ligand to target protein, the association rate will have slowed and the dissociation rate will have increased such that these two rates are equal. At that point, while ligand continues to associate and dissociate from the target protein, the fraction of the total population of target proteins occupied by ligand is no longer changing. This condition is referred to as equilibrium binding.
For most ligands, the fraction of targets occupied at equilibrium increases in a hyperbolic manner with increasing ligand concentration. The reason for this increase in the fraction of targets occupied at equilibrium is quite straightforward. At higher ligand concentrations, the association rate of the ligand with unoccupied targets is higher, because the association rate is equal to the product of the unbound ligand concentration, the unoccupied target concentration, and the association rate constant, kon. To achieve equilibrium binding, the dissociation rate therefore must also be higher, to match the increased association rate. The only way by which dissociation rate can increase is for the concentration of the complex at equilibrium to be higher, since dissociation rate equals the concentration of the complex multiplied by the dissociation rate contant, koff.
When performing an assay designed to yield a binding curve for a ligand, it is important to ensure that equilibrium binding has been reached before quantifying the fraction of targets occupied. While many ligands will reach binding equilibrium within seconds of being introduced to their targets, other ligands could take hours or even days to achieve binding equilibrium. This occurs most commonly with ligands that have low association rate constants for their target protein, or with ligands that have a very low KD value for their target, wherein the effective therapeutic dose may be very low and thus the concentration of the ligand at the target site may also be very low, resulting in a very slow association rate.
Assays designed to study binding behaviour at equilibrium are referred to as steady-state kinetics studies. In contrast, assays designed to study the kinetics of association and dissociation processes prior to equilibrium being attained are referred to as transient-state kinetics studies.
