The determination of equilibrium constants for heterogeneous macromolecular interactions. Systems forming 2:1 complexes

In developing a method for analyzing the heterogeneous association nA + mB in equilibrium AnBm, we have specifically investigated the case of n = 2, m = 1 for both the specific case of no appreciable intermediates and the more general case allowing intermediates. Computer-simulated three-dimensional surfaces of the 2:1 model generated from total concentrations of species A and B and the resulting weight-average molecular weights were analyzed with a Gauss-Newton nonlinear least-squares minimization routine. The surfaces generated included normalized random error of varying standard deviations imposed upon both the concentrations and weight-average molecular weights. For comparison purposes, these surfaces were analyzed not only by using the correct 2:1 model, but also by an incorrect (1:1) model and by the other (incorrect) 2:1 model. Except for those situations where the 'experimental' noise was consistently higher than the concentration of one of the species, correct K values were obtained and the correct model was easily distinguished from the incorrect model. The computer routine similarly distinguished between data correctly described as 1:1 and the same data incorrectly analyzed as either 2:1 model. For those cases in which a microscopic Ki value predicts an association such that all species involved for that particular Ki are in appreciable amounts, the Ki value is returned correctly. Correct overall equilibrium constants are also converged upon as long as adequate amounts of A2B, B and A are present.