Diabetes mellitus in Homo sapiens. For validating our results biologically, we have used sensitivity analysis, both local and global, as well as for identifying the role of feedbacks in spreading infection in metabolic pathways. Moreover, information in literature has also been used to validate the results. The metabolic network datasets have been collected from the Kyoto Encyclopedia of Genes and Genomes (KEGG).Disease Systems Biology is an area of life sciences, which is not very well understood to date. Analyzing infections and their spread in healthy metabolite networks can be one of the focussed areas in this regard. We have proposed a theory based on the classical forest fire model for analyzing the path of infection spread in healthy metabolic pathways. The theory suggests that when fire erupts in a forest, it spreads, and the surrounding trees also catch fire. Similarly, when we consider a metabolic network, the infection caused in the metabolites of the network spreads like a fire. We have constructed a simulation model which is used to study the infection caused in the metabolic networks from the start of infection, to spread and ultimately combating it. For implementation, we have used two approaches, first, based on quantitative strategies using ordinary differential equations and second, using graph-theory based properties. Furthermore, we are using certain probabilistic scores to complete this task and for interpreting the harm caused in the network, given by a ‘critical value’ to check whether the infection can be cured or not. We have tested our simulation model on metabolic pathways involved in Type I  An important aspect of metabolic pathway analysis is studying the impact of infections or disease spread in healthy metabolic pathways. Tackling the growth of infection in a healthy metabolic pathway as well as curing it simultaneously is rather complex. Let us consider a scenario, wherein, a metabolite in a healthy metabolic network becomes infected due to some mutation or external perturbation. Moreover, a metabolite is said to be infected if its formation, in a metabolic pathway, is somehow impaired. The major problem lies in tracking the progress of this infection to other non-infected neighboring metabolites and understand the nature of this spread In this study we have implemented the forest fire strategy for analyzing the infection spread in a healthy metabolic pathway. The classical forest fire algorithm suggests that when fire erupts in a forest, it spreads to its surrounding trees, resulting in their further burning. At each step of this process, the burning trees have a probability of staying on fire and burning out, whereas the surrounding trees also have a probability of ignition Recent literature shows that some basic disease models have been developed to analyze the spread of certain diseases in real-world networks. These models describe the susceptibility, infection scenario and recovery rates of populations from a particular disease. In all these models information related to infection progress is not taken into account because of the differences in response among individuals in a specific population. Moreover, based on the epidemiological studies of individuals, two standard models, namely, susceptible-infectious-recovered (SIR) and susceptible-infectious-susceptible (SIS), have been proposed (discussed in section ‘Methodology’) for analyzing the study of disease spread in populations in-silico but may fail when implemented on a real dataset. For this purpose, we have modeled and analyzed a prevalent property of metabolic pathways, namely, occurrence of feedback reactions and studied its role in disease spread To understand the feature of fire spread, we have selected two strategies, first, based on quantitative studies, and second, based on graphs. The first strategy implements the fire spread using mathematical models and expressions. We have used ordinary differential equations (ODEs) for this purpose. We use ODEs for representing the complete metabolic pathway, its constituents as well as their ongoing interactions. As these metabolic processes are dynamic in nature, modeling them using ODEs is extremely useful Diabetes mellitus in H. sapiens. Diabetes mellitus is a metabolic disorder of multiple aetiology that is characterized by chronic hyperglycaemia affecting carbohydrate, fat and protein metabolism, which results from improper insulin production. Diabetes mellitus affects in various manners, which include long-term damage, dysfunction and failure of multiple organs. Furthermore, certain genes play a vital role in the development of Diabetes mellitus. To date, more than 250 candidate genes have been investigated, and results have shown a very high variability in gene association with Diabetes mellitusDiabetes mellitus. Even if mutations are known, some investigations have found that people with low risk genes can still develop Diabetes mellitus. Moreover, it has been observed that the combination of susceptible genes and environmental factors may initiate this disease process that is associated with the formation of an autoimmune response to the insulin-producing cells. This autoimmune reaction is reflected by the presence of antibodies against prominent antigens in the pancreatic For testing our simulation tool, we have selected Type I Diabetes mellitus. It contributes about 10% toward Diabetes mellitus susceptibility Diabetes mellitus in H. sapiens by studying the role of GAD and INS genes in metabolic pathways involving Type I Diabetes mellitus from a Systems Biology perspective. For this purpose, we have used the SBML format of metabolic pathway datasets under Type I Diabetes mellitus of H. sapiens for our study. We have downloaded the metabolic pathway datasets which have shown role in the expression of GAD and INS genes, known from Kyoto Encyclopedia of Genes and Genomes (KEGG) Type I is usually characterized by the presence of anti-Glutaric acid decarboxylase (GAD), islet cell or insulin antibodies which identify the autoimmune processes that lead to H. sapiens, analyzing their tendency to become infected giving rise to Type I Diabetes mellitus. We have collected the metabolic pathway datasets involving GAD and INS genes from Kyoto Encyclopedia of Genes and Genomes (KEGG). One of the criteria for handling our algorithm requires input to be given in Systems Biology Markup Language (SBML) format. We used the KEGG2SBML tool for converting the metabolic pathway datasets from KEGG to SBML format compartment which acts as a container of finite volume where reactions take place, species which represents an entity that takes part in a reaction, reaction which describes some transformation process converting one or more species, parameter which describes a quantity taking part in a reaction process, unit definition which specifies a name of a unit used in the expression of quantities in a reaction model, and rule which acts as a mathematical expression that is added to the model equations constructed from the set of reactions.Here we describe the method we have developed for implementing fire spread in healthy metabolic networks in five steps, which are performed one after another in successive manner. The first step is quantitative formulation of the metabolic pathways using ordinary differential equations (ODE), which deals with conversion of the entire metabolic pathways in the form of ODEs. This is one of the preliminary aspects of quantitative modeling. The second step is fire spread analysis, which involves modeling the fire spread mathematically using information from the first step and implementing it into the healthy metabolic pathway. The third step is handling the presence of feedback reactions, analyzing their role in fire spread and combat. This step has two sub-steps, namely, modeling feedback reactions and identifying them in the metabolic pathways. The fourth step deals with analyzing the sensitivity threshold of metabolic pathways against this fire spread. We performed both local as well as global sensitivity analysis. The fifth and last step is damage analysis, which calculates the extent of infections that spread throughout the metabolic pathway and the metabolites that remain uneffected/healthy or which have become cured after becoming susceptible to infection attack. For implementation purpose, we selected glutamate metabolism for further explanation.The complete methodology is divided into Here, we have used ODEs to model the entire glutamate metabolism in terms of the metabolites participating in various reactions as shown below. Our intention of performing this step was to model the spread of infection mathematically, for which initial structure of the healthy glutamate metabolism needs to be converted into ODE form. For this purpose, we assumed some notations, namely, Now, considering the ODE for H. sapiens to analyze their susceptibility for T1D. The original SIR model was first proposed by Lowell Reed and Wade Hampton Frost in 1920. It discussed the growth of an epidemic in a population of individuals, where the population is divided into three states, namely, susceptible (S), infection (I) and removed (R). Susceptible individuals are those who have higher chance of getting infected from some already infected individuals, whereas removed state corresponds to those individuals who are either dead or removed from the populations H. sapiens for checking its susceptibility against infection spread. One of the widely analyzed epidemic models is the susceptible-infected-removed or SIR models In the previous section, we generated the ODEs for the healthy metabolites in glutamate metabolism which are still uneffected from infection spread. Now, we focus on the structure of the same metabolic pathway after it gets infected. For the same purpose, certain notations have been considered, namely, First, we model the rate of change of the structure of pathway with time against possible infection attack. Thus, we haveChange in number of metabolites that are susceptible to infection attack = Current pathway architecture−metabolites that are infected directly or actively with a certain infection rate−susceptible metabolites getting infected with a certain susceptibility rate+metabolites that are cured actively with active curing rate+metabolites