CALCULATION OF SITE AFFINITY, COOPERATIVITY BETWEEN SITES AND SELF-ASSOCIATION IN POLYMER-LIGAND-PROTON COMPLEXES

The statistical probability of state of a solution containing a reacti ng receptor M, a ligand A (and eventually proton H) is described by a molar partition function Z(M) = exp(-Delta G/RT) referred to M, or Z(A ) or Z(H), respectively. The partition function for one class of sites can be expressed as the function of site constants k(j) and cooperati vity functions gamma(j,i) = exp{b(j)(i - 1)}. Binding in a single clas s can be represented by a vector J(p(t)) whose elements correspond to single species. For more classes of sites, the joined probability is o btained as tenser product of single class vectors giving rise to compl exation matrices M-pqr. There is one partition function for each compo nent of the system. If the complexes are of type H(P)M(Q)A(R) there ar e three partition functions Z(H), ZM and ZA The relationships between partition functions and total analytical amounts T-H, T-M, T-A, respec tively are given. The experimental data obtained in a potentiometric t itration with electrode reversible to [H] or other free component can be reproduced as the function of site constants k(j) and cooperativity functions exp{b(j)(i - 1)} for each class j. The best values of k(j) and b(j), can be calculated following a nonlinear least squares proced ure by means of a computer program that is here presented. (C) 1998 El sevier Science B.V. All rights reserved.