Isothermal titration calorimetry (ITC) is a powerful technique for probing biomolecular interactions. However, accurate and precise determination of binding parameters-such as enthalpy and free energy, as well as associated uncertainties-can be hindered by noise and concentration variability. In particular, the recently noted mathematical ambiguity surrounding analyte concentrations intrinsically limits the precision with which binding parameters can be determined. Here, we compare several Bayesian approaches to validate a pipeline that resolves this ambiguity by combining two key strategies: simultaneous analysis of multiple ITC data sets and a hierarchical Bayesian treatment of analyte concentration priors. Together, these strategies lift the degeneracy inherent in single-data-set studies and remove an ambiguity typically present in Bayesian analysis by self-consistently refining concentration estimates. This enables optimal joint inference of binding parameters and concentrations while delivering a precision gain that surpasses conventional square-root-of-n averaging expectations through hierarchical information sharing across data sets. Leveraging modern Monte Carlo methods, our pipeline performs robust posterior sampling for more than 10 data sets and 40 total parameters. We validate the framework with synthetic ITC data sets for single- and multisite binding models and demonstrate its utility on experimental data, including 14 data sets for 1:1 binding of Mg(II) to the chelator EDTA and four data sets of the hub protein LC8 with its binding partner VP35. This work serves as a foundation for improving the precision of binding constants using multiple ITC data sets while providing a systematic framework for assessing the reliability of experimental concentration estimates, paving the way for more accurate biomolecular interaction studies.
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