Some pitfalls in curve-fitting and how to avoid them: a case in point

When curve-fitting is used to support a complex nonlinear model containing several exponential terms, some of which have closely-spaced time constants, a particular burden of proof must be assumed. Most important, the uniqueness of the solution must be explored and discussed. Statistical tests for the degree of error and independence of the parameters should be provided, as well as information relating to the steps actually used in the fitting procedures. As an example of the need for the procedures we recommend in this communication, we have chosen an important case in point that has been published recently, and which deals with the kinetics of electron transfer from fully-reduced cytochrome oxidase to O2, analyzed by the method of SVD-based least squares. The problems we deal with in this case are applicable to a wide variety of other cases that involve curve-fitting to mathematical models.