Biology Reference
In-Depth Information
includes exchange reactions that allow the exchange of metabolites
(either substrates or byproducts) with the environment.
Given the stoichiometric matrix S for a metabolic network, one
could write a system of ordinary differential equations to describe the
time evolution of the metabolite concentrations X of the system:
dX
dt
(1)
=
Sv X
()
where v = v ( X ) are the metabolic fluxes through each reaction. Note
that eq. (1) assumes that all the metabolites are in a single well-mixed
compartment in the cell. Since metabolic reactions have relatively short
characteristic time scales, for most purposes the equation above can
be simplified by assuming that the system is in a steady state, that is,
Sv = 0
(2)
This equation represents the conservation of mass in the metabolic net-
work under steady-state conditions, that is, the production rate of each
metabolite equals its consumption rate. Equation (2) defines all the flux
distributions allowed by the stoichiometry of the entire reaction net-
work under steady-state conditions and hence represents a constraint
on the allowable range of functionalities of the metabolic network.
Reaction stoichiometry is the most fundamental of the constraints
acting on the overall functionality of the metabolic network, but other
constraints are also commonly imposed on the system in constraint-
based analysis. By separating reversible reactions into separate forward
and backward reactions, all fluxes are restricted to be nonnegative:
v i
0
(3)
Directionality constraints that restrict the flux through a reaction to
proceed in one direction due to thermodynamic reasons can be enforced
by only retaining the reaction operating in the desired direction in the
model. Further constraints on individual fluxes can be imposed in the
form of maximum reaction rates:
v i
v i max
(4)
Typically maximal reaction rates are not known for intracellular
reactions, but upper limits for these rates can be estimated based on
enzyme concentrations in a cell. For exchange reactions, on the other
hand, the maximal rates are usually at least partially known, since
these rates can be experimentally measured as a function of substrate
concentrations [26]. Alternatively, one can measure condition-dependent
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