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Metabolic Network Reductions

Genome-scale metabolic networks are exceptionally huge and even efficient algorithms can take a while to run because of the sheer size of the problem instances. To address this problem, metabolic network reductions can substantially reduce the overwhelming size of the problem instances at hand. We begin by formulating some reasonable axioms defining what it means for a metabolic network reduction to be “canonical” which conceptually enforces reversibility without loss of any information on the feasible flux distributions. Then, we start to search for an efficient way to deduce some of the attributes of the original network from the reduced one in order to improve the performance. As the next step, we will demonstrate how to reduce a metabolic network repeatedly until no more reductions are possible. In the end, we sum up by pointing out some of the biological implications of this study apart from the computational aspects discussed earlier. Author summary Metabolic networks appear at first sight to be nothing more than an enormous body of reactions. The dynamics of each reaction obey the same fundamental laws and a metabolic network as a whole is the melange of its reactions. The oversight in this kind of reductionist thinking is that although the behavior of a metabolic network is determined by the states of its reactions in theory, nevertheless it cannot be inferred directly from them in practice. Apart from the infeasibility of this viewpoint, metabolic pathways are what explain the biological functions of the organism and thus also what we are frequently concerned about at the system level. Canonical metabolic network reductions decrease the number of reactions substantially despite leaving the metabolic pathways intact. In other words, the reduced metabolic networks are smaller in size while retaining the same metabolic pathways. The possibility of such operations is rooted in the fact that the total degrees of freedom of a metabolic network in the steady-state conditions are significantly lower than the number of its reactions because of some emergent redundancies. Strangely enough, these redundancies turn out to be very well-studied in the literature.