that are cured passively with passive curing rate Change in number of infected metabolites in passive manner = Number of susceptible metabolites that are actively infected−breakdown of already actively infected metabolites−curing of infected metabolites with passive curing rate−susceptibility of cured metabolites getting infected again Change in number of infected metabolites in active manner = Number of metabolites getting degenerated due to infection of metabolites  in active manner+breakdown of infected metabolites−curing of infected metabolites with a certain curing rate−susceptibility of already infected metabolites to be getting infected again−degeneration of the infected metabolites with a degeneracy rate H. sapiens.One of the most important factors associated with this nomenclature is the critical factor  into a directed graph Here, we define a metabolite as ‘infected’ when it loses its functionality, due to some mutation and external perturbation, and becomes inefficient to form a useful product. Also, a metabolite is termed to be infected if its formation, in a metabolic pathway, is somehow impaired. We assume that higher the connectivity of this metabolite, more the probability that its neighboring metabolites are infected. Also, if the metabolite is completely infected, it no longer participates in any other reaction, thus Infection spreads from initial metabolite till the path ends where the value of re cured , 4.As we deal with metabolic pathways, there are various ongoing processes that we need to consider so that our simulation is successful and biologically relevant. One of the most important properties in metabolic pathways is the presence of feedback reactions, which can drastically effect their overall functionality. So, we studied the existence of feedbacks and related them to our model. This subsection explains the basic implementation strategy followed by us for identification of feedbacks We considered a model A directed graph is known an arborescence if, from a given node For understanding the stability of the network, inhibits  , Finally, if With all these notations regarding feedbacks that we generated, the ultimate problem was to define certain algorithms to identify and characterize them, so that they could be further analyzed. The next subsection highlights some algorithms that we devised to identify feedbacks in metabolic pathways.All the algorithms for identifying and analyzing feedback reactions were based on identifying a pattern based on graph-based properties in metabolic pathways. The property of graphs that we used were isomorphism and arborescence. The algorithm proposed by us were for identifying feedback patterns, feedback activation, feedback inhibition, monovalent link prediction, divalent link prediction, iso-functional enzyme link prediction, sequential link prediction, concerted links prediction, and cumulative links respectively.Feedback pattern identificationfor each possible pattern dolet estimate for each node in do for each node in do ifthencontinue let  fordo output Elaborateifthen return, , [5For For H. sapiens , We implemented this method in four metabolic pathways for For implementing the fire spread, we used strategies, based on quantitative studies and graphs. The quantitative strategy using ODEs implements the fire spread using mathematical models and expressions. For biological validation, we used the sensitivity analysis for identifying the nature and property of these metabolites and their role in disease spread. In our model we do not consider any metabolite to become immunized to the infection spread and consider them equally susceptible to other infected metabolites against infection spread. One of the effective approaches in this case is curing the infected metabolites and vaccinating the uneffected ones with a probability proportional to their conductivities, so that a greater proportion of metabolites of high connectivity are vaccinated than metabolites with low connectivity. Another strategy is specifically targeting the hub metabolites by vaccinating all metabolites in the pathway of connectivity higher than some threshold value. The processes of infection and curing run for a specific number of iterations, depending on the number of metabolites in the metabolic pathway. We have assigned a maximum iteration value of H. sapiens metabolic pathways under carbohydrate metabolism have a range of critical values from 1 to 7, under amino acid metabolism from 1 to 35, under lipid metabolism from 1 to 36, under energy metabolism from 1 to 4 and under metabolism of co-factors and vitamins from 1 to 8. Furthermore, from this study we want to mention that critical values ranging from 1–5 is less prone to infection, 5–10 is more prone to infection, whereas value greater than 10 are most prone to infection. We would also like to make a note on some recent advances in systems biology approaches, such as flux balance analysis, which have been successful in idenitfying optimal metabolic pathways and extreme pathways. But, the volume of work that have been done in correlating sensitivities, both local and global, with FBA, as well as judging the system states of a network is less. Furthermore, less work have been performed in areas of detecting and quantifying ‘feedback’ using certain conventional techniques like FBA. Thus, novelty of our approach lies in that we have correlated system state identification, feedback detection, as well as sensitivities studies in diseased state pathways. This investigation can be taken one step further by analyzing the density factor as well as applying time constraints to the infection caused in the metabolic networks. Finally, we can even extend this method to analyze the patterns associated with epidemiological and endemic networks.From our analysis, we have also found that in File S1Supporting information. Figure S1. Spread of infection in glutamate metabolism with infection start site as ‘3’. Figure S2. Spread of infection in glutamate metabolism with infection start site as ‘4’. Figure S3. Combat process in glutamate metabolism with infection start site as ‘3’. Figure S4. Combat process in glutamate metabolism in H. sapiens with infection start site as ‘4’. Figure S5. Plot representing distribution of critical values in all metabolic pathways in H. sapiens. Figure S6. (DOC)Click here for additional data file.


A large number of genome-scale metabolic networks is now available for many organisms, mostly bacteria. Previous works on minimal gene sets, when analysing host-dependent bacteria, found small common sets of metabolic genes. When such analyses are restricted to bacteria with similar lifestyles, larger portions of metabolism are expected to be shared and their composition is worth investigating. Here we report a comparative analysis of the small molecule metabolism of symbiotic bacteria, exploring common and variable portions as well as the contribution of different lifestyle groups to the reduction of a common set of metabolic capabilities.Escherichia coli, their cores are enriched in biosynthetic processes whereas the variable metabolisms have similar ratios of biosynthetic and degradation reactions. Conversely, the variable metabolism of obligate intracellular symbionts is enriched in anabolism.We found no reaction shared by all the bacteria analysed. Disregarding those with the smallest genomes, we still do not find a reaction core, however we did find a core of biochemical capabilities. While obligate intracellular symbionts have no core of reactions within their group, extracellular and cell-associated symbionts do have a small core composed of disconnected fragments. In agreement with previous findings in Even when removing the symbionts with the most reduced genomes, there is no core of reactions common to the analysed symbiotic bacteria. The main reason is the very high specialisation of obligate intracellular symbionts, however, host-dependence alone is not an explanation for such absence. The composition of the metabolism of cell-associated and extracellular bacteria shows that while they have similar needs in terms of the building blocks of their cells, they have to adapt to very distinct environments. On the other hand, in obligate intracellular bacteria, catabolism has largely disappeared, whereas synthetic routes appear to have been selected for depending on the nature of the symbiosis. As more genomes are added, we expect, based on our simulations, that the core of cell-associated and extracellular bacteria continues to diminish, converging to approximately 60 reactions. We now have at our disposal the full metabolic network based on genomic data for hundreds of species, mostly bacteria. The level of annotation is however widely heterogeneous across species, making it crucial for any comparative analysis to carefully choose a set of species for which we can guarantee a good enough annotation, and a same procedure for inferring the metabolic network from the annotated genomes.i.e., the presence of non-orthologous, paralogous or unrelated, genes for the same function in different organisms)[i.e., branches that proceed via different metabolites and converge to the same end product)[One question commonly raised by the availability of many complete genome sequences is the number and content of a minimal set of protein-coding genes necessary to sustain a living cell-3, whichganisms) whose enganisms). In compproduct). Their oproduct). Since mproduct), and theproduct),20, alteproduct),13,21,22product),24. One Escherichia coli[Small-scale comparative analyses of a selection of metabolic pathways were performed investigating each one individually,26 or grchia coli. This apchia coli-37.i.e., its conserved portion) of different lifestyle bacteria, aiming to characterise the contribution of each lifestyle group in the reduction of the common set of metabolic capabilities shared by the whole dataset. As concerns the impact of the obligate intracellular group, the question could be reformulated as the reactions which could not be dispensed and/or outsourced to the host in the course of genome compaction. Our major goals were to have a representative diversity in the symbiotic associations, a balanced amount of organisms in each lifestyle group, and as few biases as possible that might be related to the use of different annotation pipelines which is important when performing comparative analyses. We address this by comparing the presence of metabolic reactions as well as biochemical capabilities based on a partial Enzyme Commission (EC) number analysis at level 3 [e.g., alternative amino acid biosynthetic pathways that are often composed of enzymes which have the same partial EC numbers at level 3 . We also analysed the metabolites that each bacterium potentially acquires from its environment in order to relate them to the set of common metabolic functions found for each lifestyle group.Here, we work at the level of whole metabolic networks for each organism and we analyse the core small molecule metabolism 2.5.1.