A study of statistical error in isothermal titration calorimetry

Abstract

In isothermal titration calorimetry (ITC), the two main sources of random (statistical) error are associated with the extraction of the heat q from the measured temperature changes and with the delivery of metered volumes of titrant. The former leads to uncertainty that is approximately constant and the latter to uncertainty that is proportional to q. The role of these errors in the analysis of ITC data by nonlinear least squares is examined for the case of 1:1 binding, M+X right arrow over left arrow MX. The standard errors in the key parameters-the equilibrium constant Ko and the enthalpy DeltaHo-are assessed from the variance-covariance matrix computed for exactly fitting data. Monte Carlo calculations confirm that these "exact" estimates will normally suffice and show further that neglect of weights in the nonlinear fitting can result in significant loss of efficiency. The effects of the titrant volume error are strongly dependent on assumptions about the nature of this error: If it is random in the integral volume instead of the differential volume, correlated least-squares is required for proper analysis, and the parameter standard errors decrease with increasing number of titration steps rather than increase.