E. coli and B. subtilis without feedback from MN and illustrate their causal structure. Next we augment the GRNs with feedback from their respective MNs by including (a) links from genes coding for enzymes to metabolites produced or consumed in reactions catalyzed by those enzymes and (b) links from metabolites to genes coding for transcription factors whose transcriptional activity the metabolites alter by binding to them. We find that the inclusion of feedback from MN into GRN significantly affects its causal structure, in particular the number of levels and relative positions of nodes in the hierarchy, and the number and size of the strongly connected components (SCCs). We then study the functional significance of the SCCs. For this we identify condition specific feedbacks from the MN into the GRN by retaining only those enzymes that are essential for growth in specific environmental conditions simulated via the technique of flux balance analysis (FBA). We find that the SCCs of the GRN augmented by these feedbacks can be ascribed specific functional roles in the organism. Our algorithmic approach thus reveals relatively autonomous subsystems with specific functionality, or regulatory modules in the organism. This automated approach could be useful in identifying biologically relevant modules in other organisms for which network data is available, but whose biology is less well studied.The genetic regulatory network (GRN) plays a key role in controlling the response of the cell to changes in the environment. Although the structure of GRNs has been the subject of many studies, their large scale structure in the light of feedbacks from the metabolic network (MN) has received relatively little attention. Here we study the causal structure of the GRNs, namely the chain of influence of one component on the other, taking into account feedback from the MN. First we consider the GRNs of  The control of gene expression is central to cellular dynamics. All cellular processes—metabolism, growth, cell division, response to stimuli, etc.—are related to characteristic subsets of genes that need to be expressed for the respective processes to take place inside the cell. The expression of genes inside a cell is controlled via a complex process of inter-regulation involving, in part, a network of genes called the gene regulatory network (GRN). Due to the large number of genes and interactions in a GRN and the presence of feedback loops, it becomes difficult to track the causal regulation from one component of the GRN to another. In order to obtain a system level understanding of gene interactions of an organism, an understanding of the structure of its GRN and its design principles is necessary.Several studies have characterized the GRNs on a global and local scale. The GRNs have been found to follow an exponential in-degree distribution and a power law out-degree distribution –3. They Despite its frequent isolated treatment the GRN of an organism functions in conjunction with other networks in the cell, in particular the metabolic network (MN). It has been shown  that aboE. coli and B. subtilis, from a number of sources in literature [E. coli), and 1700 nodes and 3500 edges (B. subtilis).To this end, we obtain the data about the genetic regulatory interactions and metabolism of two microorganisms, terature –43. CertWe first organize each GRN (without including the metabolite nodes) into a hierarchical structure by using a modified form of the vertex sort algorithm of Jothi et al  which inSecond, we augment the GRN by introducing nodes and links corresponding to metabolites belonging to the MN as described above, and discuss how the hierarchical structure changes. We show that GRNs retain their characteristic hierarchical structure upon including the feedbacks from metabolism; however they become more complicated and the causal ordering governed by the relative positions of genes among the various levels in the hierarchy is significantly altered.E. coli and B. subtilis, our methodology provides an algorithmic approach for finding important sub-systems of organisms for which the GRN and MN has been obtained.Third, we exploit the fact that not all feedbacks from the MN are functional at a given time. To this end we simplify the augmented network by first identifying functionally relevant feedbacks from the MN into the GRN under a number of simulated environmental conditions (ECs) using the technique of flux balance analysis (FBA) , and theE. coli which is large and complicated and cannot be assigned a simple functional role.Finally we also attempt to find sub-modules of the largest SCC of E. coli from RegulonDB [B. subtilis from Freyre-Gonzalez et al [B. subtilis [E. coli contains 3277 nodes and 8740 edges. The GRN of B. subtilis consists of 1681 nodes and 3096 edges. Further details are given in We obtain the gene regulatory network interaction data of egulonDB , and thaez et al  which issubtilis . The GRNi and j in the subgraph, there exists a path in the sub-graph from i to j and from j to i. Together the SCCs capture all the feedbacks in the network. Furthermore, a SCC, owing to its property that any node belonging to it can affect any of its other nodes, can be thought of as forming a semi-autonomous group of nodes, or a module, of the full network. Understanding the functioning of these modules and placing them within the parent network can provide a way to understand the functional architecture of the parent network [The GRNs of bacteria are known to have a pyramidal hierarchical structure where the number of nodes in the hierarchical levels decreases as one moves to the higher levels , 27, 45. network .E. coli and B. subtilis, which produces corresponding directed acyclic graphs (DAGs). The condensation of a graph involves identification of SCCs of the graph, replacing each of the SCC by a single node (SCC node), and replacing the edges to/from the original nodes in the SCCs by new edges to/from the SCC node. The DAG, by construction, is devoid of cycles or feedback loops, and hence it is possible to unambiguously place the nodes of the network in a chain of command hierarchy. The hierarchical organization of the GRN of E. coli and B. subtilis is shown in Varying procedures of defining the hierarchical levels for a GRN exist in the literature , 15, 27.The hierarchical organization of the GRNs obtained through the procedure above clearly elucidates the causal regulatory relationships between the transcriptional regulators as well as the regions of feedbacks (SCCs) in the GRNs. In the E. coli has a total of 7 SCCs while the GRN of B. subtilis has a total of 4 SCCs  is also smaller than for E. coli (2.67) suggesting that many links may not have been documented. An earlier version of the E. coli network also did not have a giant SCC (the largest SCC in [B. subtilis network in the future a larger giant SCC may emerge in the B. subtilis network.The GRN of f 4 SCCs . Most SCSCC 7 in  has 56 ncoli see  while tht SCC in  had 11 nE. coli contains 6 (of 7) σ-factors and global TFs like crp, fis, ihf, hns. The largest SCC in B. subtilis contains the housekeeping sigma factor sigA. Quantitatively, the largest SCC of E. coli has over 80% of the top 10 global regulators (based upon out-degree of the genes), while B. subtilis has over 25%. It is clear from the respective set of SCCs that, for the present constructions of GRNs, the GRN of E. coli has more cycles than that of B. subtilis (on account of more SCCs and larger size of the LSCC). The above suggests that the GRNs of both bacteria have largely hierarchical tree like structures with mainly small and isolated feedback loops, and one larger feedback structure located near the top of the hierarchy that influences a large number of downstream genes. This picture is essentially the same as in [E. coli at the top of the hierarchy. The LSCC in E. coli in the present study is 14 times larger than the second largest SCC. Some of the smaller SCCs in [Despite these differences in size, the largest SCCs of both the organisms have two striking similarities. First, they are located at the top of the hierarchy. Second, both consist of global regulatory factors. The largest SCC in me as in  except tThe activity of some TFs is controlled by the binding of small molecules that are part of the cell’s metabolism. These metabolites typically bind to the TF to alter its capacity to bind to target promoters. The production/consumption of such metabolites may be catalysed by enzymes whose genes are regulated by the same TF. Each binding reaction of a metabolite with a TF that alters the latter’s regulatory activity thus creates a feedback from the MN to the GRN . A histogram of the potential impact of feedbacks is shown in B. subtilis, wherein the LSCC and perhaps feedback to it could emerge.Crp (coded by gene crp) in the core of the E. coli network  which binds the TF the cell –50. On tThe incorporation of feedbacks into the GRN from the metabolic network brings substantial changes in the structure and organization of the GRN. For the purpose of reference, we label the GRN augmented with feedbacks from metabolism as graph E. coli and B. subtilis respectively). For E. coli, increase in number of feedbacks further complicates the already complex structure of the largest SCC. In both the organisms, the amino acids are predominantly present in the largest SCCs, whereas the sugars mostly occupy the small SCCs. This makes sense with the following logic: The sub-networks involving the sugars function at the input end of the metabolic network. When a sugar is present as food in the environment, the corresponding sub-network is active, while sub-networks related to other sugars are inactive. Thus the sub-networks relating to the sugar molecules form individual SCCs. Once the food is taken in, a core machinery which is active in every simulated environmental condition can produce various required molecules, e.g., the building block amino acids, for the cell. We will later (section 5) describe results which will shed more light on this observation. One stark difference between the largest SCCs of the two organisms relates to the presence of σ-factors in the LSCC of E. coli while the σ-factors are absent in the LSCC of B. subtilis. On the other hand there is also a similarity: amino acid and peroxide/iron modules are in the largest SCCs for both. For B. subtilis the new largest SCC can be loosely organized into 3 communities, E. coli is densely connected and its decomposition into communities is not that obvious. We discuss some aspects of this later (section 6). Further, the number of small SCCs has grown substantially both in size and in numbers .Due to addition of feedbacks involving enzymes and metabolites, the largest SCCs were 6 fold and 14 fold bigger than SCCs of pure GRN . In graph SCC14, melR), 2 genes coding for enzymes  and 1 metabolite (Melibiose)—but also shifts to level 2 , but regulates few (low out-degree), Figs B. subtilis graph σ-factors which generally are not modulated by the metabolites, and the other 2 genes coded for TFs received no feedback from metabolism. It would be interesting to see whether, as the database for B. subtilis expands, the amino acid metabolism cluster SCC2 merges with the housekeeping