-). The pur.-. The obligate intracellular INTRA, cell associated CA, extracellular EXTRA  and the control group free-living FL. We further grouped them in subcategories on the basis of the association type and transmission mode. The lifestyle groups and the abbreviations are given in FigureWe selected 58 bacteria from the MicroScope platform and we ci.e. small molecule reactions are those in which all participants are small molecules, hence reactions involving one or more macromolecules such as proteins or nucleic acids are not represented. The comparisons of compound and reaction sets are based on the BioCyc labels[e.g., the last reaction of glycolysis consists in the transformation of phosphoenolpyruvate, ADP and H + into pyruvate and water, and its label is PEPDEPHOS-RXN. The compounds found in the metabolic networks are those which are involved as substrates or products in the inferred reactions. All metabolites directly provided by the environment and not involved in any reaction as substrate are not included.Our analysis is restricted to the small molecule metabolism as defined in the MetaCyc/BioCyc databases,45, i.e.i.e., of a conserved set of elements in bacteria with different lifestyles, was analysed in terms of common compounds, common reactions and common partial EC number sets. The core metabolism was obtained by computing the intersection of the sets of reactions  for each species. The panmetabolism was obtained by computing the union of these sets. The variable metabolism is the difference between pan- and core metabolism, i.e., the set of elements that are missing from at least one bacterium. These definitions were introduced by Vieira et al.[The presence of a metabolic core, ra et al., howeverThe metabolic networks of the 58 bacteria were obtained from MetExplore. The mace.g. 2.5.1.3) based on the chemical reactions a given enzyme catalyses. We worked with partial EC number sets at level 3 (e.g. 2.5.1.-), leaving the fourth digit open. The first digit represents which of the six main classes the enzyme belongs to . The following 3 digits provide a more detailed description of the enzymatic activity.For the analysis of the core enzymatic functions we used the EC number classification which coi.e., the produced metabolites would be consumed by other reactions in a chain of biochemical transformations. For that, the metabolic networks of the dataset were modelled as reaction graphs. In such a graph, nodes represent reactions, and arcs  between two reactions represent a compound which is produced by one reaction and consumed by the other. We set filters to exclude pairs of cofactors  and current compounds , which otherwise would connect unrelated reactions[We analysed the connectivity of the core metabolic network to check if the common reactions would be connected among themselves, eactions.i.e., the subgraph containing the nodes corresponding to these reactions as well as the arcs that link them. After that, we checked for the presence of connected components, i.e., whether for every pair of nodes there is an undirected path.Since we were working with the common reactions of a group of organisms, we computed the union graph of all the metabolic networks modelled as reaction graphs. We then calculated the graph induced by the common set of reactions, i.e., one reaction for each partial EC number, are connected in the metabolic networks. We analysed this in the union of all metabolic networks of the dataset (or of lifestyle groups) modelled as a reaction graph, as well as in the graph of each organism. This analysis was performed using MOTUS[In the case of the common partial EC number sets, we checked whether the reactions corresponding to each one of the partial EC numbers, ng MOTUS.i.e., by forming subgroups from 57 to 53 bacteria) and the intersections of the remaining subgroups were recomputed. These six organisms are: “Candidatus Hodgkinia cicadicola” (HODCD), “Candidatus Carsonella ruddii” (CARRP), “Candidatus Sulcia mueller” GWSS (SULMW), M. genitalium (MYCGE), Buchnera aphidicola Cc (BUCCC) and Mycoplasma hyopneumoniae (MYCHJ). All possible orders for removing them were tested, and then the mean of the intersection sizes for each subset size of organisms was calculated. We also performed the same analysis by removing the eight bacteria with the smallest sets of reactions .We controlled for the impact of bacteria with very reduced genomes on the size of the common set of reactions . The six organisms which possess the smallest reaction sets  were successively removed  having nl organisms, we randomly drew x (2≤x≤nl−1) organisms and computed the intersection (y) of their reaction sets. This was repeated 1000 times. In order to test if, when adding more species, the size of the intersection of reaction sets was expected to decrease to zero, we fitted exponential (El) and logistic (Ll) models to the data obtained for each lifestyle group l. Assuming normally distributed residuals,Next, we checked whether there were reactions common to subsets of organisms within the same lifestyle group. To do so, for each lifestyle group x is the subset size , αl is the asymptote, rl is the decay rate and ϵl is the residual of the lthlifestyle group. Nlis theoretically defined as the mean of the reaction sets for an empty subset size (l for xl=0). A null intersection of the reaction sets corresponds to an asymptote α=0.whereMycoplasma species on the intersection size due to their reduced genomes (data not shown). Thus, both species were removed from the CA group for this simulation. We used the R package nlstools[Preliminary analyses showed the strong impact of the two nlstools for modeGammaproteobacteria of both groups. To do so, for each Gammaproteobacteria of the MIV group (7 organisms), we randomly picked a corresponding EXTRA Gammaproteobacterium and we randomly removed reactions from its set of reactions, until we reached the size of the corresponding MIV metabolic network. Then, we replaced each remaining reaction by its partial EC number at level 3, and removed redundant partial EC numbers from this set. We therefore obtained a group of simulated MIV networks for which we computed the union, intersection and average size of their partial EC number sets. This whole procedure was repeated 1000 times. Additionally, we aimed to test the differential random loss of biochemical capabilities, meaning the loss of partial EC numbers (at level 3). For that, we performed a similar procedure to the one explained above, however we stopped removing reactions when we reached the size of the MIV partial EC number set. We used a Monte-Carlo test from the R ade4 package[In order to rule out the possibility that the small intersection of partial EC number sets could be simply explained by a differential random loss of enzymes during genome reduction of the intracellular symbionts, we simulated the MIV , we used the Borenstein method[In order to identify which metabolites each bacterium potentially acquires from its environment (n method. For thin method. In ordeCa. Hodgkinia cicadicola” (HODCD) to 7279 genes for Ralstonia eutropha (RALEH) .The three most frequent taxonomic classes among all the organisms analysed are Ca. Hodgkinia cicadicola” (HODCD) to 1970 for Mycobacterium smegmatis (MYCS2). As for the total number of genes, the number of metabolic genes is greater in the EXTRA as compared to the INTRA bacteria. However, the ratio of the number of metabolic genes over the total number of genes shows important differences depending on the organism , being significantly different from the bacteria of the other groups .The number of metabolic genes ranges from 49 for “m Figure. For theCa. Hodgkinia cicadicola” (HODCD) to 1381 compounds and 1166 reactions for M. smegmatis (MYCS2) , one hydrolase (3.5.1) and one lyase (4.2.1) Table. They code novo biosynthesis. Removing the eight bacteria with the smallest reaction sets resulted in similar intersection sizes ranging from zero to 13 reactions and mean varying from zero to 5.4. Hence, the intersection sizes did not increase much without the bacteria with reduced metabolism.Clearly, we can expect that the inclusion of bacteria with very reduced genomes will have a large impact on the size of the intersection. However, it remains unclear if the small size of the intersection could be explained only by this. We found that the shared reaction sets, obtained when decreasing the number of organisms, range from zero to five and the mean varies from 0.2 to 2.5. There are 12 common reactions without the six bacteria with the smallest reaction sets, 7 take part in the biosynthesis of peptidoglycan, which is a cell wall precursor. These reactions do not complete this biosynthetic pathway . Among the other reactions, there is an inorganic pyrophosphatase, a reaction involved in folate transformations and a couple of reactions which take part in purine nucleotides On the other hand, these bacteria had a greater impact on the common partial EC number sets. The size of the intersections when decreasing the number of organisms ranges from 4 to 19 and the mean varies from 5 to 16. This size increases to 23 partial EC numbers without the same six bacteria. When removing the eight bacteria with the smallest sets, the sizes of the intersections increase, ranging from 4 to 27, reaching 30 partial EC numbers. Therefore, a core of biochemical capabilities composed of 30 partial EC numbers is present in 50 bacteria out of the 58 analysed. This set is made of all classes of enzymes: 3 oxidoreductases, 13 transferases, 4 hydrolases, 3 lyases, 5 isomerases and 2 ligases, which