# Economic principles in cell metabolism

Protein allocation | Optimal states | Enzyme cost | Flux cost | Rate and yield |

Value structure | Kinetic models | Flux analysis | Optimal adaptation | Enzyme rhythms |

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### Optimal enzyme rhythms

Enzyme levels in cells can be an adaptions to periodic environments, but can also drive self-induced metabolic cycles. In both cases, rearranging metabolic processes in time can make them run more efficiently. If enzyme levels change periodically, how should they be coordinated within and between pathways? To predict optimal periodic enzyme profiles, I derive them from an optimality principle, which I am applying here to periodic metabolic states. I consider kinetic models controlled by periodic enzyme levels, possibly in a periodic environment. The enzyme profiles are chosen such that the metabolic performance is maximized. Assuming small perturbations, optimal static or periodic enzyme adaptions can be computed using metabolic control theory. To compute optimal enzyme rhythms, I compute pairwise fitness synergies between all periodic parameters and solve for optimal periodic enzyme profiles. They are applicable to large metabolic networks and show how factors like model structure, fitness functions, and external rhythm shape the periodic enzyme profiles. Rhythms can either be induced by the environment, or in some cases self-induced, suggesting a possible selection advantage of spontaneous metabolic cycles. Phase shifts between reactants and enzymes can affect enzyme efficiency, and orchestrated enzyme rhythms can increase and redirect fluxes and arrange metabolic processes optimally in time. The enzymes are not only passively adapted to existing periodic metabolite levels, but shape them actively to realise fitness advantages.

**Read more:**

- The economic basis of metabolic oscillations (preprint on arxiv.org)
- Models of optimal oscillations
- Metabolic oscillations in yeast