To understand complex biological systems such as cells, tissues, or even the human body, it is not sufficient to identify and characterize the individual molecules in the system. It also is necessary to obtain a thorough understanding of the interaction between molecules and pathways. This is even truer for understanding complex diseases such as cancer, Alzheimer’s disease, or alcoholism. With recent technological advances enabling researchers to monitor complex cellular processes on the molecular level, the focus is shifting toward interpreting the data generated by these so-called “–omics” technologies. Mathematical models allow researchers to investigate how complex regulatory processes are connected and how disruptions of these processes may contribute to the development of disease. In addition, computational models help investigators to systematically analyze systems perturbations, develop hypotheses to guide the design of new experimental tests, and ultimately assess the suitability of specific molecules as novel therapeutic targets. Numerous mathematical methods have been developed to address different categories of biological processes, such as metabolic processes or signaling and regulatory pathways. Today, modeling approaches are essential for biologists, enabling them to analyze complex physiological processes, as well as for the pharmaceutical industry, as a means for supporting drug discovery and development programs. Over the last decade, DNA-sequencing technologies have advanced tremendously, culminating in the deciphering of the complete human genome in 2001 . This acIn the meantime, further technological advances have led to a considerable increase in the understanding of the workings of the human body under normal conditions and in various disease states. For example, transcriptomicThis article summarizes the challenges associated with the study of complex biological systems, the benefits of systems biology approaches, and the ways in which computational models can help consolidate and interpret the experimental data obtained using these approaches. These principles are exemplified by some concrete examples from current research projects.14 individual cells, each of which is itself a complex system comprising thousands of different proteins and other biomolecules. The information specifying the composition and structure of virtually all of these molecules is encoded in the DNA. Although researchers now have information on all genes at hand, they still lack a deeper understanding of many seemingly common biological effects. The reason for this can be exemplified by an analogy with a modern passenger jet, another complex, yet man-made, system. Modern passenger jets consist of thousands of individual components, such as screws, wheels, cables, and other components that perform a specific function in a specific technical context. However, knowledge of those individual components does not reveal functions that arise through interactions with other components, such as those related to takeoff, navigation, communication, or landing. To understand how a plane flies, one must know the interplay of the various components of the plane’s controls and the dynamic regulatory feedback loops that control this interplay. Similarly, the processes that occur in living organisms during growth, metabolism, and regulation of cell functions also are interrelated and require equally tight and coordinated control mechanisms.The human body consists of approximately 10The characteristics of a complex system that arise from the interaction of various components are referred to as the emergent properties of the system. Because they are the result of interactions between the different parts, these emergent properties cannot be attributed to any single part of the system. Thus, the ability of a passenger jet to fly is not the consequence of one particular screw (even though this particular screw may be necessary for the plane to function). Similarly, the development of a complex disease  likely is not caused by a single gene, although a particular gene may be one of the elements necessary for the disease to develop. Such a system is considered irreducible—that is, the system is unlikely to be fully understood by taking it apart and studying each part on its own. To understand irreducible systems and fully appreciate their emergent properties, one must study the systems as a whole.The publication of the human genome sequence provided biological scientists with a list of all the individual parts that make up the human body. However, just like having a pile of all the pieces of a passenger jet does not allow a technician to put together a functional plane without having a blueprint of the wiring scheme, this genome sequence is not sufficient to understand the interactions between the genes and their products. Advances over the last few years in transcriptomics, proteomics, and metabolomics that allow investigators to monitor the biological response of cells, however, will allow studies of physiological systems as a whole in order to identify higher-level biological mechanisms encoded in the human genome  see fig.A major reason for the advent of systems biology activities is that only recently analyses at the molecular level of the cell have become technically feasible on a larger