It follows that in order for a flux vector
Limits on the range of individual flux values can further reduce the number of allowable solutions. These constraints have the form:
α ≤ vi≤ β
where α and β are the lower and upper limits, respectively. Maximum flux values (β) can be estimated based on enzymatic capacity limitations or, for the case of exchange reactions, measured maximal uptake rates can be used. Thermodynamic constraints, regarding the reversibility or irreversibility of a reaction, can be applied by setting the α for the corresponding flux to zero if the reaction is irreversible.
These constraints are not sufficient to shrink the original solution space to a single solution. Instead a number of solutions remain which make up the allowable solution space. Linear optimization can be used to find the solution that maximizes a particular objective function. Some examples of objective functions include the production of ATP, NADH, NADPH or a particular metabolite. An objective function with a combination of the metabolic precursors, energy and redox potential required for the production of biomass has proven useful in predicting in vivo cellular behavior [9 (link),10 (link),25 (link),26 ].