Beyond non-integer Hill coefficients: A novel approach to analyzing binding data, applied to Na(+)-driven transporters

Prokaryotic and eukaryotic Na(+)-driven transporters couple the movement of one or more Na(+) ions down their electrochemical gradient to the active transport of a variety of solutes. When more than one Na(+) is involved, Na(+)-binding data are usually analyzed using the Hill equation with a non-integer exponent n. The results of this analysis are an overall K(d)-like constant equal to the concentration of ligand that produces half saturation and n, a measure of cooperativity. This information is usually insufficient to provide the basis for mechanistic models. In the case of transport using two Na(+) ions, an n < 2 indicates that molecules with only one of the two sites occupied are present at low saturation. Here, we propose a new way of analyzing Na(+)-binding data for the case of two Na(+) ions that, by taking into account binding to individual sites, provides far more information than can be obtained by using the Hill equation with a non-integer coefficient: it yields pairs of possible values for the Na(+) affinities of the individual sites that can only vary within narrowly bounded ranges. To illustrate the advantages of the method, we present experimental scintillation proximity assay (SPA) data on binding of Na(+) to the Na(+)/I(−) symporter (NIS). SPA is a method widely used to study the binding of Na(+) to Na(+)-driven transporters. NIS is the key plasma membrane protein that mediates active I(−) transport in the thyroid gland, the first step in the biosynthesis of the thyroid hormones, of which iodine is an essential constituent. NIS activity is electrogenic, with a 2:1 Na(+)/I(−) transport stoichiometry. The formalism proposed here is general and can be used to analyze data on other proteins with two binding sites for the same substrate.