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Power law dynamics is used to describe the stability behavior in metabolicnetworks such as chemical reaction networks (CRN's). These systems allowmultiple steady states within a single stoichiometric class. On the other sidethermodynamic constraints such as loop-less fluxes represented by the Gorbantheorem of alternatives applied to these networks reveal considerablerestrictions to their dynamics by eliminating multistability of CRN's ingeneral. Thermodynamic feasible CRN's are contained in the class of injectiveCRN's. We can give an alternative proof of the detailed balance with Brewer'sFixed Point Theorem. Furthermore we can derive by the loop-less principle theextended detailed balance. This paper establishes a link between recentresearch in CRN theory and thermodynamic basics. The result has alsoconsequences for the picture of multiple steady states as assumed for celldifferentiation and regulation. CRN's provide from their perspective not enoughmeans to maintain multistability without regulation or external control.

Some consequences of thermodynamic feasibility for the multistability and injectivity in chemical reaction networks