Optimizing experimental parameters in isothermal titration calorimetry: variable volume procedures

In the study of 1:1 binding, M + X right <==> MX, isothermal titration calorimetry is generally thought to be limited to reactions in which the key parameter, c = K[M]0, can be set in the range 1-1000. In fact, the range of applicability can be extended by a factor of 10-100 at the upper end and as much as 10(5) at the lower, with certain provisos. The present work emphasizes the low-c regime, with the key heat parameter, h identical with DeltaH degrees [M]0, low, as well. Successful determination of K and DeltaH degrees in this region requires that the titration be extended to large excesses of titrant X over titrate M, and then the reaction heat is distributed strongly in favor of the early injections. With decreasing c, DeltaH degrees and the stoichiometry parameter n (often called site number) also become highly correlated and individually indeterminate. However, the product DeltaH degrees x n ( identical with Hn) is well-determined, so if n is known from other information, both K and DeltaH degrees can be determined to quite low c. By varying the titrant volume from injection to injection, one can significantly reduce the uncertainties in the estimated K and Hn values, permitting determination of K to better than 10% and Hn within 3% down to c = 10(-4), even for the low h value of 0.1 cal/L. The titrant volume optimization algorithm yields best results for the minimal number of injections - three when n is fitted, two when it is fixed. At low c, the resulting volume distributions depend nearly exponentially on injection number. This observation facilitates the derivation of similar, near-optimal volume distributions for five- and four-injection procedures that offer two statistical degrees of freedom for analysis. The volume optimization results are tested on the Ba2+/18-crown-6 ether complexation reaction at c = 0.1 and h = 0.16 cal/L, illustrating some practical complications but confirming the utility of the variable-volume protocol.