CONTRIBUTIONS OF INDIVIDUAL MOLECULAR-SPECIES TO THE HILL COEFFICIENTFOR LIGAND-BINDING BY AN OLIGOMERIC PROTEIN

New insights into the Hill coefficient (n) as a measure of cooperativi ty are obtained by resolving (Y) over bar, the fractional ligand bindi ng to an oligomeric protein, into a series of integral n(th)-order rea ctions. For identical sites within a single conformational state, the weighted sum of each reaction multiplied by its net order gives a Hill coefficient at (Y) over bar=0.5 of n(50)=1.0, indicative of non-coope rative binding, However, the disappearance of unliganded oligomers (S- 0) reflects the higher-order reactions, with their weighted sum (for a tetramer) leading to a Hill coefficient at S-0=0.5 of n(50)=-1.27. F or an oligomer with hto conformational states (such as represented by the T and R states in the Monod-Wyman-Changeux model) capable of gener ating highly cooperative binding, the same n(th)-order reactions apply , but with different weights. For oxygen binding to hemoglobin, n(50) is resolved into three components with net reaction orders of n=-2, 2, and 4 (with weights of 0.067, 0.15, and 0.754 corresponding, respecti vely, to the contributions of singly, triply and quadruply liganded mo lecules) to give n(50)=3.18. However, the cooperativity of the ''state '' function, (R) over bar' (the normalized fraction of molecules in th e R state), as characterized by n(50)' (the Hill coefficient at (R) ov er bar'=0.5) is distinct from n(50). If the T-R equilibrium lies very far in favor of either state, then even when the two stales differ wid ely in their intrinsic affinity for ligand, the lower limit of coopera tivity for (Y) over bar is n(50)=1.0, but the Hill coefficient for (R) over bar' cannot fall below n50'=1.27 (for a tetramer). Hence, the lo wer limit of n(50)' is equal to the absolute value of n(50) describin g the disappearance of S-0 for an oligomer with a single conformationa l state. (C) 1997 Academic Press Limited.