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-protein dissociation constants can be measured. CONCLUSIONS The methods that we develop constitute an optimized approach to accurately model cooperative binding. GENERAL SIGNIFICANCE The expressions and methods we develop for modeling and analyzing DNA binding and cooperativity are applicable to most cases where multiple ligands bind to distinct sites on a common substrate. The parameters determined using these methods can be fed into models of higher-order cooperativity to increase their predictive power.

BACKGROUNDThe 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. METHODSWe use standard computational and mathematical methods, and develop novel methods as described in Results. RESULTSWe 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-protein dissociation constants can be measured. CONCLUSIONSThe methods that we develop constitute an optimized approach to accurately model cooperative binding. GENERAL SIGNIFICANCEThe expressions and methods we develop for modeling and analyzing DNA binding and cooperativity are applicable to most cases where multiple ligands bind to distinct sites on a common substrate. The parameters determined using these methods can be fed into models of higher-order cooperativity to increase their predictive power.keywords: cooperative DNA binding; competition EMSA; modeling ligand-substrate interactions; Hill plots; Engrailed; Extradenticle-Homothorax; curve fitting; finding dissociation constants; quantifying cooperativity . CC-BY-NC-ND 4.0 International license It is made available under a was not peer-reviewed) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity.The copyright holder for this preprint (which . http://dx.doi.org/10.1101/170340 doi: bioRxiv preprint first posted online Jul. 31, 2017; 3 HIGHLIGHTS• Hill plots remain prominent in biology, but can mask cooperativity• Effective modeling of binding by two ligands requires the use of 3 parameters• We develop novel ways to find these parameters for two cooperating ligands• We show how they can be used to enhance the power of established methods• We describe how this framework can be extended to multiple cooperating ligands