σ-factor cluster SCC9  , 51 , as the functionality of larger modules can often be understood in terms of smaller structures.E. coli and five in B. subtilis. Each size 3 module has one metabolite, one TF gene and one enzyme gene. The modules of size 3 can be classified into two categories: negative feedback loop and positive feedback loop . While the composite logic in these modules remain either a NFL or PFL, their internal composition in terms of position and sign of the interaction may vary. UxaC converts this molecule to D-fructuronate. One can guess that the function of the module, a NFL with three inhibitory links, is to metabolize D-fructuronate when it is in excess into a further downstream product. The internal structure of the module shows how this can be achieved. D-fructuronate binds to the TF UxuR and inactivates it. UxuR was repressing the expression of gene uxuB and hence preventing the production of enzyme UxuB. When UxuR is inactivated by D-fructuronate, the enzyme UxuB is produced and this in turn catalyzes a reaction that consumes D-fructuronate. This functionality is useful when D-fructuronate is in excess, consistent with the fact that we only see it when aldehydo-D-glucoronate is the food source. It helps the assimilation of this food source into the metabolism. Further it prevents gene expression  of uxuBAlmost every topology we have found as a module has a clearly identifiable functionality or purpose which is evident from XylR and the enzyme XylA. However the proximal circuit shows that XylR also activates enzymes XylF,G,H which catalyze the intake of extracellular D-xylose and XylB which converts D-xylulose into D-xylulose-5-phosphate. The XylF,G,H do not appear as a module in our procedure because its intake reaction is outside the scope our procedure as it is not an essential reaction because another enzyme XylE provides a second pathway for the intake of extracellular D-xylose. Collectively this whole system should be considered the “D-xylose module” instead of the 3 node SCC found by our method. Thus our method sometimes detects not the whole module but what might be called as ‘kernel’ of the module from which the rest of the module can often be constructed by examining the proximal circuit. We could have discovered that XylB is also part of the SCC if we had been more liberal in including metabolic reactions that produce or consume not just metabolites that bind to TFs but also their nearest neighbour metabolites. It is a task for the future to extend our methodology to include these effects, and to see the usefulness of the results so obtained.It is important to point out that the SCCs we find often uncover a larger module of which they are a part. The larger module can be constructed once the SCC is identified by our method. An example is the D-xylose module in E. coli and B. subtilis, E. coli has a different internal structure than that in B. subtilis. In E. coli the structure of the loop is XylR → XylA ⊣ D-xylose → XylR . Whereas in B. subtilis the structure is XylR ⊣ XylA ⊣ D-xylose ⊣ XylR . In E. coli the D-xylose activates the TF XylR whose action is activation of enzyme XylA thus leading to the metabolism of D-xylose into Xylulose. Whereas in B. subtilis D-xylose is also metabolized into Xylulose by the enzyme XylA but through a different regulation: D-xylose inactivates the TF XylR whose action is repression of the enzyme XylA, with the overall effect the enzyme XylA again metabolizing D-xylose to Xylulose. Different ways of implementing the same logic can have similar effects in a steady state but could differ in transient effects.The D-xylose module also illustrates another interesting feature: the overall function is conserved across organisms in spite of the variation in the internal structure of the module. D-xylose forms a size-3 SCC in both The modules of size 4 can be broadly divided into two classes: (a) a 4-node motif associated with uptake and utilization of small molecules, (b) two essentially 3-node motifs sharing nodes and therefore forming a 4-node SCC. In the former case the full 4-node structure is essential to understand its functionality. In the latter case the individual 3-node sub-structures have a functionality in their own right.E. coli and all 3 in B. subtilis, hence 9 out of a total of 11 in both organisms) are of consumer type. Example of both the variants of the consumer motif, one where the metabolite activates the TF (the sorbitol module) and the other where the metabolite inactivates the TF (the N-acetylneuraminate module), are shown in The first class  is a strIn the second class , the funE. coli graph B. subtilis, giving a total of 13 modules. Of these 13, one is a spurious module in B. subtilis , partially for 2 (both in B. subtilis) and we were unable to do so for 2 of the modules (both in E. coli). Most (9 out of 12) of the modules of size ≥ 5 were just more complex versions of the 4-node consumer motifs and the 3-node feedback loops or their combinations. The details are given in As the size of modules increases to 5 and beyond, the complexity of the modules also increases. Several of these modules contain more than one metabolite binding to TFs, and some of them contain both more than one metabolite and TF. They also have ‘sub-modules’ which are active in different subsets of conditions. Nevertheless, an analysis of their graphs including the sign of the links, their proximal circuit diagram, and conditions in which they are active, allows us to guess their functional roles in most cases without going into further biological details. There are 10 modules of size ≥ 5 in rbsA, rbsB and rbsC contribute to the formation of the ribose-ABC transporter. The RbsD protein functions for efficient uptake of ribose when it is transported into the cell via a mutated form of glucose transporter (PtsG). This 7 node motif is thus essentially like a 4-node consumer motif in which 4 of the enzyme coding genes are performing the same function of transporting the metabolite into the cell. (2) Multiple simple motifs joined together, e.g., Idonate-Gluconate module  to produce Cysteine. Over-production of Cysteine shuts the module off by inhibition of CysE. Sulphide at high level also represses CysB to control its own over-production. This module is well known in the biological literature for the regulation of Cysteine production [The following logic can be ascribed to the Sulphide-Acetylserine (or Cysteine) module for the controlled production of Cysteine, assuming that Serine and Sulphite are available in the cell. If Cysteine levels are sufficiently high, it inhibits the enzyme oduction . This suWe emphasize that our procedure of identifying the SCCs is blind to the signs of edges between the nodes. Still the signs in the modules we obtain through our procedure conform very well to the intuitive logical functioning of these modules. This suggests thats our approach which employs construct of SCC is actually able to find out functionally relevant biological modules or dynamical systems.E. coli and active in 3 and 10 conditions respectively; see The two modules that defied a proper classification, namely, the Serine-Pyruvate-Glycine module and the Allantoin-Glyoxylate module are also more complex , B. subtilis the LSCC is in the intermediate levels (E. coli only in the remainder of this section.Consider the largest SCC (LSCC) in graph GC  and its h GC  the largest of which is of size 29, σ-factors, size 29, has predominantly genes coding for TF and involve multiple global regulators with varying functions, which prohibits assignment of a simple function to this module. The functioning of the core remains an open question.Taking out the SCC formed by E. coli and B. subtilis to produce a list of modules in these organisms and discussed the functional role of each module.In this work we have: (i) described the causal structure of GRNs without and with feedbacks from MN, (ii) presented a framework and automated method using graph theory and FBA for determining modules in organisms from a knowledge of their GRN, MN and feedbacks from the MN to GRN, and (iii) applied the method in (ii) to E. coli and B. subtilis can be organized into a causal, largely acyclic architecture, with a few islands of feedback, We employed graph theoretic procedures of strongly connected components (SCCs) and leaf-removal to identify cyclic regions of the GRN and to organize it into a hierarchical structure composed of different levels. The hierarchical organization of the GRNs in section 2 shows that the complicated looking GRNs of E. coli and B. subtilis by increasing the number and sizes of SCCs, especially the size of the largest SCC  functionality. The fact that our construction, blind as it is to the sign of the links, finds subgraphs where the signs happen to be just right for assigning a simple functionality to the subgraph, is a non-trivial validation of the approach. It should be mentioned, however, that a module with a ‘wrong’ sign might have a function that is more complex . Identifying such functionalities requires a more detailed analysis that is beyond the scope of the present work. It is interesting that most modules have a sign combination that allows for an easy-to-interpret functionality; modules that are difficult to interpret functionally are rare  In our determination of modules of E. coli and B. subtilis, we included the feedbacks from MN. In the process we considered only a subset of the MN. That subset was composed of the essential reactions of the metabolic network. Taking only the part of the metabolic model that is constituted by the essential reactions is somewhat restrictive. It may be useful to go beyond the essential reactions in order to get better modules. We have tried using a flux vector which is obtained as a solution of the FBA  to obtain condition specific graphs. This in fact yields additional modules and also adds additional nodes and links to some existing modules. However since flux vectors are not unique  a systematization of this approach is required for further extension. (b) Similarly, as discussed at the end of the penultimate para in section 5.2.1 in the context of the D-xylose module the inclusion of next to nearest neighbors in the metabolic graph will also lead to some enlarged modules. (c) Enzyme inhibition: The GRN of an organism includes genes coding for enzymes that catalyze the metabolic reactions. In our hierarchical picture these genes come in the level-0  Graph condensation. This involves identification of the SCCs of the graph, and substituting a single representative node for each SCC in place of its constituent nodes. This renders the graph acyclic. (2) Successive identification, assignment and removal of leaves (nodes with no out-degree). In the condensed graph, the leaves identified in the first iteration are identified as level 0 nodes. They are removed. The new leaves identified in the second iteration are identified as level 1 nodes. This process is repeated until all the nodes in the graph are assigned to a level. We demonstrate this using a toy network. This procedure is a modification/combination based on works by Jothi et al  and Yu eA of B indicates the non-trivial SCC in the same network by enclosing nodes ‘2’, ‘3’, ‘4’ and ‘5’ of the