Reliability engineering identifies cytosolic fumarase as a fail-safe in the metabolic system
The above results and Figures S5 and S6 show that there is not a simple linear relationship between diurnal leaf carbon accumulation and temperature. Using an existing genome-scale metabolic model of Arabidopsis carbon metabolism in the leaf, we have taken a network topology approach to understand how organic acid accumulation changes with temperature treatment. By adapting a Failure Mode and Effect Analysis (FMEA), as outlined in the Materials and Methods, we were able to identify metabolites that pose a high risk to the metabolic system.
High-risk metabolites are those which, in the event of failure, will create the greatest disturbance to the metabolic system. In engineering, the risk factor is calculated based on the probability of failure (PM ) and the severity of failure (SM ). Here, we estimatedPM based on the length of the shortest path and the number of paths that lead to a metabolite M .SM can be associated with the number of neighbours of a metabolite and the number of paths that lead to a metabolite (see Materials and Methods). The latter is calculated as the betweenness centrality (i.e. the number of shortest paths that pass through that metabolite).
Table 1 shows the metabolites with the 10 highest risk factors. The average risk factor of all metabolites was 0.005. Malate, oxaloacetate and glucose-6-phosphate stand out as high-risk metabolites in the cytosol (Table 1). In the chloroplast, α-ketoglutarate, glyceraldehyde 3-phosphate, pyruvate, fructose 6-phosphate, ribose 5-phosphate, glucose 6-phosphate, and phosphoenolpyruvate have a high factor. Metabolites related to carbon metabolism and found in the mitochondria have an average or below average risk factor. Only the chloroplast, mitochrondrion, cytosol and peroxisomes compartments were taken into consideration, as specified in the Arnold and Nikoloski (2014) model. The full list of risk factor calculations are available on Zenodo and Github (DOI: 10.5281/zenodo.3596623.
The network structure that connects all high-risk metabolites shows that these are well-connected nodes and are located only a few reactions upstream of a carbon sink (Table 1, Fig. 4). Carbon sinks are generally low-risk metabolites (R < 0.001). In particular, fumarate is an endpoint in the system and has a null betweenness centrality (CM ). Therefore, changing the concentration of fumarate has a negligible effect on the overall metabolic system. Because changes in the concentration of high-risk metabolites could have a negative effect on system functionality, we hypothesized that adjusting the flux to the nearest carbon sink could minimize the overall system disturbance. Thus, for instance, fumarate could act as a fail-safe, buffering changes in malate, oxaloacetate and other upstream metabolites under different temperature conditions (Fig. 4). To test this hypothesis, we adopted a kinetic modelling approach.