During the transition from a healthy state to a cancerous one, cells alter their metabolism to increase proliferation. The underlying metabolic alterations may be caused by a variety of different regulatory events on the transcriptional or post-transcriptional level whose identification contributes to the rational design of therapeutic targets. We present a mechanistic strategy capable of inferring enzymatic regulation from intracellular metabolome measurements that is independent of the actual mechanism of regulation. Here, enzyme activities are expressed by the space of all feasible kinetic constants (k-cone) such that the alteration between two phenotypes is given by their corresponding kinetic spaces. Deriving an expression for the transformation of the healthy to the cancer k-cone we identified putative regulated enzymes between the HeLa and HaCaT cell lines. We show that only a few enzymatic activities change between those two cell lines and that this regulation does not depend on gene transcription but is instead post-transcriptional. Here, we identify phosphofructokinase as the major driver of proliferation in HeLa cells and suggest an optional regulatory program, associated with oxidative stress, that affects the activity of the pentose phosphate pathway. During the development of cancer, cells undergo major metabolic changes to increase their capacity for proliferation. In many cases, that transition is characterized by an increased usage of fermentation, which is independent of the presence of oxygen and caused by a higher flux through glycolysis and diminished activity of the TCA cycle3468910Therefore, it comes as no surprise that there has been an ongoing effort to combine data from the genome with the metabolome, the concentrations of all of the cells’ metabolites1212While there exists a wide selection of methods to analyze genomic data and infer regulation events in cancer up to the enzyme level, metabolome data are often analyzed solely on the abundance level with only limited ability to extend this information to the entire biological system or even connect metabolome data to the inferences made from genome data. However, there exist some notable exceptions where methods from Systems Biology have been applied successfully16181920212425In this manuscript, we present the first metabolome profiles for the cancerous HeLa and non-cancerous HaCaT cell lines. We use the k-cone formalism to obtain a differential analysis of enzyme activities between the two cell lines, as that formulation can use metabolome data to provide a mathematical transformation between the normal and disease state. Our analysis identifies alterations in the enzyme activities of HeLa cells, many of which are consistent with previously identified changes. Furthermore, we also show that there exists a set of optional enzyme regulations that may help HeLa cells to alleviate oxidative stress without compromising proliferation. Taken together, we propose that differential k-cone analysis, which may integrate genome-scale metabolic reconstructions and metabolome data, is a suitable conceptual scheme to identify and suggest the regulatory mechanisms required to establish the phenotype in cancer cell lines.K-cone analysis is closely related to the steady state, the state of homeostasis for a metabolic system. During the steady state, metabolite concentrations are constant which gives rise to the steady state equationi = kimi(x). This case holds for mass-action kinetics with stoichiometries sjiHere, S denotes the stoichiometric matrix and v the vector of steady state fluxes. The space of all v that fulfill that equation is commonly known as the flux cone. The k-cone is based on the same equation but further assumes a distinct structure of the fluxes, where each flux can be decomposed into a kinetic constant and a metabolic term given by the metabolite concentrations x as vand gives rise to the k-cone equationi(x) on its diagonal24in vivo equilibrium constants .where M denotes a diagonal matrix containing the mass-action terms mants see 24. Becaun or kd, in its respective k-cone, Kn or Kd. In the case where the fluxes are known along with the metabolome one can use the mass-action kinetics, vi = kimi(x), to pinpoint the kinetic constants directly through dividing the fluxes by the corresponding mass-action terms mi(x). Based on this argumentation, one can derive a relation that incorporates flux data and where kd = TWkn , possibly incorporating other genome-scale data, such as gene expression and growth rate measurementsHowever, one particular normal or disease state only occupies one distinct point, kd = TWkn . Here, WMetabolome measurements were obtained for the HaCaT keratinocyte and HeLa cell lines, which are both selected for their ability to proliferate independently and have very similar doubling times28291531The measured metabolite concentrations were mapped to a model of the central carbon metabolism, extending a previously published model to yield one with 100 irreversible reactions assuming mass-action kineticsin vivo equilibrium constants (Keq) obtained from the equilibrator databasehttp://equilibrator.weizmann.ac.il/) which reduced the k-cone to only 40 basis vectors which were then mapped onto two dimensions by PCA  on the fold-changes and their statistics. Thus, we performed all analyses in log-space considering logshown in . This asThere is the possibility that only a subset of the reactions are actually required to maximize proliferation, leaving a large window of variation for fluxes that do not directly influence the growth rate. Due to the identical model, and thus identical flux cone, for both conditions, those differences would not be detectable with standard methods to calculate metabolic fluxes such as sampling from the flux cone or flux balance analysis that would both result in the same fluxes for both conditions in average. Because the accuracy of our approximation of differential enzyme activity is compromised by large changes in the fluxes between the cell lines, we performed flux variability analysis to identify the maximum log-fold change that could be caused by variation in the fluxes. Here, we first added a biomass reaction to the model and maximized its flux. This step was followed by flux variability analysis to obtain upper bounds for the absolute log-fold change for each reaction fluxThe mean log-fold changes for the EDAs in each reaction are shown in  Notably, many of the enzymes with significant EDAs are already known to be altered in cancer. Those enzymes include phosphofructokinase, phosphoglycerate mutase, pyruvate kinase, 6-phosphogluconate dehydrogenase, pyruvate dehydrogenase and aconitase394041424344Fig. 1vice versa; also see Given our predictions of differential enzyme activity based on metabolome data (EDAs), we also investigated how well these data would correlate with differential gene expression in HaCaT and HeLa cells and, thus, whether the observed changes in enzyme activity are due to changes in gene expression. For this purpose, we assembled a data set consisting of 58 microarray samples (20 HaCaT and keratinocytes and 38 HeLa) on a single platform (HGU133Plus 2.0) obtained from the GEO databaseGenomic analysis of human cancers has already shown that metabolic regulation in cancer can be highly heterogeneous and varies greatly among different cancers and even within patients with the same cancerTo identify reactions with specifically increased heterogeneity in cancer, we selected reactions whose variation increased by at least 3-fold in HeLa cells compared to HaCaT cells. For the EDAs, this selection produced a set of 11 reactions involved in the pentose phosphate pathway, glycolysis and respiration as well as increased ATP usage see . Log-folBecause in our results phosphofructokinase up-regulation is the most prominent change necessary for proliferation, we suggest the mechanism illustrated in As we have shown, differential k-cone analysis is capable of suggesting regulated enzymes in the transition to cancer for the central carbon metabolism of HeLa cells. We feel that this method is particularly well-suited to examining the regulation of non-essential enzymes or enzymes that are not visibly affected on the genome level, as it detects regulation on the metabolome level, explicitly including post-transcriptional regulation events. Analysis based on the k-cone, as performed here, combines well with existing methods such as FBA or control theory by integrating data from the metabolome and thus giving a more appropriate description of the phenotypeHowever, it is also important to note the limitations of our results. At least in the analysis we performed here, the method assumed the kinetics to be governed by the mass-action law, which is, at best, an approximation of the most likely more complex underlying kinetics. Another limitation is lacking metabolite measurements for metabolites included in the used model. The analyses, as we performed here, aimed to be conservative, meaning that we treated cases with missing data as non-differential.B. subtilis suggest that large parts of the central carbon metabolism are regulated on a post-transcriptional level rather than on a transcriptional level, which seems to be the case particularly for the pentose phosphate pathway and late glycolysis, which we also find strongly regulated here225354Our results suggest that the activities of many enzymes in the central carbon metabolism of HeLa cells are similar to the activities found in the non-cancerous HaCaT cells. However, there is a small set of enzymes that can alter their activities in the two cell lines, and those changes do not seem to affect the stability of the system. Those regulation events can be further subdivided into a small set of necessary regulations required for proliferation and a slightly larger set of enzymes that can be regulated on a on-demand basis. Here, the up-regulation of phosphofructokinase (PFK) seems to be the major driver for maintaining proliferation, which explains the requirement of the Warburg effect, as a high concentration of lactate, citrate or unused ATP can allosterically inhibit phosphofructokinase4651We also observed that the metabolic differences between cancer and healthy cells are caused by the alteration of only a few enzymes. This result stands in contrast to mRNA measurements, which often suggest that cancer alters the expression of the majority of enzymes in the central carbon metabolism6 cells were harvested at 70% confluence with 2 ml MeOH including the internal standards. Then, 1.6 ml of cell suspension was transferred to microcentrifuge tubes containing 1.6 ml of CHCl3 plus 640 μl of milliQ water, vortexed and then centrifuged at 2300 g and 4 °C for 5 minutes. 