Maria Luz Cardenas
Date: April 09, 2019. 12:00
Location: CCU Seminar Room
Title: (M,R) systems of Robert Rosen as the essence of living organisms: Metabolic circularity as a guiding vision in Biology
Affiliation: Institut de Microbiologie de la Mediterranee in Marselille
The question of Erwin Schrodinger “What is Life? has excited little interest among molecular biologists during the past half-century, and the enormous development in biology during this time has been largely based on an analytical approach in which all biological entities are studied in terms of their components.
The benefits of this reductionism are obvious, but there have been costs as well, and future advances, for example for creating artificial life, need development of theory and to give more serious attention to the question of what makes a living organism living.
There have been some researchers that have tried, during the 20th century, to answer this question. One was Robert Rosen, with his theory of (M, R)-systems (metabolism-repair systems) based on the central idea that organisms are closed to efficient causation, which means that all the specific catalysts needed for the organism to maintain itself must be produced by the organism itself (but of course open to material causation). This crucial idea of metabolic circularity (closure), however, tends to be absent from biological studies.
Rosen’s work remains very obscure and, in all our work we have tried to clarify his line of thought. In particular, we started by clarifying 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 have replaced the term Repair used by Rosen, by Replacement. We defined 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.
We provided a minimal example of a (M,R system), which has been afterwards simulated. In addition, by extending Rosen’s construction, we showed 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 represents a valuable tool for understanding metabolic networks.
(M, R) systems are usually discussed in relation to individual organisms, but they can also be applied to interactions between different organisms, allowing analysis, for example, of how two or more species can exist in symbiotic relationships with one another, able to live together, but not separately. Application of Rosennean complexity to fields other than life is possible, because Rosen’s holistic vision of organisms, in which all components affect all others, has implications for the concepts of hierarchy and upward causation that are sometimes invoked in philosophical discussions, because it means that there is no hierarchy and no upward causation in (M,R) systems.