scale. With the development of these new, large-scale technologies to identify and quantify molecules on the DNA, mRNA, protein, and metabolite level, researchers for first time are in a position to gather comprehensive data on the molecular state of a given biological system in a systematical manner. These technologies are sometimes collectively referred to as “–omics” technologies see . In addiThe new –omics technologies are characterized by three distinct features. First, they allow for analyses on different molecular levels, such as the DNA, RNA, protein, or metabolite level. These different molecular levels sometimes behave asynchronously—that is, although some proteins are highly abundant in a cell, the levels of the corresponding mRNAs from which they are produced may be very low or vice versa. Because asynchronous behavior can indicate the effects of complex regulatory interactions, it is important to examine the role and degree of synchronization of the transcriptome, proteome, and metabolome. For example, metabolites produced in certain biochemical pathways sometimes exert a feedback on key enzymes in the pathway by modifying the expression of the genes that encode these enzymes. The –omics technologies allow researchers to systematically discover such interactions and incorporate them into models aiming to capture the essential regulatory features of a pathway.Second, –omics technologies are highly parallelized. This means that for a single biological sample many different biological “readouts” can be measured simultaneously. For example, with today’s microarrays researchers can simultaneously measure the expression of virtually all genes of the organism being studied rather than having to perform numerous separate experiments focusing on different genes. This parallelization enables scientists to detect not only the expected but also unforeseen responses of an organism. For example, microarrays in toxicology research allow for a broad screen for unexpected biological side effects caused by new drugs . The higThird, –omics technologies are highly standardizable and thus amenable to a high degree of automation, allowing researchers to handle and process large numbers of biological samples. The ease of sample processing and experimentation has a huge impact on how experimental studies are performed today. For instance, comparison of larger numbers of replicate experiments allows researchers to validate biological effects with a greater statistical certainty. The ease of use of –omics technologies is particularly relevant for clinical studies, in which large patient populations must be tested to obtain a sound statistical basis for confirming drug efficacy and identifying potential side effects.The huge amounts of data gathered require tools to automatically process, compare, and interpret the data in a manner that identifies the most relevant pieces of information and which can be used to generate models of, for example, regulatory or metabolic pathways. These tools include computerized data analysis strategies that result in the formulation of mathematical models of the biological systems analyzed.Biological systems are inherently complex, and many of their emergent properties result from the interplay of numerous molecular components. Moreover, biochemical reactions often obey nonlinear reaction kinetics—that is, an increase in the amount of the starting material of the reaction does not necessarily lead to a proportional increase in the amount of the reaction product. Finally, other complexities, such as cell structure and compartmentalization or random  effects, also often result in unexpected behavior of the entire system. Mathematical models that take these factors into consideration allow researchers to capture the features of complex biological systems and to understand how biological systems respond to external or internal signals and perturbations, such as different growth or development conditions or stress triggered by agents such as alcohol.Mathematical models have the big advantage of being amenable to computer simulations. Models describing biological systems generally are too complex to be solved analytically  and therefore typically are solved numerically—that is, using computers to solve the mathematical equations that help predict the response of a biological system. With the availability of computer-based techniques for solving mathematical equations, the response of a biological system to different conditions can be relatively easily simulated in silico once a mathematical model is available. These computer simulations  in many cases require much lower investment and much less time compared with the typically more time-consuming and expensive biological experiments (sometimes referred to as “wet experiments”).The general approach for creating and using mathematical models in biological sciences is similar to the one followed in other scientific disciplines such as physics and provides the basis for communication between experimental and theoretical scientists. Thus, the theories and mathematical formulas developed by theoretical biologists on the basis of existing experimental data can be tested by experimentalists and used to predict the behavior of biological systems under as-yet-unexplored conditions. Any discrepancies between the predicted