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author:("segr, Daniel")
1.  Species interactions differ in their genetic robustness 
Conflict and cooperation between bacterial species drive the composition and function of microbial communities. Stability of these emergent properties will be influenced by the degree to which species' interactions are robust to genetic perturbations. We use genome-scale metabolic modeling to computationally analyze the impact of genetic changes when Escherichia coli and Salmonella enterica compete, or cooperate. We systematically knocked out in silico each reaction in the metabolic network of E. coli to construct all 2583 mutant stoichiometric models. Then, using a recently developed multi-scale computational framework, we simulated the growth of each mutant E. coli in the presence of S. enterica. The type of interaction between species was set by modulating the initial metabolites present in the environment. We found that the community was most robust to genetic perturbations when the organisms were cooperating. Species ratios were more stable in the cooperative community, and community biomass had equal variance in the two contexts. Additionally, the number of mutations that have a substantial effect is lower when the species cooperate than when they are competing. In contrast, when mutations were added to the S. enterica network the system was more robust when the bacteria were competing. These results highlight the utility of connecting metabolic mechanisms and studies of ecological stability. Cooperation and conflict alter the connection between genetic changes and properties that emerge at higher levels of biological organization.
PMCID: PMC4396422  PMID: 25926820
cooperation; competition; genetic robustness; E. coli; Salmonella; community stability; metabolic modeling
2.  Predicting Growth Conditions from Internal Metabolic Fluxes in an In-Silico Model of E. coli 
PLoS ONE  2014;9(12):e114608.
A widely studied problem in systems biology is to predict bacterial phenotype from growth conditions, using mechanistic models such as flux balance analysis (FBA). However, the inverse prediction of growth conditions from phenotype is rarely considered. Here we develop a computational framework to carry out this inverse prediction on a computational model of bacterial metabolism. We use FBA to calculate bacterial phenotypes from growth conditions in E. coli, and then we assess how accurately we can predict the original growth conditions from the phenotypes. Prediction is carried out via regularized multinomial regression. Our analysis provides several important physiological and statistical insights. First, we show that by analyzing metabolic end products we can consistently predict growth conditions. Second, prediction is reliable even in the presence of small amounts of impurities. Third, flux through a relatively small number of reactions per growth source (∼10) is sufficient for accurate prediction. Fourth, combining the predictions from two separate models, one trained only on carbon sources and one only on nitrogen sources, performs better than models trained to perform joint prediction. Finally, that separate predictions perform better than a more sophisticated joint prediction scheme suggests that carbon and nitrogen utilization pathways, despite jointly affecting cellular growth, may be fairly decoupled in terms of their dependence on specific assortments of molecular precursors.
PMCID: PMC4264753  PMID: 25502413
3.  The average enzyme principle 
FEBS letters  2013;587(17):2891-2894.
The Michaelis-Menten equation for an irreversible enzymatic reaction depends linearly on the enzyme concentration. Even if the enzyme concentration changes in time, this linearity implies that the amount of substrate depleted during a given time interval depends only on the average enzyme concentration. Here, we use a time re-scaling approach to generalize this result to a broad category of multi-reaction systems, whose constituent enzymes have the same dependence on time, e.g. they belong to the same regulon. This “average enzyme principle” provides a natural methodology for jointly studying metabolism and its regulation.
PMCID: PMC3983706  PMID: 23892076
Enzyme regulation; Michaelis-Menten; Metabolic networks; Enzyme kinetics; Systems biology
4.  Metabolic resource allocation in individual microbes determines ecosystem interactions and spatial dynamics 
Cell reports  2014;7(4):1104-1115.
The inter-species exchange of metabolites plays a key role in the spatio-temporal dynamics of microbial communities. This raises the question whether ecosystem-level behavior of structured communities can be predicted using genome-scale models of metabolism for multiple organisms. We developed a modeling framework that integrates dynamic flux balance analysis with diffusion on a lattice, and applied it to engineered consortia. First, we predicted, and experimentally confirmed, the species-ratio to which a 2-species mutualistic consortium converges, and the equilibrium composition of a newly engineered 3-member community. We next identified a specific spatial arrangement of colonies, which gives rise to what we term the “eclipse dilemma”: does a competitor placed between a colony and its cross-feeding partner benefit or hurt growth of the original colony? Our experimentally validated finding, that the net outcome is beneficial, highlights the complex nature of metabolic interactions in microbial communities, while at the same time demonstrating their predictability.
PMCID: PMC4097880  PMID: 24794435
5.  On the Stability of Metabolic Cycles 
Journal of theoretical biology  2010;266(4):536-549.
We investigate the stability properties of two different classes of metabolic cycles using a combination of analytical and computational methods. Using principles from structural kinetic modeling (SKM), we show that the stability of metabolic networks with certain structural regularities can be studied using exclusively analytical techniques. We then apply these technique to a class of single input, single output metabolic cycles, and find that stability is guaranteed under a wide range of conditions. Next, we extend our analysis to a small autocatalytic cycle, and determine parameter regimes within which the cycle is very likely to be stable. We demonstrate that analytical methods can be used to understand the relationship between kinetic parameters and stability, and that results from these analytical methods can be confirmed with computational experiments. In addition, our results suggest that elevated metabolite concentrations and certain crucial saturation parameters can strongly affect the stability of the entire metabolic cycle. We discuss our results in light of the possibility that evolutionary forces may select for metabolic network topologies with a high intrinsic probability of being stable. Furthermore, our conclusions support the hypothesis that certain types of metabolic cycles may have played a role in the development of primitive metabolism despite the absence of regulatory mechanisms.
