Estimation of non-constant variance in isothermal titration calorimetry using an ITC measurement model

Abstract

Isothermal titration calorimetry (ITC) is the gold standard for accurate measurement of thermodynamic parameters in solution reactions. In the data processing of ITC, the non-constant variance of the heat requires special consideration. The variance function approach has been successfully applied in previous studies, but is found to fail under certain conditions in this work. Here, an explicit ITC measurement model consisting of main thermal effects and error components has been proposed to quantitatively evaluate and predict the non-constant variance of the heat data under various conditions. Monte Carlo simulation shows that the ITC measurement model provides higher accuracy and flexibility than variance function in high c-value reactions or with additional error components, for example, originated from the fluctuation of the concentrations or other properties of the solutions. The experimental design of basic error evaluation is optimized accordingly and verified by both Monte Carlo simulation and experiments. An easy-to-run Python source code is provided to illustrate the establishment of the ITC measurement model and the estimation of heat variances. The accurate and reliable non-constant variance of heat is helpful to the application of weighted least squares regression, the proper evaluation or selection of the reaction model.

Fig 1. Comparison of SDR predicted by ITC measurement model and variance function.

(A) When c = 10, the results of two methods are the same. (B) When c = 1000, the variance function cannot describe the specific changes in the transition region.

Fig 2. The influence of K_a and c-values on the distribution of SDR.

Theoretical titration curves and SDR for simulated reactions with different K_a (A, B) and c-value (C, D). With the increase of K_a or c-value, the SDR increases significantly in the transition region (B, D).

Fig 3. The influence of ΔH and V_inj on the distribution of SDR with c = 1000.

(A) As ΔH decreases, the heat residual decreases until the heteroscedasticity disappears. (B) When the injection volume is large, the SDR peak weakens.

Fig 4

Theoretical titration curves without error components (A) and distribution of SDR for reactions with different error components (B). The orange curve is the control curve with three basic error components (σ_bpv), the red curve has additional error components (σ_{H Ka}) in reaction parameters K_a and ΔH, and the green curve has additional error component (σ_conc) in titrant concentration. The additional error components obviously change the distribution characteristics of the heat residual, resulting in a significant deviation from the prediction result of the variance function.

Fig 5. The 95% confidence interval estimates of the three error parameters for 100 samples.

The vertical red lines are the true value of the three error parameters. The blue bars indicate the 95% confidence intervals (total four standard deviations wide) containing the true value, while the orange bars indicate the opposite.