# 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 metabolic states in cells

Cells need to make an efficient use of metabolites, proteins, energy, membrane space, and time, and resource allocation is also an important aspect of metabolism. How, for example, should cells distribute their protein budget between different cellular functions, e.g. different metabolic pathways, to maximise growth? Cellular resource allocation can be studied by combining biochemical network models with optimality problems that choose metabolic states by their cost and benefit. Various types of resource allocation problems have been proposed. The underlying mechanistic models may describe different cellular systems (e.g. metabolic pathways, networks, or compromises between metabolism and protein production) on different level of detail and using different mathematical formulations (e.g. stoichiometric or kinetic). The optimality problems may use metabolite levels, enzyme levels, or fluxes as variables, assume different cost or benefit functions, and describe different kinds of trade-offs, in which cell variables are either constrained or treated as optimisation objectives. Due to all these differences, optimality problems may be hard to compare or combine. To bring them under one umbrella, I show that they can be derived from a common framework, and that their optimality conditions all show the same mathematical form. This unified view on metabolic optimality problems can be used to justify and combine various modelling approaches and biochemical optimality problems.

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