Minimization of intermediate concentrations as a suggested optimality principle for biochemical networks. I: Theoretical analysis
The present paper investigates the relationship between two problems: (1) the optimization problem of minimizing the total osmolarity of intermediates in biochemical reaction networks, and (2) the multiple criteria optimization problem of simultaneously minimizing all intermediate concentrations. It is proved that each solution of problem (1) is contained in the set of all non-dominated outcomes for problem (2). Turning out that in each optimal state, the network can be subdivided into a slow and a fast subsystem, an algorithm is developed for transforming reaction systems into ones without convex conservation relations (i.e. relations with only non-negative coefficients), and the implications of such relations to the optimization problem are investigated. For the biochemical reaction network resulted from a system with convex conservations relations that the efficient solutions can easily be interpreted in terms of the original system. The present theoretical approach can be considered as an approximate mathematical representation of the wide separation of rate constants, a characteristic feature of biochemical systems further analyzed and applied in the second part of this paper, see the following review, Zbl 0731.92007.
minimizing the total osmolarity of intermediates
minimizing all intermediate concentrations
scientific article; zbMATH DE number 4209922
scientific article