J =tj =nji v jfor metabolite C i(11)xi =s vj
J =tj =nji v jfor metabolite C i(11)xi =s vj =1 nnij jfor metabolite C i(6)xi =s vj =1 nij jfor methaolite C i(12)xi =j =t ji v jfor metabolite C i(7)xi =tj =ji v jfor metabolite C i(13)Li et al. BMC Systems Biology 2011, 5(Suppl 1):S11 http://www.biomedcentral.com/1752-0509/5/S1/SPage 6 of0 vj Uj,j = 1,2, … ,n (14) aj xi bi, i ?P (15)a i x i + d i- – d i+ b i , i Nexperimental methods can also determine the suitable dose to cure the disease. (14)where N is the set of non-disease-causing compounds and P is the set of disease-causing compounds, a i b i are respectively the healthy lower and upper bounds of the mass flow of the target compound C i and d i- , d i+ are variables representing the deviation of the mass flow of Ci from its healthy range. Constraint (11) is only for intermediate metabolites. Constraint (12) is for intermediate metabolites and those metabolites that are only consumed (not produced) in the system. Constraint (13) is for intermediate metabolites and those metabolites that are only produced (not consumed) in the system.Identifying drug targets and drug dose for diseasesResults In this section, we use an illustrative simulated metabolic network and a real human metabolic pathway to test the effectiveness of our method in detecting potential drug targets. The algorithm is coded by Python script and the LP models are solved by GLPK linear programming/MIP solver GLPSOL.An illustrative simulated metabolic networkAfter we obtain the flux vector of reactions v 0 in the pathologic state and the flux vector of reactions v 1 in the medication state, by comparing v0 and v1 , we can easily find the reactions whose flux has been changed by medication. We construct a sub-metabolic network by using all these reactions whose fluxes have been changed by medication along with their reactants and products. All the compounds with zero in-degree are then deleted, that is, delete all the compounds which is not a product of any reaction in this subnetwork. These compounds come into the metabolism process from the outside of the system. In the sub-metabolic network consisting of changed reactions and their related compounds, all the reactions that have no reactants are identified. These reactions (equivalently, enzymes catalyzing these reactions are actually the Metformin (hydrochloride) chemical information boundary or source of the system and determined as drug targets. This indicates that manipulating the concentration of enzymes that catalyze these reactions by drugs can adjust the reaction fluxes so that the mass flows of disease-causing compounds are changed back to the healthy ranges following the paths in the sub-metabolic network. This alignment strategy for finding drug targets is reasonable. For example, Chu and Chen constructed protein-protein interaction networks involved in the apoptosis of cancerous and normal cells to determine cancer-perturbed protein-protein interactions which allows identification of potential apoptosis drug PubMed ID:https://www.ncbi.nlm.nih.gov/pubmed/25609842 targets for anti-cancer drugs [33]. In [34], it has been indicated that the flux of a reaction is correlated with the concentration level of the enzymes catalyzing this reaction. The concentration of enzymes can be controlled by drugs, so drug dose can be determined according to the flux change of reactions between the pathologic and medication states. PrimaryFigure 2(a) is a simulated metabolic network of 12 metabolites and 8 reactions, which can be expressed by the following chemical reaction equations. R1 : 2C1 + C2 5 + C6 R2 : 4 C3.