Diagram of a simple metabolic network.

A primary carbon source S is consumed by the cell at a rate u ≥ 0. It is processed into an intermediate P, generating N_F energy units per unit S consumed. The intermediate P can be excreted in the form of a waste product W (rate −v ≤ 0), or it can be completely oxidized (rate r ≥ 0) generating an additional N_R energy units (N_R ≫ N_F). The respiration rate is capped, r ≤ r_max.