network in a red dashed ellipse. Panel C shows the directed acyclic graph (DAG) obtained after the condensation of the toy network. The nodes forming the SCC have been clubbed into one node represented by the bigger circle. Panel D shows the nodes of the condensed graph, i.e., the obtained DAG, arranged in a tree layout. The network in panel D can be used to assign nodes to different hierarchical levels.Panel E illustrates levels of the hierarchical organization. The categorization of the nodes of the network into finer levels employs iterative leaf removal algorithm on the DAG in panel D. The leaves of a network are the nodes with no out-degree. The leaves are assigned to a level and then removed from the DAG which modifies the DAG and exposes new leaves. This procedure is iterated until all the nodes of the DAG are exhausted and the nodes assigned to subsequent levels. This is done as follows. In the DAG in panel D, the nodes ‘8’, ‘9’ and ‘10’ has no out-degree and are the leaves. We assign these nodes to level 0 (see panel E) and remove them along with their in coming links from the DAG. This leaves us with the modified DAG where ‘7’ is the new leaf. Then ‘7’ is assigned to the higher level, 1, and removed. This procedure is iterated assigning ‘6’ to level 2, ‘2,3,4,5’ to level 3 and finally ‘1’ to level 4. The hierarchical levels along with the nodes are shown in panel E for the original toy network where we have expanded the SCC into its constituents nodes. In a GRN, level 0 generally contains many nodes and depending upon the need or for purposes of clarity, the level 0 might not have been shown in the hierarchical pictures used in the other sections of the paper.Panel E. coli [B. subtilis [E. coli, iJR904 [B. subtilis, iBsu1103 [E. coli, while for B. subtilis this information was obtained from Goelzer et al [iJR904 for E. coli and iBsu1103 for B. subtilis) which were catalyzed by the enzymes whose coding genes were also present in the GRN  only 89 produced viable minimal media in aerobic conditions and 69 in anaerobic conditions. Thus we had a list of 158 viable minimal media for E. coli. For B. subtilis out of a total of 212 EC  we had only 118 viable media, all aerobic. The list of viable minimal media is given in M (M = 158 for E.coli and 118 for B. subtilis).First, we consider the utilization of metabolic pathways by the organism in multiple environmental conditions (ECs). Each EC considered is characterized by a ‘minimal’ medium in which there is a unique and limited source of carbon together with specified but unlimited other nutrients like nitrogen, phosphorous, sulphur, etc. An EC is characterized as aerobic if external oxygen is available, otherwise anaerobic. We use the computational technique of flux balance analysis (FBA) , 51 to dE. coli in aerobic glucose minimal growth condition, FBA deemed 218 reactions out of 904 to be essential. Thus for a given EC, in augmenting the GRN with feedbacks from MN, instead of using all 462 links from enzyme coding genes to metabolites we only used the subset corresponding to essential reactions in glucose which were 71 in number. The metabolites that were not participating in the essential reactions were also excluded. We determined the set of essential reactions under each of the 158 ECs for E. coli and 118 ECs for B. subtilis. The essential reactions for each EC are listed in E. coli, and 118 versions for B. subtilis. We designate these instances of GRN with condition dependent allosteric feedbacks from metabolic network as graph i indicates that the graph is for a given growth condition, labelled by i; i goes from 1 to M. E. coli or B. subtilis) to be union of graph We then determine the essential reactions of the MN for each of the above ECs. An essential reaction in a metabolic model in a given viable EC, as the name suggests, is one, which, if blocked, results in zero simulated growth . The determination of essential reactions under a given EC is done in the following standard way. The reaction to be tested for essentiality is first constrained to have a zero flux in the metabolic model, and then the metabolic model is simulated for growth in the particular EC using FBA. If this results in a zero growth value, then the reaction tested is an essential reaction in that EC, else it is not. This procedure is repeated for each reaction in the metabolic model and its essentiality is determined for the given EC. For example, in case of M media considered. A link from an enzyme node to a metabolite node in M media considered.The graph The advantage of using essential reactions of a metabolic model under an EC lies in their unambiguous determination. An alternative approach (which we have explored but not discussed in detail here) is to use all the reactions with non-zero flux in a flux-vector. It is well known that in a given medium FBA has multiple flux vectors as solutions with the same maximal growth rate and the set of non-zero flux reactions is different for different flux vectors. This gives rise to an ambiguity in the set of reactions to be included if one works with all reactions with non-zero flux. However in a given medium the set of essential reactions is unique for a FBA model.E. coli [B. subtilis [2, Iron, Water, H+, Potassium, Na+, singleRxnDeletion along with a growth rate cut-off of 1e-6 was used to determine the set of essential reactions for a particular EC. The set of viable food sources, and essential reactions under each EC is given in We used the COBRA toolbox in Matlab  to perfoE. coli  and B. ssubtilis . We simuS1 TableThe excel sheets list the genes, interactions, regulators, sigma-factors, TFs, ncRNAs, regulated genes, details of SCCs, and hierarchical levels of the GRNs.(XLSX)Click here for additional data file.S2 TableLists the genes, metabolites, regulatory interactions, links from the GRN to respective MNs, feedbacks from MN into the respective GRNs, details of SCCs, and hierarchical levels of the GRNs.(XLSX)Click here for additional data file.S3 TableE. coli and B. subtilis: potential carbon food sources, viable carbon food sources, essential reactions of the organism for each viable minimal medium i.Contains information about flux balance analysis of the MN of (XLSX)Click here for additional data file.S4 TableHas sheets related to the GRN augmented with environmental condition dependent feedbacks from MN, (XLSX)Click here for additional data file.S5 TableE. coli classified according to their size (number of nodes) accompanied with respective proximal regulatory logic circuit diagrams, the list of environmental conditions in which they are active, and a discussion of their possible functional role.The functional modules of (XLS)Click here for additional data file.S6 TableB. subtilis instead of E. coli.This file contains the same information as in (XLS)Click here for additional data file.S7 TableThis file contains the details regarding randomization of a graph to create appropriate null model for comparison of results concerning the number and size of SCCs with those in the original graph.(PDF)Click here for additional data file.S1 FigE. coli.This is a pdf file which contains the figure showing hierarchical structure of graph (PDF)Click here for additional data file.S2 FigB. subtilis.This is a pdf file which contains the figure showing hierarchical structure of graph (PDF)Click here for additional data file.


Understanding the fundamental thermodynamic limits of photo-electrochemical (PEC) water splitting is of great scientific and practical importance. In this work, a ‘detailed balance’ type model of solar quantum energy converters and non-linear circuit analysis is used to calculate the thermodynamic limiting efficiency of various configurations of PEC design. This model is released as freely accessible open-source (GNU GPL v3) code written in MATLAB with a graphical user interface (GUI). The capabilities of the model are demonstrated by simulating selected permutations of PEC design and results are validated against previous literature. This tool will enable solar fuel researchers to easily compare experimental results to theoretical limits to assess its realised performance using the GUI. Furthermore, the code itself is intended to be extendable and so can be modified to include non-ideal losses such as the over-potential required or complex optical phenomena. In light of the current social and political pressures to move towards a more immediately sustainable future, there has been much hope in realising an economically feasible ‘artificial photosynthesis’ process capable of meeting the modern energy demand. One such photo-synthetic fuel commonly studied is hydrogen produced through photo-electrochemical reduction of water.Photosynthesis harnesses the solar resource by converting the energy incident on the earth into a storable fuel which has enabled great change in the history of life. A vast quantity of our primary energy use continues to come from fossil fuelsG° under standard conditions can be expressed as a cell potential n is the number of electrons transferred per product formed and F is the Faraday constant. In an electrochemical process, the oxidation reaction occurs at the anodic interface and is spatially separated by an electronic conductor, from the reduction reaction at cathodic interface. Correspondingly, the standard cell potential is expressed as The overall chemical equation for water splitting is found in eq. , where t5 Pa) with H2 and O2, respectively, will be −1.23 V. In reality, kinetic losses will mean a voltage greater than this is required to drive the reaction, and this difference is termed the over-potential, Vo for each cell. As the ideal thermodynamics limits of solar fuel conversion for different configurations is studied here, it is assumed Vo = 0.It can be derived from the Nernst equation for each half reaction ΔH° = 286 kJ mol−1) must be provided as electrical energy. Hence, the thermo-neutral cell potential  will be −1.48 V. If heat is supplied reversibly from the ambient surroundings at 298.15 K , the minimum electrical energy required will therefore be the Gibbs energy of reaction and the minimum cell potential required will be −1.23 V. Therefore, this value will be used in this analysis and for convenience the negative sign will be dropped henceforth: Under adiabatic conditions, the total enthalpy of reaction (i.e. positive Gibbs energy) indicates that this process is not thermodynamically spontaneous, and hence requires free energy in order to drive the reaction. In a solar driven photo-electrochemical cell, this free energy is generated through the excitation of charge carriers in one or more photo-absorbers by absorption of incoming solar photons. The number of photo-absorbers is denoted by Nphoto, and systems where Nphoto = 2 are commonly referred to as tandem PEC cells. Some designs can employ multiple electrolysers and in this case, the total voltage that the photo-absorber(s) are required to produce is therefore A negative cell potential  and PV is often stated at maximum power point (mpp), rather than the operating point of electrolysers. A decoupled system that ultilses DC–DC converters, would allow the PV to operate at the mpp whilst maintaining a voltage suitable for electrolysis, though there