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Analysis and synthesis of regulator networks in terms of feedback circuits

par Thomas, René
Référence Self-Organization and Emergence in Life Sciences, Springer Netherlands, page (63-73)
Publication Publié, 2006

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Résumé :

Studies on the biological role of feedback circuits were initially centered on systems with sigmoid or stepwise interactions. It turned out recently that reasoning in terms of feedback circuits (rather than of individual interactions) can be used in a more general context, and, in particular, help understanding the behavior of weakly non-linear systems " la Rssler" (with a single non-linear term) known to generate multiple periodicity or deterministic chaos. The obvious way to formalize biological and other regulatory systems consists of using sets of differential equations. Since most regulatory interactions are non-linear, these differential systems usually cannot be treated analytically. In many cases, the shape of these non-linearities is sigmoid, i.e., the effect of a regulator is negligible below a "threshold" value and it rapidly levels off beyond this threshold value. For this reason, it is tempting to caricature these interactions as step functions. This is the justification of the efforts to develop logical methods, hoping for qualitative, yet analytical tools. It is our experience that differential and logical methods nicely complement each other, and often gain to be used in conjunction. The purpose of this paper is to show that although the logical approach has been developed to treat systems with step- or steep sigmoid interactions, the type of reasoning used can be fruitfully applied to weakly non-linear systems (the Rssler type of differential systems) which can generate complex behavior, including deterministic chaos. This paper includes : 1) a brief account of recent developments in the logical description of regulatory systems; 2) a section on the properties and roles of feedback circuits; 3) a section on the recent concept of circuit-characteristic states; 4) a discussion on how differential systems can be treated in terms of feedback circuits; 5) an application to the Rssler-type differential systems. It is realized that the brief description of items 1 to 4 is not self-sufficient, but these matters have been amply discussed elsewhere (bibliography below).© 2006 Springer. Printed in the Netherlands.