Power-law modeling based on least-squares minimization criteria

The power-law formalism has been succesfully used as a modeling tool in man y applications. The resulting models, either as Generalized Mass Action or as S-systems models, allow one to characterize the target system and to sim ulate its dynamical behavior in response to external perturbations and para meter changes. The power-law formalism was first derived as a Taylor series approximation in logarithmic space for kinetic rate-laws. The especial cha racteristics of this approximation produce an extremely useful systemic rep resentation that allows a complete system characterization. Furthermore, th eir parameters have a precise interpretation as local sensitivities of each of the individual processes and as rate-constants. This facilitates a qual itative discussion and a quantitative estimation of their possible values i n relation to the kinetic properties. Following this interpretation, parame ter estimation is also possible by relating the systemic behavior to the un derlying processes. Without leaving the general formalism, in this paper we suggest deriving the power-law representation in an alternative way that u ses least-squares minimization. The resulting power-law mimics the target r ate-law in a wider range of concentration values than the classical power-l aw. Although the implications of this alternative approach remain to be est ablished, our results show that the predicted steady-state using the least- squares power-law is closest to the actual steady-state of the target syste m. (C) 1999 Elsevier Science Inc. All rights reserved.