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

Equilibrium binding constants (Kb) between chemical compounds and target proteins or between interacting proteins provide a quantitative understanding of biological interaction mechanisms. Reported 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 ΔGb 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 ΔGb 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 ΔGb values is to consistently report 95% confidence intervals, in line with other authors' suggestions. The ways to obtain such error ranges are discussed in detail and exemplified for a binding reaction obtained by ITC.