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Flux Imbalance Analysis and the Sensitivity of Cellular Growth to Changes in Metabolite Pools

Figure 1

Shadow prices in FBA capture the sensitivity of growth to flux imbalances.

Consider the FBA problem with one metabolite and two reactions, formulated as: , ; ; . The solid red line indicates the feasible solution space, and the red dot indicates the optimal solution. When the flux balance condition is relaxed and the outgoing flux from M is allowed to increase, the feasible space moves to the right (dashed blue line) and the optimal solution increases. Since the objective function increases as the right-hand-side of the flux balance constraint decreases, the metabolite has a negative shadow price. In general for intracellular metabolites, negative shadow prices correspond to growth-limiting metabolites.

Figure 1