Metabolic network

A metabolic network is a connected system of chemical reactions that transform the metabolites of a biological cell or organism. One reaction's product can be another reaction's substrate, so the activity of one enzyme cannot by itself determine flow through the whole system.

A minimal example has input $u$ into metabolite $A$, conversion $A\to B$ at rate $v$, and removal of $B$ at rate $w$:At a steady state, $u=v=w$. Doubling the maximum capacity of the middle enzyme does not double throughput if the input remains fixed. In a larger metabolic network, the same bookkeeping is expressed as $\dot{\mathbf{x}}=S\mathbf{v}$, with stoichiometric matrix $S$ and metabolic flux vector $\mathbf{v}$.

A genome-scale reconstruction for Escherichia coli combined annotated genes, biochemical literature and strain information to specify possible reactions. The network constrains which conversions are possible; predicting actual rates still needs environmental constraints and modelling assumptions.^[ref]

A stoichiometric matrix records how each reaction changes the amounts of the species in a chemical reaction network. Rows correspond to species and columns to reactions; an entry is positive for production and negative for consumption. For a well-mixed system of fixed volume, with concentration vector $\mathbf{x}$ and reaction-rate vector $\mathbf{v}$, the mass-balance model is $\dot{\mathbf{x}}=S\mathbf{v}$.

Consider input to $A$, conversion $A\to B$, and removal of $B$, at rates $u,v,w$. Counting only the two internal species givesAt a steady state, $S\mathbf{v}=0$, so $u=v=w$. All three rates can be equal at many different magnitudes: stoichiometry constrains the allowable balance without supplying the chemical kinetics that sets the actual rate. Genome-scale metabolic networks use this same bookkeeping for many reactions.^[ref]