1.5 ml of the transferred aqueous layer was filtered through a Millipore 5-kDa cutoff and evaporated to dryness using a centrifugal evaporator. The measurement and quantification of extracted metabolites were performed by a commercial provider using a capillary electrophoresis (CE) connected to an ESI-TOF-MS with an electrophoresis buffer .Measurement of the ionic metabolites was performed using the CE-MS system. The HeLa cell line was provided by the oncology laboratory of the Centro Medico Siglo XXI, which belongs to the Instituto Mexicano del Seguro Social. The HaCaT cell line was donated by the Centro de Investigación Sobre Enfermedades Infecciosas, which belongs to the Instituto Nacional de Salud Pública. Cell lines were cultured in RPMI-advanced as previously described by our group6 cells, assuming an individual cell volume of 1.54 flAbundances were transformed into concentrations by dividing by the total volume of the 10Missing metabolite concentrations required in the model were imputed in multiple steps. First, missing data were imputed from measurements within the same cell line, followed by imputation across the two cell lines. Concentrations for metabolites that could not be detected in either of the two cell lines were obtained from the Human Metabolome database, primarily using cytosolic concentration measurements and falling back to blood measurements if cytosolic measurements were not availablehttps://github.com/cdiener/dycone together with installation instructions (doi: 10.5281/zenodo.49987). A detailed protocol describing the steps taken to generate all figures and results in this paper is given in the https://github.com/cdiener/kcone-paper and can be used to reproduce all analyses in this manuscript.The raw data used for the analysis are provided in The underlying kinetic model was obtained by extending a previously published model that had been validated by experimental data. The model was updated by annotating all reactions with their respective IDs from KEGG and adjusting the hydrogen balances to coincide with the ones reported in KEGG. We added additional reactions summarizing core mechanisms such as the neutralization of peroxide, import of glutamine, as well as the production of ATP and reduction of NADH in the mitochondria. Appropriate exchange reactions were added to molecules that could either be produced or consumed by metabolic processes not included in the model or obtained from the extracellular environment. The complete model specification can be found in et al.https://cran.r-project.org/web/packages/rcdd) on a H-representation with redundancies removed. Basis elements were normalized to unit length. The non-reduced individual k-cones, individual k-cones were calculated as M−1V, where M denotes the diagonal matrix with the mass action terms on its diagonal. The k-cones which where additionally constrained by equilibrium constants were calculated individually by adding the respective equilibrium constraints to the k-cone equation  = log2 (k2/k1) for T = M1M2−1, as derived in the Approximations of changes in enzyme activities were either obtained by the transformation T via calculating its log-diagonal logbm, this procedure gave rise to the following linear programming program for the flux balance analysisi:Necessity for proliferation was performed by first appending a biomass reaction to the model and identifying the maximum permissible flux through that reaction. The biomass reaction was adapted from Recon 2−16 to ensure a non-zero flux for each reaction, as all reactions of the central carbon metabolism should be active in the cell lines used.Here, the upper bound could be chosen arbitrarily, as later calculations used only the flux ratios, which are invariant to the upper bound. Lower bounds for the fluxes were chosen as 10max, the upper and lower flux limits were obtained by solving two linear programming problems for each flux vi:After obtaining the maximum biomass flux vThe largest absolute log-fold change that could be explained by flux variability analysis could now be obtained asmax were deemed necessary for proliferation.Finally, all individual log-fold changes obtained from the EDAs whose absolute value exceeded that of lfcAll log-fold changes, obtained by the transformation T, were handled in the same way. Significance measures were obtained by performing Welch t-tests on the log-transformed mass-action terms after validating their normal distributions . Sample 36Fifty-eight microarray samples were manually selected from the GEO database by selecting for samples from a single platform (HGU133Plus 2.0), in untreated conditions and only for the previously used cell lines . The analysis of gene expression was performed by normalizing the raw data for the 58 samples by Frozen Robust Multiarray Analysis (fRMA), followed by differential analysis using the limma package, particularly its empirical Bayes method36c and the differential standard deviation σd (obtained from the log-fold change samples described before), a reaction was considered differentially heterogeneous if σd/σc > 3, based on the visualization in Standard deviations for log-fold changes of enzyme activities were obtained from the 9 possible Hela/HaCaT sample combinations of log-fold changes as used in the approximation of credible intervals. To obtain an estimate for the standard deviation in untreated conditions we used the control samples obtained from the paired permutations of HaCaT samples, as previously described. Given the control standard deviation σHow to cite this article: Diener, C. et al. The space of enzyme regulation in HeLa cells can be inferred from its intracellular metabolome. Sci. Rep.6, 28415; doi: 10.1038/srep28415 (2016).


Metabolic reactions have been extensively studied and compiled over the last century. These have provided a theoretical base to implement models, simulations of which are used to identify drug targets and optimize metabolic throughput at a systemic level. While tools for the perturbation of metabolic networks are available, their applications are limited and restricted as they require varied dependencies and often a commercial platform for full functionality. We have developed MetaNET, an open source user-friendly platform-independent and web-accessible resource consisting of several pre-defined workflows for metabolic network analysis.MetaNET is a web-accessible platform that incorporates a range of functions which can be combined to produce different simulations related to metabolic networks. These include (i) optimization of an objective function for wild type strain, gene/catalyst/reaction knock-out/knock-down analysis using flux balance analysis. (ii) flux variability analysis (iii) chemical species participation (iv) cycles and extreme paths identification and (v) choke point reaction analysis to facilitate identification of potential drug targets. The platform is built using custom scripts along with the open-source Galaxy workflow and Systems Biology Research Tool as components. Pre-defined workflows are available for common processes, and an exhaustive list of over 50 functions are provided for user defined workflows.http://metanet.osdd.net, provides a user-friendly rich interface allowing the analysis of genome-scale metabolic networks under various genetic and environmental conditions. The framework permits the storage of previous results, the ability to repeat analysis and share results with other users over the internet as well as run different tools simultaneously using pre-defined workflows, and user-created custom workflows.MetaNET, available at  Systems biology investigates the components of complex biological networks and can pinpoint drug targets through a combination of experimental and computational research . Over thi.e. genes, proteins, reactions and metabolites involved in various activities of the network. The reconstructed network is then converted into a matrix Sm×n where m rows represent metabolites, n columns represent reactions and each element of the matrix represents the stoichiometric coefficient of the metabolite in the corresponding reaction. The dynamic mass balance of the metabolic system isFundamentally, FBA requires four steps: (i) reconstruction of the metabolic network (ii) obtaining the stoichiometry matrix of the metabolic network (iii) defining the objective function and biochemical relevant constraints and (iv) optimization . Reconstn×1 =  is the vector of the unsolved fluxes and ×n×1 is the vector representing metabolite concentration. At steady state, the flux distribution is defined by a system of linear equations aswhere νIn general, for a biological metabolic system the number of reactions is more than the number of metabolites leading to an under-determined solution of steady state. Therefore, additional biologically relevant constraints are imposed on fluxes of reactions in order to find substantive solutions of the system.