Graphic method for determination of allosteric constants

The maximum slope of the plot, appearing in the paper of Watari & Isogai (1976), was derived algebraically as a function of allosteric constants c and α_mor β_m (= cα_m), and the relation between L, c, and α_mor β_m, was also obtained, where $\text{L =}\text{T}{}_{\mathrm{o}}\text{R}{}_{\mathrm{o}}\text{, c =}\text{K}{}_{\mathrm{R}}\text{K}{}_{\mathrm{T}}\text{, α}{}_{\mathrm{m}}\text{=}\text{F}{}_{\mathrm{m}}\text{K}{}_{\mathrm{R}}\text{, β}{}_{\mathrm{m}}\text{=}\text{F}{}_{\mathrm{m}}\text{K}{}_{\mathrm{T}}\text{, R}{}_{\mathrm{o}}\text{and}\text{T}{}_{\mathrm{o}}$ are concentrations of unligated R and T states respectively, K_Rand K_T are microscopic dissociation constants, and F_m is the ligand concentration at the maximum slope of the plot. When the maximum slope is increased by one, the value becomes Hill constant, n. Nomographs which enable easier estimation of allosteric constants, L and c, were constructed from the two given values, the maximum slope of the plot, n ? 1, and α_mor β_m, in the cases where the maximum number of ligands, N, was 2 and 4. In the nomograph, log c is plotted against log L²c^N keeping the value of the maximum slope of the plot and that of α_mor β_m constant. These nomographs show that the representation is symmetrical in the cases of L²c^N > 1 and L²c^N < 1.