PMCID: PMC4038548  PMID: 20673772
metabolic networks; structural kinetic modeling; autocatalytic cycles
6.  Resource Competition May Lead to Effective Treatment of Antibiotic Resistant Infections 
PLoS ONE  2013;8(12):e80775.
Drug resistance is a common problem in the fight against infectious diseases. Recent studies have shown conditions (which we call antiR) that select against resistant strains. However, no specific drug administration strategies based on this property exist yet. Here, we mathematically compare growth of resistant versus sensitive strains under different treatments (no drugs, antibiotic, and antiR), and show how a precisely timed combination of treatments may help defeat resistant strains. Our analysis is based on a previously developed model of infection and immunity in which a costly plasmid confers antibiotic resistance. As expected, antibiotic treatment increases the frequency of the resistant strain, while the plasmid cost causes a reduction of resistance in the absence of antibiotic selection. Our analysis suggests that this reduction occurs under competition for limited resources. Based on this model, we estimate treatment schedules that would lead to a complete elimination of both sensitive and resistant strains. In particular, we derive an analytical expression for the rate of resistance loss, and hence for the time necessary to turn a resistant infection into sensitive (tclear). This time depends on the experimentally measurable rates of pathogen division, growth and plasmid loss. Finally, we estimated tclear for a specific case, using available empirical data, and found that resistance may be lost up to 15 times faster under antiR treatment when compared to a no treatment regime. This strategy may be particularly suitable to treat chronic infection. Finally, our analysis suggests that accounting explicitly for a resistance-decaying rate may drastically change predicted outcomes in host-population models.
PMCID: PMC3862480  PMID: 24349015
7.  Metabolic Proximity in the Order of Colonization of a Microbial Community 
PLoS ONE  2013;8(10):e77617.
Microbial biofilms are often composed of multiple bacterial species that accumulate by adhering to a surface and to each other. Biofilms can be resistant to antibiotics and physical stresses, posing unresolved challenges in the fight against infectious diseases. It has been suggested that early colonizers of certain biofilms could cause local environmental changes, favoring the aggregation of subsequent organisms. Here we ask whether the enzyme content of different microbes in a well-characterized dental biofilm can be used to predict their order of colonization. We define a metabolic distance between different species, based on the overlap in their enzyme content. We next use this metric to quantify the average metabolic distance between neighboring organisms in the biofilm. We find that this distance is significantly smaller than the one observed for a random choice of prokaryotes, probably reflecting the environmental constraints on metabolic function of the community. More surprisingly, this metabolic metric is able to discriminate between observed and randomized orders of colonization of the biofilm, with the observed orders displaying smaller metabolic distance than randomized ones. By complementing these results with the analysis of individual vs. joint metabolic networks, we find that the tendency towards minimal metabolic distance may be counter-balanced by a propensity to pair organisms with maximal joint potential for synergistic interactions. The trade-off between these two tendencies may create a “sweet spot” of optimal inter-organism distance, with possible broad implications for our understanding of microbial community organization.
PMCID: PMC3813667  PMID: 24204896
8.  Flux Imbalance Analysis and the Sensitivity of Cellular Growth to Changes in Metabolite Pools 
PLoS Computational Biology  2013;9(8):e1003195.
Stoichiometric models of metabolism, such as flux balance analysis (FBA), are classically applied to predicting steady state rates - or fluxes - of metabolic reactions in genome-scale metabolic networks. Here we revisit the central assumption of FBA, i.e. that intracellular metabolites are at steady state, and show that deviations from flux balance (i.e. flux imbalances) are informative of some features of in vivo metabolite concentrations. Mathematically, the sensitivity of FBA to these flux imbalances is captured by a native feature of linear optimization, the dual problem, and its corresponding variables, known as shadow prices. First, using recently published data on chemostat growth of Saccharomyces cerevisae under different nutrient limitations, we show that shadow prices anticorrelate with experimentally measured degrees of growth limitation of intracellular metabolites. We next hypothesize that metabolites which are limiting for growth (and thus have very negative shadow price) cannot vary dramatically in an uncontrolled way, and must respond rapidly to perturbations. Using a collection of published datasets monitoring the time-dependent metabolomic response of Escherichia coli to carbon and nitrogen perturbations, we test this hypothesis and find that metabolites with negative shadow price indeed show lower temporal variation following a perturbation than metabolites with zero shadow price. Finally, we illustrate the broader applicability of flux imbalance analysis to other constraint-based methods. In particular, we explore the biological significance of shadow prices in a constraint-based method for integrating gene expression data with a stoichiometric model. In this case, shadow prices point to metabolites that should rise or drop in concentration in order to increase consistency between flux predictions and gene expression data. In general, these results suggest that the sensitivity of metabolic optima to violations of the steady state constraints carries biologically significant information on the processes that control intracellular metabolites in the cell.
