Rate, maximization of ATP production, and minimization of nutrient uptake. These objectives can be represented by a linear combination of reaction fluxes of interest, which results in a linear programming model: max cT (1) s.t. S ?v = 0 (2) Vmin v vmax (3) where c in the objective function (1) is a vector of weights for the fluxes v, (2) is the set of mass balance constraints, and (3) is the set of enzymatic capacity constraints. FBA has been widely used for in silico phenotype prediction. For more methodological details of FBA, one can refer to [31,32]. Given a metabolic network in the pathologic state, we delete the reactions that cannot take place because its catalyzing enzyme is inhibited in the disease state. Although the metabolic network is in the pathologic state, it still can produce as much biomass or energy (e.g. ATP) as possible so as to maintain tissue growth. So we can determine the flux of each reaction and the mass flow of each PM01183 solubility metabolite in the pathologic state by a FBA optimization model. Let v j denote the flux of reaction R j , x i denote the mass flow of metabolite C i, that is, the mass flow of metabolite C i produced (or consumed) by all the reactions it involves in the metabolic network. We use the following linear programming model to determine the mass flows of metabolites and the fluxes of reactions in the pathologic state:max z =n0 vj Uj,j = 1,2, … , n (8) 0 xi qi,i = 1,2, … , m (9) The objective function denotes the maximization of mass flows of certain metabolites. For example, if we want to maximize the mass flows of metabolites in the biomass reaction, we can set cbiomass,i = 1 and Cj,i= 0, j biomass. Eq. (5) is the mass balance constraint of each intermediate metabolite. Constraint (6) defines that the mass flow of each metabolite is equal to the weighted sum of the fluxes of all reactions (if any) that consume this metabolite. Similarly, constraint (7) guarantees that the mass flow of each metabolite is equal to the weighted sum of the fluxes of all reactions (if any) that produce this metabolite. Constraints (14) and (15) represent the capacity limits of reaction flux and metabolite mass flow in the pathologic state, where Uj and q i are the upper bounds of variables v j and x i respectively.Determining medication metabolite mass flows and reaction fluxesIn the pathologic state, the mass flows of some metabolites are out of healthy ranges which directly result in the disease symptoms. For example, if the healthy range of the jth metabolite’s mass flow is [a i ,b j ], it means that xj should satisfy aj xj PubMed ID:https://www.ncbi.nlm.nih.gov/pubmed/26226583 bj . If xj >bj or xj