Mapping PF component diagrams onto space of shape parameters for four-site binding curves. (A) Examples of PF spectra for four-site binding curves. Spectra show cases in which PF constants q, r, s, and t are real-valued. Spacing parameters Δ1, Δ2, and Δ3 are shown in subpanel o. (B) Root-locus map for PF components of four-site binding curves. Lowercase roman numerals identify points in the (a, b, c) parameter space corresponding to the PF spectra in A. Blue sheet represents all (a, b, c) triples for which r = s (corresponding to subpanel i in A); red and black sheets represent all (a, b, c) triples for which s = t and q = r, respectively (corresponding to subpanels iii and v in A, respectively). The “seam” where blue and red sheets intersect corresponds to all (a, b, c) triples for which r = s = t (corresponding to subpanel ii in A). The seam where blue and black sheets intersect corresponds to all (a, b, c) triples for which q = r = s (corresponding to subpanel iv in A). The seam where red and black sheets intersect corresponds to all (a, b, c) triples for which q = r and s = t (corresponding to subpanel vi in A). Volume inside of the blue, red, and black sheets corresponds to all (a, b, c) triples for which the PF constants q, r, s, and t are real and distinct. In the volume outside of the blue, red, and black sheets, the PF constants will contain one or two pairs of complex conjugate values. The cube in B is bounded by the planes defined by the critical values of shape parameters a, b, and c (see Table 1).
