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