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.
Average cooperativity effect and site binding constants in homotropic complexes / A. Braibanti; E. Fisicaro; M. C. Monguidi; F. Dallavalle. - In: INORGANICA CHIMICA ACTA. - ISSN 0020-1693. - 138(1987), pp. 17-24. [10.1016/S0020-1693(00)]
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