Optimizing experimental parameters in isothermal titration calorimetry

In isothermal titration calorimetry, the statistical precisions with which the equilibrium constant (K) and reaction enthalpy (Delta H degrees) can be estimated from data for 1:1 binding depend on a number of quantities, key among them being the products c K[M](0) and h Delta H degrees[M](0), the stoichiometry range (R-m, ratio of total titrant X to total titrate M after the last injection), and the number of injections of titrant. A study of the statistical errors as functions of these quantities leads to the following prescription for optimizing throughput and precision: (1) Make 10 injections of titrant. (2) Set the concentrations in accord with the empirical equation R-m = 6.4/c(0.2) + 13/c (but no smaller than 1.1). (3) Make the starting concentration [M](0) as large as possible within the large-signal limits of the instrumentation but limited to c < 10(3) for estimating K. With this procedure, both K and [M](0) are predicted to have relative standard errors < 1% over large ranges of K. Systematic errors in the concentrations, [X](0) and [M](0), are fully compensated by the "site number" or stoichiometry parameter (n). On the other hand, altering and freezing any of the fit parameters leads to a deterioration of the fit quality and to predictable changes in the other parameters. Fit divergence at very small c is avoidable through a simple redefinition of the fit parameters; however, unless n can be fixed from other information, Delta H degrees may be statistically ill-defined in this region.