Failure Mode and Effect Analysis (FMEA)
Metabolism can be represented in the form of a metabolic network (or graph), such that metabolites (nodes) are connected to one another (i.e. share an edge) if there exists a metabolic reaction that converts one metabolite to the other (Jeong et al. , 2000). If the graph is undirected, all reactions are considered to be reversible. If the graph is directed, edges connected nodes only in the direction that the reaction is presumed to proceed. An existing genome-scale metabolic model of Arabidopsis plant leaf metabolism, constructed by Arnold and Nikoloski (2014) and updated by Herrmann et al . (2019c) was converted to a directed metabolite-metabolite graph and analysed using the networkx package (Version 2.2) in Python (Version 3.6.9). Reversible reactions were accounted for by applying two separate edges between the respective metabolites, one in either direction. All non-carbon compounds, small molecules and cofactors were removed from the graph. The model is leaf specific and is compartmentalized to include the chloroplast, mitochondrion, cytosol and peroxisomes.
We applied the FMEA framework to primary carbon metabolism. We considered metabolites as the components of the metabolic system. We calculated the risk of failure for each component considering, for instance, failure to be that the concentration of a particular metabolite falls outside a concentration range required to sustain metabolic activity. The FMEA analysis does not presume what the required concentration of a metabolite should be at a given condition and can therefore be considered an unbiased approach (Lewis et al. , 2012).
The probability of failure for a given metabolite M downstream of ribulose-1,5-bisphosphate carboxylase/oxygenase (Rubisco) was calculated as:
\(P_{M}=\frac{L_{\mathrm{R,M}}}{L_{\mathrm{R,X}}\sum d_{\mathrm{R,M}}}\),
where LR,M is equal to the shortest path length from Rubisco to metabolite M, LR,X is the longest of all the shortest paths to metabolites in the network, and\(\sum d_{\mathrm{R,M}}\) is the number of alternative paths to metabolite M having the shortest length. LR,X is a normalization constant and is equal to 14 in all calculation ofPM . Overall, PM considers the probability of failure of M as a calculation of the number of upstream reactions and metabolites that are required for the production of M . The severity of failure for each metabolite (SM ) was calculated such that:
\(S_{M}\mathrm{=N}_{M}\times C_{M}\),
where NM is the degree of metabolite M(i.e. number of direct neighbours) and CM is the normalized betweenness centrality of M . The number of neighbours of M indicates the number of reactions that would fail ifM was not present in the system. Betweenness centrality is defined as the normalized sum of the total number of shortest paths that pass through a node and can thus be considered a proxy for how important that metabolite is in the production of other metabolites.SM calculates a severity for M based of the number of reactions and down-stream metabolites that cannot occur in the absence of M .
The risk factor (RM ) was calculated for each metabolite such that
\(R_{M}\mathrm{=P}_{M}\times S_{M}\) .
The risk factor takes into consideration how heavily the production ofM is dependent on other metabolites and other reactions in the system. It also considers how many other metabolites and reactions in the system are dependent on the production of M .RM therefore considers how important M is to the overall system functionality.
Although we could equally well calculate the risk factor of individual reactions in a metabolic system, we have here chosen to consider metabolites as the individual components of the system. This is because metabolites are the fundamental building blocks of the metabolic system, whereas reactions are the means to producing these building blocks. For example, it is possible for one reaction to fail but for all metabolites in the system to still be produced as required.