Uncertainty in protein–ligand binding constants: asymmetric confidence intervals versus standard errors

Abstract

Equilibrium binding constants (Kb) between chemical compounds and target proteins or between interacting proteins provide a quantitative understanding of biological interaction mechanisms. Reporting uncertainties of measured experimental parameters are critical for decision making in many scientific areas, e.g., in lead compound discovery processes and in comparing computational predictions with experimental results. Uncertainties in measured Kb values are commonly represented by a symmetric normal distribution, often quoted in terms of the experimental value plus-minus the standard deviation. However, in general the distributions of measured Kb (and equivalent Kd) values and the corresponding free energy change Gb are all asymmetric to varying degree. Here, using a simulation approach, we illustrate the effect of asymmetric Kb distributions within the realm of isothermal titration calorimetry (ITC) experiments. Further we illustrate the known, but perhaps not widely appreciated, fact that when distributions of any of Kb, Kd and Gb are transformed into each other their degree of asymmetry is changed. Consequently, we recommend that a more accurate way of expressing the uncertainties of Kb, Kd, and Gb values is to consistently report 95% confidence intervals, in line with other author's suggestions. The ways to obtain such error ranges are discussed in detail and exemplified for a binding reaction obtained by ITC.

Re-Use of Caco-2 Monolayers in Permeability Assays—Validation Regarding Cell Monolayer Integrity

“…The quality of the best fit is sign proved when a LogNormal distribution is considered (black line), which is in tistical distribution expected for rate constants [37]. Due to the asymmetry in tion, the uncertainty associated with this parameter should be expressed as interval [37]. This interval may be calculated from the parameters of the Log FOR PEER REVIEW 8 of 18 obtained for the TEER values of cell monolayers not previously used on permeability assays are undistinguishable from those of the cell monolayers previously used and incubated in culture media for two full days.…”

“…The characteristic values and uncertainty associated with this parameter cannot therefore be obtained directly from the average and standard deviation of the values measured. Instead, the most probable value was obtained from the average of LogP app , and uncertainty is expressed as 95% confidence intervals, calculated from the standard deviation of LogP app [37,38].…”

“…A clear misfit is observed when the best fit of a d (grey dashed line), with the experimental data showing Papp values. The quality of the best fit is significantly imribution is considered (black line), which is in fact the starate constants [37]. Due to the asymmetry in the distribuwith this parameter should be expressed as a confidence be calculated from the parameters of the LogNormal dis- on the average values obtained for each experimental esults for each individual cell monolayer is presented in ure S2.1 and shows that: (i) a large decrease in the value assay was only observed in 1/3 of the cell monolayers, inserts, TEER varied by less than 20% (increase or defore the permeability assay in both days), the TEER value e decrease observed after the assay on day 22 was fully nalyzing the results between the 2nd and the 3rd use of bility assays, a full recovery of TEER was also observed EER suggest that the procedure developed in this work monolayer integrity and that they can be re-used in per-/or 28 after being used on day 22.…”

“…A clear misfit is observed when the best fit of a (grey dashed line), with the experimental data showing Papp values. The quality of the best fit is significantly imbution is considered (black line), which is in fact the staate constants [37]. Due to the asymmetry in the distribuith this parameter should be expressed as a confidence e calculated from the parameters of the LogNormal dis- obtained for the TEER values of cell monolayers not previously used on permea says are undistinguishable from those of the cell monolayers previously used bated in culture media for two full days.…”

Community-building and promotion of technological excellence in molecular biophysics: the ARBRE–MOBIEU network

“…But the network also led to the development of new and exciting methods and ways of using instrumentation, for example in the development of improved intrinsic viscosity measurements using the Viscosizer TD instrument (Brule et al 2021), the complementary use of X-ray scattering and analytical ultracentrifugation to understand re-assembly of bacterial fimbriae (Solovyova et al 2021), the improvement of FTIR spectra by partial deuteration of samples (De Meutter and Goormaghtigh 2021a) and the use of attenuated total reflection Fourier transform IR spectroscopy as a tool to characterize peptide/membrane interactions (Claro et al 2021). The network has also contributed to the improvement of data analysis, for instance for evaluating FTIR spectra (De Meutter and Goormaghtigh 2021b), gaining increased information from MST experiments (López-Méndez et al 2021b) and accurately determining binding constant uncertainties in ITC experiments (Paketurytė et al 2021).…”