Nucleotide binding to 5-iodoacetamidofluorescein (IAF) labelled Na+/K+-ATPase was measured by steady state fluorescence quenching of the fluorescein label via energy transfer to trinitrophenyl (TNP) labelled nucleotide. TNP-nucleotides are valuable probes of nucleotide binding to ATPases. Interpretation of these and other experiments in our laboratory using TNP-nucleotides with the Na+/K+-ATPase rely on having a good model for the interaction of TNP-nucleotide with the enzyme. Sets of fluorescence quenching curves obtained by titrating the enzyme with TNP-ADP in the presence of various concentrations of ADP could not be adequately modelled using a simple model with a single nucleotide binding site. Therefore, we compare various models which allow for additional TNP-nucleotide binding to the enzyme. In the two-site model, the additional binding is to a second specific site for which TNP-nucleotide and unlabelled nucleotide compete. In two other models, the additional binding (in one case saturable, and in the other case non-saturable) of TNP-nucleotide is not blocked by or affected by unlabelled nucleotide, and is, therefore, referred to as non-specific binding of the TNP-nucleotide. The goal of this work is to determine which of the distinctly different physical pictures associated with these models most accurately describes the interaction of TNP-nucleotide with the enzyme. We find that the interaction of TNP-ADP with IAF-labelled Na+/K+-ATPase is best described by a model in which there are two classes of binding: TNP-ADP and ADP compete for a specific binding site with dissociation binding constants of 0.13 mu M for TNP-ADP and 2.0 mu M for ADP; and non-saturable non-specific binding of TNP-ADP. (C) 1997 Elsevier Science B.V.