νi represents internal fluxes and bi signifies the exchange fluxes in the system. Next, a reaction of interest is defined as the objective function which formulate FBA as the following linear programming problem.where E.coli [where c represents a vector with the reaction of interest set to one, while all other reactions are set to zero ,6 . ExamE.coli .13C-based metabolic flux analysis, using the Bio-jETI workflow framework [Over the last decade, FBA and other methods for metabolic network analysis have been implemented through various resources ,9. The mramework . Webcoliramework  providesramework  is a valramework  and MetRramework  in its rMetaNET has been implemented with different functionalities of the SBRT under a GNU/Linux operating system. Although, many processes to analyze biological networks are available in SBRT, it was designed with a basic non-interactive GUI which hinders its widespread use within the research community. More importantly, users of SBRT have to create various input files manually or through programs, which are time-consuming and prone to error while handling large metabolic networks. To overcome these limitations, we extended SBRT with a user friendly platform for metabolic network studies by integrating SBRT functions with the open source platform Galaxy, available over the internet . Galaxy http://wiki.galaxyproject.org/Admin/Get%20Galaxy & installed intentionally as a normal user – “galaxy”, to permit easy migration and for reasons of security. The application runs using HTTP with a user-specified port, and does not need root privileges. This results in the easy migration by porting the entire user space to another system and as root privileges are not required, it also secures the base operating system. SBRT was downloaded from www.ieu.uzh.ch/wagner/software/SBRT and installed with the same user i.e. “galaxy”. Sybil [All the three applications: Galaxy, SBRT and R were installed on a development machine running CentOS 6.5 with the prerequisites– python version 2.6.6 & Java Development kit. Galaxy was downloaded from ”. Sybil  was usedXML files were written for each integrated SBRT and in-house tool which include all the information required to execute the tool. Using these files, Galaxy automatically generates the user interface for user to select input files & parameters required by the tool. On execution, Galaxy calls the respective Perl/Java wrapper and runs the tool. Table For SBRT based methods, wrappers were written in Java to call functions of SBRT. These wrappers use SBRT as an application programming interface (API) by calling its respective functions.For in-house tools, a second set of wrappers were written in Perl that provide missing functionality in SBRT. Additional Perl scripts were also written that take input from Galaxy and generate plots in MetaNET using R.The application was implemented using XML files, Java and Perl wrappers at the following levels, as shown in Figure Custom workflows were designed by combining different tools using workflow editor. The framework can filter the coupling of tools for permitting only those cases where the output from one process can be used as input of the other. Sample workflows, created to perform common metabolic simulation tasks, are listed along with a description of their functionality in Table MetaNET currently has over 50 tools grouped into different categories , from Reed et. al. [MetaNET provides various tools for simulation using FBA by applying different genetic or environmental constraints. To emphasize the core features of MetaNET, three case studies were performed with the publicly available genome-scale metabolic  et. al. . The sysTo predict optimal biomass growth under aerobic conditions, the network was optimized through the biomass reaction by flux balance analysis using the “Single Objective optimizer” tool for the wild type strain Figure A. The grTo predict optimal biomass growth under anaerobic conditions, the flux of the reaction which corresponds to exchange of oxygen from the extracellular to cytosolic compartment was constrained to zero using the “Replace constraint” tool and the network was again optimized using the “Single Objective optimizer” tool Figure A. The grTo identify the critical reactions of the network, all 1075 reactions were iteratively knocked-out and its effect on biomass was calculated using the “Reaction knock-out optimizer” tool . Using “Essential Reactions Reporter”, we found 135 reactions to be essential as their deletion reduce the flux of biomass significantly (Figure This category consists of tools designed to determine robustness and modularity based on the topology of the metabolic network. “SLP cyclic identifier” and “Extreme path identifier” are Java-based functions available within SBRT that have been have been integrated in MetaNET. Additionally, many tools are available in MetaNET which have been implemented using in-house Perl scripts. For instance, choke points are reactions present in the metabolic network which uniquely consume a particular substrate or produce a particular product ,37. Any One of the most powerful feature of MetaNET is to utilize the workflow support provided by the galaxy framework to couple tools into higher order solutions. Keeping this in mind, we designed different tools in such a way that these can be joined to create workflows in the MetaNET. Users can create custom workflows for analysis by linking appropriate tools of MetaNET using the workflow editor. The tools can only be joined if the output of one is compatible with the input of other. We have implemented eight different workflows which are generally used during metabolic network simulation Table . These wThis is the simplest workflow which reads the SBML file and plots the flux distribution after optimization Figure . It callGenes are said to be lethal if their deletion stops the growth of the organism. This workflow finds lethal genes in the given metabolic network by iteratively knocking down each gene and optimizing the metabolic network of the mutant strain Figure . This woPairwise reactions deletion experiments require considerable time and effort to perform on a large scale. This workflow is designed to rapidly predict the biomass flux by deleting a pair of reactions simultaneously. This workflow may predict some interesting pairs of reactions whose simultaneous deletion reduce the biomass, which otherwise are found to be non-essential during single-reaction deletion analysis. It calls the tools “Fetch Reaction IDs”, “Fetch objective function”, ”“Fetch flux constraints” and “PalssonSBML Reader” which parse the reaction identifiers, objective function, reactions constraints and reactions respectively from input SBML file. As the numbers of possible pairs is very large, it first finds the choke point reactions using “Find Choke Point Reactions” tool. The resulting output i.e. reaction Identifiers of choke point reactions is used by the tool “Make Pairs” tool implemented in Perl which makes all the possible pairs of reactions. Finally, another tool “Reaction knock-out optimizer” deletes the pairs sequentially and optimizes the objective function.http://metanet.osdd.net. The framework is built with a set of tools for data management including data upload/download, format conversion, file operations and data extraction capabilities from SBML files, optimizing network using FBA, flux variability analysis [MetaNET is a user-friendly, extensible and platform independent framework for metabolic network analysis freely available at analysis , perturbProject Name: MetaNETProject home page:http://metanet.osdd.net/Operating system: Platform IndependentProgramming Language: Language independentOther requirements: InternetAny restrictions to use by non-academics: None


Escherichia coli in a minimal medium and we find that synthetic lethal pairs divide in two different groups depending on whether the synthetic lethal interaction works as a backup or as a parallel use mechanism, the first corresponding to essential plasticity and the second to essential redundancy. In E. coli, the analysis of pathways entanglement through essential redundancy supports the view that synthetic lethality affects preferentially a single function or pathway. In contrast, essential plasticity, the dominant class, tends to be inter-pathway but strongly localized and unveils Cell Envelope Biosynthesis as an essential backup for Membrane Lipid Metabolism. When comparing E. coli and Mycoplasma pneumoniae, we find that the metabolic networks of the two organisms exhibit a large difference in the relative importance of plasticity and redundancy which is consistent with the conjecture that plasticity is a sophisticated mechanism that requires a complex organization. Finally, coessential reaction pairs are explored in different environmental conditions to uncover the interplay between the two mechanisms. We find that synthetic lethal interactions and their classification in plasticity and redundancy are basically insensitive to medium composition, and are highly conserved even when the environment is enriched with nonessential compounds or overconstrained to decrease maximum biomass formation.We unravel how functional plasticity and redundancy are essential mechanisms underlying the ability to survive of metabolic networks. We perform an exhaustive computational screening of synthetic lethal reaction pairs in  Plasticity and redundancy are essential features of biological systems, from brain to genome, that underlie the ability of organisms to survive. In metabolic networks, these essential mechanisms are unveiled by the analysis and categorization of synthetic lethal pairs of reactions. We find that plasticity acts as a backup mechanism that reorganizes metabolic fluxes, while redundancy corresponds to a simultaneous use of different flux channels that increases fitness. Both capacities ensure viability and are highly insensitive to environmental conditions, but plasticity seems a more sophisticated mechanism requiring a more complex functional organization. Our results have clear implications for biotechnology and biomedicine, since targeting a plasticity or a redundancy synthetic lethal pair will certainly have different requirements and peculiar specific effects. Homeostasis in living systems balances internal states over a possibly wide range of internal or external variations, and organisms unable to maintain stability in front of internal disruptions or changing environments can experience dysfunction and even collapse. At the level of cellular metabolism, multiple regulatory mechanisms control homeostasis, including allosteric or posttranslational activation of enzymes and modulation of enzymatic activity by transcriptional regulation Escherichia coli –with catalytic action in purine biosynthesis and thus important as crucial components of DNA, RNA or ATP– require exogenously added purine for growth, while single knockout mutants do not result in purine auxotrophy Beyond the molecular level, plasticity and redundancy are large-scale strategies that offer the organism the ability to exhibit no or only mild phenotypic variation in front of environmental changes or upon malfunction of some of its parts. In particular, these mechanisms protect metabolism against the effects of single enzyme-coding gene mutations or reaction failures such that most metabolic genes are not essential for cell viability. However, some mutants fail when an additional gene is knocked out, so that specific pair combinations of non-essential metabolic genes or reactions become essential for biomass formation. As an example, double mutants defective in the two different phosphoribosylglycinamide