New JTB paper on (M,R)-system

[Tim Gwinn <***>]

I have received word from one of the authors that their new paper on (M,R)-systems is now in the "Articles In Press" section of the Journal of Theoretical Biology. I think this paper will be very useful to those seeking a better understanding of (M,R)-systems -- it is a relatively lengthy paper which - among other things - includes several illustrative examples and discussions of replication and self-referential relations. 

DOI: doi:10.1016/j.jtbi.2005.07.007

 

The abstract page is as follows:

 

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doi:10.1016/j.jtbi.2005.07.007      
Copyright © 2005 Elsevier Ltd All rights reserved.

Organizational invariance and metabolic closure: Analysis in terms of (M,R) systems

Juan-Carlos Letelier^{a, ,} , Jorge Soto-Andrade^b, Flavio Guíñez Abarzúa^b, Athel Cornish-Bowden^c and María Luz Cárdenas<sup>c

a</sup>Departamento de Biología, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago, Chile
^bDepartamento de Matemáticas, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago, Chile
^cBioénergétique et Ingénierie des Protéines, Institut de Biologie Structurale et Microbiologie, Centre National de la Recherche Scientifique, 31 chemin Joseph-Aiguier, 13402 Marseille Cedex 20, France

Received 21 February 2005;  revised 5 July 2005;  accepted 7 July 2005.  Available online 24 August 2005.

Abstract

This article analyses the work of Robert Rosen on an interpretation of metabolic networks that he called (M,R) systems. His main contribution was an attempt to prove that metabolic closure (or metabolic circularity) could be explained in purely formal terms, but his work remains very obscure and we try to clarify his line of thought. In particular, we clarify the algebraic formulation of (M,R) systems in terms of mappings and sets of mappings, which is grounded in the metaphor of metabolism as a mathematical mapping. We define Rosen's central result as the mathematical _expression_ in which metabolism appears as a mapping f that is the solution to a fixed-point functional equation. Crucially, our analysis reveals the nature of the mapping, and shows that to have a solution the set of admissible functions representing a metabolism must be drastically smaller than Rosen's own analysis suggested that it needed to be. For the first time, we provide a mathematical example of an (M,R) system with organizational invariance, and we analyse a minimal (three-step) autocatalytic set in the context of (M,R) systems. In addition, by extending Rosen's construction, we show how one might generate self-referential objects f with the remarkable property f(f)=f, where f acts in turn as function, argument and result. We conclude that Rosen's insight, although not yet in an easily workable form, represents a valuable tool for understanding metabolic networks.

Keywords: (M,R) systems; Metabolic network; Metabolic closure; Infinite regress; Systems biology

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