(a) Fractional saturation binding curves of a MWC protein as a function of the logarithm of the scaled concentration α, with parameter values that give rise to systematically higher maximum cooperativity nH values. The pairs of L and c values for all curves obey the maximum cooperativity criterion and are listed in Table 1. (b) Dependence of the logarithm of the scaled affinity (logα1/2) of the curves presented in (a) on the maximum cooperativity Hill value (nHmax). (c) Dependence of the substrate unbinding sensitivity (Δ/Δlogα) of a tetrameric MWC protein on nHmax (filled black symbols). The array of open yellow symbols decorating each maximum cooperativity point corresponds to changes in the Y axis values due to changes in L that reside within the correspondingly encoded buffering of cooperativity regime (see text) (d) Dependence of on the logarithm of the allosteric constant L around the different maximum cooperativity points indicated in (a) and Table 1 (and assuming their different c values). For each curve, the portion highlighted in yellow corresponds to the logL range fulfilling the ‘buffering of cooperativity’ regime, that is the L range around the maximum Hill point that gives rise to fractional saturation curves all exhibiting less than 1% change in the maximum Hill coefficient value. Such a physiological dataset is observed for the maximum point of ~2.8, characteristic of human Hb in panel (e) (calculated using its appropriate c value; see Supplementary file 1). Similar data for different maximum cooperativity values are presented in Figure 4—figure supplement 1. In each physiological dataset, the curve indicated in red corresponds to the maximum cooperativity curve (f) Dependence of the broadness of the ‘buffering of cooperativity’ regime (the dynamic range), as defined above, on the maximum cooperativity Hill value. In all figure panels, the curves indicated in red were calculated using the experimental values for human Hb reported in the literature. The red data points in several of the panels represent approximated values of human Hb.