correspond to 958 reactions in our dataset  is quite large when compared to the mean number of compounds, indicating a relative diversity of the metabolome in these organisms  and M. hyopneumoniae J (MYCHJ) which are obligate parasites that have undergone extreme reductive genome evolution[Mycoplasma species increases to 167 compounds and 88 reactions. These values are similar to the ones found for the EXTRA, the reactions take part in the same metabolic pathways observed for this group and the classification into biosynthetic and degradation processes present similar ratios  are classified as biosynthetic processes . Indeedp<10−15) and depleted in degradation reactions .As there is only one reaction common to INTRA, it is not possible to analyse whether there is a majority of biosynthesis reactions in their core as we found in the EXTRA and CA. Instead, we analyse the content of biosynthesis and degradation reactions in the variable metabolism (see Methods for definition). The total number of reactions in the variable metabolism is 704 (62% in biosynthetic and 24% in degradation processes) for the intracellular group while it is 2049 (38% in biosynthesis and 35% in degradation) in the EXTRA  and EXTRA groups (results not shown). We therefore tested a logistic model, which has a smoother decay than the exponential model, and found that it fitted much better this data. As expected, the asymptote for the INTRA group (αINTRA) was not significantly different from zero . We found no occurrence of connected reactions in either group .The differential random loss of enzymes or of biochemical capabilities  was compared with the small intersection size of the partial EC number sets. Comparing the simulated values with the ones of the real MIV ia Table, we founi.e., potential inputs) ranged from 29 in “Candidatus Sulcia muelleri” (SULMW) to 341 in M. smegmatis (MYCS2) with a mean of 133 [The absence of a metabolic core in the INTRA might be linked to the differences in their environment. The number of metabolites that each bacterium potentially acquires from its environment (isation). OverallWhen we allowed distance one from the topological precursors (see Methods for details), the number of common inputs increased inside the lifestyle groups that have less organisms, such as PIV. In the broader lifestyle groups, the number of shared inputs remained equal. The number of bacteria that has glucose as input increased from 3 to 40. Furthermore, the size of the intersection augmented between the groups, such as MEH and PEH.Overall, we find that neither EXTRA nor INTRA symbionts exhibit a common core of input metabolites. The absence of such a core is an intuitive explanation for the absence of a metabolic core of degradation pathways: different metabolic environments imply different metabolic pathways. However, this observation alone does not explain the total lack of a metabolic core for the INTRA symbionts. In this case, the specificity of the symbiosis with the host has to be considered.In this paper, we investigated to what extent there is any reaction common to a set of bacteria, including obligate intracellular symbionts, as well as the influence and the trend of each lifestyle group concerning shared reactions or biochemical capabilities. In order to do this, we considered 58 bacteria carefully selected to represent a wide range of lifestyles.Previous studies have found small sets of common metabolic genes even when including bacteria with reduced genomes,7. BasedM. hyopneumoniae (MYCHJ). It is catalysed by the hydrolase peptide deformylase (Def), which releases the formyl group from the N-terminal methionine residue of most nascent polypeptides[Phytoplasma sp. and Mycoplasma arthritidis[et al.[Ca. Hodgkinia cicadicola” (HODCD)) is potentially capable to code for this enzyme. Nevertheless, recently an even smaller cellular genome (approx. 139 base pairs and 121 protein-coding genes) of “Candidatus Tremblaya princeps” has been described[Even though there was no reaction common to all bacteria, we actually found one reaction  presentpeptides, an oblipeptides. The abspeptides, and it thritidis,68. For is[et al. identifiescribed which isescribed,8,19.Such small sets found raised the question whether they could be explained only by the (6 or 8) bacteria with the smallest genomes. These bacteria had a weak impact on the number of shared reactions, while they had a strong effect on the common partial EC number set. Removing them, the shared set increased to 12 reactions mainly involved in the synthesis of a cell wall precursor, which is not considered as an essential pathway and is kGammaproteobacteria as having lost a greater diversity of biochemical capabilities. This indicates that there is a set of partial EC numbers (capabilities) which are kept in subsets of organisms  and accounts for a reduced union.The reduced set of common partial EC numbers raised the question whether it could be simply explained by a differential random loss of enzymes. This was not the case. We further identified the MIV Hence, we did not find a core of metabolic reactions shared by the symbiotic bacteria which agrees with the idea that searching for ubiquity as more genomes are included may ultimately reduce to nothing. ConversMycoplasma species. Even if this group presents other host-dependent bacteria, their genome sizes at least double when compared to the Mycoplasma species, and a core of reactions similar in size to the EXTRA is found. The other lifestyle groups (EXTRA and FL), which include just free-living bacteria, did not contribute to the size of the common set.Among the different types of classification that we considered – (i) obligate intracellular, extracellular, cell associated, (ii) mutualistic, commensalist, parasitic, (iii) vertically or horizontally transmitted – the first is by far the one that explains best the differences in terms of metabolism. The CA group also accounted for the small common sets exclusively because of the Mycoplasma species in the small sets can be directly related to their extremely reduced genomes[W. pipientis wBm (WOLTR)) are the most integrated[Furthermore, the impact of the INTRA and of the  genomes-75. Theytegrated and are tegrated,57-64. Itegrated,77,78. Ttegrated.Mycoplasma species - the CA mentioned henceforward is without these bacteria). The shared reactions are involved in metabolic pathways that are also included in the minimal metabolism described by[In the analyses of each lifestyle group, we did not find a core of reactions for the INTRA, however we found it for the EXTRA and CA [E. coli, but at the same time, it is even more enriched in biosynthetic reactions. The reason for such an enrichment could be that, while the needs of the CA and the EXTRA symbionts are very similar in terms of building blocks for protein and DNA synthesis, the nutrients they uptake in their respective environment may be extremely variable. When variable environments are considered, degradation pathways, which are closer to the inputs of the network, are the first to be modified. This explanation is also corroborated by our observations on the lack of common inputs to all bacteria.The common sets of reactions of the CA and EXTRA groups are enriched in biosynthesis (approx. 88%) according to the metabolic processes defined in the BioCyc databases. In the core metabolism of ed (57%), thus ouE. coli (36% biosynthesis and 35% degradation) and the CA and EXTRA bacteria (approx. 39% biosynthesis and approx. 35% degradation), but the numbers are quite different for obligate intracellular bacteria (62% biosynthesis and 24% degradation). A possible explanation for this is that degradation pathways have largely disappeared in obligate intracellular bacteria, as the host provides an interface between the environment and the bacterium, while synthetic routes have not all disappeared but have been selected for, depending on the nature of the symbiosis[Considering now the proportion of biosynthesis and degradation reactions in the variable metabolism, we find that it is quite similar in ymbiosis,75,77,78et al.[Here, we worked with whole metabolic networks enabling to check whether the metabolic core would represent chains of biochemical reactions regardless of specific metabolic pathways. The core of reactions found was not entirely connected, most likely because of the existence of alternative pathways as highlighted by Gil et al.. This merCA and rEXTRA) were similar, while the two other parameters were different. In principle we cannot give a direct biological interpretation to Nl(it corresponds to the mean of the reaction sets for an empty subset size of organisms), we found its estimates are close to the size of the union of reactions of the corresponding lifestyle group, e.g., NEXTRA was estimated at 1643, while the size of the union of EXTRA was 1725 reactions. As expected, the asymptote estimated for the INTRA was not significantly different from zero, which agrees with the absence of a core of metabolic reactions found for this group. Conversely, the asymptotes estimated for the CA and the EXTRA groups were significantly different from zero; thus, based on the analysed dataset, neither group is expected to have an empty common set of reactions when more genomes of these groups are added. One should be aware that adding one organism that has a very particular niche could certainly change this trend. This result is nevertheless interesting given the fact that there are organisms from distinct taxonomic classes inside these groups, that moreover present different types of association with their hosts. To have an idea of the subset of reactions that would be “asymptotically” kept in organisms with lifestyles similar to those two groups, we analysed the reactions shared by the EXTRA and CA groups in our dataset. These 62 reactions are involved in the synthesis of purine and pyrimidine, of peptidoglycan and glycolysis. These findings are similar in number of enzymatic steps and in the content of pathways to the minimal metabolism described by Gabaldón et al.