will be energy losses associated with this voltage conversion.The efficiency of a directly coupled PV + electrolyser or integrated PEC cell is not simply 12 which is summarised in Table et al.4, which demonstrated the equivalence of many of the historical models. In more recent work, many researchers have investigated practical efficiency limits of solar fuel processes15 and different optical configurations10.There has been much work into the fundamental efficiency limits of quantum energy converters and in particular photo-electrochemical energy conversionet al.12 aims to address this and they maintain a web based efficiency model (www.solarfuelsmodeling.com). This is a javascript implementation for a single or tandem configuration , which can model both maximum and practical losses. Whilst an undeniably useful tool for the solar fuels community, the configuration is fixed as a two photo-absorber cell, optically and electrically in series. Therefore the solution offered here is unique in its flexibility to model configurations previously understudied.Whilst the models used to calculate the efficiency are often well documented, the method of numerical solution is often less clear and any code used not openly available. Recent work by Seger et al.4, calculation of the photo-electrochemical efficiency assuming no free energy losses is thermodynamically impossible at feasible device and sun temperatures. Intrinsic free energy losses in any heat engine, which includes solar quantum energy converters, are unavoidable16. We have reviewed the literature and found numerous examples of calculated photo-electrochemical energy conversion efficiencies which neglect the inescapable radiative emission Fig. 2a10,Fig. 218, Fig. 719.It is possible that the reason the second law of thermodynamics is neglected, is due to a lack of easily available tools to calculate the limiting photo-electrochemical efficiency.As explained by Bolton et al.20.Here, we outline a methodology and an open-source implementation to calculate the limiting efficiency of various configurations of solar water splitting devices. The script is written in MATLAB, a language common to engineers. Both the script and a stand-alone executable (packaged with the MATLAB Compiler) are provided under an open-source license meaning that it can be modified by researchers to suit their needs. There are various configurations for which the limiting efficiencies have not been well studied, such as those outlined by Brillet Figure 21, and the following assumptions were made in order to use the standard ideal diode equation: Each cell is planar with an abrupt absorption threshold and complete absorption of above band gap photons. Carrier generation from ambient and from radiative emission from other cells was neglected. Furthermore, one photon excites one electron (i.e no carrier multiplication). Therefore, the current-voltage relationship of a single photo-absorber is given in eq. , and equal to two if radiative emission can leave from both front and back sides. Henceforth, fg = 1 is assumed for all sub-cells except sub-cells optically in series, where unabsorbed light must pass through the photo-absorber to the next (and therefore fg = 2). Finally, unless otherwise stated, AM1.5 G spectrum (ASTM G17322) and an ambient temperature of 298.15 K was used henceforth.A geometric factor The full derivation of the model and information about the numerical methods used, is outlined in the supplementary information.The theoretical limiting efficiency is defined by the conceptual configuration of the photo-electrochemical system. Any PEC configuration can be categorised by: 1) Number of photo-absorbers 2) Electrical configuration 3) Optical configuration.The generic photo-electrochemical cell components are shown in Fig. 23.The various components outlined in Fig. 9 and there will be multiple optical configurations for any conceptual design that has more than one photo-absorber. Light may pass through one photo-absorber and upon to others, allowing for portions of the light spectrum not utilised by the first to be captured by the second. Such a configuration, henceforth, is referred to as ‘optically in series’. Alternatively, photo-absorbers could be placed ‘optically in parallel’, where each photo-absorber is placed side-by-side.The optical configuration has a significant impact on the limiting efficiency of the conceptual designOptically in series: →1 → 2Optically in parallel: In order to represent the optical configuration, a directed graph schematic will be used. Edges indicate the path of the light to nodes which represent each numbered photo-absorber. The first node is the incoming solar spectrum where there is no photo-absorber and so it is unlabelled. For example, a two photo-absorber system could be:i.e. at any node which has 2+ successor nodes), the edge weight defines both the fraction split in the photon flux and the relative area of the subsequent node. In the previous ‘optically in parallel’ example, the edge weight of 1/2 denotes that half the light is transferred to a photo-active area of half the previous node. Currently, optical losses (such as reflection) or spectrum specific optics such as dichroic mirrors are not included in this analysis. Furthermore, it is assumed each photo-absorber has an abrupt absorption threshold and absorbs above bandgap light entirely. As the open-source code is easily extendible, such complex configurations and optical non-idealities could be incorporated in the future.In order to simplify the current schematic, at any split , and hence Fig. et al.27.The table in Fig. Vmpp matches with the required voltage to drive the electrochemical cell Vtot. At lower bandgaps than this maximum, the system becomes voltage limited. At higher bandgaps, the system provides a greater voltage than required and so this mismatch leads to an efficiency lower than if the voltage is unconstrained and the system can operate at the maximum power point potential.As seen in Fig. Repeating units electrically in series and optically in parallel - Demonstrates that the efficiency of PV + EC systems can be optimised by matching the maximum power point to the loadEffect of solar concentration - Demonstrates that for PEC systems under certain conditions, solar concentration can improve the maximum efficiency to a much larger degree than the efficiency improvement for PV aloneEg,1 and Eg,2)Permutation of tandem designs - Maximum efficiency versus both bandgaps  to number of repeating units (NRU) have the same theoretical limiting efficiency. An example of this schematically  is shown in eq. 4 for the case where this ratio is unity.(4)There is an interesting property for repeating units (of photo-absorber configurations) that are electrically in series and optically in parallel, with each unit getting the same fraction of the total light. It can be shown that all systems with the same ratio of the number of electrochemical cells  of a single photo absorber , we will define the repeating unit connection ratio as S is fixed at unity), this method of optimisation will not be available and the maximum efficiency will then be 30.7%. If S is allowed to vary, the maximum is 33.8% found at a value of S = 0.801 with Eg = 1.34 eV, which approximately corresponds to 5 single photo-absorber repeating units connected to 4 electrolysers. This type of analysis has been extensively discussed by Patel et al.14, where they investigated repeating unit which consisted of a 1 to 7 junction solar cells that were optically in series.For the simplest repeating unit  systems are investigated. Figure Nelec.Next, two photo-absorber .For the optically in parallel systems shown in Fig. etc. The results of this can be found in the table in Fig. Nphoto = 3.For each conceptual design, the bandgaps can be optimised to produce the global limiting efficiency. Mathematically, this is represented as eq. 12, in that the code can handle various configurations. This distinction is most apparent when studying systems such as the final entries in Fig. et al.29 and Brillet et al.20.This clearly demonstrates the large variety of designs possible, many of which could obtain high STH efficiencies. Whilst many of these configurations have been studied previously, it can be difficult to compare each subset when different models are used. Therefore, this demonstrates the distinction from previous open access modelsThis analysis, particularly the table in Fig. 23. With bandgaps of 1.895, 1.414, 0.965 eV and a solar concentration of 42 Suns, the maximum theoretical efficiency is 34.3% (assuming −2 as found from integrating AM1.5 G). The global maximum for that configuration, is found at bandgaps of 1.73, 1.17, 0.68 eV and is 45.9%. Therefore, the 30% demonstrates a significant realised potential of that particular configuration.For example, the current solar-to-hydrogen efficiency record of 30% is comprised of triple junction cell  and 2 electrolyserset al.4), there are a number of simplifying assumptions made. For example, this work does not take into account the built in optical concentration of nanostructured solar cell when compared to planar cells. The code could be modified to account for this by following the work of Xu et al.32. Furthermore, this analysis currently does not include the realistic performance of the solar cell or electrolysers11, radiative coupling of sub-cells8, semi-transparent upper absorbers9, or carrier multiplication7. Once again, as the code aims to be extendible, such analysis could be easily incorporated. The authors aim to extend the code so as to be able to include realistic performance losses following the methodologies previously published12.Whilst this approach is significantly better than assuming a non-radiative model . A GUI interface was built. Open source code available from 33 in order to validate the model. Overall, it compares very closely to previous work.As shown in Fig. et al.6, historical AM1.5 G data was used34 as opposed to the more current standard: ASTM G17322. However, the results are still slightly different and could be due to different numerical methods used. Interestingly, for the tandem cell case (referred to as D4 in the paper) the authors suggested a second threshold wavelength of 2,610 nm, yet the spectral distribution given by Bird et al.34 finishes at 2,450 nm. Therefore a second possible reason for any discrepancies here could perhaps arise from a different interpolation method of the solar spectrum data.For the comparison with Bolton et al.8 and Seitz et al.9 as both aimed to model practical theoretical limits rather than fundamental limits. Furthermore, whilst work by Jacobsson et al.10 compares well with our analysis, direct comparison is not applicable as it is not a detailed balance approach, but assumes a fixed energy loss due to charge carrier separation of 0.4 eV.We did not compare our data to work by Hu Supplementary Information


