Metabolic networks are biochemical reaction networks. Metabolites are chemical species, reactions convert substrate into product metabolites. Metabolic networks can be visualized as a hypergraph, metabolites usually as nodes and reactions as directed hyperedges between the nodes.
Alternatively, the stoichiometric matrix is frequently used, containing the stoichiometric coefficients. Metabolites are associated with the matrix rows, reactions with columns. Negative entries stand for the consumption of a metabolite and positive entries indicate production. Using matrix notation, the concentration change can be described by the following formula:
dc/dt = N * r(t)Here, c1 × m/dt is a vector containing concentration changes, Nm × q is the stoichiometric matrix and r(t) is a 1 × q flux vector or flux distribution. The flux vector r(t) contains a flux value for each of the q reactions, m denotes the number of metabolites.
Many common applications assume quasi steady state, assuming that for a balanced network, concentrations of (internal) metabolites remain constant. This simplifies the above equation to
N * r = 0reducing possible flux values r to the nullspace of N. The irreversibility of reactions (reversible reactions can be split into two irreversible ones) leads to
r ≥ 0Both constraints together define a convex polyhedral cone -- the flux cone -- a well studied object in computational geometry and convex analysis. Applications based on the given (and possibly additional) constraints are thus subsumed as constraint based approaches.
Elementary modes -- minimal functional pathways for metabolic networks -- can be defined for the network, and an implementation for such computation is contained in the {@link ch.javasoft.metabolic.efm metabolic.efm} package and subpackages.
Other common applications like flux balance analysis (FBA) use linear programming and related techniques to find obtimal solutions for different objective functions. Typical objectives are maximization of biomass yield or of ATP, a typical energy carrier in biochemical networks. For more information, we refer to the following selected wiki pages: