Minimal cut sets and their use in modelling flavonoid metabolism

Abstract

This research makes use of the genome-scale metabolic information of the Arabidopsis thaliana (Arabidopsis) plant to better understand the systemic behaviour of a multicellular cell, using mathematical and in silico methods. To avoid combinatorial explosion resulting from the large network size, an appropriate subnetwork is first extracted. This results in an Arabidopsis flavonoid subnetwork that is self-contained, in the sense that all its exchange fluxes are accounted for and it is representative of flavonoid metabolism in the context of whole cell metabolism. This subnetwork is verified by comparing its compounds and reactions with a recently reconstructed and verified Arabidopsis network. The research focusses on anthocyanins, a major flavonoids subgroup responsible for colour pigmentation in plants. To determine the anthocyanin biosynthetic pathway (ABP), elementary modes (EMs) or non-decomposable pathways that allow the system to operate at steady state, are calculated. These EMs are classified into groups and those responsible for the formation of anthocyanin compounds are taken to constitute the ABP. The central analysis approach in the research is that of minimal cut sets (MCSs), a fairly new metabolic pathway analysis (MPA) concept. A review of various development stages of the MCS concept and its relationship to other similar approaches is given for the first time in this thesis. MCSs provide a mathematically complete list of candidate genes for eliminating a certain objective function from a holistic perspective, without needing prior knowledge of genes. They are used to identify target genes for loss of colour pigmentation in plants. Other methods, such as reaction participation, are then used to study the implications that the elimination of these target genes would have on other processes in the cell. MCSs are also used to look at the fragility coefficient of the ABP genes and how crucial they are to the pathway. These analyses provide quantitative support for experimental results e.g., gene connectivity determines the number of EMs the ABP genes are connected to, and backs the pleiotropic characteristics of the “early” ABP genes and how it relates to where they occur in the pathway. The research also uses flux balance analysis (FBA) to simulate fluxes (reaction rates) for the different MCSs eliminating anthocyanin compounds. The FBA provides a quantitative measure of the relative impact that the different MCSs would have on the production and processes of other flavonoids and related compounds. Certain simulation outcomes correspond to experimental observations, e.g., the simulated fluxes from eliminating the MCS containing the CHS gene, support the observation that the suppression of the anthocyanin pathway, via CHS silencing, dramatically reduces flavonoids but does not affect scent (benzenoids) production. The research also develops a method for determining which genes are being expressed in a tissue, using EMs and MCSs in conjunction with information about compound products. This involves developing an algorithm and writing a program to determine which reactions are being expressed in a tissue. The algorithm and program worked both on an example network and on the flavonoid network used to determine reactions taking place in the Arabidopsis flower. Information obtained from the results includes identifying reactions that are critical to the flower as well as reaction sets that would represent gene sets. The program still needs further development to incorporate analytical clustering methods and a user-friendly interface.