Author Summary
Cellular metabolism is composed of a complex network of biochemical reactions that convert environmental nutrients into biosynthetic building blocks and energetic currency. Genome-scale mathematical models of metabolic networks focus largely on trying to predict the rates – or fluxes - of these reactions. By assuming that the concentrations of intracellular metabolites are at steady-state (flux balance), and invoking optimality, these constraint-based methods for modeling metabolism have offered abundant insight into how metabolic flux is routed through the cell. Here we ask how cellular growth would respond to deviations from steady state (flux imbalance) of every possible intracellular metabolite. This question can be addressed through a sensitivity analysis inherent to linear optimization theory, known as duality. We show how some features of metabolite concentrations, such as their growth-limitation and their transient response, are captured by this sensitivity analysis. Our results suggest that, in addition to predicting fluxes, stoichiometric models offer a valuable route towards probing the metabolites themselves and their relevance to growth dynamics.
PMCID: PMC3757068  PMID: 24009492
9.  The COMBREX Project: Design, Methodology, and Initial Results 
Anton, Brian P. | Chang, Yi-Chien | Brown, Peter | Choi, Han-Pil | Faller, Lina L. | Guleria, Jyotsna | Hu, Zhenjun | Klitgord, Niels | Levy-Moonshine, Ami | Maksad, Almaz | Mazumdar, Varun | McGettrick, Mark | Osmani, Lais | Pokrzywa, Revonda | Rachlin, John | Swaminathan, Rajeswari | Allen, Benjamin | Housman, Genevieve | Monahan, Caitlin | Rochussen, Krista | Tao, Kevin | Bhagwat, Ashok S. | Brenner, Steven E. | Columbus, Linda | de Crécy-Lagard, Valérie | Ferguson, Donald | Fomenkov, Alexey | Gadda, Giovanni | Morgan, Richard D. | Osterman, Andrei L. | Rodionov, Dmitry A. | Rodionova, Irina A. | Rudd, Kenneth E. | Söll, Dieter | Spain, James | Xu, Shuang-yong | Bateman, Alex | Blumenthal, Robert M. | Bollinger, J. Martin | Chang, Woo-Suk | Ferrer, Manuel | Friedberg, Iddo | Galperin, Michael Y. | Gobeill, Julien | Haft, Daniel | Hunt, John | Karp, Peter | Klimke, William | Krebs, Carsten | Macelis, Dana | Madupu, Ramana | Martin, Maria J. | Miller, Jeffrey H. | O'Donovan, Claire | Palsson, Bernhard | Ruch, Patrick | Setterdahl, Aaron | Sutton, Granger | Tate, John | Yakunin, Alexander | Tchigvintsev, Dmitri | Plata, Germán | Hu, Jie | Greiner, Russell | Horn, David | Sjölander, Kimmen | Salzberg, Steven L. | Vitkup, Dennis | Letovsky, Stanley | Segrè, Daniel | DeLisi, Charles | Roberts, Richard J. | Steffen, Martin | Kasif, Simon
PLoS Biology  2013;11(8):e1001638.
Experimental data exists for only a vanishingly small fraction of sequenced microbial genes. This community page discusses the progress made by the COMBREX project to address this important issue using both computational and experimental resources.
PMCID: PMC3754883  PMID: 24013487
10.  Invariance and optimality in the regulation of an enzyme 
Biology Direct  2013;8:7.
The Michaelis-Menten equation, proposed a century ago, describes the kinetics of enzyme-catalyzed biochemical reactions. Since then, this equation has been used in countless, increasingly complex models of cellular metabolism, often including time-dependent enzyme levels. However, even for a single reaction, there remains a fundamental disconnect between our understanding of the reaction kinetics, and the regulation of that reaction through changes in the abundance of active enzyme.
We revisit the Michaelis-Menten equation under the assumption of a time-dependent enzyme concentration. We show that all temporal enzyme profiles with the same average enzyme level yield identical substrate degradation– a simple analytical conclusion that can be thought of as an invariance principle, and which we validate experimentally using a β-galactosidase assay. The ensemble of all time-dependent enzyme trajectories with the same average concentration constitutes a space of functions. We develop a simple model of biological fitness which assigns a cost to each of these trajectories (in the form of a function of functions, i.e. a functional). We then show how one can use variational calculus to analytically infer temporal enzyme profiles that minimize the overall enzyme cost. In particular, by separately treating the static costs of amino acid sequestration and the dynamic costs of protein production, we identify a fundamental cellular tradeoff.
The overall metabolic outcome of a reaction described by Michaelis-Menten kinetics is ultimately determined by the average concentration of the enzyme during a given time interval. This invariance in analogy to path-independent phenomena in physics, suggests a new way in which variational calculus can be employed to address biological questions. Together, our results point to possible avenues for a unified approach to studying metabolism and its regulation.
This article was reviewed by Sergei Maslov, William Hlavacek and Daniel Kahn.