transformylases present in in silico prediction of SL pairs These synthetic lethal (SL) combinations E. coli in a glucose minimal medium and we find that SL reaction pairs divide in two different groups depending on whether the SL interaction works as a backup or as a parallel use mechanism, the first corresponding to essential plasticity and the second to essential redundancy. When comparing the metabolisms of E. coli and Mycoplasma pneumoniae, we find that the two organisms exhibit a large difference in the relative importance of plasticity and redundancy. In E. coli, the analysis of how pathways are entangled through SL pairs supports the view that redundancy SL pairs preferentially affect a single function or pathway E. coli, tends to be inter-pathway but concentrated and unveils Cell Envelope Biosynthesis as an essential backup for Membrane Lipid Metabolism. Finally, different environmental conditions are tested to explore the interplay between these two mechanisms in coessential reaction pairs.With this perspective, we unveil how functional plasticity and redundancy are essential systems-level mechanisms underlying the viability of metabolic networks. In previous works on cellular metabolism iJO1366 E. coli metabolic network reconstruction iJW145 M. pneumoniae model E. coli  reaction pairs those in which both reactions are active and used in parallel . Of all  are RSL   that is able to reorganize metabolic fluxes turning on inactive reactions when coessential counterparts are removed in order to maintain viability in a specific medium, while redundancy corresponds to a simultaneous use of different flux channels (mainly intra-pathway in E. coli) that ensures viability and besides increases fitness. Apparently, it could seem extremely improbable that the removal of an inactive reaction together with a non-essential active one, like in PSL pairs, could have any lethal effect on an organism. However, we found that this situation is indeed overwhelmingly dominant in E. coli as compared to redundancy synthetic lethality, and it is still relatively frequent even in a less complex organism like M. pneumoniae.Synthetic lethals are complex functional combinations of genes or reactions that denote at the same time both vulnerability in front of double deletions and robustness in front of the failures of any of the two counterparts. Although synthetic lethal genes could be associated to the plasticity and redundancy categories, approaching directly pairs of reactions without the  scaffold of enzymes and genes allows us to determine in a clean and systematic way the minimal combinations of reactions that turn out to be essential for an organism. Working at the level of reactions, we showed that this synthetic lethality is meditated by two different mechanisms, essential plasticity and essential redundancy, depending on whether one reaction is active for maximum growth in the medium under consideration and the second inactive, or in contrast both reactions have non-zero flux. Plasticity sets up as a sophisticated backup mechanism . To do this, we follow an approach similar to Flux Variability Analysis (FVA) in silico prediction of SL pairs Flux Balance Analysis is a method to compute the fluxes of reactions in metabolic networks at steady state. In its standard version, FBA optimizes biomass production without using kinetic parameters We implement FBA using GNU Linear Programming Kit (GLPK) to compute synthetic lethality of reaction pairs. Once we have determined the space of reactions to be considered in potential SL pairs using FVA , we computed E. coli, we use the information given in Ref. M. pneumoniae, we use results from a genome-wide transposon study in M. genitalium given in Ref. M. genitalium can be assigned to 128 metabolic genes in iJW145, and we associate the essentiality of that ortholog to the corresponding gene in M. pneunomiae. The other M. genitalium and the high similarity of the metabolic networks of both organisms  associated to isoenzymes (2 occurrences) and multifunctional enzymes (1 occurrence) are classified as inconsistencies.We model metabolism as a bipartite directed network We considered the set of 333 minimal media given in Ref. E. coli that we use in this work. However, an amino acid-enriched medium  can be constructed from the glucose minimal medium given in Amino acid-enriched medium exchange bounds have not been measured yet for the version of E. coli model we are using. The exchange constraints bounds of these compounds are set to −10 mmol/Click here for additional data file.Table S2Synthetic lethal pairs of Escherichia coli. They are divided into 4 categories: RSL , RSL I , PSL , PSL I . We show also the associated gene or genes and pathways of all reactions.(XLS)Click here for additional data file.Table S3Synthetic lethal pairs of Escherichia coli in the amino acid-enriched medium. They are divided into 2 categories: RSL , PSL . We show also the associated gene or genes and pathways of all reactions.(XLS)Click here for additional data file.Table S4Compounds added to construct the rich medium of Escherichia coli. They are given in Refs. (XLS)Click here for additional data file.Table S5Synthetic lethal pairs of Escherichia coli in the rich medium. They are divided into 2 categories: RSL , PSL . We show also the associated gene or genes and pathways of all reactions.(XLS)Click here for additional data file.Table S6Synthetic lethal pairs of Escherichia coli in the growth reduced to 30 of the maximum value medium by constraining mineral salts. They are divided into 2 categories: RSL , PSL . We show also the associated gene or genes and pathways of all reactions.(XLS)Click here for additional data file.Table S7Synthetic lethal pairs of Escherichia coli in the growth reduced to 30 of the maximum value medium by constraining the 4 basic sources . They are divided into 2 categories: RSL , PSL . We show also the associated gene or genes and pathways of all reactions.(XLS)Click here for additional data file.Table S8Compounds present in the medium of Mycoplasma pneumoniae. They are given in Ref. (XLS)Click here for additional data file.Table S9Set of candidate reactions of Mycoplasma pneumoniae obtained with modified FVA computations. All possible pair combinations of these reactions lead to potential SL pairs.(XLS)Click here for additional data file.Table S10Synthetic lethal pairs of Mycoplasma pneumoniae. They are divided into 4 categories: RSL , RSL I , PSL , PSL I . We show also the associated gene or genes and pathways of all reactions.(XLS)Click here for additional data file.


Leishmania major, which is transmitted by sandfly vector. There are specific differences in biochemical profiles and metabolite pathways in logarithmic and stationary phases of Leishmania parasites. In the present study, 1H NMR spectroscopy was used to examine the metabolites outliers in the logarithmic and stationary phases of promastigotes in L. major to enlighten more about the transmission mechanism in metacyclogenesis of L. major. Cutaneous leishmaniasis is one of the most important parasitic diseases in humans. In this disease, one of the responsible organisms is 1H NMR spectroscopy was applied, and outliers were analyzed using principal component analysis. Promastigote was cultured, logarithmic and stationary phases were separated by the peanut agglutinin, and cell metabolites were extracted. The most altered metabolites in stationary and logarithmic phases were limited to citraconic acid, isopropylmalic acid, L-leucine, ornithine, caprylic acid, capric acid, and acetic acid. 1H NMR spectroscopy could play an important role in the characterization of metabolites in biochemical pathways during a metacyclogenesis process. These metabolites and their pathways can help in exploiting a transmission mechanism in metacyclogenesis, and outcoming data might be used in the metabolic network reconstruction of L. major modeling.  Cutaneous leishmaniasis is the most popular form of the disease causing ulcers on skin[2]. Leishmania major and L. tropica are the main causes of this disorder found in Iran, Iraq, and their neighboring countries. Leishmania cells exist in two morphological forms: free extracellular, flagellated promastigote in the gut of the sandfly vector, which changes into the intracellular, non-flagellated amastigote in the mammalian macrophage phagolysosome. Parasites experience several developmental transitions during their infectious cycle. Procyclic promastigotes, similar to in vitro logarithmic promastigotes, are flagellated and motile forms that exist in the gut of sandfly. They divide rapidly but do not infect the vertebrate host. After developing into the metacyclic phase resembling the in vitro stationary phase, which is non-dividing and infective, promastigots are transferred to the sandfly's mouth. This metacyclogenesis process transforms from non-infective dividing procyclics to infective non-dividing metacyclics[7-9].Protozoan Leishmania spp. parasites involve about 20 species that infect humans by the bite of the sandfly vectorL. major Fredlin was the first protozoan model that its metabolic network was reconstructed by Chavali et al.[10] in 2008. The reconstructed metabolic network contained 560 gene spanning, 36 chromosomes of the genome, 1112 reaction, and 1047 metabolites[10]. Since there is a lack of complete information on L. major proteins and metabolites, the reconstruction was mostly based on protein expression from L. infantum, which is a related Leishmania spp[11]. In 2007, Leifso et al.[11] reported that the stage-specific metabolism in amastigotes and promastigotes of L. major. They postulated that alcohol dehydrogenase enolase adenosine triphosphate synthase were preferentially expressed on promastigote stages while hexokinase was preferentially expressed in amastigotes. Alteration in enzyme level often functions as an intermediate step that leads to functionally relevant variation at the metabolite level[12].