Experimental data analysis - An algorithm for determining rates and smoothing data

Reaction rate determination from experimental data is generally an essential part of evaluating enzyme or microorganism growth kinetics and the effects on them. Commonly used methods include forward, centered, or backward finite difference equations using two or more data points. Another commonly applied method for determining rates is least-square regression techniques, and when the sought function is unknown, polynomials are often applied to represent the data. The cubic spline functions presented in this article represent a versatile method of evaluating rates. The advantage in using this method is that experimental error may be largely accounted for by the incorporation of a smoothing step of the experimental data without force-fitting of the data. It also works well when data are unevenly spaced (often the case for experiments running over long periods of time). The functions are easily manipulated, and the algorithm can be written concisely for computer programming. The development of spline functions to determine derivatives as well as integrals is presented.