Simulating a Model of Metabolic Closure

Abstract

The goal of synthetic biology is to create artificial organisms. To achieve this it is essential to understand what life is. Metabolism-replacement systems, or (M, R)-systems, constitute a theory of life developed by Robert Rosen, characterized in the statement that organisms are closed to efficient causation, which means that they must themselves produce all the catalysts they need. This theory overlaps in part with other current theories, including autopoiesis, the chemoton, and autocatalytic sets, all of them invoking some idea of closure. A simple model of an (M, R)-system has been implemented in the computer, and behaves in ways that may shed light on the requirements for a prebiotic self-organizing system. In addition to a trivial steady state in which nothing happens, it can establish a non-trivial steady state in which all intermediates have finite concentrations, with their rates of degradation balanced by their rates of synthesis. The sys tem can be regenerated from the set of food components plus a single intermediate, and maintain itself in that stateindefinitely, despite continuous degradation. At the very low compartment volumes that may have existed in pre- biotic conditions, for example in cavities in minerals, or in micelles formed by simple amphiphiles, statistical fluctu ations in the numbers of molecules need to be taken into account. With the stochastic approach there is no nontrivial steady state in strict mathematical terms, because the system will always collapse to the trivial state after suffi- cient time. However, the average time before collapse is so long for volumes greater than 10À19 l (much smaller than the volume of the order of 10À15 l for a typical bacterial cell) that for practical purposes the self-maintaining state of non-null concentrations becomes significant, recalling the situation of bistability that is observed in deterministic analysis. In turn, there exists a minimum size below which the self-organizing system cannot maintain itself on chemically relevant time scales. The value of the critical volume depends on the particular concentrations and rate constants assumed, but the principle could apply generally.