[13]. It is also a method for the high-throughput identification and quantification of metabolites in the metabolome of the cells, tissues, and organisms[14]. Proton NMR spectroscopy is a powerful, simple, reproducible, reliable, and quantitatively accurate tool that is typically applied to acquire metabolomics data[15]. Direct analysis of cellular metabolome is being applied to get more information about metabolic pathways and has been extensively used in many organisms[16]. There are several examples of its application in analyzing the metabolome of pathogenic microorganisms[12]. Therefore, to know the gradual changes in enzyme expression or drug inhibition of a special pathway, the full understanding of Leishmania metabolism, by detailed analysis of metabolic networks in different phases, is needed. There are specific differences in biochemical characters and metabolite pathways in the two phases of procyclic and metacyclic biochemical pathways of L. major[17], which annually causes 20,000 infection cases in Iran[18].Metabolomics is a new field in post-genomic era and analyzes the changes of the whole metabolome simultaneously in response to environmental or cellular changesL. major. In addition, the out coming data might be used in the metabolic network reconstruction of L. major modeling. Thus, in the present pilot study, we examined the metabolites outliers of procyclic and metacyclic phases to better enlighten the transmission mechanism in metacyclogenesis of ParasitesL. major promastigote (MRHO/IR/75/ER) was originally obtained from the infected BALB/c mice in Immunology Department of Pasture Institute of Iran (Tehran). The starting parasite inoculation was 2×106/ml. Promastigotes were adapted at 23-25ºC in a Scheneider's medium  supplemented with 10% inactivated fetal calf serum, 2 mM L-Glutamine, 100µg/ml streptomycin, and 100 U/ml penicillin . The promastigotes were incubated with medium refreshment intervals for 15 days and then transferred into two flasks. Each flask contained a total volume of 80 ml with a cell density of approximately 14×106 viable cells/ml. Content of one flask was cultured for 5-7 days and represented as procyclic promastigote. The content of other flask was cultured from day15 to day 20 without adding fresh media, and then metacyclic promastigotes were harvested. In the current study, the purification of metacyclic promastigotes was accomplished by agglutination with peanut agglutinin [19]. In brief, PNA was added to washed metacyclic promastigotes to a final concentration of 50 µg/ml for 3×108 parasite/ml. In the next step, PNA- parasites (metacyclic promastigotes) were separated from agglutinated PNA+ parasites (procyclic promastigotes) by centrifugation at 200 ×g for 10 min. The non-agglutinated metacyclic promastigotes were then collected from the supernatant. Metacyclic and procyclic promastigotes were washed in PBS and collected by centrifugation at 3500 ×g at 4°C for 20 min. Then the increased infectivity of the PNA-metacyclic promastigotes was tested in 10 BALB/c mice (6–8 weeks old). The animals were selected randomly and divided into two groups: one group received subcutaneous injections of106 procyclic promastigotes, and the other group received 106 metacyclic promastigotes in the left hind footpad. The footpad inflammation of the two groups were measured weekly, and their sizes were deﬁned as the mean of thickness and the width of footpad. Ten samples, each containing 6×108 promastigote/ml, were used for proton NMR spectroscopy from each phase.The Cell extraction for metabolite analysis8 cell/mL were obtained from each vial, centrifuged at 1000 ×g at 4°C for 15 min and washed twice with ice-cold normal saline. Chilled perchloric acid (1.8 M) was added to the cell suspension, vortexed and sonicated at 4°C for 5 min, followed by centrifugation at 12000 ×g for 10 min at 4ºC. The pH of the supernatant was adjusted to 6.8, and then the supernatant was kept on ice for one hour to allow precipitation of potassium perchlorate and finally centrifuged again. The supernatant was lyophilized and taken for NMR spectroscopy[22]. In total, 6×101HNMR experiments2O with 0.2 mM trimethylsilyl propionate  as the NMR chemical shifts reference. Samples were centrifuged at 45,000 ×g at 4ºC for 20 min. The extracted samples were analyzed on a Bruker AV-500 NMR spectrometer with filed gradient operating at 500.13 MHz for proton observation at 298K. One-dimensional 1H NMR spectra were obtained using a 10-μs pulse, 6009.6 Hz spectral width, 0.1 s mixing time, 3.0 s relaxation delay, and 3000 transients with standard 1D NOESY (nuclear Overhauser spectroscopy) pulse sequence to suppress the residual water peak. Lyophilized powder samples (n=10) from each phase were resuspended in DData analysis[23]. Principal component analysis, which is an unsupervised pattern recognition method that converts multidimensional data space into low dimensional model, was used. The spectral areas of above 6 ppm were removed. The outliers were identified, and the corresponding metabolite was extracted from metabolome database. Using MetaboAnalyst 2.0 , biochemical pathways were also investigated.The resulting NMR spectra were imported into MATLAB (v.7.8.0.347) software and preprocessed with ProMetab software (version 1.1). Chemical shifts between 0 and 10 ppm were taken and normalized. Spectra were binned in 0.004 units, and water peak (4.7 ppm) was removed for data analysisResults from the present study showed that many metabolites pathways, influenced by Leishmania cell differentiations, were altered. The comparison of the metabolites patterns in stationary and logarithmic phases is depicted in The PCA results  showed tL. major metabolism is remarkably complex and unique in their capability for polycistronic transcription[24], the presence of kinetoplast DNA, glycosome, acidocalcisome, flagellar compartments[25], and the occurrence of fatty acid synthesis mechanism. Chavali and coworkers[10] reported that 12% of single-gene knockout in the L. major network are lethal and 10% are growth-reducing factors, which control the metabolism network of growth in parasites. Focusing on the metabolic cause of pathogenicity of L. major promastigotes, H1NMR spectroscopy of the logarithmic and stationary phases showed that there are P values  three-four-fold faster than the logarithmic phase in the medium to induce oxidative phosphorylation in glycosomes and mitochondria and finally gain energy in these stages. Therefore, it can be postulated that caprylic acid and capric acid have an important role in the stationary phase of L. major metabolic network, and our results are in consistent with those data.As promastigotes age and/or transform into amastigotes[39]. In Trypanosome brucei, acetate, which is produced from glucose and threonine amino acid in the mitochondrion, is synthetically essential to feed the necessary fatty acid biosynthesis and ATP production through the acetate shuttle. This shuttle has been recently described in the procyclic form of the parasite in insect[40]. Therefore, the utilization of high glucose, which is correlated with acetate production in this pathway and the presence of acetate shuttle in the procyclic phases, could be considered as a factor that makes acetate to be altered more in the logarithmic phase than stationary phase of promastigotes.The current study indicates the alteration of acetate metabolite in the sulfur metabolism pathway as well. Some amino acids contain different levels of sulfur that finally could degrade to acetate by a simple hydrolysis of the thioester bondL. major. It could be concluded that the main sources of the energy backbone are affected by promastigotes differentiations in the metacyclogenesis process, and these metabolic outliers could be used in coming in silico metabolic modeling and gene knockout.Overall, our findings show how the application of metabonomics approaches can play an important role in the characterization of biochemical pathways in different stages of promastigotes by identifying metabolites outliers in infective and non-infective forms of the promastigote in


Boolean models have been instrumental in predicting general features of gene networks and more recently also as explorative tools in specific biological applications. In this study we introduce a basic quantitative and a limited time resolution to a discrete (Boolean) framework. Quantitative resolution is improved through the employ of normalized variables in unison with an additive approach. Increased time resolution stems from the introduction of two distinct priority classes. Through the implementation of a previously published chondrocyte network and T helper cell network, we show that this addition of quantitative and time resolution broadens the scope of biological behaviour that can be captured by the models. Specifically, the quantitative resolution readily allows models to discern qualitative differences in dosage response to growth factors. The limited time resolution, in turn, can influence the reachability of attractors, delineating the likely long term system behaviour. Importantly, the information required for implementation of these features, such as the nature of an interaction, is typically obtainable from the literature. Nonetheless, a trade-off is always present between additional computational cost of this approach and the likelihood of extending the model’s scope. Indeed, in some cases the inclusion of these features does not yield additional insight. This framework, incorporating increased and readily available time and semi-quantitative resolution, can help in substantiating the litmus test of dynamics for gene networks, firstly by excluding unlikely dynamics and secondly by refining falsifiable predictions on qualitative behaviour. Since tIndeed, as the maxim goes in genetics, ‘no genotype is superior in all environments’ , neitherWhile Boolean functions present an intuitive approach to capture interactions, they become increasingly harder to specify as the number of interaction partners of a particular gene increases, starting with the choice between AND/OR gates at 2 inputs . At the Over the years, many qualitative modelling approaches have been developed to address these two limitations ,12,13. FSecondly, several adaptations to the standard Boolean framework augment the time resolution. A first strategy is to fine-tune the update rules. For instance, priority classes, introduced in GINsim, achieve this by enforcing that nodes in a higher priority class are updated first . A similIn this paper we introduce a discrete dynamical framework that addresses the aforementioned issues arising in the Boolean framework. The all or nothing response is mitigated by introduction of continuous normalized values in combination with an additive approach. Qualitative information on time aspects is included by dividing the model interactions into two separate speed classes. The increased model complexity