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

Equilibrium binding constants (K_b) 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 K_b 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 K_b (and equivalent K_d) values and the corresponding free energy change ΔG_b are all asymmetric to varying degree. Here, using a simulation approach, we illustrate the effect of asymmetric K_b 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 K_b, K_d and ΔG_b are transformed into each other, their degree of asymmetry is changed. Consequently, we recommend that a more accurate way of expressing the uncertainties of K_b, K_d, and ΔG_b 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.