Figure 1.

(A) A monovalent binding event between a receptor and ligand is characterized by a dissociation constant (K_d^inter) with units of concentration (M). (B) When the ligand is tethered to the receptor, the dissociation constant (K_d^intra) is now dimensionless and is related to K_d^inter by the effective molarity, M_eff (eq 1). (C) Analogous to (A) for a binding event between a protein and ligand. (D) Analogous to (B) for an intramolecular protein-ligand binding event. In this case, however, the distance (d) between the two ends of the linker in the bound state is non-zero (unlike the case in (B)). (E) Dissociation of a bivalent ligand from a bivalent receptor. This process can be conceptualized as occurring in two steps: the first step (with dissociation constant 2K_d^intra*) is intramolecular, and the second step (with dissociation constant ¼K_d^inter) is intermolecular. The equation given provides a means of estimating M_eff from the observed dissociation constant (K_d^avidity) and the intermolecular dissociation constant (K_d^inter) by assuming that the dissociation constant for the first step is equivalent to the product of a statistical factor of 2 and K_d^intra (defined in (D); i.e., this procedure assumes that K_d^intra* = K_d^intra). This assumption is often quite poor because of complications arising from the influence of binding at one site on binding at the other site (e.g., cooperativity between binding sites, enthalpy/entropy compensation).⁴