Statistical aspects of van't Hoff analysis: a simulation study.

The thermodynamics of biological interactions is frequently studied by the van't Hoff analysis whereby data on variation of the binding constant K(D) with temperature are used to obtain estimates of standard enthalpy (Delta H degrees ), entropy (Delta S degrees ), and heat capacity (Delta C degrees P) of complex formation. A Monte Carlo simulation demonstrates that the absolute error of the above parameters is proportional to the relative error of KD and independent of the actual values of KD and of the way they vary with temperature. The error of Delta H degrees is approximately the same as that of T Delta S degrees (within 14% in the temperature range 5-45 degrees C). The error depends both on the number of temperature points within the experimental temperature range and on the size of the range, but it is more sensitive to the latter. Using the linear form of the van't Hoff equation to fit data with non-zero Delta C degrees P gives erroneous Delta H degrees and DeltaS degrees estimates at standard temperature except for the case when the T points are placed symmetrically with respect to the standard temperature. With the range of Delta C degrees P values usual for protein-protein interactions, the KD error must be very low to confidently infer that Delta C degrees P is non-zero or to claim that two interactions have different Delta C degrees P.