A Simple Self-Maintaining Metabolic System: Robustness, Autocatalysis, Bistability

Abstract

A living organism must not only organize itself from within; it must also maintain its organization in the face of changes in its environment and degradation of its components. We show here that a simple (M,R)-system consisting of three interlocking catalytic cycles, with every catalyst produced by the system itself, can both establish a non-trivial steady state and maintain this despite continuous loss of the catalysts by irreversible degradation. As long as at least one catalyst is present at a sufficient concentration in the initial state, the others can be produced and maintained. The system shows bistability, because if the amount of catalyst in the initial state is insufficient to reach the non-trivial steady state the system collapses to a trivial steady state in which all fluxes are zero. It is also robust, because if one catalyst is catastrophically lost when the system is in steady state it can recreate the same state. There are three elementary flux modes, but none of them is an enzyme-maintaining mode, the entire network being necessary to maintain the two catalysts.

Biological organisation as closure of constraints

“…Let us just mention that, recently, several studies have made substantial contributions to re-examining, interpreting and developing Rosen's ideas (Piedrafita et al, 2010;Letelier et al, 2003Letelier et al, , 2006Wolkenhauer & Hofmeyr, 2007). What matters for our present purposes is that closure, and therefore self-determination, is located at the level of efficient causes: what constitutes the organisation is the set of efficient causes subject to closure, and its maintenance (and stability) is the maintenance of the closed network of efficient causes.…”

Autonomy and Enactivism: Towards a Theory of Sensorimotor Autonomous Agency

“…And, finally, the lack of a good model of sensorimotor autonomy. In contrast with the operationally explicit models of basic or material autonomy that have provided maturity and empirical support for autopoietic theory at the level of metabolic or molecular interactions (Barandiaran and RuizMirazo 2008;Bechtel 2007a;Bourgine and Stewart 2004;Luisi 2003;Piedrafita et al 2010;Varela et al 1974), early models of neuronal or sensorimotor autonomy (in particular Bittorio as a model of the operational closure of the nervous system, to be discussed below) failed to provide conceptual consistency within enactivism. By analysing these difficulties in detail we might gain not just a therapeutic grasp on how to reconcile autonomy back with enactivism but we might also be capable to specify the demands for a more precise characterization of autonomy that becomes useful and compatible with contemporary enactivist approaches.…”

“…The neurodynamic signature or neuronal correlate of photototaxis is precisely that shape, the carving out of a specific, functionally distinct, form within the undifferentiated space of possible oscillatory relationships. Neither the intrinsic and spontaneous (Smithers 1995(Smithers , 1997) and Piaget's sensorimotor grounding of cognitive development (Piaget 1969(Piaget , 1975. activity of the system, nor the shape of the system under behaviourally-structured input can produce and sustain such a pattern.…”

Simulating a Model of Metabolic Closure

“…1 to study the range of behavior possible in a simple (M, R)-system (Piedrafita et al 2010(Piedrafita et al , 2012a. It is based on one proposed earlier (Letelier et al 2006;Cornish-Bowden et al 2007) that was itself derived from that of Morán et al (1996).…”

“…The initial simulations (Piedrafita et al 2010) were deterministic, done in terms of concentrations, so the numbers of molecules were essentially infinite and no statistical fluctuations were considered. These simulations were done with the commercial software MatLab and checked with COPASI (Hoops et al 2006), or vice versa.…”