Methylocystis parvus is a type II methanotroph characterized by its high specific methane degradation rate (compared to other methanotrophs of the same family) and its ability to accumulate up to 50% of its biomass in the form of poly-3-hydroxybutyrate (PHB) under nitrogen limiting conditions. This makes it a very promising cell factory.M. parvus OBBP. The model is compared to Genome Scale Metabolic Models of the closely related methanotrophs Methylocystis hirsuta and Methylocystis sp. SC2. Using the reconstructed model, it was possible to predict the biomass yield of M. parvus on methane. The prediction was consistent with the observed experimental yield, under the assumption of the so called “redox arm mechanism” for methane oxidation. The co-consumption of stored PHB and methane was also modeled, leading to accurate predictions of biomass yields and oxygen consumption rates and revealing an anaplerotic role of PHB degradation. Finally, the model revealed that anoxic PHB consumption has to be coupled to denitrification, as no fermentation of PHB is allowed by the reconstructed metabolic model.This article reports the first Genome Scale Metabolic Model of The “redox arm” mechanism appears to be a general characteristic of type II methanotrophs, versus type I methanotrophs that use the “direct coupling” mechanism. The co-consumption of stored PHB and methane was predicted to play an anaplerotic role replenishing the serine cycle with glyoxylate and the TCA cycle with succinyl-CoA, which allows the withdrawal of metabolic precursors for biosynthesis. The stored PHB can be also used as an energy source under anoxic conditions when coupled to denitrification.The online version of this article (10.1186/s12934-019-1154-5) contains supplementary material, which is available to authorized users. Methylocystis parvus is a type II methanotroph characterized by a specific growth rate higher than other species of the genus Methylocystis (such as Methylocystis hirsuta or Methylocystis sp. SC2) and that, under nitrogen limiting conditions, is able to accumulate poly-3-hydroxybutyrate (PHB) up to 50% of its dry biomass.Methylomicrobium buryatense and Methylomicrobium alcaliphilum [Methylocystis, rely on the serine cycle for methane assimilation. Type II methanotrophs, so far, have not been used as metabolic engineering platforms, not even at a research level, even if successful gene knockouts have been reported for Methylocystis sp. SC2 [Methylocystis are natural producers of PHB, a biodegradable polymer, similar to polypropylene in terms of mechanical properties, that is synthesized under nitrogen starvation conditions. Methylocystis parvus has been reported to accumulate up to 50% of its dry weight in the form of PHB [M. hirsuta can accumulate up to 45% of PHB on a dry weight basis using methane as a feedstock [Methane is a powerful green-house effect gas, which is currently being emitted at a rate over 70 million tonnes per year  in anthrliphilum , 5. Type sp. SC2 . On the eedstock . PHB proeedstock , and it M. parvus OBBP was reconstructed [M. hirsuta CSC1 [M. sp. SC2 [M. parvus was used to elucidate some relevant aspects of the physiology of PHB accumulating methanotrophs. The first question addressed was the mechanism of methane oxidation used by methanotrophic organisms. Methane is initially oxidized to methanol, thus consuming a molecule of oxygen. This step also requires a reduced redox co-factor carrying two electrons, which are transferred to the second oxygen atom to produce a molecule of water. There is no general agreement on the identity of this redox co-factor, and three alternative mechanisms have been proposed [c, which is reduced back during the oxidation of methanol to formaldehyde by the enzyme methanol dehydrogenase (MeDH). Finally, a third mechanism consists of the reduction of ubiquinone by cytochrome-c in the so called “uphill electron transfer” mechanism. GSMMs of type I methanotrophs [M. parvus OBBP were consistent with any of the three hypothesized methane oxidation mechanisms.In this work, the first GSMM of structed . This GSuta CSC1  and M. s sp. SC2 . The recproposed . The so-notrophs , 5 were Methylocystis parvus has been shown to use the stored PHB for protein synthesis in the absence of methane and in the presence of nitrogen sources [M. parvus consumes simultaneously PHB and methane while decreasing significantly its cell division time [M. parvus has been shown to produce acetic acid and butane-2,3-diol [ sources . Howeverion time , which p2,3-diol , which wM. parvus OBBP was reconstructed using SEED [M. parvus was made publicly available in SBML and tab-separated formats at https://github.com/SergioBordel/ModelsMethanotrophs. The same repository also contains the lists of essential reactions, lists of the top connected metabolites and RAST genome annotations in Excel format. The model is presented compared to GSMMs of two other species of Methylocystis, namely M. hirsuta and M. sp. SC2 [A metabolic model of ing SEED  after aning SEED  and manu sp. SC2 . GeneralM. parvus 28.7% of its metabolic reactions are essential for growth on methane. The overlap between the reactions and metabolites in the three different models is shown in Fig. Essential reactions are defined as those in whose absence, no biomass production from methane is possible. For M. parvus, 8 of them are catalyzed by a purine nucleoside phosphorylase (EC. 2.4.2.1). This enzyme is involved in salvage pathways that allow recovering nucleotides from the degradation of nucleic acids such as messenger RNA. This enzyme could be related to the higher specific growth rate of M. parvus by contributing to a faster turnover rate of messenger RNA. A similar function could be that of a nicotinamide phosphoribosyltranspherase (EC. 2.4.2.12), which is also specific to M. parvus and is absent in the metabolic networks of M. hirsuta and M. sp. SC2. An interesting enzyme unique to M. parvus is homoserine O-succinyltransferase (EC. 2.3.1.46), which synthesizes O-succinyl-l-homoserine from succinyl-CoA and l-homoserine. In contrast, the two other considered species appear to synthesize O-succinyl-l-homoserine from succinate and cystathionine using the reverse activity of a cystathionine-γ-synthase (EC. 1.4.1.2). Other two important metabolic genes, present uniquely in M. parvus, are the transporters of l-proline (l-proline/glycine betaine transporter ProP) and 3-hydroxybutanoate (d-β-hydroxybutyrate permease). The presence of these transporters could make M. parvus a suitable cell factory for these compounds. Indeed, this strain has been reporter to secrete butane-2,3-diol [Among the 40 reactions that are unique to 2,3-diol  under anl-threonine 3-dehydrogenase (EC. 1.1.1.103), involved in the synthesis of amino acids, nicotinamidase (EC. 3.5.1.19), that degrades nicotinamide to niacin, adenosine deaminase (EC. 3.5.4.4) or adenosine deaminase (EC 3.5.4.4), rank among the main enzymes absent in M. parvus and present in both M. hirsuta and M. sp. SC1.The enzymes cystathionine-γ-synthase (EC. 2.5.1.48) and c (direct coupling mechanism), has been included in the model with the identifier “pMMO1”. A second reaction, in which methane oxidation is coupled to ubiquinol-8 oxidation, has been included with the identifier “pMMO2” . The “uphill electron transfer mechanism” was herein modelled by allowing the reaction corresponding to the complex III of the respiratory chain (with identifier “rxn10113_c0”) to proceed backwards.Depending on the redox-carrier involved in methane oxidation, there are three possible mechanisms of methane oxidation (previously described). A reaction in which methane oxidation is coupled to the oxidation of cytochrome-4. In order to obtain an estimation of the non-growth associated ATP requirements (which in the absence of methane are supplied by endogenous respiration), oxygen consumption was monitored following total methane depletion (in triplicate serum bottles), leading to a value of 0.71 ± 0.2 mmolO2 g-DW−1 h−1. In this context, assuming five molecules of ATP produced per oxygen molecule, the non-growth associated ATP maintenance would be 3.5 mmol ATP g-DW−1 h−1.Experiments in closed serum flasks containing different methane concentrations in the headspace, were carried out see “”. The toM. parvus OBBP was 6.45 h, which corresponded to a growth rate of 0.107 h−1 [M. parvus OBBP was 14.9 mmolCH4 g-DW−1 h−1. This experimental value, together with the estimated ATP consumption rate for non-growth associated maintenance, were set as constraints and biomass production was optimized under the assumption of each of the three possible methane oxidation mechanisms  [During the 15 h of PHB and methane co-consumption by d medium ), the PH bottle) . Conside2 consumed. These predictions are remarkably close to the experimental values [In order to test the performance of the model, the consumed methane and PHB were set as constraints and biomass formation was optimized, leading to predictions of 21.59 mg of non-PHB dry biomass produced and 2.7 mmol of Ol-erytro-3-methylmalyl-CoA, which becomes dissociated into glyoxylate and propionyl-CoA . The glyoxylate originated from l-erytro-3-methylmalyl-CoA is incorporated into the serine cycle, while propionyl-CoA is carboxylated into succinyl-CoA and thus incorporated into the TCA cycle  to produce glycine. This glycine is incorporated into the serine cycle allowing withdrawal of serine for biosynthetic purposes. The simulations using the GSMM herein constructed predicted a rate of glycine synthesis of 1.3 mmol hl-erytro-3-methylmalyl-CoA, whose rate is equal to the PHB degradation rate. Therefore, it seems reasonable that the increased rate of l-erytro-3-methylmalyl-CoA lysis from zero to 0.608 mmol h−1 g-DW−1 is concomitant to a drop in the rate of malyl-CoA lysis from 12.3 to 11.8 mmol h−1 g-DW−1 due to a competitive inhibition mechanism.At this point it should be stressed that the enzyme malyl-CoA lyase catalyzes both the lysis of malyl-CoA in the serine cycle as well as the lysis of M. parvus, in the absence of oxygen, can secrete acetate and butane-2,3-diol [M. parvus cells as an energy source under anoxic conditions only if nitrate is present as electron acceptor. Production of acetate and butane-2,3-diol from PHB, using nitrate as electron acceptor, was also modeled. The simulations were carried out by setting the PHB consumption to 1 mol and optimizing ATP production for different productions of acetate and butane-2,3-diol. Maximal ATP production corresponded to zero production of acetate and butane-2,3-diol. Thus, the optimal production of any of these two compounds appeared to be incompatible with ATP production. Figure 2).It has been reported that 2,3-diol . This phM. parvus OBBP during PHB and methane co-consumption (which was accompanied by a slightly lower specific methane degradation rate), seems to confirm this hypothesis. Other evidence suggesting that methane oxidation is typically a limiting step was provided by knockout experiments in M. sp. SC2 [M. parvus has a specific growth rate at 30 °C of 0.107 h−1 [M. sp. SC2 was reported to have a specific growth rate of 0.074 h−1 [M. hirsuta has a specific growth rate of only 0.048 h−1 [Methane oxidation is likely to be the step limiting the growth rate of methanotrophs. The reduced duplication time observed in  sp. SC2 . M. parv.074 h−1  and M. h.048 h−1 . TherefoM. sp. SC2 possesses two different gene clusters referred as pmoCAB1 and pmoCAB2 (the order of letters reflects the order in which the genes of the three different subunits are arranged), of which pmoCAB2 expression appears to be