(A) Plots of the binding function, whose shape reflects the interactions between binding sites, as described in the text. (B) The Monod, Wyman and Changeux (MWC) model with a population of dimers in two quaternary conformations, with each monomer having one binding site and ligand binding shown by a solid black disc. The two monomers are considered to be distinguishable, leading to four microstates. Directed arrows show transitions between microstates. This picture anticipates the graph-theoretic representation used later in this paper. (C) Schematic of the end points of the allosteric pathway between the tense, fully deoxygenated and the relaxed, fully oxygenated conformations of a single haemoglobin tetramer, , showing the tertiary and quaternary changes, based on Figure 4 of Perutz, 1970. Haem group (red); oxygen (cyan disc); salt bridge (positive, magenta disc; negative, blue bar); DPG is 2–3-diphosphoglycerate.