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Network, MFA and FBA

S·v = 0. A small network with glucose, pyruvate, NADH and ATP. Measure fluxes and see when the rest are determined (MFA), or set bounds and an objective and let a linear program choose (FBA).

Network

Line thickness follows the flux. Dashed grey lines are fluxes that the data cannot determine. Hover a reaction to find its column in the S matrix.

Stoichiometric matrix S

Fluxes

How it works

Every reaction is a column of S and every metabolite a row. At steady state S·v = 0 for all metabolites, including the cofactors NADH and ATP. This toy network has 10 reactions and rank(S) = 4, so 6 fluxes can be chosen freely.

MFA measures some fluxes and calculates the rest from S·v = 0. With as many independent measurements as degrees of freedom, every flux is determined. With more, the extra balances check the data. With fewer, some fluxes stay free.

FBA does not measure anything. It adds bounds and an objective and solves a linear program. Many flux distributions can reach the same optimum, so the page shows one (the one with the smallest total flux) and the range of each flux at the optimum.

The network is invented for teaching. Respiration gives 1 ATP per NADH, and surplus ATP is burned in the ATP use reaction, whose lower bound is the maintenance.