Using competition assays to quantitatively model cooperative binding by transcription factors and other ligands

Background: The affinities of DNA binding proteins for target sites can be used to model the regulation of gene expression. These proteins can bind to DNA cooperatively, strongly impacting their affinity and specificity. However, current methods for measuring cooperativity do not provide the means to accurately predict binding behavior over a wide range of concentrations. Methods: We use standard computational and mathematical methods, and develop novel methods as described in Results. Results: We explore some complexities of cooperative binding, and develop an improved method for relating in vitro measurements to in vivo function, based on ternary complex formation. We derive expressions for the equilibria among the various complexes, and explore the limitations of binding experiments that model the system using a single parameter. We describe how to use single-ligand binding and ternary complex formation in tandem to determine parameters that have thermodynamic relevance. We develop an improved method for finding both single-ligand dissociation constants and concentrations simultaneously. We show how the cooperativity factor can be found when only one of the single-ligand dissociation constants can be measured. Conclusions: The methods that we develop constitute an optimized approach to accurately model cooperative binding.