Protein-ligand binding with a missing species

Considerable experimental evidence has been produced recently that shows that in the binding of oxygen or carbon monoxide to certain tetrameric hemoglobins, the triply-ligated species is virtually non-existent. The binding polynomial representing this phenomenon for the general case is P(x) = 1 + beta 1x + ... + beta n-1xn-1 + beta nxn, where beta n-1 is nearly zero. The zeros, factorization and associated Hill plots of such binding polynomials with beta n-1 = 0 are investigated for the general case, and are analyzed in detail for n = 3 and n = 4. These results are then compared with the results obtained from experimental data on a number of tetrameric hemoglobins for which beta 3 is small. One concludes that, apart from the slope of the high-saturation asymptote of the Hill plot, a small perturbation of beta 3 from zero produces small changes in other properties associated with the binding process, such as fractional saturation, maximum Hill slope, and zeros and factorization of the binding polynomial.