Isothermal titration calorimetry (ITC) is the only technique able to determine both the enthalpy 18 and entropy of noncovalent association in a single experiment. The standard data analysis method based 19 on nonlinear regression, however, provides unrealistically small uncertainty estimates due to its neglect 20 of dominant sources of error. Here, we present a Bayesian framework for sampling from the posterior 21 distribution of all thermodynamic parameters and other quantities of interest from one or more ITC 22 experiments, allowing uncertainties and correlations to be quantitatively assessed. For a series of ITC 23 measurements on metal:chelator and protein:ligand systems, the Bayesian approach yields uncertainties 24 which represent the variability from experiment to experiment more accurately than the standard data 25 analysis. In some datasets, the median enthalpy of binding is shifted by as much as 1.5 kcal/mol. A Python 26 implementation suitable for analysis of data generated by MicroCal instruments (and adaptable to other 27 calorimeters) is freely available online. 28 29 33 be used to study more complex processes such as competitive binding [15, 36], binding cooperativity [2], 34 and binding events coupled to changes in the protonation state [6, 28] or tautomeric state [11] of one or 35 more components. Provided reaction rates are slower than cell mixing times, ITC can even be used to study 36 the kinetics of association [23]. 37 Here, we focus on the thermodynamics of simple two-component association (one-to-one binding). A 38 unique and powerful property of ITC is that it can not only determine the free energy of binding (Δ ), but 39 1 of 21 Bayesian ITC also decompose it into enthalpy (Δ ) and entropy (Δ ) without having to resort to multiple experiments 40 at different temperatures to determine these quantities via the van 't Hoff equation. This decomposition 41 has been used to draw conclusions into, for example, how entropy is related to antibody flexibility [35] 42 and ordering of disordered loops [4] during antibody affinity maturation. It has also been used to suggest 43 that iterative improvements in generations of drugs result in their interactions being increasingly driven by 44 enthalpy [14]. Furthermore, it has been used to suggest how force fields might be improved [9]. 45 It is possible to perform enthalpy-entropy decomposition with ITC because the instrument not only 46 detects a binding process, but can determine the heat of binding. The raw data from an ITC instrument is the 47 differential power required to maintain a reference cell at the same temperature as the titrand in a sample 48 cell (usually a macromolecule dissolved in buffer) as a titrant (usually a small molecule ligand) is injected into 49 it. The experimental data can be summarized as the measured heats of injection, ≡ { 1 , 2 , … , } ob-50 tained by integrating the differential power over the duration of each injection. Thermodynamic parameters 51 are then determined by fitting binding heat m...