Mathematical problems in fitting kinetic models - Some new perspectives

Fitting kinetic data with kinetic rate expressions has been a challenge for many years. In hopes of providing some guidelines for tackling this problem, kinetic parameter estimation is revisited, covering such topics as data transformations, nonlinear single and multi-response techniques, optimization techniques, and parameter confidence measures. Among the optimization techniques discussed are direct and indirect methods, use of higher-order derivatives, and global optimization. New perspectives on statistical tests for model and parameter confidence are discussed, paying particular attention to exact, nonlinear methods and pointing out the distinct lack of these tests throughout the kinetics literature. In each section, either a single-site or a dual-site Langmuir-Hinshelwood (L-H) example model is shown for illustration of the aforementioned concepts.