Fitting physiological models to data

Methods of fitting models to experimental data obtained from biological systems are reviewed. The Michaelis-Menten model is used as the working example of a familiar and well-studied biological model. Criteria for selecting models include goodness of fit, freedom from systematic errors, and simplicity. A given model is usually fitted and the optimal parameters determined by minimization of an objective function, usually the sum of the squared errors. Freedom from systematic errors is best judged graphically. The important mathematical methods of fitting models are derived from the calculus and include linear and quadratic programming. The latter leads to minimization of the sum of squares of errors. Optimal search procedures, which also perform this minimization, are surveyed. Other properties of models, such as the proper number of parameters and whether linearization is appropriate, are discussed. The specialized problems of biological models and data are considered.