Differential equation systems for heat‐loss corrections of isoperibolic microcalorimeters: A computer‐modeling approach

The problem of adequately correcting thermal titration curves for heat losses in isoperibolic microcalorimeters during rapid reactions in small volumes has been examined. With a data‐acquisition system for the simultaneous encoding of changes in heat, pH, and time linked directly to a DEC‐20 computer, various possible mechanisms for heat‐loss corrections were tested using computer‐modeling techniques. Models expressed by series exponential terms, as commonly used in linear pharmacokinetics to describe the time‐course concentration of a drug, proved to be inadequate to reconstruct the “adiabatic” thermal curve, since its apparent magnitude increased with the time taken for its generation. However, models based on mechanisms incorporating at least two heat sinks, one of which can be equated to the surroundings, have proved successful. The differential equations descriptive of the various models examined have rate constants characteristic of the reaction cell and its inserts, the reaction volume, and the calorimeter used. These can be evaluated by a curve‐fitting algorithm (MLAB) using standard thermal‐titration data (the neutralization of HCL with KOH). Once the rate constants are known, the differential equation solver of MLAB is then used to deconvolute any time: heat‐change matrix to that which would obtain in the absence of heat loss (the “adiabatic” state). With an appropriate differential equation model, the magnitude of the corrected heat change is independent of the time taken for its production and so‐called best model(s) have been judged on the basis of Akaike's information criterion. The application of the heat‐loss correction procedure to the thermal titration of chymotrypsinogen is illustrated.