Structural identifiability analysis of parameters for three-site allosteric binding model. (A) Relation between mean number of bound ligands (v) and free ligand concentration (x) for the model in Fig. 4 A. Terms are color coded as in Fig. 4. (B) Linearized form of binding equation from A. (C) Matrix representation of system of equations obtained by evaluating the equation in B at seven ligand concentrations x1 through x7. Dashed red and blue boxes indicate identical columns in design matrix and corresponding parameters in parameter vector derived from states with one and two bound ligands, respectively. (D) Reduced matrix equation obtained by summing parameters KI, KII, and KIII from C into a single parameter and by summing parameters fI(II) KI KII, fI(III) KI KIII, and fII(III) KII KIII into a single parameter. This operation causes the identical red and blue columns to collapse into a single red and single blue column in the reduced design matrix. (E) General form of the reduced matrix equation in D, in which model-specific parameters are replaced by model-independent fit parameters {p1, p2, p3}.
