Power-law modeling based on least-squares criteria: consequences for system analysis and simulation

The power-law formalism was initially derived as a Taylor series approximat ion in logarithmic space for kinetic rate-laws. The resulting models, eithe r as generalized mass action (GMA) or as S-systems models, allow to charact erize the target system and to simulate its dynamical behavior in response to external perturbations and parameter changes. This approach has been suc cesfully used as a modeling tool in many applications from cell metabolism to population dynamics. Without leaving the general formalism, we recently proposed to derive the power-law representation in an alternative way that uses least-squares (LS) minimization instead of the traditional derivation based on Taylor series [B. Hernandez-Bermejo, V. Fairen, A. Sorribas, Math. Biosci. 161 (1999) 83-94]. It was shown that the resulting LS power-law mi mics the target rate-law in a wider range of concentration values than the classical power-law, and that the prediction of the steady-state using the LS power-law is closer to the actual steady-state of the target system. How ever, many implications of this alternative approach remained to be establi shed. We explore some of them in the present work. Firstly, we extend the d efinition of the LS power-law within a given operating interval in such a w ay that no preferred operating point is selected. Besides providing an alte rnative to the classical Taylor power-law, that can be considered a particu lar case when the operating interval is reduced to a single point, the LS p ower-law so defined is consistent with the results that can be obtained by fitting experimental data points. Secondly, we show that the LS approach le ads to a system description, either as an S-system or a GMA model, in which the systemic properties (such as the steady-state prediction or the log-ga ins) appear averaged over the corresponding interval when compared with the properties that can be computed from Taylor-derived models in different op erating points within the considered operating range. Finally, we also show that the LS description leads to a global, accurate description of the sys tem when it is submitted to external forcing. (C) 2000 Elsevier Science Inc . All rights reserved.