Computer Simulation of Sedimentation Equilibrium Distributions for Systems Involving Heterogeneous Associations

Two methods are presented for computing the concentration of a species at sedimentation equilibrium as a function of radial distance, for systems wherein the species is involved in a set of chemical equilibria. The treatments are exemplified with a system involving a polymerizing acceptor and a series of acceptor-ligand complexes. It is shown that analytical expressions are available for the computation of exact distributions even in cases where volume changes accompany the several interactions, provided the activity coefficient of each species is taken as unity. This aspect of the work extends previously reported simulation procedures pertaining to simple interacting systems considered thermodynamically ideal. Secondly, a numerical integration procedure is presented for the solution of cases where both volume changes and non-ideality effects operate. The potential use of computer-simulated sedimentation equilibrium distributions is illustrated in relation to experimental results obtained with interacting mixtures of lysozyme (monomer and dimer) and N-acetylglucosamine at pH 8.0, Γ/2 = 0.15, and 15°. First, it is shown that the apparent weight average molecular weight approaches that of the monomer-inhibitor complex at saturating concentrations of the inhibitor, behavior consistent with the effective loss of binding sites on dimer formation. Further analysis involves the direct comparison of simulated distributions with those obtained experimentally using different inhibitor concentrations. The results indicate that the monomeric and dimeric forms of lysozyme bear one binding site with essentially identical affinity for the inhibitor.