| Resumo: |
Background: Flux balance and network-based pathway analyses are theoretical tools aimed to find optimal steady state flux distributions in a metabolic network subject to additional constraints on the rates of the reaction steps. Although these methods are mathematically accurate, there are several physicochemical and computational aspects that are questionable and misleading. In particular, it is well known that the flux balance analysis may result in multiple flux distributions for the same objective function. 

Results: The flux balance and network-based pathway analyses are reformulated in terms of reaction routes (RRs), a theoretical framework that has been developed by Horiuti over 50 years ago. Not only does the theory of RRs provide the most general and rigorous definition of a pathway, but it also relates the steady state rates of the reaction steps with the rates along RRs or pathways. In this work, we employ the simple relation between the steady state rates of the reaction steps and the rates along RRs (fluxes) established by Horiuti to eliminate the steady state constraints. 
	
Conclusion: The newly proposed RR approach represents a powerful tool for a deeper understanding of optimal flux distributions in metabolic reaction systems. Application of the RR approach to several typical systems from the literature surprisingly reveals that an infinite number of flux distributions for the same optimal objective function may be a rule rather than the exception

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