State diagrams and state populations for two-site allosteric binding models that include multiple protein conformations. (A–C, left) Models for proteins occupying one (A), two (B), or three (C) conformations. States Rij, Sij, and Tij designate molecules in conformations R, S, and T with i and j ligands bound to sites I and II, respectively (i, j = 0 or 1). KIR, KIS, and KIT represent microscopic equilibrium association constants for site I when the macromolecule is in the R, S, and T conformations, respectively. KIIR, KIIS, and KIIT are the corresponding constants for site II. Cooperativity factors fR, fS, and fT represent the fold change in binding to a site when the adjacent site is occupied and the protein is in the indicated conformation. MRS and MST are the conformational equilibrium constants for the equilibria between states R00 and S00 and between states S00 and T00, respectively. (A–C, right) Expressions for state populations for models shown on the left and relation between model parameters and fit parameters {p0, p1, p2}. States and expressions are color coded black, red, and blue for zero, one and two bound ligands, respectively.
