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Figure 6 | BMC Systems Biology

Figure 6

From: Morphisms of reaction networks that couple structure to function

Figure 6

Examples of chemical reaction network morphisms. Circles are species and squares are reactions. Red arrows are species mappings m S and blue arrows are reaction mappings m R . Solid arrows indicate morphisms that are emulations. More examples are given in Additional file2. (A) A simple stoichiomorphism: the species in the source reactions are distinct. In general, multiple separate copies of a system will map to it via a trivial map that is a homomorphism and stoichiomorphism. (B) This is a homomorphism, but is not a stoichiomorphism. For s 0 , r ^ 0 : Σ r m R - 1 r ^ 0 φ s 0 , r =-2-1=φ m S s 0 , r ^ 0 . (C) This is a stoichiomorphism, but is not a homomorphism or a reactant morphism. r 0 = ρ → π with ρ s 0 =1 but m R r 0 = r ^ 0 = ρ ^ π ^ with ρ ^ m S s 0 = ρ ^ s ^ 0 =2, so ρ ^ m S ρ and m r 0 m S ρ π ^ . (D) This is a homomorphism but not a stoichiomorphism. For s 1 , r ^ 0 : Σ r m R - 1 r ^ 0 φ s 1 , r =12=φ m S s 0 , r ^ 0 . (E) This stoichiomorphism is not a homomorphisms, but is a reactant morphism. r 0 = ρ → π and m R r 0 = r ^ 0 = ρ ^ π ^ with ρ ^ = m S ρ and m R r 0 = m S ρ π ^ . (F) This reactant morphism is not a homomorphism but is a stoichiomorphism. E.g., for s 1 , r ^ 0 : Σ r m R - 1 r ^ 0 φ s 1 , r =φ s 1 , r 0 +φ s 1 , r 1 =2·k+0·k=1·2k=φ m S s 1 , r ^ 0 .

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