Bayesian Regression Quantifies Uncertainty of Binding Parameters from Isothermal Titration Calorimetry More Accurately Than Error Propagation.

We compare several different methods to quantify the uncertainty of binding parameters estimated from isothermal titration calorimetry data: the asymptotic standard error from maximum likelihood estimation, error propagation based on a first-order Taylor series expansion, and the Bayesian credible interval. When the methods are applied to simulated experiments and to measurements of Mg(II) binding to EDTA, the asymptotic standard error underestimates the uncertainty in the free energy and enthalpy of binding. Error propagation overestimates the uncertainty for both quantities, except in the simulations, where it underestimates the uncertainty of enthalpy for confidence intervals less than 70%. In both datasets, Bayesian credible intervals are much closer to observed confidence intervals.

Bayesian regression and model selection for isothermal titration calorimetry with enantiomeric mixtures.

Bayesian regression is performed to infer parameters of thermodynamic binding models from isothermal titration calorimetry measurements in which the titrant is an enantiomeric mixture. For some measurements the posterior density is multimodal, indicating that additional data with a different protocol are required to uniquely determine the parameters. Models of increasing complexity-two-component binding, racemic mixture, and enantiomeric mixture-are compared using model selection criteria. To precisely estimate one of these criteria, the Bayes factor, a variation of bridge sampling is developed.