Abstract
In this paper, we consider the Minimum Reaction Insertion (MRI) problem for finding the minimum number of additional reactions from a reference metabolic network to a host metabolic network so that a target compound becomes producible in the revised host metabolic network in a Boolean model. Although a similar problem for larger networks is solvable in a flux balance analysis (FBA)-based model, the solution of the FBA-based model tends to include more reactions than that of the Boolean model. However, solving MRI using the Boolean model is computationally more expensive than using the FBA-based model since the Boolean model needs more integer variables. Therefore, in this study, to solve MRI for larger networks in the Boolean model, we have developed an efficient Integer Programming formalization method in which the number of integer variables is reduced by the notion of feedback vertex set and minimal valid assignment. As a result of computer experiments conducted using the data of metabolic networks of E. coli and reference networks downloaded from the Kyoto Encyclopedia of Genes and Genomes (KEGG) database, we have found that the developed method can appropriately solve MRI in the Boolean model and is applicable to large scale-networks for which an exhaustive search does not work. We have also compared the developed method with the existing connectivity-based methods and FBA-based methods, and show the difference between the solutions of our method and the existing methods. A theoretical analysis of MRI is also conducted, and the NP-completeness of MRI is proved in the Boolean model. Our developed software is available at “http://sunflower.kuicr.kyoto-u.ac.jp/~rogi/minRect/minRect.html.”
Highlights
Metabolism is one of the most important biological processes in organisms
The computational complexity of the Boolean model is large, we develop an efficient method based on integer programming (IP) [27,28], which is often used as a formalization of NP-complete problems and there is an efficient free solver for IP called CPLEX [29]
As for species, a reference network includes the chemical reactions of all species, whereas the metabolic networks of E. coli are used for the host networks
Summary
Metabolism is one of the most important biological processes in organisms. Relations between reactions and chemicals in the metabolism are often represented by metabolic networks [1]. Since many of these metabolic processes can produce commodity and specialty chemicals, the manipulation of metabolisms has been extensively studied in the field of metabolic engineering. Techniques for production of desired chemicals using a microbial host are roughly classified into the following three types [5]: (a)combinations of existing pathways, (b)engineering of existing pathways, and (c) de novo pathway design. In (a), partial pathways can be recruited from independent organisms and co-localized in a single host. It is to be noted that (a) focuses on the topology of the given metabolic networks, while (b) and (c) utilize the information of the structures of chemicals as well
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