We discuss a simple model formed by two iterated maps of the interval, m and r: The map r, named regulatory map, controls the behavior of the map m, which is seen as an abstraction of the metabolism concept.

An optimization problem is naturally established for the pair (m, r). For given parameters, we define a maximizing function, which depends on the metabolic orbit during a certain time interval. The problem is to obtain the maximization of this function, depending on the initial conditions for the metabolic system. We discuss further developments for which the system is perturbed by an external system.