Robert Rosen's concept of (M,R)-systems was a fundamental advance in our understanding of the essential nature of a living organism as a self-organizing system, one that is closed to efficient causation, synthesizing, and maintaining all of the catalysts necessary for sustained operation during the whole period of its lifetime. Although it is not difficult to construct a model metabolic system to represent an (M,R)-system, such a model system will typically appear to lack organizational invariance, an essential property of a living (M,R)-system. To have this property, an (M,R)-system must not only be closed to external causation, it must also have its organization coded within itself, i.e., the knowledge of which components are needed for which functions must not be defined externally. In this paper, we discuss how organizational invariance may be achieved, and we argue that the apparent failure of previous models to be organizationally invariant is an artifact of the usual practice of treating catalytic cycles as 'black boxes'. If all of the steps in such a cycle are written as uncatalyzed chemical reactions, then it becomes clear that the organization of the system is fully defined by the chemical properties of the molecules that compose it.