[We found a core of metabolic reactions for the CA and EXTRA, however we did not find one for the INTRA. This raised the question whether, as we add organisms, the decay of shared reactions and its limit was the same in these groups. First, we fitted the exponential model with asymptote to the data of all groups. This model described well the decay of shared reactions in the INTRA group. However, it was not appropriate to fit the EXTRA and CA data, since their behaviour of decay was not the same as that for the INTRA. Conversely, the logistic model was well adapted for these two groups. We also tested for common parameters for the two groups, but model fitting was better with each group having its separate parameter values. The decay rates (ón et al..In this paper, we explored to which extent each lifestyle group contributes to the reduction of a core metabolism as well as the composition of this core in the different groups, with a special focus on bacterial species only, in particular those that entertain a symbiotic relationship with a host. Moreover, we considered reactions instead of genes. Although we might then have expected to find a core, none common to all bacteria was observed. Symbionts with the most reduced genomes in our dataset had a weak impact on the number of shared reactions, but had a strong effect on the common partial EC number set which increased to 30 without those bacteria, covering a quite broad set of biochemical capabilities similar to those described for a minimal metabolism, with however an enrichment in transferases.Mycoplasma species were eliminated from the group. Extremely reduced genomes such as those of the two Mycoplasma and of the intracellular group remain thus the main factor behind the absence of a core, even though the loss of genes primarily concerns the non metabolic ones.Obligate intracellular symbionts appeared as the main reason for such absence of a core of metabolic reactions due to their high specialisation. However, hostdependence alone is not an explanation for this absence. Indeed, although the cell associated group contained host-dependent bacteria, their core of reactions was observed to be similar in size to the one of extracellular bacteria once the two E. coli, we observed that it is even more enriched in biosynthetic reactions, which might be due to the extreme variability of the nutrients that cell-associated and extracellular bacteria uptake in their respective environment. On the other hand, the proportion of biosynthesis and degradation reactions in the variable metabolism appears quite similar to the one found in E. coli. The same is not the case for obligate intracellular bacteria where degradation pathways have largely disappeared but synthetic routes appear instead to have been selected for depending on the nature of the symbiosis.A core of reactions was found for the cell-associated and the extracellular bacteria. This core roughly corresponds to the minimal metabolism previously described in the literature. It is not entirely connected and therefore does not result in one functional metabolic network. Although smaller than the core previously identified for strains of Finally, by using simulation, we tested whether the decay of shared reactions and its limit would be the same for cell-associated and extracellular bacteria as for the intracellular ones. Although one should be aware that adding one organism that has a very particular niche could certainly change the result observed, it appears that a subset of around 60 reactions would be “asymptotically” kept in cell-associated and extracellular bacteria. These are involved in the synthesis of purine and pyrimidine, of peptidoglycan and glycolysis, and are similar in number of enzymatic steps and content of pathways to the minimal metabolism described in the literature.The authors declare that they have no competing interests.CCK selected the dataset and LC prepared the data. CCK conducted the computational analyses described in the paper. JK and CCK performed the simulation of the decay of the reaction sets. All authors contributed equally to coordinating the analyses and writing the manuscript. All authors read and approved the final manuscript.Additional results. Additional results exemplifying the issue of NOGD, controlling for the structuring ofMIV and connectivity of the partial EC number set for obligate intracellular and extracellular bacteria.Click here for fileThe full list of the bacteria selected and their detailed classification. Additional fileClick here for fileNumber of Genes vs lifestyles. Additional fileClick here for fileCompounds common to all dataset. Additional fileClick here for fileCompounds and reactions common to groups of lifestyle. Additional fileClick here for fileThe full list of the reactions analysed and the list of organisms that lack them. Additional fileClick here for filePartial EC numbers common to groups of lifestyle. Additional fileClick here for fileMetabolic core of the extracellular bacteria. Additional fileClick here for fileDistribution of reactions across metabolic processes. Additional fileMycoplasma species.Click here for fileSimulation of partial EC number sets of the MIV bacteria. Simulation of partial EC number sets of theMIV bacteria. Additional fileClick here for fileNumber of potential inputs. Additional fileClick here for filePotential inputs common to groups of lifestyle. Additional fileClick here for file


A grand challenge in synthetic biology is to push the design of biomolecular circuits from purely genetic constructs towards systems that interface different levels of the cellular machinery, including signalling networks and metabolic pathways. In this paper, we focus on a genetic circuit for feedback regulation of unbranched metabolic pathways. The objective of this feedback system is to dampen the effect of flux perturbations caused by changes in cellular demands or by engineered pathways consuming metabolic intermediates. We consider a mathematical model for a control circuit with an operon architecture, whereby the expression of all pathway enzymes is transcriptionally repressed by the metabolic product. We address the existence and stability of the steady state, the dynamic response of the network under perturbations, and their dependence on common tuneable knobs such as the promoter characteristic and ribosome binding site (RBS) strengths. Our analysis reveals trade-offs between the steady state of the enzymes and the intermediates, together with a separation principle between promoter and RBS design. We show that enzymatic saturation imposes limits on the parameter design space, which must be satisfied to prevent metabolite accumulation and guarantee the stability of the network. The use of promoters with a broad dynamic range and a small leaky expression enlarges the design space. Simulation results with realistic parameter values also suggest that the control circuit can effectively upregulate enzyme production to compensate flux perturbations. The seminal works published in 2000 ,2 kick-sOne of the most prominent applications of synthetic biology is the manipulation of bacterial metabolism for chemical production in sectors such as energy, biomedicine and food technology . EffectiThe goal of this paper is to reveal new insights into the design limitations and trade-offs arising from the interplay between gene circuits and metabolic pathways. To that end, we analyse a dynamic model for a feedback system comprising nonlinear kinetic equations for the metabolic species, together with product-dependent enzyme expression controlled by a synthetic gene circuit. We focus on the existence and stability of the steady state, the dynamic response of the network under perturbations and the dependence of these on the design knobs of the synthetic gene circuit.et al. [et al. [et al. [et al. [Two landmark implementations of engineered genetic–metabolic circuits are the genetic control of lycopene production  and the et al. . These w [et al. , whereby [et al. , only a  [et al.  demonstr [et al.  as an ON [et al.  exploreda. The design of the genetic controller must then account for two complementary control objectives: firstly, it must dynamically adjust pathway activity to match the cellular demand for product and sustain the homeostatic balance of native cellular processes. Secondly, a common strategy in metabolic engineering is to modify host microbes by expressing heterologous enzymes that convert metabolic intermediates into a chemical of interest [figure 1b), and, therefore, the controller must also alleviate the impact of these engineered pathways on the native flux.From a control engineering standpoint, catalytic enzymes act as inputs to a metabolic pathway in order to drive the metabolite dynamics (i.e. the outputs). The pathway outputs are then sensed by metabolite-responsive molecules that can modulate enzyme expression levels (e.g. transcription factors (TFs) or riboswitches ). In thefigure 1interest . The conIn this paper, we study an unbranched metabolic pathway under transcriptional repression from the product. The synthetic circuit consists of an operon encoding all the catalytic enzymes that is repressed by a product-responsive TF (§2). The operon feedback architecture mimics natural circuits enabling cellular adaptations to environmental perturbations . These constraints must be satisfied to guarantee the existence of an equilibrium point, to prevent the accumulation of metabolites and to ensure the stability of the network under small perturbations. The feasible set for the RBS strengths depends critically on the promoter leakiness and substrate availability. Within the feasible set, RBS strengths may be used to fine-tune the balance between the intermediate metabolite levels and the gene expression burden imposed on the host cell. We also obtained analytical formulae for the modes of the feedback system; these showed that the operon architecture leads to slow fixed modes, and suggests a separation principle between the effect of RBS strengths and the promoter characteristic (§3.2).Escherichia coli (§§3.2 and 4.2). The simulations show that the control circuit can effectively upregulate enzyme production to compensate an increase in the cell's native demand for product and the impact of engineered pathways. These also suggest that, in terms of both flux and product homeostasis, the synthetic circuit always outperforms an uncontrolled pathway (i.e. with constant enzyme levels), thus highlighting the advantages of using a dynamic feedback control