Average cooperativity effect and site binding constants in homotropic complexes

The equil. between metals or receptors and ligands are described by the formation function ‾n = ligand bound/total receptor. From the exptl. formation function, the binding polynomial ΣM = 1 + β1[A]+... + β1[A]i+... +βt[A]t or formation (gran canonical) partition function is obtained as function of the cumulative consts. βi. The Σm can be related to the stepwise equil. consts. by introducing a dissocn. partition function and a satn. function FMc = ΣM/ΣD. The std. value, FM coincides with βt = K1K2...Ki...Kt of the completely satd. receptor or metal. By calcg. K‾γ = (βi1/i/K1)(1/kst(y)), one obtains an av. cooperativity effect between binding mols. In NiNH3 system at 30° the cooperativity effect Δμ° γ(i) = -0.752 + 0.621(i-1) kJ/mol and in the system of bovine serum albumin (BSA) with Cu(II) at 25° is Δμ°γ(i) = 0.034 + 0.123(i-1)kJ-mol. By comparing the exptl. binding polynomial with a model partition function for cooperative equal binding, ΣM.CE, e.g. for 3 site receptors or metals Σm.ce = 1 + 3k[A]2+y3k3[A]3 with k = equal intrinsic site const., one obtains γ2 = Ky2 and y3 = Kγ3. The values of γ2, γ3 thus obtained are then introduced in a cor. formation function ‾ncorr which gives very good linear correlations on the Scatchard plot. From these plots the values of the intrinsic binding const. k are obtained which are k = 92.4 for Ni-NH3 at 30° and k = 1.3 × 103 for copper-BSA at 25°. These values correspond to values Δμ°k =-RTn k of -11.41 kJ/mol and -17.8 kJ/mol, resp. Also the equil. consts. of the Ni-NH3 system at other temps. and ionic strengths as well those of the Co(II)-NH3 system, were analyzed following the same procedure. In the Ni-hydrazine system, the cooperativity is almost O and in the Cd-NH3 system, 2 different sets of sites are put in evidence. The strict parallelism and possible coupling of chem. and biochem. systems are discussed.