and measured results then need to be resolved, either by extending the theoretical framework  or by refining the experimental setup or data interpretation.Mathematical models for biological systems and the associated computer simulations offer numerous benefits. First, discrepancies between systems behaviors predicted by a mathematical model and actual behaviors measured in experiments can point to components that still are missing from the mathematical model, thereby assisting in developing a more comprehensive picture of a biological process. And even if it is not clear which components are missing from the system under investigation, the results obtained with the mathematical model may help to guide the design of additional experiments to clarify the issue see .Second, mathematical models provide a systematic approach for investigating systems perturbations—for example, those induced by drug administration, genetic alterations, developmental signals, or other factors. To this end, scientists can modify the values of the model parameters  and re-run the computer simulations. This approach is relatively straightforward once a reasonable base model is available.Third, mathematical simulations are not as limited by experimental constraints as wet experiments. Computer simulations can quickly investigate different experimental conditions for the biological system of interest, and only the most relevant cases can be assessed afterwards in the laboratory. This allows researchers to investigate novel scenarios and to develop hypotheses to guide the design of new and promising experiments. This approach is particularly helpful if the wet experiments are difficult and expensive to perform. The combination of dry and wet approaches is at the heart of systems biology and already is being used widely in the metabolic engineering industry, which uses live cells  to produce complex chemicals  based on fermentation processes. In these cases, mathematical models are used to suggest directed genetic modifications that may improve the productivity of the microorganisms.Fourth, mathematical models can be very helpful for systematically determining the relevance of a specific molecule or pathway for the overall behavior of the system. Not all components of a reaction or pathway are equally important, and many biological processes are controlled by relatively small subsystems. Comparison of computer simulations and actual experimental data may help the researcher to readily identify such simpler subsystems that are sufficient to understand the features of the much more difficult-to-treat full biological system.For choosing the optimal modeling approach it is essential to understand the nature of the biological process of interest because different mathematical frameworks have been developed for modeling the behavior of different types of biological systems. For example, most cellular phenomena are governed by dynamic processes so that the cell can adapt to environmental changes or control inherently dynamic cellular functions, such as periodic cell division. For describing such time-dependent phenomena, it is imperative to choose mathematical equations that can capture these dynamic effects. For other biological processes, however, it often is not necessary to describe all the details of the underlying dynamics because some molecules’ concentrations do not change over time . For most types of applications, appropriate modeling methods have been developed. Two examples are described below—modeling of metabolic processes and modeling of signaling and regulatory pathways.Metabolic processes are essential for all living organisms and provide the cell’s energy, deliver building blocks for the synthesis of larger molecules, or degrade toxic substances. Although biological research has focused on metabolism for several decades, many metabolic processes still are not fully understood, and, in particular, the regulatory mechanisms controlling even well-investigated metabolic pathways often are unknown.A key parameter in any metabolic study is the metabolic flux—that is, the conversion rate of metabolites along a metabolic pathway. For many research and industrial applications, it is crucial to predict the metabolic flux patterns that indicate which biochemical routes are utilized . Modeling techniques are widely used in the field of metabolic engineering to identify any steps in the production of a desired molecule by cultured cells or bacteria that limit the overall rate with which the process occurs . The results of these analyses can guide researchers on how to genetically modify the cells or bacteria to optimize the yield of the desired end product  to the sugar glucose, yielding a compound called glucose-6-phosphate. This reaction must be balanced in terms of atoms and electrical charges. In a chemical notation, the balanced reaction is written as C13C-method)   that wilSignaling pathways serve as the cell’s central control machinery, which tightly regulates the cell’s response to external and internal stimuli. These pathways involve the transmission of external and internal signals through the cell’s membrane and interior into the cell’s nucleus, where they activate or deactivate specific sets of genes. All of these processes are inherently dynamic events that require different mathematical