associated to higher affinity for methane at low concentrations [M. hirsuta has a pmoCAB1 cluster identical to the one present in M. sp. SC2 and an alternative cluster named pmoABC3. The cluster pmoCAB2 is absent in M. hirsuta. In contrast, M. parvus OBBP has a gene cluster closely related but not identical to the pmoCAB2 cluster from M. sp. SC2. This gene cluster was herein referred to as pmoCAB2parv. A second cluster with only 2 subunits (A and B), which are similar  to the A and B subunits of the cluster pmoCAB1, was found in M. parvus. This cluster was referred to as pmoAB1parv. Finally, two separate C sub-units, very similar to each other and similar to the C sub-unit of pmoCAB1, are found in the genome of M. parvus. These enzymes were herein referred to as pmoC1parv and pmoC1bparv, respectively. Figure Particulate methane monooxygenases have a trimeric architecture, consisting of three copies each of the pmoA, pmoB and pmoC sub-units . These strations . M. hirsM. hirsuta. In this case, asparagine is substituted by glutathione. Multiple alignments of the catalytic sites are presented in Fig. Multiple alignments and phylogenetic trees comparing the three pMMO subunits were carried out using the software MUSCLE . The perM. parvus OBBP, the first functional GSMM for this organism was herein reconstructed. The model was able to accurately predict biomass yields on methane (under the assumption of methane oxidation using the “redox arm” mechanism). The model was equally able to predict accurately both oxygen consumption and biomass production in the case of simultaneous co-consumption of methane and stored PHB. The metabolic flux distribution predicted by the model revealed that the stored PHB is used during its co-consumption with methane to replenish the serine cycle with glyoxylate and the TCA cycle with succinyl-CoA. This allows anabolic precursors to be withdrawn from these cycles leading to higher specific growth rates (reduced cell duplication times). This anaplerotic function of the stored PHB as a source of the glyoxylate replenishing the serine cycle, had been previously suggested [M. parvus. In contrast, formate supplied to the growth medium was uptaken by the cells [l-erytro-3-methylmalyl-CoA (originated from PHB) into glyoxylate and propionyl-CoA, it is reasonable that an increased flux of the serine cycle, caused by the uptake of formate, will result in a lower rate of PHB degradation, as both pathways are competing for the same enzyme.Based on the sequenced genome of uggested . Howeveruggested  observedhe cells , which wM. parvus under anoxic conditions. The model revealed that the production of these compounds from stored PHB also requires denitrification. However, a lower nitrate consumption is required for the secretion of these compounds than for the complete oxidation of PHB. The observed production of acetate and butane-2,3-diol was therefore more likely due to an overflow mechanism caused by the faster PHB utilization compared to the denitrification rate required for full oxidation of PHB to CO2.The model also revealed that denitrification was the only mechanism for the stored PHB to be used as energy source in the absence of oxygen. Therefore, the anaerobic fermentation of PHB, previously hypothesized in literature , was notM. parvus is the same as the yields  of M. hirsuta and Methylocystis sp. SC2. However, M. parvus exhibited a higher specific growth rate, and thus a higher specific methane oxidation rate, than the two other species. M. parvus has a similar system of pMMO enzymes than that of M. sp. SC2. In particular, the metallic catalytic sites are well conserved in both organisms and no conclusive statements can be made regarding the higher specific oxidation rates of M. parvus compared to M. sp. SC2. M. hirsuta is characterized by a different pmoABC3 gene cluster (absent in the two other strains) in which the mononuclear copper site present in the B subunit of pMMO is mutated. The gene cluster pmoCAB1 is present in both M. hirsuta and M. sp. SC2. Closely related enzymes to those in the pmoCAB1 cluster are also present in M. parvus, but arranged in a pmoAB1parv cluster plus two independent pmoC1 genes. The absence of the pmoCAB2 cluster in M. hirsuta might be related to its low specific methane oxidation rate. After removing the pmoCAB2 cluster from M. sp. SC2 [M. hirsuta, which suggested that the presence of the pmoABC3 cluster does not compensate the lack of the pmoCAB2 cluster in this strain.The yield on methane of  sp. SC2 , this stM. parvus OBBP metabolism. Its high PHB accumulation capacity and high specific methane oxidation rate makes M. parvus OBBP a promising cell factory, while the availability of a predictive GSMM for this organism will foster future developments as a metabolic engineering platform.In summary, the GSMM presented in this article provided accurate quantitative predictions of M. parvus OBBP [https://github.com/SergioBordel/ModelsMethanotrophs. A draft metabolic model was obtained from the genome annotation using SEED [The genome of vus OBBP  has beenvus OBBP . The resing SEED . The resing SEED  under thAll model manipulations , as well as simulations using flux balance analysis (FBA), were carried out using the python library COBRApy .M. parvus OBBP was obtained from Biopolis S.L. . The bacterium was cultured in Whittenbury nitrate mineral medium (pH 6.8) [4 L−1. Cultures were carried out in an orbital shaker at 200 rpm and at 30 °C.The strain (pH 6.8) . Culture4, O2 and CO2 in the headspace of the serum bottles were determined using gas chromatography in a Bruker 430 GC-TCD  with two columns: a CP-Molsieve 5A (15 m × 0.53 mm × 10 mm) [Gas concentrations of CH× 10 mm)  and a CP× 10 mm) .Additional file 1. Multiple protein alignments of each of the three pMMO subunits.


Escherichia coli BL21(DE3) is an industrial model microbe for the mass-production of bioproducts such as biofuels, biorefineries, and recombinant proteins. However, despite its important role in scientific research and biotechnological applications, a high-quality metabolic network model for metabolic engineering is yet to be developed. Here, we present the comprehensive metabolic network model of E. coli BL21(DE3), named iHK1487, based on the latest genome reannotation and phenome analysis. The metabolic model consists of 1,164 unique metabolites, 2,701 metabolic reactions, and 1,487 genes. The model was validated and improved by comparing the simulation results with phenome data from phenotype microarray tests. Previous transcriptome profile data was incorporated during model reconstruction, and flux prediction was simulated using the model. iHK1487 was simulated to explore the metabolic features of BL21(DE3) such as broad spectrum amino acid utilization and enhanced flux through the upper glycolytic pathway and TCA cycle. iHK1487 will contribute to systematic understanding of cellular physiology and metabolism of E. coli BL21(DE3) and highlight its biotechnological applications. Modeling and simulation of metabolic networks are well-established computational tools for myriad applications such as designing of microbial cell factories, model-driven discovery, and phenotype prediction –4. The rEscherichia coli and their derivatives have been widely used and have had enormous impact on basic biology, medicine, and biotechnology. K-12 strains have been the primary choice for genetic studies, and hence, extensive genetic, metabolic, and omic studies of E. coli have been performed using K-12 or its derivatives. After the release of the complete genome sequence of E. coli K-12 MG1655 in 1997 . Ho. Horfb gegration ,39. The eV locus  38]. Th. Thrfb gynthesis  were homL21(DE3) , and its can synttabolism . Differe) genome  and the 2 genome . Althoug2 genome  and addigal operon , molybdate ABC transporter genes (modF and modABC), and pgl (encoding 6-phosphogluconolactonase) in the oxidative pentose phosphate pathway of BL21(DE3) (pgl is present both in B REL606 and K-12 genomes  chloride, trifluoperazine, acriflavine, furaltadone, nitrofurantoin, carbenicillin, domiphen bromide, nitrofurazone, menadione, puromycin, protamine sulfate, diamide, cinoxacin, caffeine, cefoperazone, tinidazole, plumbagin, phenethicillin, captan, orphenadrine, thioridazine, ciprofloxacin, amitriptyline, and ornidazole. BL21(DE3) grew in 28 cells containing colistin, gentamicin, kanamycin, polymyxin B, sodium arsenate, sodium hromycin , whereas studies . Compare did not B REL606  and has B REL606 . As currmyo-inositol metabolism encoded by putative genes (yhiJ and yidK) were removed as BL21(DE3) did not grow on myo-inositol in the PM tests. In conclusion, the simulated growth qualitatively agreed with PM results for 160 out of 190 carbon sources, and the predictive accuracy of our model can be considered to be 84.2%, representing 4.7% increase over 79.5% accuracy of the iECD_1391.The reconstructed model was validated by comparing the simulated growth from FBA using the model with experimental growth from PM tests . The sim13C metabolic flux analysis (13C-MFA) is the robust approach to experimentally quantify the metabolic fluxes in central carbon metabolism [13C-MFA data to evaluate prediction accuracy of a metabolic network model. As shown in 13C fluxes of BL21 [r2 = 0.95). Since BL21(DE3) and K-12 have the same metabolic gene repertoire in central carbon metabolism with the exception of absence of pgl in BL21(DE3), K-12 without PGL reaction can have flux distribution in central metabolism similar to BL21(DE3). Remarkably, the predicted fluxes using iHK1487 also agreed well with 13C fluxes of the deletion mutant of pgl in K-12 [r2 = 0.95) (pgl is an important intrinsic property of BL21(DE3) in the central carbon metabolism. The excellent agreement between in vivo measurements and in silico predictions indicate iHK1487 yielded fairly accurate flux predictions.tabolism . We used of BL21  (r2 = 0. in K-12  (r2 = 0. = 0.95) , implyinpgl involved in the oxidative PPP, the simulation results from iHK1487 (representing wild-type BL21(DE3)) were compared with those from iHK1487 added with the PGL reaction (iHK1487 + PGL) (representing BL21(DE3) having the active PGL reaction) . For the aerobic growth on glucose, total production rates of NADPH and ATP were similar in both cases. However, total production rate of NADH were 12% higher in iHK1487 (40.5 mmol gDCW-1 h-1) than in iHK1487 + PGL (36.2 mmol gDCW-1 h-1), due to the higher flux through glycolysis and TCA cycle in iHK1487. And then, the increased NADH in iHK1487 was converted to NADPH by transhydrogenase to compensate the loss of NADPH production by the block of the oxidative PPP. Total ATP production rates were very similar in iHK1487 (78.3 mmol gDCW-1 h-1) and iHK1487 + PGL (79.4 mmol gDCW-1 h-1), and the majority of ATP was produced from oxidative phosphorylation (> 71%) via oxidation of NADH. Taken together, these results demonstrate that absence of PGL reaction in BL21(DE3) considerably affects the way of NADH/NADPH generation.To expand insights on energy metabolism, we calculated production and consumption rates of major co-factors of the redox carriers (NADH and NADPH) and the energy carrier (ATP). As the major feature of BL21 in the central metabolism is the absence of eaction) . For