Canonical modeling: Review of concepts with emphasis on environmental health

The article reviews concepts of canonical modeling in the context of enviro nmental health. Based on biochemical systems theory, the canonical approach was developed over the past thirty years and applied to complex systems pr imarily in biochemistry and the regulation of gene expression. Canonical mo deling is based on nonlinear ordinary differential equations whose right-ha nd sides consist of products of power-law functions. This structure results from the linearization of complex processes in logarithmic space. The cano nical structure has many intriguing features. First, almost any system of s mooth functions or ordinary differential equations can be recast equivalent ly in a canonical model, which demonstrates that the model structure is ric h enough to deal with all relevant nonlinearities. Second, a large body of successful applications suggests that canonical models are often valid and accurate representations of quite complex, real-world systems. third, a set of guidelines supports the modeler in all phases of analysis. These guidel ines address model design, algebraic and numerical analysis, and the interp retation of results. Fourth, the structure of canonical models, especially those in S-system form, facilitates algebraic and numerical analyses. Of pa rticular importance is the derivation of steady-state solutions in an expli cit symbolic or numerical form, which allows further assessments of stabili ty and robustness. the homogeneous structure of canonical models has also l ed to the development of very efficient, customized computer algorithms for all steps of a typical analysis. Fifth, a surprising number of models curr ently used in environmental health research are special cases of canonical models. The traditional models are thus subsumed in one modeling framework, which offers new avenues of analysis and interpretation.