modeling strategies than the quasi-stationary (metabolic) processes discussed above.Many signaling pathways are triggered by the binding of extracellular biomolecules  to a docking molecule  embedded in the membrane surrounding the cell. Receptors are proteins, often spanning the membrane, which expose one part of their structure to the exterior environment  and one part to the cell’s interior . If a signaling molecule binds to the extracellular region of the receptor, the receptor’s three-dimensional structure may change—a process that can trigger cascades of biochemical reactions within the cytoplasm. These cascades often involve specialized signaling molecules such as enzymes known as kinases, which transfer phosphate groups from one molecule (the donor) to a specific target molecule (the substrate) and which are used extensively to transmit and integrate signals to control complex cellular processes. In many cases, kinases act on and modify the activity of specific proteins. The addition of the phosphate group changes the substrate protein’s biochemical behavior so that it, in turn, can modify additional signaling molecules in the signaling cascade. Ultimately, this chain reaction results in the activation of proteins called transcription factors that bind in the cell nucleus to DNA, triggering expression of distinct sets of target genes. It is this gene activation that alters the cell’s behavior and represents the cell’s response to the initial stimulus.56.Obviously, signal transduction is an inherently dynamic phenomenon, as the cell has to be able to flexibly respond to changes within the organism and in the environment. To model the dynamics of signaling cascades such as those described above, researchers primarily rely on so-called differential equations . Such differential equations are used to model the dynamic behavior of, for example, the changes in the concentration of signaling molecules over time as well as the signaling molecules’ distribution across different cellular compartments. Modeling of even relatively simple signaling networks has revealed that signal transmission through the cell often shows unexpected behaviors, such as periodic activation patterns or enhancement  of the initial signals . A speciAny equation in a mathematical model will contain one or more parameters that describe certain biophysical characteristics of the molecules involved in the reaction or pathway being studied. For example, when modeling the dynamics of a network of biochemical reactions, the mathematical equations must incorporate parameters that reflect the kinetic properties of the involved enzymes—for example, the number of reactions the enzyme can perform during a given period of time . Researchers must know these kinetic parameters before they can set up well-defined systems of differential equations representing appropriate models of biological processes.In principle, the kinetic parameters for all the relevant enzymes can directly be experimentally determined. In practice, however, many kinetic parameters, even for otherwise well-investigated enzymes, still are unknown, primarily because the relevant experimental data are lacking . But even if the kinetic parameters have been measured, these data often are based on experiments performed in a test tube with purified enzymes , and it is unlikely that the enzymes behave similarly under the conditions found in a living cell . To overcome this limitation, one can use dynamic measurements of the overall system. Computational procedures are available to estimate the appropriate model parameters by testing different parameter sets until they fit the available experimental data. However, this process is critically dependent on the quality of the experimental data, and unreliable experimental data will lead to unreliable predictions of kinetic parameters and therefore to models of very limited value . The lacIt must be pointed out that some biological phenomena cannot be described by using models that are just based on continuous concentration fields , ignoring the existence and relevance of individual molecules. For instance, on a molecular scale random molecular movements can have a major impact on cellular processes. The molecules in a cell are closely packed, and thermally induced random movements of these molecules as well as interactions between them can strongly affect the transmission of signals. To account for such effects, a random  component must be integrated into the mathematical equations of the model. Particularly for rare signaling molecules, of which only a few copies may be present in the cell, the effects of such a stochastic component are significant and must not be neglected.Another issue that complicates modeling of biological systems is that the different components of a pathway often act over different time and distance scales. For example, metabolic reactions can happen within seconds or minutes, whereas genetic regulatory processes that are induced by these metabolic reactions may occur over several hours or even days. Similarly, some regulatory reactions occur over small distances , whereas others involve greater distances . To couple relevant effects occurring on very different length and time scales, researchers use so-called multiscale models as a compromise to avoid making the model