Structural identifiability analysis of parameters for two-site binding models. (A) Relation between mean number of bound ligands (v) and free ligand concentration (x) for two-site allosteric model from Fig. 1. Terms are color coded as in Fig. 1 B (bottom). (B) Linearized form of binding equation from A. (C) Synthetic total binding curve. The symbols v1, v2, and v3 represent the mean number of bound ligands at free ligand concentrations x1, x2, and x3. (D) System of equations obtained by evaluating equation in B at three ligand concentrations, as illustrated in C. (E) Matrix form of system of equations in D. Dashed red boxes indicate two identical columns in design matrix and corresponding parameters in parameter vector. (F) Reduced matrix equation obtained by combining parameters KI and KII into a single parameter: KI + KII. This procedure collapses the two identical red columns in the design matrix into a single column. (G) General form of reduced matrix equation in F, in which model-specific parameters {KI + KII, f KI KII} are replaced by model-independent fit parameters {p1, p2}. (H) Expressions for state populations for model in Fig. 1 A and relation between model parameters and fit parameters: p1 = KI + KII and p2 = f KI KII.
