Numerical and experimental demonstrations of the need for caution in the use of zonal gel chromatography for characterizing ligand interactions with small acceptors.

Quantitative expressions are presented for the evaluation of equilibrium constants for interactions of the type A + B in equilibrium C from experiments entailing the application of a small zone of acceptor-ligand mixture to a column of gel preequilibrated with ligand solution [J.P. Hummel and W.J. Dreyer (1962) Biochim. Biophys. Acta 63, 530-532]. Only in the event that identical elution volumes pertain to acceptor and complex does the steady-state binding constant (Kss) obtained by that method equal the thermodynamic equilibrium constant (K). Simulated elution profiles are then generated with parameters relevant to gel chromatography of the ATP-Mg2+ system on Sephadex G-10 in order to demonstrate the practical importance of the need for distinction between Kss and K in situations where acceptor and complex do not comigrate. A study of the interaction between soybean trypsin inhibitor and cytochrome c by gel chromatography on Sephadex G-75 is then used to illustrate the feasibility of combining information from Hummel-Dreyer experiments with the theoretical expressions to characterize systems under the more general conditions that the elution volumes of A and C differ. A finding of considerable theoretical interest in relation to the simulation of mass migration behavior is the demonstration that a truncation error is the source of zonal spreading in the theoretical-plate model of chromatography. This truncation error is shown to be the source of spreading generated whenever solution of an abbreviated (diffusion-free) continuity equation involves substituting first differences for first derivatives in the differential equation describing mass transport.