Closure to efficient causation, computability and artificial life.

The major insight in Robert Rosen's view of a living organism as an (M,R)-system was the realization that an organism must be "closed to efficient causation", which means that the catalysts needed for its operation must be generated internally. This aspect is not controversial, but there has been confusion and misunderstanding about the logic Rosen used to achieve this closure. In addition, his corollary that an organism is not a mechanism and cannot have simulable models has led to much argument, most of it mathematical in nature and difficult to appreciate. Here we examine some of the mathematical arguments and clarify the conditions for closure.

Beyond reductionism: metabolic circularity as a guiding vision for a real biology of systems.

The definition of life has excited little interest among molecular biologists during the past half-century, and the enormous development in biology during that time has been largely based on an analytical approach in which all biological entities are studied in terms of their components, the process being extended to greater and greater detail without limit. The benefits of this reductionism are so obvious that they need no discussion, but there have been costs as well, and future advances, for example, for creating artificial life or for taking biotechnology beyond the level of tinkering, will need more serious attention to be given to the question of what makes a living organism living. According to Robert Rosen's theory of metabolism-replacement systems, the central idea missing from molecular biology is that of metabolic circularity, most evident from the obvious but commonly ignored fact that proteins are not given from outside but are products of metabolism, and thus metabolites. Among other consequences, this implies that the usual distinction between proteome and metabolome is conceptually artificial -- however useful it may be in practice -- as the proteome is part of the metabolome.

Programming paradigms and mind metaphors: convergence and cross-fertilization in the study of cognition.

This paper describes a notable convergence between biological organization and programming language abstractions. Our aim is to explore possibilities of cross-fertilization, at both conceptual and empirical levels, towards the understanding of what cognition and cognitive systems might be.

Programming Paradigms and Mind Metaphors: Convergence and Cross-fertilization in the Study of Cognition

This paper describes a notable convergence between biological organization and programming language abstractions. Our aim is to explore possibilities of cross-fertilization, at both conceptual and empirical levels, towards the understanding of what cognition and cognitive systems might be.

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

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.

Understanding the parts in terms of the whole.

Metabolism is usually treated as a set of chemical reactions catalysed by separate enzymes. However, various complications, such as transport of molecules across membranes, physical association of different enzymes, giving the possibility of metabolite channelling, need to be taken into account. More generally, a proper understanding of the nature of life will require metabolism to be treated as a complete system, and not just as a collection of components. Certain properties of metabolic systems, such as feedback inhibition of the first committed step of a pathway, make sense only if one takes a broader view of a pathway than is usual in textbooks, so that one can appreciate ideas such as regulation of biosynthesis according to demand. More generally still, consideration of metabolism as a whole puts the emphasis on certain systemic aspects that are crucial but which can pass unnoticed if attention is always focussed on details. For example, a living organism, unlike any machine known or conceivable at present, makes and maintains itself and all of its components. Any serious investigation of how this can be possible implies an infinite regress in which each set of enzymes needed for the metabolic activity of the organism implies the existence of another set of enzymes to maintain them, which, in turn, implies another set, and so on indefinitely. Avoiding this implication of infinite regress represents a major challenge for future investigation.