(M,R)-systems

An (M,R)-system is a formal model of a living system developed by theoretical biologist Robert Rosen. The name stands for metabolism-repair: the system is organized as a network of processes that produce its own components (metabolism) and a network of processes that produce the metabolic processes themselves (repair). The result is a closed loop of self-production that Rosen proved cannot be reduced to a finite algorithm.

The (M,R)-system is one of the most rigorous mathematical attempts to capture the organizational property that distinguishes living systems from non-living mechanisms. It anticipates and formalizes many of the insights later developed in autopoiesis theory, though Rosen's approach is more explicitly concerned with the functional organization of metabolism rather than the spatial boundary of the cell.

Rosen proved that any (M,R)-system must contain at least one component that is not produced by any process in the system — a non-repairable repair — which he identified with the system's genetic material. This result connects (M,R)-systems to the origin of life problem: the first living system must have achieved metabolic closure before it achieved complete repair closure.