PMCID: PMC3665469  PMID: 23522082
11.  Temporal Expression-based Analysis of Metabolism 
PLoS Computational Biology  2012;8(11):e1002781.
Metabolic flux is frequently rerouted through cellular metabolism in response to dynamic changes in the intra- and extra-cellular environment. Capturing the mechanisms underlying these metabolic transitions in quantitative and predictive models is a prominent challenge in systems biology. Progress in this regard has been made by integrating high-throughput gene expression data into genome-scale stoichiometric models of metabolism. Here, we extend previous approaches to perform a Temporal Expression-based Analysis of Metabolism (TEAM). We apply TEAM to understanding the complex metabolic dynamics of the respiratorily versatile bacterium Shewanella oneidensis grown under aerobic, lactate-limited conditions. TEAM predicts temporal metabolic flux distributions using time-series gene expression data. Increased predictive power is achieved by supplementing these data with a large reference compendium of gene expression, which allows us to take into account the unique character of the distribution of expression of each individual gene. We further propose a straightforward method for studying the sensitivity of TEAM to changes in its fundamental free threshold parameter θ, and reveal that discrete zones of distinct metabolic behavior arise as this parameter is changed. By comparing the qualitative characteristics of these zones to additional experimental data, we are able to constrain the range of θ to a small, well-defined interval. In parallel, the sensitivity analysis reveals the inherently difficult nature of dynamic metabolic flux modeling: small errors early in the simulation propagate to relatively large changes later in the simulation. We expect that handling such “history-dependent” sensitivities will be a major challenge in the future development of dynamic metabolic-modeling techniques.
Author Summary
Understanding the dynamic response of microorganisms to environmental changes is a major challenge in systems biology. In many cases, these responses manifest themselves through changes in gene transcription, which then propagate to adjust flow through metabolism. Here, we implement a Temporal Expression-based Analysis of Metabolism (TEAM) by dynamically integrating a genome-scale model of the metabolism of S. oneidensis with high-throughput measurements of gene expression and growth data. TEAM recapitulates the complex cascade of secretion and re-uptake of intermediary carbon sources that S. oneidensis exhibits in the experimental data. We show that these complicated metabolic behaviors are best captured when TEAM explicitly accounts for each gene's unique transcriptional signature. Furthermore, by way of a newly proposed sensitivity analysis, we reveal and study the inherent difficulty of dynamic metabolic flux modeling: small changes early in a simulation can easily spread and lead to significant changes towards the end of it. We expect that further development of robust dynamic flux balance methods will need to overcome such “history-dependent” sensitivities in order to achieve increased predictive accuracy.
PMCID: PMC3510039  PMID: 23209390
12.  Comparative multi-goal tradeoffs in systems engineering of microbial metabolism 
BMC Systems Biology  2012;6:127.
Metabolic engineering design methodology has evolved from using pathway-centric, random and empirical-based methods to using systems-wide, rational and integrated computational and experimental approaches. Persistent during these advances has been the desire to develop design strategies that address multiple simultaneous engineering goals, such as maximizing productivity, while minimizing raw material costs.
Here, we use constraint-based modeling to systematically design multiple combinations of medium compositions and gene-deletion strains for three microorganisms (Escherichia coli, Saccharomyces cerevisiae, and Shewanella oneidensis) and six industrially important byproducts (acetate, D-lactate, hydrogen, ethanol, formate, and succinate). We evaluated over 435 million simulated conditions and 36 engineering metabolic traits, including product rates, costs, yields and purity.
The resulting metabolic phenotypes can be classified into dominant clusters (meta-phenotypes) for each organism. These meta-phenotypes illustrate global phenotypic variation and sensitivities, trade-offs associated with multiple engineering goals, and fundamental differences in organism-specific capabilities. Given the increasing number of sequenced genomes and corresponding stoichiometric models, we envisage that the proposed strategy could be extended to address a growing range of biological questions and engineering applications.
PMCID: PMC3484036  PMID: 23009214
Metabolism; Microorganisms; Metabolic engineering; Constraint-based modeling
13.  Epistasis from functional dependence of fitness on underlying traits 
Epistasis between mutations in two genes is thought to reflect an interdependence of their functions. While sometimes epistasis is predictable using mechanistic models, its roots seem, in general, hidden in the complex architecture of biological networks. Here, we ask how epistasis can be quantified based on the mathematical dependence of a system-level trait (e.g. fitness) on lower-level traits (e.g. molecular or cellular properties). We first focus on a model in which fitness is the difference between a benefit and a cost trait, both pleiotropically affected by mutations. We show that despite its simplicity, this model can be used to analytically predict certain properties of the ensuing distribution of epistasis, such as a global negative bias, resulting in antagonism between beneficial mutations, and synergism between deleterious ones. We next extend these ideas to derive a general expression for epistasis given an arbitrary functional dependence of fitness on other traits. This expression demonstrates how epistasis relative to fitness can emerge despite the absence of epistasis relative to lower level traits, leading to a formalization of the concept of independence between biological processes. Our results suggest that epistasis may be largely shaped by the pervasiveness of pleiotropic effects and modular organization in biological networks.
PMCID: PMC3441082  PMID: 22896647
epistasis; benefit–cost model; evolution; pleiotropy; modularity
14.  Deep Sequencing of the Oral Microbiome Reveals Signatures of Periodontal Disease 
PLoS ONE  2012;7(6):e37919.
The oral microbiome, the complex ecosystem of microbes inhabiting the human mouth, harbors several thousands of bacterial types. The proliferation of pathogenic bacteria within the mouth gives rise to periodontitis, an inflammatory disease known to also constitute a risk factor for cardiovascular disease. While much is known about individual species associated with pathogenesis, the system-level mechanisms underlying the transition from health to disease are still poorly understood. Through the sequencing of the 16S rRNA gene and of whole community DNA we provide a glimpse at the global genetic, metabolic, and ecological changes associated with periodontitis in 15 subgingival plaque samples, four from each of two periodontitis patients, and the remaining samples from three healthy individuals. We also demonstrate the power of whole-metagenome sequencing approaches in characterizing the genomes of key players in the oral microbiome, including an unculturable TM7 organism. We reveal the disease microbiome to be enriched in virulence factors, and adapted to a parasitic lifestyle that takes advantage of the disrupted host homeostasis. Furthermore, diseased samples share a common structure that was not found in completely healthy samples, suggesting that the disease state may occupy a narrow region within the space of possible configurations of the oral microbiome. Our pilot study demonstrates the power of high-throughput sequencing as a tool for understanding the role of the oral microbiome in periodontal disease. Despite a modest level of sequencing (∼2 lanes Illumina 76 bp PE) and high human DNA contamination (up to ∼90%) we were able to partially reconstruct several oral microbes and to preliminarily characterize some systems-level differences between the healthy and diseased oral microbiomes.
PMCID: PMC3366996  PMID: 22675498
15.  Detection of transcriptional triggers in the dynamics of microbial growth: application to the respiratorily versatile bacterium Shewanella oneidensis 
Nucleic Acids Research  2012;40(15):7132-7149.
The capacity of microorganisms to respond to variable external conditions requires a coordination of environment-sensing mechanisms and decision-making regulatory circuits. Here, we seek to understand the interplay between these two processes by combining high-throughput measurement of time-dependent mRNA profiles with a novel computational approach that searches for key genetic triggers of transcriptional changes. Our approach helped us understand the regulatory strategies of a respiratorily versatile bacterium with promising bioenergy and bioremediation applications, Shewanella oneidensis, in minimal and rich media. By comparing expression profiles across these two conditions, we unveiled components of the transcriptional program that depend mainly on the growth phase. Conversely, by integrating our time-dependent data with a previously available large compendium of static perturbation responses, we identified transcriptional changes that cannot be explained solely by internal network dynamics, but are rather triggered by specific genes acting as key mediators of an environment-dependent response. These transcriptional triggers include known and novel regulators that respond to carbon, nitrogen and oxygen limitation. Our analysis suggests a sequence of physiological responses, including a coupling between nitrogen depletion and glycogen storage, partially recapitulated through dynamic flux balance analysis, and experimentally confirmed by metabolite measurements. Our approach is broadly applicable to other systems.
PMCID: PMC3424579  PMID: 22638572
16.  Transcriptional Analysis of Shewanella oneidensis MR-1 with an Electrode Compared to Fe(III)Citrate or Oxygen as Terminal Electron Acceptor 
PLoS ONE  2012;7(2):e30827.
Shewanella oneidensis is a target of extensive research in the fields of bioelectrochemical systems and bioremediation because of its versatile metabolic capabilities, especially with regard to respiration with extracellular electron acceptors. The physiological activity of S. oneidensis to respire at electrodes is of great interest, but the growth conditions in thin-layer biofilms make physiological analyses experimentally challenging. Here, we took a global approach to evaluate physiological activity with an electrode as terminal electron acceptor for the generation of electric current. We performed expression analysis with DNA microarrays to compare the overall gene expression with an electrode to that with soluble iron(III) or oxygen as the electron acceptor and applied new hierarchical model-based statistics for the differential expression analysis. We confirmed the differential expression of many genes that have previously been reported to be involved in electrode respiration, such as the entire mtr operon. We also formulate hypotheses on other possible gene involvements in electrode respiration, for example, a role of ScyA in inter-protein electron transfer and a regulatory role of the cbb3-type cytochrome c oxidase under anaerobic conditions. Further, we hypothesize that electrode respiration imposes a significant stress on S. oneidensis, resulting in higher energetic costs for electrode respiration than for soluble iron(III) respiration, which fosters a higher metabolic turnover to cover energy needs. Our hypotheses now require experimental verification, but this expression analysis provides a fundamental platform for further studies into the molecular mechanisms of S. oneidensis electron transfer and the physiologically special situation of growth on a poised-potential surface.
PMCID: PMC3271074  PMID: 22319591
Regulation of metabolic enzymes plays a crucial role in the maintenance of metabolic homeostasis, and in the capacity of living systems to undergo physiological adaptation under multiple environmental conditions. Metabolic regulation is achieved through a complex interplay of transcriptional and post-transcriptional mechanisms, some of which have been experimentally characterized for specific pathways and organisms. Many of the details, however, including the values of most kinetic parameters, have proven difficult to elucidate. Hence, understanding the principles that underlie metabolic regulation strategies constitutes an ongoing challenge. In the context of genome-scale steady state models of metabolic networks, it has been shown that evolution may drive metabolic networks towards reaching computationally predictable optimal states, such as maximal growth capacity. Here we develop a new computational approach based on the hypothesis that the regulatory systems operating on metabolic networks have evolved towards an optimal architecture as well. Specifically, we hypothesize that the topology of metabolic regulation networks has been selected for optimally maintaining the system balanced around one or more steady states. Based on these hypotheses, we use methods related to flux balance analysis to construct a model of metabolic regulation based primarily on a metabolic network’s topology, bypassing the requirement for the details of all kinetic parameters. This model predicts an optimal regulatory network of metabolic interactions that can resolve perturbations to a given steady state in a metabolic system. We explore the ability of the model to predict optimal regulatory responses in both a simple toy network and in a fragment of the well-described glycolysis pathway.
PMCID: PMC3245838  PMID: 19425131
metabolic regulation; flux balance analysis; enzyme kinetics; metabolism; optimality; logistic map; chaos
Flux Balance Analysis (FBA) has been successfully applied to facilitate the understanding of cellular metabolism in model organisms. Standard formulations of FBA can be applied to large systems, but the accuracy of predictions may vary significantly depending on environmental conditions, genetic perturbations, or complex unknown regulatory constraints. Here we present an FBA-based approach to infer the biomass compositions that best describe multiple physiological states of a cell. Specifically, we seek to use experimental data (such as flux measurements, or mRNA expression levels) to infer best matching stoichiometrically balanced fluxes and metabolite sinks. Our algorithm is designed to provide predictions based on the comparative analysis of two metabolic states (e.g. wild-type and knockout, or two different time points), so as to be independent from possible arbitrary scaling factors. We test our algorithm using experimental data for metabolic fluxes in wild type and gene deletion strains of E. coli. In addition to demonstrating the capacity of our approach to correctly identify known exchange fluxes and biomass compositions, we analyze E. coli central carbon metabolism to show the changes of metabolic objectives and potential compensation for reducing power due to single enzyme gene deletion in pentose phosphate pathway.
PMCID: PMC3245841  PMID: 19425132
flux balance analysis; systems biology; data integration; metabolic objectives
19.  Diminishing returns epistasis among beneficial mutations decelerates adaptation 
Science (New York, N.Y.)  2011;332(6034):1190-1192.
Epistasis substantially impacts evolution, in particular the rate of adaptation. We generated combinations of beneficial mutations that arose in a lineage during rapid adaptation of a bacterium whose growth depended upon a newly-introduced metabolic pathway. The proportional selective benefit for three of the four loci consistently decreased when introduced upon more fit backgrounds. These three alleles all reduced morphological defects caused by expression of the foreign pathway. A simple theoretical model segregating the apparent contribution of individual alleles to benefits and costs effectively predicted the interactions between them. These results provide the first evidence that patterns of epistasis may differ for within- and between-gene interactions during adaptation, and that diminishing returns epistasis contributes to the consistent observation of decelerating fitness gains during adaptation.
PMCID: PMC3244271  PMID: 21636771
20.  Epistatic Interaction Maps Relative to Multiple Metabolic Phenotypes 
PLoS Genetics  2011;7(2):e1001294.
An epistatic interaction between two genes occurs when the phenotypic impact of one gene depends on another gene, often exposing a functional association between them. Due to experimental scalability and to evolutionary significance, abundant work has been focused on studying how epistasis affects cellular growth rate, most notably in yeast. However, epistasis likely influences many different phenotypes, affecting our capacity to understand cellular functions, biochemical networks adaptation, and genetic diseases. Despite its broad significance, the extent and nature of epistasis relative to different phenotypes remain fundamentally unexplored. Here we use genome-scale metabolic network modeling to investigate the extent and properties of epistatic interactions relative to multiple phenotypes. Specifically, using an experimentally refined stoichiometric model for Saccharomyces cerevisiae, we computed a three-dimensional matrix of epistatic interactions between any two enzyme gene deletions, with respect to all metabolic flux phenotypes. We found that the total number of epistatic interactions between enzymes increases rapidly as phenotypes are added, plateauing at approximately 80 phenotypes, to an overall connectivity that is roughly 8-fold larger than the one observed relative to growth alone. Looking at interactions across all phenotypes, we found that gene pairs interact incoherently relative to different phenotypes, i.e. antagonistically relative to some phenotypes and synergistically relative to others. Specific deletion-deletion-phenotype triplets can be explained metabolically, suggesting a highly informative role of multi-phenotype epistasis in mapping cellular functions. Finally, we found that genes involved in many interactions across multiple phenotypes are more highly expressed, evolve slower, and tend to be associated with diseases, indicating that the importance of genes is hidden in their total phenotypic impact. Our predictions indicate a pervasiveness of nonlinear effects in how genetic perturbations affect multiple metabolic phenotypes. The approaches and results reported could influence future efforts in understanding metabolic diseases and the role of biochemical regulation in the cell.
Author Summary
An epistatic interaction between two genes occurs when the phenotypic impact of one gene is dependent on the other. While different phenotypes have been used to uncover epistasis in different contexts, little is known about how cell-scale genetic interaction networks vary across multiple phenotypes. Here we use a genome-scale mathematical model of yeast metabolism to compute a three-dimensional matrix of interactions between any two gene deletions with respect to all metabolic flux phenotypes. We find that this multi-phenotype epistasis map contains many more interactions than found relative to any single phenotype. The unique contribution of examining multiple phenotypes is further demonstrated by the fact that individual interactions may be synergistic relative to some phenotypes and antagonistic relative to others. This observation indicates that different phenotypes are indeed capturing different aspects of the functional relationships between genes. Furthermore, the observation that genes involved in many epistatic interactions across all metabolic flux phenotypes are found to be highly expressed and under strong selective pressure seems to indicate that these interactions are important to the cell and are not just the unavoidable consequence of the connectivity of biological networks. Multi-phenotype epistasis maps may help elucidate the functional organization of biological systems and the role of epistasis in the manifestation of complex genetic diseases.
PMCID: PMC3037399  PMID: 21347328
21.  COMBREX: a project to accelerate the functional annotation of prokaryotic genomes 
Nucleic Acids Research  2010;39(Database issue):D11-D14.
COMBREX ( is a project to increase the speed of the functional annotation of new bacterial and archaeal genomes. It consists of a database of functional predictions produced by computational biologists and a mechanism for experimental biochemists to bid for the validation of those predictions. Small grants are available to support successful bids.
PMCID: PMC3013729  PMID: 21097892
22.  Environments that Induce Synthetic Microbial Ecosystems 
PLoS Computational Biology  2010;6(11):e1001002.
Interactions between microbial species are sometimes mediated by the exchange of small molecules, secreted by one species and metabolized by another. Both one-way (commensal) and two-way (mutualistic) interactions may contribute to complex networks of interdependencies. Understanding these interactions constitutes an open challenge in microbial ecology, with applications ranging from the human microbiome to environmental sustainability. In parallel to natural communities, it is possible to explore interactions in artificial microbial ecosystems, e.g. pairs of genetically engineered mutualistic strains. Here we computationally generate artificial microbial ecosystems without re-engineering the microbes themselves, but rather by predicting their growth on appropriately designed media. We use genome-scale stoichiometric models of metabolism to identify media that can sustain growth for a pair of species, but fail to do so for one or both individual species, thereby inducing putative symbiotic interactions. We first tested our approach on two previously studied mutualistic pairs, and on a pair of highly curated model organisms, showing that our algorithms successfully recapitulate known interactions, robustly predict new ones, and provide novel insight on exchanged molecules. We then applied our method to all possible pairs of seven microbial species, and found that it is always possible to identify putative media that induce commensalism or mutualism. Our analysis also suggests that symbiotic interactions may arise more readily through environmental fluctuations than genetic modifications. We envision that our approach will help generate microbe-microbe interaction maps useful for understanding microbial consortia dynamics and evolution, and for exploring the full potential of natural metabolic pathways for metabolic engineering applications.
Author Summary
Microbial metabolism affects biogeochemical cycles and human health. In most natural environments, multiple microbial species interact with each other, forming complex ecosystems whose properties are poorly understood. In an effort to understand inter-microbial interactions, and to explore new metabolic engineering avenues, researchers have started building artificial microbial ecosystems, e.g. pairs of genetically engineered strains that require each other for survival. Here we computationally explore the possibility of creating artificial microbial ecosystems without re-engineering the microbes themselves, but rather by manipulating the environment in which they grow. Specifically, using the framework of flux balance analysis, we predict environments in which either one or both microbes in a pair would not be able to grow without the other, inducing commensal (one-way) or mutualistic (two-way) interactions, respectively. Our algorithms can successfully recapitulate known inter-microbial interactions, and predict millions of new ones across any pair amongst different microbial species. Surprisingly, we find that it is always possible to identify conditions that induce mutualistic or commensal interactions between any two species. Hence, our method should help in mapping naturally occurring microbe-microbe interactions, and in engineering new ones through a novel, environment-driven branch of synthetic ecology.
PMCID: PMC2987903  PMID: 21124952
23.  Signatures of Arithmetic Simplicity in Metabolic Network Architecture 
PLoS Computational Biology  2010;6(4):e1000725.
