Canonical form of reduced design matrices for binding models that include multiple protein conformations. (A–D) Reduced design matrices for proteins containing two (A), three (B), four (C), or n (D) binding sites.Matrix elements derived from states with zero, one, two, three, four, and n bound ligands are color coded black, red, blue, purple, green, and orange, respectively. The general form of the matrix elements in all cases is given by Eq. 15, with the row and column numbering ranging from 0 to n.