overly complex.One important signaling factor is nuclear factor kappa B (NFκB), which regulates numerous processes relevant for inflammatory reactions, immune responses, cell proliferation, and survival of the cell. NFκB is a transcription factor—that is, it activates specific genes required for these processes by binding to the DNA in front  of these so-called target genes.Because of its important functions in the cell, the levels and actions of NFκB must be tightly regulated. NFκB normally is found in the fluid filling the cell  and must move to the nucleus to exert its effects on its target genes. To prevent inappropriate movement of NFκB to the nucleus, the molecule normally is linked to a phosphate group  and interacts with proteins called inhibitory molecules of NFκB (IκBs). When the NFκB pathway is activated by another signaling molecule, IκBs are degraded, allowing NFκB to move to the nucleus and activate its target genes. One of these target genes codes for one of the inhibitory molecules, IκBα. Thus, NFκB activation leads to production of new IκBα, which can then bind to NFκB and shut off the NFκB pathway. This is known as a negative feedback loop. Continuous cycles of IκBα degradation and synthesis give rise to regular changes  in NFκB activity that can be observed experimentally. Mathematical models have been used to investigate these oscillations in more detail, and comparisons between “dry” and “wet” experimental results generally have shown good agreement. The mathematical equations for modeling NFκB activation also have been used to identify potential contributions of other molecules that are thought to modulate the NFκB/IκB-mediated regulatory process. For example, modeling approaches using experimental data derived from mice in which specific IκB genes had been inactivated  demonstrated that certain IκBs had a damping effect on cyclic NFκB/IκBα oscillations  .Finally, it is important to recognize that any model can be only as good as the assumptions upon which it is based. By definition, any model is an abstraction and simplification of reality. All currently available, tractable mathematical models of biological systems neglect the majority of the molecular players in an organism. Moreover, all models make assumptions about relevant time and length scales. For example, the discussion in this article focuses on modeling approaches for cellular pathways that neglect molecular details . It is essential to keep these limitations in mind when discussing the value and validity of mathematical models or when developing a specific model to capture the characteristics of a given biological process.Systems biology approaches have great potential for enhancing the drug discovery and development process. Currently, the productivity of the pharmaceutical industry is lagging behind its investments in research and development. The output of new chemical entities , which is considered an indicator of the innovation potential of pharmaceutical research, is only slowly growing . The whoSystems biology is expected to play an increasingly important role in the establishment of innovative drug discovery strategies. Today, the industrialized drug discovery process relies, to a large degree, on highly automated processes for screening the biological activity of large chemical libraries in order to identify new drug candidates. These screening assays enable a systematic assessment of candidate compounds by testing their activity on therapeutic targets—that is, biomolecules that are causally involved in disease outbreak or disease progression .Systematic compound screening provides the starting point for further chemical development to optimize the drug-like features of the lead compound. Computational models of disease-relevant pathways that allow for dry experiments to support the assessment of a candidate molecule’s safety and efficacy most likely will play an increasingly important role in this process, and the pharmaceutical industry is greatly interested in establishing new predictive, computer-supported methods to systematically identify the most promising drug candidates. In this context, a number of pharmaceutical companies recently have initiated dedicated systems biology programs to support their in-house drug discovery and development programs .58). One of the pioneering systems biology programs is the publicly funded German HepatoSys initiative, in which more than 40 German research centers cooperate in a joint program investigating the systems biology of the liver cell using numerous complementary approaches. The liver is an organ of great medical interest with relevance to many disease areas, including alcohol-related diseases. The different groups participating in HepatoSys apply a broad spectrum of technologies, ranging from classical cell biological methods to imaging, transcriptomics, proteomics, and metabolomics; in addition, several groups conduct dry experiments by applying pathway modeling to liver cell pathways. Within the overall consortium, different technology platforms are organized into subgroups, or networks, which focus on specific medically relevant themes, such as liver regeneration or detoxification processes. In a first step, the researchers seek to reconstruct liver-specific pathways using wet and dry methods. Later, liver metabolism and