Metabolic networks perform some of the most fundamental functions in living cells, including energy transduction and building block biosynthesis. While these are the best characterized networks in living systems, understanding their evolutionary history and complex wiring constitutes one of the most fascinating open questions in biology, intimately related to the enigma of life's origin itself. Is the evolution of metabolism subject to general principles, beyond the unpredictable accumulation of multiple historical accidents? Here we search for such principles by applying to an artificial chemical universe some of the methodologies developed for the study of genome scale models of cellular metabolism. In particular, we use metabolic flux constraint-based models to exhaustively search for artificial chemistry pathways that can optimally perform an array of elementary metabolic functions. Despite the simplicity of the model employed, we find that the ensuing pathways display a surprisingly rich set of properties, including the existence of autocatalytic cycles and hierarchical modules, the appearance of universally preferable metabolites and reactions, and a logarithmic trend of pathway length as a function of input/output molecule size. Some of these properties can be derived analytically, borrowing methods previously used in cryptography. In addition, by mapping biochemical networks onto a simplified carbon atom reaction backbone, we find that properties similar to those predicted for the artificial chemistry hold also for real metabolic networks. These findings suggest that optimality principles and arithmetic simplicity might lie beneath some aspects of biochemical complexity.
Author Summary
Metabolism is the network of biochemical reactions that transforms available resources (“inputs”) into energy currency and building blocks (“outputs”). Different organisms have different assortments of metabolic pathways and input/output requirements, reflecting their adaptation to specific environments, and to specific strategies for reproduction and survival. Here we ask whether, beneath the intricate wiring of these networks, it is possible to discern signatures of optimal (i.e., shortest and maximally efficient) pathway architectures. A systematic search for such optimal pathways between all possible pairs of input and output molecules in real organic chemistry is computationally intractable. However, we can implement such a search in a simple artificial chemistry, which roughly resembles a single atom (e.g., carbon) version of real biochemistry. We find that optimal pathways in our idealized chemistry display a logarithmic dependence of pathway length on input/output molecule size. They also display recurring topologies, including autocatalytic cycles reminiscent of ancient and highly conserved cores of real biochemistry. Finally, across all optimal pathways, we identify universally important metabolites and reactions, as well as a characteristic distribution of reaction utilization. Similar features can be observed in real metabolic networks, suggesting that arithmetic simplicity may lie beneath some aspects of biochemical complexity.
PMCID: PMC2848538  PMID: 20369010
24.  Metabolic Network Model of a Human Oral Pathogen▿ ‡  
Journal of Bacteriology  2008;191(1):74-90.
The microbial community present in the human mouth is engaged in a complex network of diverse metabolic activities. In addition to serving as energy and building-block sources, metabolites are key players in interspecies and host-pathogen interactions. Metabolites are also implicated in triggering the local inflammatory response, which can affect systemic conditions such as atherosclerosis, obesity, and diabetes. While the genome of several oral pathogens has been sequenced, quantitative understanding of the metabolic functions of any oral pathogen at the system level has not been explored yet. Here we pursue the computational construction and analysis of the genome-scale metabolic network of Porphyromonas gingivalis, a gram-negative anaerobe that is endemic in the human population and largely responsible for adult periodontitis. Integrating information from the genome, online databases, and literature screening, we built a stoichiometric model that encompasses 679 metabolic reactions. By using flux balance approaches and automated network visualization, we analyze the growth capacity under amino-acid-rich medium and provide evidence that amino acid preference and cytotoxic by-product secretion rates are suitably reproduced by the model. To provide further insight into the basic metabolic functions of P. gingivalis and suggest potential drug targets, we study systematically how the network responds to any reaction knockout. We focus specifically on the lipopolysaccharide biosynthesis pathway and identify eight putative targets, one of which has been recently verified experimentally. The current model, which is amenable to further experimental testing and refinements, could prove useful in evaluating the oral microbiome dynamics and in the development of novel biomedical applications.
PMCID: PMC2612419  PMID: 18931137
25.  Model-driven analysis of experimentally determined growth phenotypes for 465 yeast gene deletion mutants under 16 different conditions 
Genome Biology  2008;9(9):R140.
An iterative approach that integrates high-throughput measurements of yeast deletion mutants and flux balance model predictions improves understanding of both experimental and computational results.
Understanding the response of complex biochemical networks to genetic perturbations and environmental variability is a fundamental challenge in biology. Integration of high-throughput experimental assays and genome-scale computational methods is likely to produce insight otherwise unreachable, but specific examples of such integration have only begun to be explored.
In this study, we measured growth phenotypes of 465 Saccharomyces cerevisiae gene deletion mutants under 16 metabolically relevant conditions and integrated them with the corresponding flux balance model predictions. We first used discordance between experimental results and model predictions to guide a stage of experimental refinement, which resulted in a significant improvement in the quality of the experimental data. Next, we used discordance still present in the refined experimental data to assess the reliability of yeast metabolism models under different conditions. In addition to estimating predictive capacity based on growth phenotypes, we sought to explain these discordances by examining predicted flux distributions visualized through a new, freely available platform. This analysis led to insight into the glycerol utilization pathway and the potential effects of metabolic shortcuts on model results. Finally, we used model predictions and experimental data to discriminate between alternative raffinose catabolism routes.
Our study demonstrates how a new level of integration between high throughput measurements and flux balance model predictions can improve understanding of both experimental and computational results. The added value of a joint analysis is a more reliable platform for specific testing of biological hypotheses, such as the catabolic routes of different carbon sources.
PMCID: PMC2592718  PMID: 18808699

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