FBAargI, cysU, cysW, and cysA) which were not predicted to be essential in K-12. Ornithine carbamoyltransferase is involved in the L-arginine biosynthetic pathway, which is encoded by two genes in K-12  and by one gene in BL21(DE) (argI) [cysPUWA, which encode an ATP-dependent sulfate/thiosulfate uptake system, and by modABC, which encodes a molybdate ABC transporter. The modABC operon is missing in BL21(DE3) [cysUWA becomes essential for BL21(DE3). All the 199 genes associated with 382 reactions predicted to be essential for BL21(DE3) were expressed in more than one condition among the five culture/growth conditions of our transcriptome analysis [FBA was performed to predict the reactions essential for cell growth of BL21(DE3) and K-12 strains. In BL21(DE3) and K-12, 195 genes were predicted to be essential. In addition, BL21(DE3) harbored four more essential genes  (argI) ,59. In t) (argI) , sulfateL21(DE3) , and henanalysis  (S8 TablgltA encoding citrate synthase and icd encoding isocitrate dehydrogenase) were predicted to be essential from FBA using iML1515 of K-12 [lpd, gapA, eno, fbaA, pgk, pfkA, and tpiA) represent false positives . The false growth prediction can be used to refine the model when more biochemical information is available [Among 69 metabolic genes involved in central metabolic pathways, nine were reported to be essential for K-12 growing aerobically on glucose . Of the  of K-12 , which wvailable .Integrating transcriptome data into constraint-based models of metabolic network can improve flux prediction –62. In tde novo or were increased  were not synthesized in flask cultures using defined medium without fatty acid [ydiO) in the β-oxidation cycle. This case study demonstrates that the prediction power of the metabolic model can be improved by incorporating transcriptome data into metabolic simulation.When all the 238 fluxes corresponding to the 336 genes that were not expressed at the exponential phase in the defined medium were set to zero, the growth objective value was almost identical to that when such restriction was not imposed on the fluxes. Regarding flux distribution, most of the flux values did not change (< 5%), 44 fluxes disappeared or decreased, and 57 appeared ncreased . Notablyncreased . Anotherncreased . Previoutty acid , which apgl, which encodes 6-phosphogluconolactonase (Pgl) that is involved in the oxidative branch of the pentose phosphate pathway (PPP) [The major genetic difference in the central metabolism between BL21 and K-12 strains is the lack of ay (PPP) ,64. Abseay (PPP) . Simulatay (PPP) . Our simE. coli BL21(DE3) is widely used for the mass-production of recombinant proteins [E. coli B and K-12 strains showed that most of the genes involved in amino acid biosynthetic pathways were expressed more in B strains [E. coli could not grow on glutamate [E. coli strains.li BL21DE is widel strains ; howeverlutamate  and grewlutamate . The eff+ symporter (KgtP) of BL21(DE3) and K-12 MG1655 are identical. α-Ketoglutarate lies at the intersection between the carbon and nitrogen metabolic pathways and is a master regulator metabolite for nitrogen-assimilatory reactions [gltF adjacent to the gltBD operon encoding glutamate synthase, which converts α-ketoglutarate to glutamate [Interestingly, compared to K-12, BL21(DE3) did not grow well on α-ketoglutarate in PM tests . The proeactions . In addilutamate . GltF walutamate . SimulatThe automatically reconstructed metabolic model should be considered as a draft model, which requires extensive expert review. iECD_1391, the metabolic model of BL21, which is the predecessor of BL21(DE3), was first reconstructed in an automatic manner . The BL2Gene expression data can provide experimental evidences for the addition of model entities. We also used the transcriptome data to improve the flux prediction in a condition-specific manner . Set of IgoR and dcuS) affecting 11 transport reactions, the iHK1487 can be further improved by integrating more regulatory rules. For example, FBA using iHK1487 predicted no flux through the glyoxylate shunt pathway regardless of glucose concentration (cra (encoding catabolic repressor/activator) [arcA , iclR (repressor of aceBAK operon) [We showed that addition of BL21(DE3)-specific regulation into the metabolic model made the metabolic model congruent with the carbon source utilization data obtained from PM tests. As the regulatory rules of the current model were limited to two regulatory genes (ntration . This istivator) , reduced operon) , and ind operon) , althougBL21DE3) is one of the primary choices for overproduction of recombinant proteins, biofuels, and biorefineries ,76. Unti is one oS1 Fig(DOCX)Click here for additional data file.S2 Fig(DOCX)Click here for additional data file.S3 Fig(DOCX)Click here for additional data file.S4 Fig(DOCX)Click here for additional data file.S5 Fig(DOCX)Click here for additional data file.S6 Fig(DOCX)Click here for additional data file.S1 Table(XLSX)Click here for additional data file.S2 Table(XLSX)Click here for additional data file.S3 Table(XLSX)Click here for additional data file.S4 Table(XLSX)Click here for additional data file.S5 Table(XLSX)Click here for additional data file.S6 Table(XLSX)Click here for additional data file.S7 Table(XLSX)Click here for additional data file.S8 Table(XLSX)Click here for additional data file.S9 Table(XLSX)Click here for additional data file.S10 Table(XLSX)Click here for additional data file.S1 File(XML)Click here for additional data file.


Saccharomyces cerevisiae metabolic network. Partial functional impairment of the genes involved in the maturation of iron‐sulphur (Fe‐S) proteins was investigated employing the model and the in silico analysis revealed extensive rewiring of the fluxes in response to this functional impairment, despite its marginal phenotypic effect. The optimal turnover rate of enzymes bearing ion cofactors can be determined via this novel approach; yeast metabolism, at steady state, was determined to employ a constant turnover of its iron‐recruiting enzyme at a rate of 3.02 × 10−11 mmol·(g biomass)−1·h −1.Metabolic networks adapt to changes in their environment by modulating the activity of their enzymes and transporters; often by changing their abundance. Understanding such quantitative changes can shed light onto how metabolic adaptation works, or how it can fail and lead to a metabolically dysfunctional state. We propose a strategy to quantify metabolic protein requirements for cofactor‐utilising enzymes and transporters through constraint‐based modelling. The first eukaryotic genome‐scale metabolic model to comprehensively represent iron metabolism was constructed, extending the most recent community model of the  Baker’s yeast, the first eukaryote to have its genome sequenced . A specific growth rate of 0.1 hr−1 was used unless otherwise specified. The iron and copper supplementations of the system was determined from a standard defined medium for S. cerevisiae :For any metabolic reaction catalysed by a cofactor requiring enzyme (A and B) and products (C and D) are denoted by their cognate lower case letters, a cofactor (X) of enzyme N enters the metabolic reaction as a substrate and leaves as a catalytically unreactive product:where the stoichiometric coefficients of the substrates  were used in this study  and non‐reductive  iron uptake mechanisms were incorporated into the metabolic network. High‐affinity iron uptake, as both free and xenosiderophore‐bound iron, was represented by the reductive pathway. The intracellular transport of iron and complex iron entities, such as haem and sirohaem, across intracellular boundaries and the storage of residual components and excess iron were also considered , enterobactin and ferrioxamine B  or for other mitochondrial Fe‐S proteins —was introduced to the metabolic network to model Fe‐S cluster biogenesis (the ISC machinery) in the mitochondria and Fe‐S cluster assembly (the CIA machinery) in the cytosol and nucleus. This allowed the maturation of the Fe‐S clusters and the ensuing transfer to their cognate apoenzymes  the yeast‐specific haem‐regulated positive feedback route  of the pathway, was reported to be an indicator of low‐iron uptake in yeast . AS activated the iron regulon in the nucleus, relaying a message to the cell envelope to activate the uptake of iron Figure d. PS was3.2Cofactor representation.” This allowed us to establish the connectivity between iron metabolism, described above, and the primary metabolic network of yeast. For this purpose, the copper, iron, haem, sirohaem, pyridoxine and Fe‐S requirements of the metabolic network were identified  were used as substrates and untransformed reactants in those reactions that were catalysed by enzymes activated by these cofactors, as described in “3.3Although the elemental iron content of yeast has long been determined , 13 species types (11 metabolites and two enzymes), and 53 existing reactions, as well as the removal of three reactions from Y7.6. Some 90 species types , representing 173 species  and 104 new enzymatic and transport reactions were introduced to the model. Here, “species” denotes both metabolites and enzymes as the standard nomenclature adopted in the model. Thus the new version of the model, Y7.Fe, has improved the gene coverage of the existing model by 6%.Reactions, which were reported to take place at the membrane but did not have a detailed mechanism explained, were represented to occur across the membrane. This device simplified the model without compromising on the details of iron metabolism. The enzymes associated with these reactions were localised to the membrane to highlight the transmembrane nature of the reaction. Pseudo‐metabolites were introduced such that they did not interfere with the material, energy, or redox balances of the network. They were introduced in coupled reactions to avoid accumulation, and these reactions were unbounded so that the system was not constrained by the flux limitations through these reactions when the underdetermined system was optimised for a given objective.2 (in vacuole) and FMNH2 (in the mitochondria). Some by‐products of iron metabolism are allowed to accumulate in the yeast cell as reported in the literature: bilirubin and ferrioxamineB (in the vacuole), coprogen, ferrichrome and enterobactin (in the cytoplasm). l‐Cysteine is transported into the mitochondrion in our model for the assembly of the sulphonylated scaffold for Fe‐S cluster formation. Although recent reports have suggested a putative cysteine synthase (Mcy1p) identified in the mitochondrial outer membrane , NADPH, NADP, FMN and FMNHp < 10–38) along with other metabolic processes in line with our observations on the analysis involving the purine intermediates used as flux constraints. We carried out a sensitivity analysis to investigate robustness by selecting the fluxes that displayed a change more than 15–35% (in 5% increments), and observed that the genes encoding the enzymes that catalysed these reactions were significantly enriched for the same, or very similar processes . The variability of the flux distributions was taken into consideration in conducting this analysis .Some 97% of the reactions contained in Y7.Fe were comparable to those of Y7.6 and only 823 (ca. 23%) reactions had