strategy.We also show that engineered pathways consuming an intermediate add further constraints to the RBS strengths design space, which can be relaxed by using promoters with a high dynamic range and small leakiness (§4.1). We performed numerical simulations of the model with physiologically realistic parameters in 2.b, where s0 denotes the concentration of substrate, s1 and s2 are intermediate metabolites and s3 is the metabolic product. The metabolic reactions occur at a rate vi  and d denotes the rate of product consumption by the cell. The metabolic genes are encoded in a single operon controlled by a product-responsive TF that represses enzyme expression. This kind of transcriptional feedback is common, for example, in bacterial nutrient uptake systems (e.g. the lactose operon [We consider an unbranched metabolic pathway as in figure 2e operon ) and amie operon ).Figure2.1.s0 and the product consumption rate d. We are interested in biologically meaningful phenotypes, and, therefore, we assume that s0 is constant to ensure that, the network can reach a non-zero steady state [s0 is an extracellular substrate pool shared by a low-density cell population (so that the effects of cell-to-cell competition are negligible).The network in dy state . Note thn reactions and n metabolites, the rate of change of metabolite concentrations can be described byi = 1, 2, … , n and vn+1 = d(sn). This model arises from the mass balance between the reactions that produce and consume si, and the enzyme kinetics are included in the reaction rates vi. To keep a general analysis, we will not presuppose a specific form for the enzyme kinetics. Instead, we will generically assume that the metabolic reaction rates are linear in the enzyme concentrations [gi(0) = 0. We will also assume that the enzyme turnover rates are increasing and saturable functions of the metabolite concentrations, so thatIn a pathway with trations 2.2where kinetics ,25.d(sn) is typically modelled as a saturable function of Michaelis–Menten type [d(sn) satisfying d(0) = 0, dmax is proportional to the enzyme concentration, and therefore in our model we can describe changes in cellular demand as changes in the parameter dmax.The rate of product consumption ten type , but, fo2.2.i = 1, 2, …, n. This model comes from the balance between protein synthesis and degradation. We consider a first-order degradation process with kinetic constants γi, which accounts for the aggregate effect of degradation and dilution by cell growth. A common strategy in synthetic biology is to control protein degradation by adding a degradation tag to the gene sequence [γi = γ. In the model (2.5), we have parameterized enzyme expression in terms of the promoter characteristic and RBS strengths, both of which are common design elements in synthetic gene circuits (a):Promoter characteristic. It describes the regulatory effect of the TF on gene transcription. The function σ(0) = 1, — tightness (κ0) and strength (κ1); see figure 3b. The tightness refers to the level of baseline transcription (i.e. under full repression by the product), whereas the strength is the gap between the ON and OFF transcription levels. The promoter strength is quantified in terms of the dynamic rangeμ,μ ≥ 1, and we can model the uncontrolled case (i.e. pure constitutive expression without regulation) by taking μ = 1.Promoters are typically described in terms of their Ribosome binding site strengths. RBSs are mRNA sequences that are bound by the ribosomes to initiate translation [bi.— nslation . The translation . We modeWith the above assumptions and definitions, we can write the complete model for the feedback system asIn an operon architecture all the enzymes are under the control of a single promoter (for the multi-promoter case see ), and thsequence , and thucircuits a:— Prom3.3.1.The operon circuit must be able to sustain a metabolic flux that feeds the product into the downstream native processes of the host. In this section, we show how this essential requirement translates into constraints on the RBS strength design space.We will denote the steady-state metabolite concentrations, enzyme concentrations and reaction rates as i ≥ 2,bi/b1. Note that because the enzyme turnover rates gi are monotonically increasing functions, increasing the bi/b1 ratio leads to a lower steady-state concentration of the intermediate si−1. From equations (Effect of the promoter characteristic. From the steady-state equation in (3.2), we can calculate (see appendix A.1 for a detailed derivation) the sensitivity of the product concentration to changes in promoter tightness κ0, promoter strength κ1 or RBS strength b1,κ0 and κ1) or RBS strength b1 will lead to a higher steady-state product concentration, which in turn translates into a higher flux. Moreover, since the genes cannot be transcribed at a rate beyond (κ0+κ1), from (3.2), we observe that the flux is constrained by the promoter parameters according to— Effect of the RBS strengths. Using (3.1), we can write the steady state of the downstream enzymes asbi/b1 ratio leads to a higher concentration for the ith enzyme. Taken together, equations (bi/b1. Comparing the dependencies of (3.3) and (3.8) on the RBS ratio reveals a design trade-off between enzyme expression and the intermediate metabolite concentrations (a): low bi/b1 ratios lead to low enzyme expression levels at the expense of high concentrations for the intermediates. Conversely, high bi/b1 ratios tend to increase enzyme expression (and therefore the gene expression burden on the host cell) in favour of low concentrations for the intermediates.— quations  and (3.8trations a: low biThe equilibrium concentrations of the intermediates can be obtained by setting quations  and (3.3d) and enzyme kinetics (gi), both equations may lack a solution. Firstly, the solution of (3.2) can be computed as the intersection of the two curves shown in dmax/g1(s0 ) > b1κ0/γ, or equivalentlyIn the above discussion, we have implicitly assumed that a solution to equations  and 3.33.3 existequation , the exibi/b1 ratio. Taken together, conditions (3.9) and (3.10) define a feasible region in the RBS strengths design space that prevents the accumulation of intermediates and product (b). If the condition in (3.9) is not satisfied, the substrate will be consumed at a higher rate than the maximal product consumption, and therefore the design will lead to an infinite accumulation of the product. Likewise, violation of at least one of the bounds in (3.10) will cause enzymatic saturation and lead to infinite accumulation of an intermediate.Secondly, since the enzyme turnover rates saturate at equation  has a fi product b. If thebi and promoter tightness κ0, together with the substrate availability s0 and the enzyme saturation c,d, we illustrate the effect of promoter tightness and substrate availability on the feasible region for the RBS strengths. Tighter promoters relax condition (3.9) and therefore enlarge the feasible region (figure 5c). In the limit case of a perfect leak-less promoter (i.e. κ0 = 0), condition (3.9) does not limit the RBS strength of the first enzyme. Conversely, by conditions (3.9) and (3.10), a higher substrate tends to tighten the feasible region (figure 5d).Conditions (3.9) and (3.10) link together genetic and metabolic parameters  as n eigenvalues can be classified into three categories λfixed, λiRBS and λprom. The system has the following:n−1) stable eigenvalues at λfixed = −γ < 0. These eigenvalues are independent of the circuit design parameters, and therefore they lead to fixed modes, which can be adjusted only by changing the degradation rate (e.g. with various degradation tags). They cannot be suppressed or changed by tuning the circuit design knobs, and, from (3.11), we see that they translate into (n − 1) modes of the form et/γ−, t et/γ−, … , tn−2 et/γ−. The enzyme degradation rates γ are inversely proportional to their half-lives, which are in turn much longer than metabolic time scales . Therefn−1) stable eigenvalues atbi/b1 . We also see that, as shown by the steady-state relation b, we plot the location of the promoter-dependent eigenvalues λprom in the complex plane. These indicate that, in the case of weak promoters, the eigenvalues λprom lie on the real axis, becoming complex only for a sufficiently broad dynamic range μ. For strong promoters, the real part b suggest that flux maximization may entail a reduction in the response speed.— Two stable eigenvalues atequation ). To stuIn the case of the feedback system in (2.7), we can exploit the structure of the Jacobian matrix to obtain analytic expressions for its eigenvalues in terms of the design knobs of the gene circuit (see appendix A.2 for details). We found that the 2a). We modelled a change in the cell demand as a slow S-shaped temporal increase in the maximal product consumption rate dmax (see the inset in figure 7a). This describes, for example, cases in which the demand increase is due to native processes upregulating the enzyme that metabolizes the product. Note that, from the steady-state equation in (3.2), a higher dmax inevitably leads to a higher flux and a lower steady-state product concentration . Before the perturbation, the network is in steady state with a pre-stimulus flux dpre = 19.5 µM min−1. We considered a Michaelis–Menten consumption rate of the form d(sn) = dmaxsn/(Kd + sn), with Kd being the product concentration needed for half-maximal consumption. Upon the increase in dmax at t = 50 min, we observe that the promoter responds to the drop in product concentration and upregulates enzyme expression so as to drive the pathway to a new post-stimulus flux dpost that is approximately 40 per cent higher than dpre, and a product concentration that is approximately 20 per cent lower than its pre-stimulus value. Using equations . The uncontrolled pathway is unable to increase the flux, and we observe that this leads to a considerable decrease in product concentration (approx. 