permits us to capture a wider range of the system’s behaviour then would otherwise be possible in a standard Boolean model. We show that the incorporation of these features can yield new insights into the behaviour of the system.To illustrate that the increase in the model’s complexity is justified by an increased scope of possible behaviour, we apply it to two gene networks, the first driving differentiation of cartilage cells (chondrocytes) in the growth plate (derived from ) and theThe chondrocyte model is based on an extensive literature study and is an expansion of a model we previously published . Note thEssentially, any mathematical model of a gene network relies on two distinct parts, the representation of the topological information in the form of a directed graph, and a framework for the simulation of the dynamics of the network, for which a variety of methods is available –45.G consists of a set of nodes (or vertices) V and a set of edges (or arcs) E. Each edge is an ordered pair, giving the source node and the target node . The slow and fast variables are then set to reflect this activity. If the node is subject to both slow and fast control, the initial conditions of the fast and slow variable are the square root of this value. If control is uniquely fast or slow, this variable also takes on the activity value whereas the other variable is set to 1. An example of a non-viable state would be a fast node where the slow variable is not 0, which cannot occur without intervention. The Monte Carlo analysis of the attractor basins is similar to the algorithm included in the BN/PBN toolbox by Lähdesmäki and Shmulevich . For theThe Monte Carlo algorithm can determine the attractors for both networks. For the chondrocyte gene network, the Monte Carlo analysis indicates that three stable states exist, one of which is the trivial state . As expected, of the other two states one is characterized by Sox9 and the other by Runx2. The exact values of the attractors are given in For the Th network, the attractors are given in Next, we demonstrate how the additional features in our framework, the introduction of priority classes and the additive control combined with normalised activities, broaden the scope of behaviour that the model can successfully capture/investigate. We also show that this advantage is context-specific, since for some networks the effects will not be worth the extra computational cost.To illustrate the advantages of normalized continuous values, the first of two major differences with standard Boolean modelling, we perform a perturbation analysis on the growth factors in the network. It is a long standing tenet in developmental biology that timing and dosage are crucial considerations to determine a growth factor’s impact on differentiation, hence the need for network models to allow for examination of these effects. In terms of the gene network the first factor (timing) is equivalent to the network state at the moment the signal is received, and dosage determines how effectively the perturbed node’s outgoing edges are activated. The continuous activities of the nodes allow for a straightforward dissemination of the effect of dosage, summarised in Specifically, we perturbed the six growth factors in the chondrocyte network from the Sox9 stable attractor. The results of perturbations of 1%, 5% and 10% to 50% are summarised in A second major difference is the introduction of priority classes, in this case limited to two, allowing for a more straightforward breakdown of their contribution to model dynamics. To indicate their significance, we will investigate their influence on the canalisation of the Th network. For the Th network without priority classes, which boils down to using random asynchronous updating, the distribution of the Th1 vs the Th2 attractor is around 57% versus 43%. To assess the impact of the priority classes, we assigned a priority class to each interaction. The assigned priority class for each reaction is found in Since the mutual repression of T-bet and GATA3 is a hypothesis , exact mThe observed change is solely quantitative. For a model that is qualitative in nature, the obtained difference is perhaps not worth the added computational effort. That cannot be stated, however, when the change is qualitative. Though priority changes do not alter the attractors themselves, they can adversely affect its reachability. We illustrate this with a fictive example in the Th network, where we made the interactions that make up the GATA3 positive feedback  fast, and all others interactions in the network slow. Thus these nodes are exclusively controlled by a fast variable, whereas all other nodes are determined by a slow variable. This shifts the equilibrium in favour of GATA3 to about 65%, but more importantly, 35% of random states end up in the Th0 state, while the Th1 state becomes unreachable.The introduction of priority classes and normalized values in combination with additive logic hence has significant advantages in the above examples. However, these advantages have to be weighed against increased model complexity. Moreover, the advantages are not always present, as in some cases the extra features offer no, or relatively little, benefit over more basic models. For example the introduction of normalized values in the Th network does not change the effect of growth factors at all, mainly since dominant inhibitions prevent them from having an effect on the attractor. Hence in that case, a perturbation analysis in the Boolean framework will not differ qualitatively from one using normalized values. The same holds true for the influence of priority classes in the chondrocyte network. To illustrate this, we investigated the effect of a change in priority class for all nodes exclusively controlled by one priority class. The results can be found in This study highlights that extra features added to the Boolean framework give rise to a broader scope of model behaviour. Firstly, the introduction of continuous normalized values shows more diverse qualitative responses to growth factor perturbation. Secondly, the introduction of priority classes can affect the reachability of attractors. However, the extended scope must be balanced with limited availability of quantitative information, as models may keep to behaviour that the Boolean framework can capture as well.As stated in the methods section, we employ an adapted form of general asynchronous updating, where each step an eligible node is selected to be updated randomly until a stable state is reached, rather than a fixed or synchronous updating scheme ,57. SincLimited time information is added to the framework by dividing interactions into priority classes based on the expected rate of the underlying biological phenomenon. This division of the updating scheme in two priority classes equates to a quasi-steady state approach as we implicitly assume the fast variables to be in equilibrium as the slow variables evolve. The updating of nodes within the same priority class is random. Hence the time resolution of the model is improved by poising a balance between deterministic updating that requires more detailed time information and general asynchronous updating that requires none . An impoThe overall effect of the introduction of priority classes, as shown by the analysis of the chondrocyte network, could potentially be small in comparison to uncertainties that are incorporated by the weights, implicitly or explicitly  and even more so by uncertainties on the type of the interactions  and the The underlying assumption of the division of the model’s reactions into two priority classes is an ideal separation of the time scales on which these interactions take place. That is, the fast variables should reach equilibrium in a time frame where the slow variables only change marginally. This boils down to a quasi-steady state approach were we assume the fast reactions are always in equilibrium as the slow reactions evolve . How welThe control functions employed in the framework are additive. Additive functions have shown to be capable of adequately simulating biological systems . The useFrom a methodological perspective, our use of additive control functions prevents having to make choices between implementing OR and AND gates to combine multiple signals, which are mostly arbitrary in the absence of information. An alternative to this approach could be to investigate an ensemble of networks with possible control functions, by for example varying the strength of the interactions, using different combinations of logical operators or probabilistic control functions . HoweverIn the control functions the strength of interactions was assumed equal for all actors, in the absence of additional information. Sometimes information on, for example, the steady state is available allowing these to be tuned somewhat to reflect the data. A change in the importance of the interactions can skew the distribution of stable states in the canalisation analysis, though qualitative results are expected to be similar. For example, increasing the weight of any nodes’ outgoing edges’ impact will result in more influence of changes in that node’s activity on the stable state distribution and will also affect the ‘wild type’ canalization of stable states. Of course, the influence of any factor can be increased or decreased up to the point that its expression becomes dominant or inconsequential. In the former case this amounts to changing network topology by removing all other incoming links from nodes on which that particular node impacts, whereas the latter changes network topology by removing all of the node’s outgoing connections. Therefore it is recommended that any conclusions drawn from this generic framework should be subjected to a sensitivity analysis, for example by varying model assumptions.There are several limitations to the additive approach presented here. The activities of complexes are represented by the product of the activities of its constituents, comparable to mass action kinetics . This representation has a few limitations, the first being that normalisation of the variables entails the inherent assumption that the concentrations of both constituents are the same order of magnitude. Secondly, it assumes one molecule of each constituent is present in the complex. Finally, the constituents don’t lose activity due to being holed up in the complex . This is only valid when a relatively