We discuss chemical reaction networks and metabolic pathways based on stoichiometric network analysis, and introduce deformed toric ideal constraints by the algebraic geometrical approach.  With the deformed toric ideal constraints, the shape of flux is constrained without introducing ad hoc constraints. To illustrate the effectiveness of such constraints, we discuss two examples of chemical reaction network and metabolic pathway; in the former the shape of flux is constrained completely by deformed toric ideal constraints, and in the latter, it is shown the deformed toric ideal constrains the  parameters of flux at least partially  .
We discuss chemical reaction networks and metabolic pathways based on stoichiometric network analysis, and introduce deformed toric ideal constraints by the algebraic geometrical approach. This paper concerns steady state flux of chemical reaction networks and metabolic pathways. With the deformed toric ideal constraints, the linear combination parameters of extreme pathways are automatically constrained without introducing ad hoc constraints. To illustrate the effectiveness of such constraints, we discuss two examples of chemical reaction network and metabolic pathway; in the former the flux and the concentrations are constrained completely by deformed toric ideal constraints, and in the latter, it is shown the deformed toric ideal constrains the linear combination parameters of flux at least partially . Even in the latter case, the flux and the concentrations are constrained completely with the additional constraint that the total amount of enzyme is constant .
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This paper concerns steady state flux of chemical reaction networks and metabolic pathways.
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shape of flux is
linear combination parameters of extreme pathways are automatically
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shape of flux is
flux and the concentrations are
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linear combination
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. Even in the latter case, the flux and the concentrations are constrained completely with the additional constraint that the total amount of enzyme is constant