Computational Design of Reduced Metabolic Networks

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Abstract
Cellular functions are based on thousands of chemical reactions and transport processes, most of them being catalysed and regulated by specific proteins. Systematic gene knockouts have provided evidence that this complex reaction network possesses considerable redundancy, that is, alternative routes exist along which signals and metabolic fluxes may be directed to accomplish an identical output behaviour. This property is of particular importance in cases where parts of the reaction network are transiently or permanently impaired, for example, due to an infection or genetic alterations. Here we present a computational concept to determine enzyme-reduced metabolic networks that are still sufficient to accomplish a given set of cellular functions. Our approach consists of defining an objective function that expresses the compromise that has to be made between successive reduction of the network by omission of enzymes and its decreasing thermodynamic and kinetic feasibility. Optimisation of this objective function results in a linear mixed-integer program. With increasing weight given to the reduction of the number of enzymes, the total flux in the network increases and some of the reactions have to proceed in thermodynamically unfavourable directions. The approach was applied to two metabolic schemes: the energy and redox metabolism of red blood cells and the carbon metabolism of Methylobacterium extorquens. For these two example networks, we determined various variants of reduced networks differing in the number and types of disabled enzymes and disconnected reactions. Using a comprehensive kinetic model of the erythrocyte metabolism, we assess the kinetic feasibility of enzyme-reduced subnetworks. The number of enzymes predicted to be indispensable amounts to 14 (out of 28) for the erythrocyte scheme and 13 (out of 77) for the bacterium scheme, the largest group of enzymes predicted to be simultaneously dispensable amounts to 3 and 37 for these two systems. Our approach might contribute to identifying potential target enzymes for rational drug design, to rationalising gene-expression profiles of metabolic enzymes and to designing synthetic networks with highly specialised metabolic functions.

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