low percentage of the constituents is in complex. Other formalisms, such as petri nets or mass action kinetics, may be better suited to model complexes .Another caveat is that the examples discussed do not involve limit cycles. As such, the supplied implementation files  do not dIt is interesting to note that the framework presented here has qualitatively different attractors for the Th network from the ones obtained in Mendoza et al. . This isCompared to existing methods, our approach specifically applies additive logic and is tailored to information typically found in biological literature. As such, the presented framework is particularly suited for exploratory modelling of differentiation networks. Typically, these networks deal with growth factors that through a variety of signalling events influence a set of transcription factors that are needed to sustain a certain phenotype. In our experience, the type of interactions this involves  lend themselves to division into two distinct priority classes. Moreover, the framework is of qualitative nature and geared towards systems where data is sparse. In the absence of combinatorial data, we employ an additive approach to deal with the multitude of pathways that converge on critical growth factors as a first step in exploring the system’s behaviour. The division of nodes into a fast and slow variable also helps in limiting the number of interactions that have to be combined in a single variable. The use of additive logic and normalisation of the variables can organically reveal dosage effects.Somewhat paradoxically, our understanding of intracellular networks has progressed to a point that we can no longer comprehend them without resorting to mathematical models. Indeed, the fact that human intuition does not take dynamics into account, while these exploratory models do, is precisely their main contribution ,75,76. MUncertainties on the priority classes, parameters and often also the network structure itself make predictions on the dynamic properties, e.g. canalisation, highly challenging, even if only qualitative. In these exploratory models, a key aspect to match the dynamics of the biological system is the topology . Indeed,S1 Appendix(PDF)Click here for additional data file.S1 FigNo values lower than 0,03 are detected. There is a clear trend for lower values to be less likely.(PDF)Click here for additional data file.S1 FileTo capture the structure of the model presented here, each node is split into a slow and fast variable. Fast variables are identified by _PTM suffix. Slow variables have a _protein suffix. The final activity has no suffix. Fast reactions are identified by their reaction id. Inhibitions are identified by a negative sign in the kinetic law.(XML)Click here for additional data file.S2 FileAttractorThnetwork.m performs a random initialisation Monte Carlo analysis on the Th network without priority classes. AttractorThnetworkpriority.m does include priority. Attractorchondrocyte.m network performs a random initialisation Monte Carlo analysis on the chondrocyte network. Dosageeffect.m performs a perturbation analysis on the chondrocyte network.(ZIP)Click here for additional data file.S1 TableThis table shows the attractors of the chondrocyte network. The three attractors are dubbed ‘None’, ‘Sox9’ and ‘Runx2’ representing the attractors where neither Sox9 or Runx2 is active, Sox9 is active and Runx2 is active, respectively. The first column gives the activity of the node. This activity is composed of the slow variable (second column), which gives the influence of the slow processes leading to protein formation, and the fast variable (third column), giving the influence of post translation modifications (PTMs).(PDF)Click here for additional data file.S2 TableAs can be seen in this table the results for Wnt, FGF, IGF and PTHrP are qualitatively the same. A difference arises in the qualitative response for BMP and Ihh due to the saturation of Sox9 activity at 1. However, it can be seen that the underlying unsaturated control function does show a similar dynamic for Sox9 activity.(PDF)Click here for additional data file.S3 TableFast interactions consist of post translation modifications, receptor binding, and other interactions that take place in this time scale. Slow interactions include transcription, translation and degradation.(PDF)Click here for additional data file.S4 TableS → F means the priority class was changed from fast to slow and vice versa. The third column gives the associated change in size of the Runx2 attractor basin.(PDF)Click here for additional data file.


RNA or RNA-like polymers are the most likely candidates for having played the lead roles on the stage of the origin of life. RNA is known to feature two of the three essential functions of living entities : it is capable of unlimited heredity and it has a proven capacity for catalysing very different chemical reactions which may form simple metabolic networks. The Metabolically Coupled Replicator System is a class of simulation models built on these two functions to show that an RNA World scenario for the origin of life is ecologically feasible, provided that it is played on mineral surfaces. The fact that RNA templates and their copies are of complementary base sequences has an obvious dynamical relevance: complementary strains may have very different structures and, consequently, functions – one may specialize for increasing enzymatic activity while the other takes the role of the gene of the enzyme.Incorporating the functional divergence of template and copy into the Metabolically Coupled Replicator System model framework we show that sequence complementarity 1) does not ruin the coexistence of a set of metabolically cooperating replicators; 2) the replicator system remains resistant to, but also tolerant with its parasites; 3) opens the way to the evolutionary differentiation of phenotype and genotype through a primitive version of phenotype amplification.phenotype amplification characteristic of our recent DNA-RNA-protein World.The functional asymmetry of complementary RNA strains results in a shift of phenotype/genotype (enzyme/gene) proportions in MCRS, favouring a slight genotype dominance. This asymmetry is expected to reverse due to the evolved trade-off of high “gene” replicability and high catalytic activity of the corresponding “enzyme” in expense of its replicability. This trade-off is the first evolutionary step towards the “division of labour” among enzymes and genes, which has concluded in the extreme form of The online version of this article (doi:10.1186/s12862-014-0234-8) contains supplementary material, which is available to authorized users. In a series of simulation studies -6 we havThe original MCRS is a toy model neglecting important physical-chemical details of the supposed RNA World scenario . Some ofvice versa), but its 3D structure, and, consequently, its physico-chemical properties – like its enzymatic activity [In the present study we address the dynamical consequences of the fact that the replication of RNA or any known RNA-like macromolecule yields a copy with a monomer sequence different from that of the template – a property directly following from nucleotide base-pairing rules . The complementary string of nucleotides in the copy carries the same sequence information as the original  toy model framework (MCRS) has been specified in detail in our previous publications ,3,5,6,17i at any point of time. Each replicator type has two forms different with respect to their enzymatic activities and complementary sequence-wise: the phenotype form  and the genotype form , i.e., the size of the system.MCRS is implemented as a stochastic cellular automaton (SCA) model on a square lattice representing the mineral surface to which the replicators are anchored. The topology of the lattice is toroidal (opposite sides merged), to avoid edge effects on the dynamics. Each site may be empty or occupied by a single replicator asynchronous random update. The first step of the updating algorithm is the random choice of a grid site, the next state of which (at time t +1) depends on its own state and those of its neighbours at time t. If the focal site is occupied by a replicator, then it becomes empty with a constant probability pd. If it is empty, then it may remain so with probability pe . r is the size of replication neighbourhoods . The size of the replication neighbourhood is a parameter of the model: increasing r means that the template may be further away from the empty site on which it claims to place a copy of itself.Each grid site is updated once on average in one generation time using y pi Eq. .1\documepe and pi. The next state of the empty site is determined by a random draw using probabilities ki , a replicator specific constant (replicability), and the local metabolic (monomer) supply (Mi) of replicator i:The “claim” of a replicator to put a complementary copy of itself to the focal empty site depends on two components: Mi of replicator i depends on the presence of the enzymatically active phenotype forms of all the metabolic replicator types, each type with at least one copy, within the metabolic neighbourhood of replicator i  of all the different phenotype-forms j within the metabolic neighbourhood of replicator i: h is the size of the metabolic neighbourhood . Mi is either zero , or it is greater than or equal to 1. Obviously, Mi = 0 implies Ci = 0  to be catalytically active [kip) of the “enzyme” form of an evolved replicator species (i) must be smaller than that (kig) of the “gene” form of the same species . Ivica et al. [kip < kig).Template-directed replication produces “enzymes” from “genes” and a Figure C and D. y active  has an ey active . The coma et al.  show thaParasitic replicators differ from metabolic ones in that neither of their complementary forms is enzymatically active. That is, both the “phenotype” and the “genotype” of a parasite use monomers produced by the metabolic replicator “phenotypes” for their replication, but neither form contributes to monomer production Figure D.2×2 blocks of sites are rotated 90° clockwise or anticlockwise with equal (0.5) probabilities. The intensity of replicator diffusion is scaled by the average number D of such sub-lattice rotations per update, so that D = 1 means four random steps per replicator per generation on average, because one rotation moves four replicators. Note, however, that even with D = 0 a minimum of