Average cooperativity effect and site binding constants in homotropic complexes

Abstract

The equilibria between metals or receptors and ligands are described by the formation function n̄ = ligand bound/total receptor From the experimental formation function, the binding polynomial Σ M = 1 + β 1[A] + … + β i[A] i + … + β t[A] t or formation (gran canonical) partition function is obtained as function of the cumulative constants β i. Σ M can be related to the stepwise equilibrium constants by introducing a dissociation partition function and a saturation function F c M = Σ M/Σ D. The standard value, F e⊝ M coincides with β t = K t = K 2 … K i… K t of the completely saturated receptor or metal. By calculating K γ =(β i 1/i/ K 1)(1/ k st( γ ) ) one obtains an average cooperativity effect between binding molecules. In nickel-ammonia system at 30 °C the cooperativity effect comes out to be Δμ° γ (i) = −0.752 + 0.621( i − 1) kJ/mol and in the system of bovine serum albumin (BSA) with copper(II) at 25 °C is Δμ° γ (i) = 0.034 + 0.123( i − 1) kJ/mol. By comparing the experimental binding polynomial with a model partition function for cooperative equal binding, Σ M.CE, e.g. for three site receptors or metals Σ M.CE = 1 + 3 k[A] + 3 γ 2 k 2 [A] 2 + γ 3 k 3[A] 3 with k = equal intrinsic site constant, one obtains γ 2 = K γ 2 and γ 3 = K γ 3. The values of γ 2, γ 3 thus obtained are then introduced in a corrected formation function n̄ corr which gives very good linear correlations on the Scatchard plot. From these plots the values of the intrinsic binding constant k are obtained which are k = 92.4 for nickel-ammonia at 30 °C and k = 1.3 × 10 3 for copper-BSA at 25 °C. These values correspond to values Δμ° k = − RT In k of −11.41 kJ/ mol and −17.8 kJ/mol, respectively. Also the equilibrium constants of the nickel-ammonia system at other temperatures and ionic strengths as well those of the cobalt(II)-ammonia system, have been analysed following the same procedure. In the nickel-hydrazine system the cooperativity is almost null and in the cadmium-ammonia system two different sets of sites are put in evidence. The strict parallelism and possible coupling of chemical and biochemical systems are discussed.