Evaluation and Minimization of Uncertainty in ITC Binding Measurements: Heat Error, Concentration Error, Saturation, and Stoichiometry

Abstract

Background Isothermal titration calorimetry (ITC) is uniquely useful for characterizing binding thermodynamics, because it straightforwardly provides both the binding enthalpy and free energy. However, the precision of the results depends on the experimental setup and how thermodynamic results are obtained from the raw data. Methods Experiments and Monte Carlo analysis are used to study how uncertainties in injection heat and concentration propagate to binding enthalpies in various scenarios. We identify regimes in which it is preferable to fix the stoichiometry parameter, N, and evaluate the reliability of uncertainties provided by the least squares method. Results The noise in the injection heat is mainly proportional in character, with ~1% and ~3% uncertainty at 27C and 65C, respectively; concentration errors are ~1%. Simulations of experiments based on these uncertainties delineate how experimental design and curve fitting methods influence the uncertainty in the final results. Conclusions In most cases, experimental uncertainty is minimized by using more injections and by fixing N at its known value. With appropriate technique, the uncertainty in measured binding enthalpies can be kept below ~2% under many conditions, including low C values. General Significance We quantify uncertainties in ITC data due to heat and concentration error, and identify practices to minimize these uncertainties. The resulting guidelines are important when ITC data are used quantitatively, such as to test computer simulations of binding. Reproducibility and further study are supported by free distribution of the new software developed here.

ITC and SPR Analysis Using Dynamic Approach

“…ITC thermogram is sensitive to various parameters such as protein concentration, ligand concentration, cell volume and injection volume [33]. In dynamic analysis, when an experimental thermogram is fitted against a kinetic model, the initial few data points may not fit well to the model.…”

“…ITC thermogram is sensitive to various parameters such as protein concentration, ligand concentration, cell volume and injection volume [32]. The dilution effect of protein/ligand due to injected ligand, can be calculated as explained in SI (1.…”

Accounting for Apparent Deviations between Calorimetric and van’t Hoff Enthalpies

“…It is worthwhile to note that even the ionic guests give negligible heats of dilution (Supplemental Figure 1). It is reasonable to assume then, that most of the error in the measurements will stem from heat and concentration error, which we have characterized experimentally 16 . Table 1: Binding enthalpies and free energies (kcal/mol) for amantadine and rimantadine with beta-cyclodextrin, from 300 to 340 K. Uncertainties are one standard deviation, generated from bootstrapping during fitting as described in Methods.…”

“…ΔH VH " magnitude and character of both the concentration error and heat error used here are chosen to reflect typical experimental conditions, as determined in our prior empirical study 16 . A central observation of this work is that realistic levels of concentration error and heat error lead to strikingly different patterns of error in ΔH Direct and ΔH VH , as illustrated by representative data drawn from the 1,000 bootstrapped datasets for N floating (Figure 4) and N fixed at 1 ( Figure 5).…”

“…Following our prior investigation into heat error for this instrument 16 , we estimated the standard deviation of the measured heat of a given injection as where is the standard deviation of the measured injection heat; is the temperature dependent coefficient of the proportional error component; and is the standard deviation of the temperaturedependent irreducible heat noise. Based on our prior study 16 , we set ζ to 0.01 (1%) for T=27-57C, and to 0.03 (3%) for experiments at 67C. Similarly, σ irr was set to 0.13 µcal and 0.39 µcal for experiments at 27-57C and at 67C, respectively.…”