70% reduction). In the uncontrolled case, the rate of substrate uptake is fixed to v1unc so that the equilibrium product satisfiesdmax translates into a lower product concentration d(sn). In contrast, the feedback-controlled pathway can partly compensate the drop in product by dynamically upregulating enzyme expression, substantially outperforming the uncontrolled case.As a way of comparison, in figure 7b, where we show the drop in product concentration relative to the pre-stimulus level as a function of the change in flux and dynamic range of the promoter. We observe that stronger promoters can significantly improve the compensation of the drop in product concentration (a perfect compensation would correspond to a flat curve at 0% in figure 7b). For example, under a 50 per cent increase in the pathway flux, a mild promoter (μ = 10) leads to a drop in product of approximately 47 per cent, whereas a strong promoter (μ = 100) can bring down the drop in product to approximately 20 per cent (the latter corresponds to the design simulated in figure 7a). As predicted by the upper bound in (3.7), the flux is limited by the promoter strength, and therefore weak promoters do not allow for large increases in flux ; for example, for the weakest promoter tested, the flux could not be increased beyond approximately 10 per cent.We study the performance of the control circuit in more detail in figure 74.A common strategy in metabolic engineering is to modify bacteria by expressing heterologous enzymes that convert natural metabolic intermediates into a compound of interest . The tar4.1.dext, we include dext as a consumption rate in the ODE for a, and in this case the steady-state equation for the product and the first enzyme isbi/b1 can be used to fine-tune the balance between enzyme expression and the concentrations of the intermediates. In addition, in this case, we see that the intermediates after the branch point also depend on the promoter characteristic.To account for an engineered pathway consuming the intermediate dext = 0. Since the design must also prevent the accumulation of intermediates in the absence of perturbations, we conclude that (3.10), i.e.b). As in the case without the branch (b), the limits (4.5) and (4.7) prevent the accumulation of the product and intermediates, respectively. The condition in (4.6), however, adds a new type of constraint to the design space: it guarantees that the synthetic gene circuit can upregulate enzyme expression strongly enough to cope with the flux through the branch, hence preventing the depletion of the product. This new constraint also depends on the promoter dynamic range, which was absent in the case without a branch. From (4.5) and (4.6), we can compute the gap between the upper and lower bounds for the first RBS strength (see b)c).Using similar arguments to those in equation  to have ates see b. As in e branch b, the lingth see b4.8whichpace see c.4.2.s1 (see a). Before the perturbation, the network is in steady state with a native flux dpre = 19.5 µM min−1. We modelled the engineered branch as an S-shaped increasing rate dext(t) (see the inset in figure 9a). Upon the activation of the branch, induced at t = 50 min, the synthetic operon circuit upregulates enzyme expression by approximately 45 per cent to drive the pathway to a new native flux dpost. Using equation  indicates that all enzymes are upregulated by an identical fold-factor that depends on the promoter design and the first RBS strength.a, we have also simulated the response of a pathway without feedback regulation (i.e. with constant enzyme levels dpre of the controlled case). In terms of both flux and product concentration, we observe that the feedback-controlled network displays a dramatic improvement compared with the uncontrolled case: the operon circuit reduces the loss in native flux from 50 per cent to approximately 5 per cent, whereas the decrease in steady-state product concentration is brought down from approximately 82 per cent to 20 per cent. In the uncontrolled case, the rate of substrate uptake is fixed to v1unc and therefore the post-stimulus flux is given byb, we show this linear dependence together with the feedback-regulated case for a wide span of the promoter dynamic range. We observe that the feedback control circuit outperforms the uncontrolled case even with promoters with a narrow dynamic range, and that this improvement can be achieved with a relatively low enzyme upregulation factor.In figure 95.In this paper we have presented a detailed analysis of a synthetic gene circuit designed to dynamically control metabolic pathways. The goal of this feedback control system is twofold: to adjust pathway activity so as to match the cell demand for product, and to dampen flux perturbations that divert the native flux to the synthesis of foreign molecules. The control strategy relies on encoding the metabolic genes in a single operon repressed by a product-responsive TF. The TF can sense a drop in product concentration and upregulate enzyme expression to bring the pathway close to its homeostatic levels.Since the seminal operon paper , the intA typical complication in engineered pathways is that enzymatic saturation may cause intermediates to accumulate in prohibitively large concentrations, thus affecting the viability of the host due to toxic effects . MetabolThe steady-state equations reveal a trade-off between the steady-state enzyme expression levels and the concentration of intermediates: the enzyme concentrations are inversely proportional to the concentration of the intermediate they catalyse. We found that a critical parameter is the RBS ratio, i.e. the relative strength of an RBS with respect to the strength of the first one in the operon, which can be used to fine-tune the circuit between high-enzyme/low-intermediate or low-enzyme/high-intermediate designs.The two considered design knobs, promoter characteristic and RBS strengths, seem to have decoupled roles in the steady state and transient behaviour of the network. The promoter characteristic together with the first RBS determine the steady state of the product and the first enzyme. A strong promoter and a strong RBS for the first enzyme can be used to increase the pathway flux, but this may come at the expense of slow modes in the transient response. In the absence of an engineered pathway consuming an intermediate, the remaining RBS strengths can be used to independently adjust the concentrations of the intermediates and the remaining enzymes. In the case of consumption of an intermediate, however, this design rule applies only to the metabolites upstream of the consumed intermediate, i.e. the steady state of the downstream metabolites depends on a combination of the RBS strength, promoter characteristic and the size of the perturbation.n modes of an n-step pathway, we found that only two depend on the promoter characteristic, whereas further (n − 1) modes depend exclusively on the RBS ratio. The remaining (n − 1) modes correspond to the enzyme half-lives and are independent of the promoter characteristic and RBS strengths. Since enzyme half-lives are considerably slower than metabolic time constants (even with the use of protein degradation tags), the system dynamics can be dominated by slow transients.The closed-form expressions for the transient modes of the feedback system show further evidence of the separation principle between promoter and RBS design. From the 2E. coli, the synthetic operon control circuit can dramatically compensate the loss in flux by sensing the drop in product concentration and subsequently upregulating the enzyme concentrations. The feedback-controlled pathway outperforms the uncontrolled one even when weak promoters are used, thus underscoring the tremendous advantage of taking a feedback approach to metabolic control.We ran numerical simulations that demonstrate the potential of the proposed control strategy. Using physiologically realistic parameter values for et al. [In this work we focused on a control circuit with an operon architecture, a choice inspired by the fact that operons are one of the building blocks in genome-wide bacterial networks . The ubiet al. .We should point out that the derived design constraints guarantee the existence and stability of the metabolic steady state, and thus they are only baselines for the correct functioning of the genetic control circuit. In most applications, the design must also account for more demanding objectives such as maximization of flux, minimization of energy expenditure, or a combination of these. Since these objectives may conflict with each other, selecting an appropriate combination of circuit parameters requires the use of multi-objective optimization methods within the feasibility sets derived here (see, for example, figures n-step pathway with reversible reactions, the steady-state equations form a system of 2n coupled algebraic equations. These equations may admit an analytic solution for specific enzyme kinetics (see Heinrich & Klipp [As a consequence of a compromise between model complexity and the generality of the analytic results, our results have two main limitations. Firstly, we have restricted the analysis to pathways with irreversible reactions, and, secondly, our results are limited to unbranched pathways operating in isolation of the remaining metabolism of the host cell. Enzymatic reactions are inherently reversible processes and, although many biosynthetic reactions operate in a regime where the forward reaction is much more likely to occur than its backward counterpart , their r & Klipp  for the A possible workaround to deal with reversible kinetics is to exploit the natural timescale separation between enzyme expression and metabolic reactions. In this approach, the metabolite trajectories are assumed to evolve in a much faster time scale than the enzyme concentrations. This allows us to approximate the metabolite concentrations as algebraic functions of the enzymes, leading to an enzyme-only ODE model subject to the algebraic relations between metabolites and enzymes. We have previously used such an approach in the case of ON–OFF promoters  (i.e. prWe are exploring a number of extensions to this work, aiming primarily at the use of alternative feedback topologies and at quantifying the impact of biochemical noise on the pathway performance. The implementation of genetic–metabolic circuits, let alone parameter fine-tuning, can be costly and time-consuming. Our work provides a first step towards understanding the fundamental limitations and trade-offs that must be addressed at the design stage, potentially facilitating the implementation using a model-guided rationale.


