Effects of anomalous migration and DNA to protein ratios on resolution of equilibrium constants from gel mobility‐shift assays

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Abstract
Numerical resolution of binding constants from data generated by the gel mobility‐shift assay is dependent on the experimental resolution of the different ligation states of the DNA. Previously we showed that the populations of the intermediate ligation states at partial saturation with the protein ligand are extremely sensitive to cooperativity (Senear, D. F. and Brenowitz, M. J. Biol. Chem. 1991, 266, 13661–13671). This makes accurate gel mobility‐shift data extremely useful to the demonstration of cooperativity. However, the accuracy with which the intermediate ligation state populations are resolved has been questioned. Thus, two additional and related questions are now considered. First, what information is available if the intermediate ligation state populations are not used in the analysis of binding constants. Second, is accurate information obtained from those states under conditions of high DNA concentration. These questions are addressed by using the interactions of the λ cI repressor protein with the three site operator, OR, and the interaction of the E. coli GalR protein with the single site operator, OE. Both simulated and experimental data are analyzed. The results point to two conclusions. First, precise resolution of all macroscopic constants for binding of proteins to DNA is critically dependent on the intermediate ligation state populations; resolution is limited to at most two DNA sites if these states are not used in the analysis. Second, when the DNA and protein concentrations used in the titrations are comparable, the resolution of binding constants is extremely sensitive to experimental uncertainty in the macromolecule concentrations.