liver-specific signaling and their roles in liver regeneration and drug metabolism will be investigated.At the same time, an increasing number of publicly and privately funded initiatives and consortia aim at establishing systems biology in different domains of biological research to elucidate, for example, the functions of specific cell types relevant for medical applications or to develop comprehensive systems biology applications for metabolic engineering. In most cases, multiple research centers or companies are integrated in a decentralized research network to which investigators from numerous disciplines  contribute see , p. 58. For HepatoSys and other systems biology consortia and research centers, it is essential that the different research groups are connected via a central, dedicated data transfer and exchange infrastructure to facilitate the close collaboration among groups and disciplines. Such an infrastructure must include a specialized data management system that allows the participating groups to deposit their wet and dry data in a central location, which is accessible to the experimentalists as well as to the modelers. Although the focus of publicly funded systems biology consortia primarily is on basic research, the results produced will likely also be critical for applications in the healthcare and biotechnology sectors.In summary, the various systems biology approaches developed in recent years provide an extraordinary amount of new information on many functions of human and other organisms relevant to research and biotechnology applications. Only with the help of computerized modeling efforts, however, can researchers make sense of all the different bits and pieces of information that are accumulating at an ever-increasing pace. Just as an engineer can turn a heap of metal pieces, wires, screws, and bolts into a jet plane only if he has a comprehensive blueprint, biomedical scientists can understand the workings of living organisms only if they have comprehensive models that enable them to connect the often disparate pieces of information derived from experimental approaches. The Greek philosopher Aristotle said more than 2,000 years ago, “The whole is more than the sum of its parts,” and today, systems biology research and modeling efforts are helping to obtain a more comprehensive understanding of life.


Escherichia coli, Corynebacterium glutamicum, Bacillus licheniformis, and Saccharomyces cerevisiae during well-controlled bioreactor cultivations. Most surprisingly, in all cases a great diversity of central metabolic intermediates and amino acids is found in the culture medium with extracellular concentrations varying in the micromolar range. Different hypotheses for these observations are formulated and experimentally tested. As a result, the intermediates in the culture medium during batch growth must originate from passive or active transportation due to a new phenomenon termed “extended” overflow metabolism. Moreover, we provide broad evidence that this could be a common feature of all microorganism species when cultivated under conditions of carbon excess and non-inhibited carbon uptake. In turn, this finding has consequences for metabolite balancing and, particularly, for intracellular metabolite quantification and 13C-metabolic flux analysis.Overflow metabolism is well known for yeast, bacteria and mammalian cells. It typically occurs under glucose excess conditions and is characterized by excretions of by-products such as ethanol, acetate or lactate. This phenomenon, also denoted the short-term Crabtree effect, has been extensively studied over the past few decades, however, its basic regulatory mechanism and functional role in metabolism is still unknown. Here we present a comprehensive quantitative and time-dependent analysis of the exometabolome of  Saccharomyces cerevisiae.13C-MFA) is the standard method for quantifying intracellular fluxes + mode at an electron energy of 70 eV. The source temperature was set to 180°C. The MS was tuned and calibrated with the mass fragmentation pattern of Heptacosa (heptacosafluoro-tributylamine). During analysis, the accurate masses were corrected to a single point lock mass of CPFB (chloropentafluorobenzene) as an external reference at 201.9609 m/z. Data acquisition was done in centroid mode at a scan rate of 0.09 s and an interscan delay of 0.01, i.e. 10 scans s-1. For the identification of known metabolites a baseline noise subtracted fragment pattern was used and compared to the in-house database JuPoD, the commercial database NIST and the freely available database GMD. Unknown peaks were identified by a structural combination of elemental compositions and verified by virtual derivatization and fragmentation of the predicted structure.Prior to analysis, 13 μl aliquots of the samples were lyophilized overnight in a Christ LT-105 freeze drier and then stored at −20°C. The dried samples were consecutively derivatized with 50 μl MeOX (20 mg mlThe authors declare that they have no competing interests.NP, AN and TL conducted the experiments and analyzed the data; JG performed GC-TOF-MS analysis; SN wrote the paper with substantial input from NP and WW. All authors read and approved the final manuscript.Supplementary Information. Click here for file


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