One of the most common goals in this field is the generation of a high rate chemical producing strain. A major hurdle with this approach is that many chemicals do not have easy to recognize attributes, making their screening expensive and time consuming. To address this problem, it was previously suggested to use microbial biosensors to facilitate the detection and quantification of chemicals of interest. Here, we present novel computational methods to: (i) rationally design microbial biosensors for chemicals of interest based on substrate auxotrophy that would enable their high-throughput screening; (ii) predict engineering strategies for coupling the synthesis of a chemical of interest with the production of a proxy metabolite for which high-throughput screening is possible via a designed bio-sensor. The biosensor design method is validated based on known genetic modifications in an array of E. coli strains auxotrophic to various amino-acids. Predicted chemical production rates achievable via the biosensor-based approach are shown to potentially improve upon those predicted by current rational strain design approaches. (A Matlab implementation of the biosensor design method is available via  A rational design approach - focused on the engineering of cellular phenotypes using rational modifications  based on existing stoichiometric, kinetic, and regulatory knowledge of a system A combinatorial approach - generating genetic diversity in a population followed by screening and selection for improved phenotypes inverse metabolic engineering (IME), which aims to discover the genetic factors that confer the phenotype and transfer them to another strain by directly applying these genetic modifications In recent years, metabolic engineering has emerged as a discipline that utilizes modern genetic tools for the construction of organisms capable of fuel and chemical production. Metabolically engineered microbial strains are now being used in the industry for the production of various chemicals Computational modelling in metabolic engineering has traditionally been used to rationally design the effect of genetic modifications on metabolism. However, such modeling approaches commonly involve either kinetic analysis E. coliThe combinatorial approach for metabolic engineering via random mutagenesis followed by screening for specific phenotypes of interest, has long been the gold standards for strain improvement in industry. A variety of recombinant DNA techniques are available for generating random genetic changes, thus introducing the possibility of uncovering regulatory, kinetic, or unknown/poorly understood targets not encompassed in current models  design microbial biosensors for chemicals of interest based on substrate auxotrophy  that canC, and a definition of a growth medium denoted by M, the biosensor design method aims to search for genetic modifications such that: (i) The bio-sensor strain would grow in a medium that consists of at least nutrients that are in M and C, and (ii) would not grow in a medium where C is absent, even if it consists of all metabolites (other than C) that can be transported into the biosensor strain. Notably, the common definition of substrate-auxotrophy is less restrictive than the above, and in many cases, strains considered auxotrophic for a chemical C, may actually also grow in the absence of C, utilizing a different substrate as input to synthesize C. We hence refer to a microbial strain that realizes the above growth constraints as being ultra-auxotrophic for chemical C. A microbial strain that is ultra-auxotrophic for C (considering some medium M), can be used as a biosensor within combinatorial metabolic engineering experiment, to detect and quantify the concentration of C , with the total biomass of the grown biosensor strain reflecting the concentration of C (as further explained below). The requirement for ultra-auxotrophy guarantees that the biosensor strain would not grow in case C is absent from the spent media, regardless of which additional chemicals were potentially secreted by the producer strains.Given a metabolic network model for some microbial species, a chemical to be sensed denoted by The search for a set of gene knockouts that would give rise to ultra-auxotrophy is performed via a bi-level optimization problem, considering stoichiometric mass-balance, reaction directionality, and knockout constraints . The latter medium, in which a large number of nutrients are expected to be manually added to the spent media is more complex from an experimental perspective, though as shown below, it increases the number of designed biosensors and enables to better quantify the concentration of sensed chemicals. We restricted the analysis to allowing up to a total of three knockouts. When considering a minimal medium, we predict biosensor designs for 43 chemicals, and when considering a rich medium, we predict additional biosensor designs for 10 chemicals  shows a good match between the two (E. coli should be able to utilize indole as a substrate to produce tryptophan (Comparing the predicted amino-acids biosensors with a list of known amino-acid auxotrophic strains (extracted from the Coli Genetic Stock Center (CGSC);  the two . Specifi the two . Our anayptophan . NotablyE. coli). Hence, in this case, the concentration of the sensed chemical can be accurately determined based on the total biomass of the grown biosensor strain. When only glucose minimal medium is assumed to be added to the spent media, the biosensor's biomass yield may change depending on the secretion of additional chemicals by the producer strain. For example, the xylose biosensor achieves a significantly higher biomass yield when additional metabolites (other than xylose) not included in glucose minimal media are present in the media . FBA is applied to predict the maximal theoretical production yield of a chemical of interest, while enforcing a minimal growth rate of 0.1 mmol/gr(DW)h to maintain viability . The results show that combinatorial metabolic engineering experiments aiming to over-produce chemicals using the predicted biosensors would enable to produce 25 metabolites with a rate greater than zero . RobustKnock is a robust variant of OptKnock that searches for knockout combinations that maximizes the minimal  secretion rate of the chemical, considering the presence of the alternative pathways in a metabolic network that may prevent the organism from reaching the maximal theoretical chemical production rate predicted by OptKnock  by coupling their production with biomass formation. Furthermore, the maximal possible production yields predicted by OptKnock and RobustKnock for these chemicals are significantly lower than the optimal yields that may theoretically be achieved by the biosensor-based approach , testifyE. coli under glucose minimal medium. To over-produce the remaining 25 metabolites, we suggest a novel approach, this time focused on engineering the producer strain  via gene knockouts to couple the production of a metabolite of interest with the production of a proxy metabolite for which a biosensor design has already been found . The latter approach is predicted to improve the potential production and secretion rates of several metabolites.In this paper, we describe a computational method for designing microbial biosensors that can be used to perform high-throughput measurements of the concentration of various small molecules. Applying our method to design biosensors based on A major limitation of current constraint-based rational design approaches in metabolic engineering is that they all aim to couple the production of a chemical of interest with biomass formation, such that evolutionary pressure towards growth rate maximization would lead to increased chemical production rates E. coli , which is a common target of metabolic engineering experiments and has a highly accurate metabolic network model. Considering the growing interest computational approaches in metabolic engineering and the current rapid reconstruction of metabolic networks  is a mathematical modeling approach for metabolic networks that utilizes knowledge of the network structure together with constraints on its possible behaviors, to predict possible functional metabolic states. Mass-balance constraints imposed by stoichiometry in a chemical network at steady state enforce the sum of all production and consumption rates of each metabolite to be zero:S denotes a stoichiometric matrix in which ijS corresponds to the stoichiometric coefficient of metabolite i in reaction j. S dimensions are n is the number of metabolites in the network and m is the number of reactions. m-dimensional vector of flux rates, where j at steady state. Additional constraints, including those pertaining to the availability of nutrients in the growth media or to the maximal flux that can be supported by specific enzymes can be introduced via the following inequality:Φ that represents the phenotypic potential of an organism. For an underdetermined system, as is typically the case in models of cellular metabolism Φ is a convex set in the m-dimensional space of fluxes Flux Balance Analysis (FBA) is a particular CBM method that assumes that the network is regulated to maximize a certain cellular function Taken together, the constraints limit the allowable functional states of a metabolic network. In mathematical terms, the range of allowable network states is described by a solution space C is present in the spent media and no growth when it is absent. The problem is formulated as following:The biosensor design method is based on a bi-level optimization problem that searches for gene knockouts such that a feasible flux distribution that satisfies stoichiometric mass-balance, reaction directionality, and knockout constraints, will enable high growth rate when chemical i'th reaction is represented by k . The uptake of the sensed chemical is enabled only for flux distribution Stoichiometric mass-balance, enzyme directionality and knockout constraints are enforced for the flux distribution Figure S1The predicted growth rate of the D-xylose (a) and D-galactose (b) biosensors, as a function of sensed chemical update rate, under both poor and rich media. As shown, the growth yield (represented by the slope of the curve) of the D-xylose biosensor significantly differ between poor and rich spent media. Hence if the D-xylose biosensor is grown after a minimal medium is supplemented to the spent medium, the potential secretion of additional metabolites by the producer strain may affect its biomass yield, leading to inaccurate estimation of the chemical concentration  to the spent. On the other hand, the D-galactose biosensor is predicted to have the same biomass yield in both poor and rich medium, facilitating the direct quantification of chemical concentration also in poor medium.(TIF)Click here for additional data file.Table S1The specific details of the predicted knockout combinations for each bio-sensor.(XLS)Click here for additional data file.Table S2Secretion rates of chemical as predicted by OptKnock and RobustKnock.(XLS)Click here for additional data file.Table S3Secretion rates of chemical (using different proxies) as predicted by OptKnock-proxy and RobustKnock-proxy.(XLS)Click here for additional data file.