BackgroundThe numerous diverse metabolic pathways by which plant compounds can be produced make it difficult to predict how colour pigmentation is lost for different tissues and plants. This study employs mathematical and in silico methods to identify correlated gene targets for the loss of colour pigmentation in plants from a whole cell perspective based on the full metabolic network of Arabidopsis. This involves extracting a self-contained flavonoid subnetwork from the AraCyc database and calculating feasible metabolic routes or elementary modes (EMs) for it. Those EMs leading to anthocyanin compounds are taken to constitute the anthocyanin biosynthetic pathway (ABP) and their interplay with the rest of the EMs is used to study the minimal cut sets (MCSs), which are different combinations of reactions to block for eliminating colour pigmentation. By relating the reactions to their corresponding genes, the MCSs are used to explore the phenotypic roles of the ABP genes, their relevance to the ABP and the impact their eliminations would have on other processes in the cell.ResultsSimulation and prediction results of the effect of different MCSs for eliminating colour pigmentation correspond with existing experimental observations. Two examples are: i) two MCSs which require the simultaneous suppression of genes DFR and ANS to eliminate colour pigmentation, correspond to observational results of the same genes being co-regulated for eliminating floral pigmentation in Aquilegia and; ii) the impact of another MCS requiring CHS suppression, corresponds to findings where the suppression of the early gene CHS eliminated nearly all flavonoids but did not affect the production of volatile benzenoids responsible for floral scent.ConclusionsFrom the various MCSs identified for eliminating colour pigmentation, several correlate to existing experimental observations, indicating that different MCSs are suitable for different plants, different cells, and different conditions and could also be related to regulatory genes. Being able to correlate the predictions with experimental results gives credence to the use of these mathematical and in silico analyses methods in the design of experiments. The methods could be used to prioritize target enzymes for different objectives to achieve desired outcomes, especially for less understood pathways.

A minimal cut set is a minimal set of reactions whose inactivation would guarantee a failure in a certain network function or functions. Minimal cut sets (MCSs) were initially developed from the metabolic pathway analysis method (MPA) of elementary modes (EMs); they provide a way of identifying target genes for eliminating a certain objective function from a holistic perspective that takes into account the structure of the whole metabolic network. The concept of MCSs is fairly new and still being explored and developed; the initial concept has developed into a generalized form and its similarity to other network characterizations are discussed. MCSs can be used in conjunction with other constraints-based methods to get a better understanding of the capability of metabolic networks and the interrelationship between metabolites and enzymes/genes. The concept could play an important role in systems biology by contributing to fields such as metabolic and genetic engineering where it could assist in finding ways of producing industrially relevant compounds from renewable resources, not only for economical, but also for sustainability, reasons.

Different genes are expressed in different tissues, depending on functional objectives and selection pressures. Based on complete knowledge of the structure of the metabolic network and all the reactions taking place in the cell, elementary modes (EMs) and minimal cut sets (MCSs) can relate compounds observed in a tissue, to the genes being expressed by respectively providing the full set of non-decomposable routes of reactions and compounds that lead to the synthesis of external products, and the full set of possible target genes for blocking the synthesis of external products. So, for a particular tissue, only the EMs containing the reactions that are related to the genes being expressed in those tissues, are active for the production of the corresponding compounds. This concept is used to develop an algorithm for determining a matrix of reactions (which can be related to corresponding genes) taking place in a tissue, using experimental observations of compounds in a tissue. The program is applied to the Arabidopsis flower and identified 20 core reactions occurring in all the viable EMs. They originate from the trans-cinnamate compound and lead to the formation of kaempferol and quercetin compounds and their derivatives, as well as anthocyanin compounds. Analyses of the patterns in the matrix identify reaction sets related to certain functions such as the formation of derivatives of the two anthocyanin compounds present, as well as the reactions leading from the network's external substrate erythrose-4P to L-Phenyla-lanine, cinnamyl-alc to trans-cinnamate and so on. The program can be used to successfully determine genes taking place in a tissue, and the patterns in the resulting matrix can be analysed to determine gene sets and the state of the tissue.