non‐zero fluxes when the unit glucose uptake rate was used as the single constraint for optimising growth. Of those 823 reactions, the flux through only 229 remained the same and the difference in fluxes through 254 of the remaining reactions was more than 25%. This indicated that introduction of iron metabolism into the genome‐scale metabolic model resulted in a substantial rewiring of nearly one‐third of the active reactions in the model under standard growth conditions. The predicted growth flux was reduced by 7% in Y7.Fe , indicating the cost of the iron metabolism to the existing network. This high metabolic burden was most likely to be associated with energy generation, and could not be captured by Y7.6. This observation was in line with the growth predictions obtained by constraining the fluxes through the purine pathways in our preliminary analysis. Revisiting the same system, the flux predictions improved substantially employing Y7.Fe with only a ±20% difference between the experimentally measured and predicted growth fluxes, at the cost of lower predictive accuracy of the growth phenotype. Indeed, an analysis of those reactions, which displayed more than 25% change in their flux between Y7.6 and Y7.Fe, showed that they were associated with genes that were significantly enriched for the nucleoside phosphate metabolism process term . The modifications were proportional enrichment in the fluxes for the production of the iron entities that were incorporated into the biomass equation. Despite being far from providing a complete picture due to the problems regarding data availability discussed above, this exercise of incorporating iron entities into biomass definition demonstrated that, in fact, it was the incorporation of the iron metabolism into the network that caused extensive rewiring of the fluxes when iron was taken into consideration as a metabolic cofactor, rather than the part Fe‐proteins played in the biomass.The predictive power of the Y7.Fe model was further investigated by determining its ability to define gene essentiality. The extended model was observed to perform very similarly to the existing primary model, Y7.6, with only marginal differences in measures evaluating predictive power of the model despite a sizeable improvement of 6% in gene coverage Table . Major i3.5–14 if the supply of iron is not to reduce the rate of growth −1·h−1 based on this model. The maximum and minimum theoretical requirements for iron‐recruiting enzymes were determined by investigating the variability of these fluxes. This analysis demonstrated that the cell employs the pathways where minimal iron recruitment of the cognate enzymes would be required, possibly to improve the energy efficiency of the system. The total turnover was only marginally (0.02‰) higher than that computed for the theoretical minimum usage. On the other hand, we observed that the fluxes through these pathways would be rewired such that the turnover of iron‐recruiting enzymes would be increased by 34% (Supporting Information S5).The stoichiometry of the cofactors introduced into the reactions was observed to be closely related to the predictions of growth rate, which meant that such predictions were very sensitive to the metabolic requirement for iron in the network. The total iron requirement of the cell was calculated from the iron composition of a standard defined medium for yeast . An alternative strategy to determine enzyme abundances from the reaction flux and the turnover rate of these enzymes (kcat) could be evaluated to replace the stoichiometric coefficient strategy. Iron, being a micronutrient, is usually provided in the growth medium at a low concentration. Therefore, constraining enzyme abundances by iron availability constrains the reaction flux altogether, since the kcat for each reaction would remain constant. Even making a favourable selection of kcat values based on available data, the constraint on iron availability indicated that material flow through high‐flux reactions, such as those involved with the mitochondrial respiratory chain, would then adopt impractically low values to satisfy the constraint on iron availability and compromise growth rate substantially. This indicated that the limiting factor concerning iron metabolism was the availability of iron, not the enzyme turnover rates, necessitating the modulation of reaction stoichiometry.The stoichiometric coefficients for cofactors were determined to be very low, as expected by their biological context. Although iron was not among the trace element cofactors, the stoichiometric coefficients were determined to be in the magnitude of 10http://www.gurobi.com/) were two orders of magnitude lower than the stoichiometric coefficients, allowing us a robust platform to conduct the analyses independent of whether the MATLAB or the Python version of Cobra was utilised. Several tests were run to ensure that Gurobi did not treat the stoichiometric coefficients as zero, and that the performance of the solver was not compromised (as described in Supporting Information 3). However, for less abundant cofactors, this is an issue that needs to be addressed.Working with such small numbers also imposes technical constraints on the analysis. The precision of the machine and the solver used can both cause problems at this stage. For the current analyses, the precision of both the machine and Gurobi  and ATM1 (the Fe‐S apocluster transporter) have essential functions outside of the metabolic network, perhaps for the supply of Fe‐S clusters for essential non‐enzyme proteins.We then investigated how Y7.Fe could be used to study the impact of the deletion of the genes p < 0.01) with the specific growth rate for all mutants remaining within 0.43±0.01h−1 as also indicated by the model predictions. Our experiments demonstrated that the hemizygous mutants did not display significant differences (p < 0.01) with respect to their utilisation of glucose or ammonium as carbon and nitrogen sources, respectively, nor in their production of ethanol or glycerol. On average, the hemizygous mutants were observed to consume more iron per unit optical density equivalent number of cells although this difference was not observed to be significant due to the high variance between replicates. However, a significant difference in the intracellular distribution of copper was observed between these mutants and the wild type was observed. That said, measurements of intracellular haem, copper, reduced or total iron content of the mutants gave no further insight into the essential roles of ARH1 , YFH1 and ATM1 inside or outside metabolism (Supporting Information S5).Despite their essentiality, the hemizygous mutants of these genes in the diploid BY4743 genetic background did not produce any significant growth defects (p < 10–40) in Y7.Fe than in Y7.6. In line with this observation, ARH1 was widely associated with reactions having non‐zero fluxes in the metabolic network. ARH1 being an essential gene also for the model, the reorganisation of the fluxes in the network could only be investigated by introducing an “in silico reduction of function.” We used flux as a proxy for the functional capacity of the enzyme catalysing that reaction and lowered the flux value by 50% to mimic the impact of heterozygosity. The flux bounds that were set to 50% of their wild‐type flux value did not relate to nutrient uptake fluxes; therefore, they did not change the nutrient limitation of the system and this has been confirmed by the glucose uptake flux being maintained at its upper bound limit under both conditions. Consequently, the predicted growth rate was reduced by 50% in response to limiting the flux through the reaction catalysed by ARH1 at 50% of its original value, the expected outcome for the remaining non‐zero‐fluxes was to be reduced by 50%, or to remain unchanged. However, 14% of all fluxes were observed to be rewired or had changed by a factor other than a 50% reduction.The reactions with non‐zero fluxes were more often catalysed by enzymes encoded by essential genes . Furthermore, fluxes were observed to be rewired away from the metabolism of glycine and serine family of amino acids (p < 10−6) towards the metabolism of neutral lipids (p < 10−4). The enzymes associated with the reactions that displayed unexpected variations in the magnitude of their fluxes were significantly associated with oxidative phosphorylation (p < 10–40), aerobic respiration (p < 10–30), and purine nucleotide metabolism (p < 10–72).Some 22% of the enzymes and transporters represented in Y7.Fe  associated with 506 fluxes were affected by these changes. The rewiring of the fluxes was predominantly observed to involve lipid metabolism .Among the reactions with unexpectedly altered fluxes, 28% were orphan reactions, mostly involved in small molecule transport or exchange, for which the relevant gene has yet to be identified. Many of these reactions were involved with the transport or exchange of lipid metabolism intermediates across organelles, as well as of amino acids including glycine, ARH1 function in the cell was in line with earlier findings on its role in biological systems. Apart from acting as an essential component of the ISC machinery, the Arh1 protein is an ortholog of the human adrenodoxin reductase , constraining the flux of such a reaction was observed to lead to a reduction in the oxygen uptake flux, also by 50%. This was observed not only upon imposing limitations on iron uptake, but also upon rendering of the Fe‐S cluster biogenesis fluxes low, as demonstrated by the simulations carried out to mimic the impact of genetic modifications on the metabolic network. This example also demonstrated the tight links across the metabolic network. Because the flow of material (i.e. flux) through the reactions, which were catalysed by iron‐requiring enzymes, would not be isolated from the flux through those that did not require iron‐bearing enzymes. The fluxes through reactions which (in theory) had no direct relationship with iron metabolism were also affected in response to this extension of the model.Because iron cofactors, specifically Fe‐S clusters, were used extensively as cofactors by enzymes catalysing mitochondrial reactions  availability, but also by the availability of an essential micronutrient, that is iron. The ability to incorporate the roles of such ion cofactors could prove essential for constructing models of biological systems at the level of the whole cell or organism.The authors declare that there are no conflicts of interest.Supplementary informationClick here for additional data file.Supplementary informationClick here for additional data file.Supplementary informationClick here for additional data file.Supplementary informationClick here for additional data file.Supplementary informationClick here for additional data file.Supplementary informationClick here for additional data file.Supplementary informationClick here for additional data file.Supplementary informationClick here for additional data file.Supplementary informationClick here for additional data file.Supplementary informationClick here for additional data file.Supplementary informationClick here for additional data file.Supplementary informationClick here for additional data file.