replicator mixing is unavoidable, because replicator movement on the surface consists of two independent components: replicative movement (Dr) and diffusive movement (D). The former is an inevitable consequence of the replication mechanism: putting a copy in a site adjacent to that of the template implies the movement of the copy. The relative intensity of replicative to diffusive mixing can be estimated, given that a single Toffoli-Margolus diffusion step (D = 1) represents 4 site swaps per replicator per generation, whereas replicative movements result in an average of 0.2 swaps per replicator in each generation (because the death rate of replicators is constant – pd = 0.2 – a nd replicator densities are stationary). That is, replicative movement corresponds to Dr ≅ pd/4 = 0.05 in our model with the parameters above, assuming that the distance between the template and the empty site where the copy is placed is 1. Then the total mobility of the replicators is Dt = Dr + D, which yields Dt = 0.05 for D = 0. If the replication neighbourhood is larger than the von Neumann neighbourhood  is larger.Replicators bind to the mineral surface reversibly, allowing them some limited mobility in the form of a slow diffusive movement on the surface. This is implemented by using the Toffoli-Margolus algorithm  in the mThe stochastic cellular automaton consists of 90.000 sites arranged in a 300×300 rectangular square lattice. All simulations were initiated with 80% of the sites occupied at random positions by the “genotype” and “phenotype” forms of all replicator types, with both complementary forms of each replicator species represented at equal (10-10%) proportions.spatial mixing in that model: the speed of replicator diffusion (D) and the size of replication neighbourhoods (r) both correspond to replicator mobility, whereas metabolic neighbourhood size (h) is the proxy for the average distance that metabolite (and monomer) molecules can cover on the surface before being used in a reaction, degraded or desorbed from the surface. Consequently, h is determined by three factors: the surface diffusibility, the degradation rate and the desorption rate of small metabolite molecules – these three components are lumped in parameter h.Replicator coexistence has been shown to critically depend on just a small number of parameters in the original toy model of MCRS ,6. The tpd = 0.2), the “claim” of the empty site (Ce = 2.0) and system size (n = 4) were the same in all simulations. Replicabilities were also fixed at kip = kig and kpp = kpg in Model I, and kip < kig and kpp < kpg in Model II .We have screened the pheno/geno version of the model for replicator coexistence at different ranges of the same three parameters, keeping all others constant: the death rate of replicators , or the replicator community died out altogether. This is just to be expected: the extinction of any one of the metabolically active species stops monomer production and thus kills all the rest, including the parasite if there is one. The survival constraint does not apply to parasites, of course: since they perform no essential function for metabolism, they may go extinct while the metabolic replicators persist.Wherever the system is persistent, its equilibrium state can be fully specified by the stationary densities of the replicator species, and the phenotype to genotype density ratio within each species. Figures D and Dr) and the size of the replication neighbourhood (r) has a positive effect on the persistence of the system, as well as on the average density of replicators on the surface. This conclusion is in line with our previous results [r means more distance between template and copy, so that with the replication rate left unchanged, the step length of a single diffusive move increases and thus replicative diffusion (Dr) becomes more intensive with r larger.Replicator mobility is clearly advantageous for the coexistence of the metabolic replicator community in general: increasing any one or both of the diffusion parameters  the system goes extinct in some cases, even though at small and high r it is persistent . The larger it is the longer the distance within which the products of metabolism – monomers – are available for replicators being copied. In accordance with the conclusions of all previous versions of the MCRS models we find that the pheno/geno version also admits replicator coexistence within an optimum range of metabolic neighbourhood size: very small and very large h values are deleterious for system persistence, for essentially the same reasons as in the previous models [h mimics the fast desorption or decay of metabolites from the mineral surface, so that most of the metabolite molecules cannot be converted to monomers before they disappear from the system. It is difficult  to fit a complete set of metabolic replicators into a very small metabolic neighbourhood, therefore it slows down or stops replication everywhere, for lack of monomers.The average distance that a metabolite molecule travels on the surface before it becomes the substrate of a metabolic reaction or disappears from the system by desorption or decay is implicit in the size of the s models ,3,5,6,17h reduces the advantage of rarity, because rare replicator types are available in the (large) metabolic neighbourhoods of most other replicator types which are capable of faster replication, and thus the more common types outcompete the rare type and the system collapses. In other words, increasing h shifts the system towards the mean-field situation in which it has been shown to go extinct invariably [h for which coexistence occurs in the simulations  parameter range of the pheno/geno version of the MCRS model is somewhat narrower than that of the non-complementary version [Comparing the results of the current model Figures , 4 and 5 version ,6. This The dynamical consequences of an evolved trade-off between enzyme activity and gene replicability are clearly beneficial for the MCRS: Model I is coexistent in a section of its parameter space that is remarkably smaller than in Model II, and the average density of persistent replicator populations is also smaller everywhere in Model I  does not change this picture, at least not radically. One of the obvious differences is that the coexistence regions of the parameter space, i.e., the parameter settings at which the system is viable, are shifted towards larger metabolic and replication neighbourhoods in the pheno/geno version. This is not very surprising, given that - from a functional point of view - the pheno/geno system is “diluted” by the “gene” forms. Since it is only the “enzyme” form that contributes to metabolism, and each site of the lattice can be home for a single replicator at most, the inevitable presence of the enzymatically inactive “gene” forms scales up effective neighbourhood sizes in inverse proportion to the relative frequency of “enzyme” forms.r). It shows up consistently on each of Figures r = 4, i.e., at the von Neumann neighbourhood) seem to be advantageous for coexistence, just as large ones are. But in most cases there exists an intermediate section of the replication neighbourhood scale at which system extinction occurs. Since the persistence of the replicator system depends on the survival of the least abundant metabolic replicator species, in fact the question is: why does a very small replication neighbourhood favour the survival of the least fit  species compared to the others? The answer probably lies in the strong stochastic fluctuation of neighbourhood composition at very small neighbourhood sizes. An empty site with a single replicator in its replication neighbourhood  and that the metabolic neighbourhood h is sufficiently large to include the whole patch. Then all the replicators of a patch fit into the same metabolic neighbourhood so that they are all supplied by monomers for copying. Very small r guarantees that the rare type survives in spite of h being quite large. Of course, too large metabolic neighbourhoods are fatal for the system because of the shift towards mean-field dynamics leading to system extinction, so the viable range of h at very small r is limited. Note that the sharp borders of the patches dissolve with increasing diffusion, and the pattern of the arena becomes “normal”, i.e., nearly homogeneous.All “enzyme” and “gene” forms are distributed on the surface homogeneously in the majority of the parameter settings, except at large metabolic advantage of phenotypes” - : since “enzymes” replicate more often and they always yield “genes”, it is the latter that become more abundant. This is especially conspicuous in the case of Model I  the system is persistent in a considerably larger part of the parameter space; 2) wherever the system persists in both models, Model II produces larger overall densities and 3) higher relative frequencies of the phenotype (“enzyme”) form (by compensating the kp < kg) is not so straightforward, because nothing guarantees ab ovo that the complementary strain of a good ribozyme has a loose spatial structure, which would make it easier to copy. To the contrary – the complementary strains of efficient ribozymes have a high chance of being compact themselves too - but this is not a strictly constrained relation either [kp < kg would eventually appear as an evolved feature of the replicator species. This is a conjecture to be studied in detail later, using the MCRS model framework combined with the Vienna algorithm of RNA folding [Recall that the enzyme activity part of the trade-off is a physico-chemical necessity: an efficient ribozyme needs to be relatively compact and energetically stable, in order to present the required spatial configuration of critical residues in a steady structure for executing the reaction it catalyses. The replicability part of the trade-off  are amplified to many copies from just a few copies of their genes. The first step of phenotype amplification might have been the evolutionary acquisition of the enzymatic activity/replicability trade-off which we have shown to be advantageous for the coexistence and the dynamical efficiency of MCRS. More advanced ways of functional differentiation or “division of labour” (including the adoption of DNA and the complicated machineries of transcription and translation) might have developed later in some vesicular forms of the metabolic replicator system (see ) on the D = 4) or hamper  the persistence of parasites.Additional file