An integrative, multi-scale, genome-wide model reveals the phenotypic landscape of Escherichia coli.

Given the vast behavioral repertoire and biological complexity of even the simplest organisms, accurately predicting phenotypes in novel environments and unveiling their biological organization is a challenging endeavor. Here, we present an integrative modeling methodology that unifies under a common framework the various biological processes and their interactions across multiple layers. We trained this methodology on an extensive normalized compendium for the gram-negative bacterium Escherichia coli, which incorporates gene expression data for genetic and environmental perturbations, transcriptional regulation, signal transduction, and metabolic pathways, as well as growth measurements. Comparison with measured growth and high-throughput data demonstrates the enhanced ability of the integrative model to predict phenotypic outcomes in various environmental and genetic conditions, even in cases where their underlying functions are under-represented in the training set. This work paves the way toward integrative techniques that extract knowledge from a variety of biological data to achieve more than the sum of their parts in the context of prediction, analysis, and redesign of biological systems

Constrained Allocation Flux Balance Analysis

New experimental results on bacterial growth inspire a novel top-down approach to study cell metabolism, combining mass balance and proteomic constraints to extend and complement Flux Balance Analysis. We introduce here Constrained Allocation Flux Balance Analysis, CAFBA, in which the biosynthetic costs associated to growth are accounted for in an effective way through a single additional genome-wide constraint. Its roots lie in the experimentally observed pattern of proteome allocation for metabolic functions, allowing to bridge regulation and metabolism in a transparent way under the principle of growth-rate maximization. We provide a simple method to solve CAFBA efficiently and propose an "ensemble averaging" procedure to account for unknown protein costs. Applying this approach to modeling E. coli metabolism, we find that, as the growth rate increases, CAFBA solutions cross over from respiratory, growth-yield maximizing states (preferred at slow growth) to fermentative states with carbon overflow (preferred at fast growth). In addition, CAFBA allows for quantitatively accurate predictions on the rate of acetate excretion and growth yield based on only 3 parameters determined by empirical growth laws.Comment: 21 pages, 6 figures (main) + 33 pages, various figures and tables (supporting); for the supplementary MatLab code, see http://tinyurl.com/h763es

Dynamic optimization of metabolic networks coupled with gene expression

The regulation of metabolic activity by tuning enzyme expression levels is crucial to sustain cellular growth in changing environments. Metabolic networks are often studied at steady state using constraint-based models and optimization techniques. However, metabolic adaptations driven by changes in gene expression cannot be analyzed by steady state models, as these do not account for temporal changes in biomass composition. Here we present a dynamic optimization framework that integrates the metabolic network with the dynamics of biomass production and composition, explicitly taking into account enzyme production costs and enzymatic capacity. In contrast to the established dynamic flux balance analysis, our approach allows predicting dynamic changes in both the metabolic fluxes and the biomass composition during metabolic adaptations. We applied our algorithm in two case studies: a minimal nutrient uptake network, and an abstraction of core metabolic processes in bacteria. In the minimal model, we show that the optimized uptake rates reproduce the empirical Monod growth for bacterial cultures. For the network of core metabolic processes, the dynamic optimization algorithm predicted commonly observed metabolic adaptations, such as a diauxic switch with a preference ranking for different nutrients, re-utilization of waste products after depletion of the original substrate, and metabolic adaptation to an impending nutrient depletion. These examples illustrate how dynamic adaptations of enzyme expression can be predicted solely from an optimization principle

Essential plasticity and redundancy of metabolism unveiled by synthetic lethality analysis

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 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.Comment: 22 pages, 4 figure

Flux imbalance analysis and the sensitivity of cellular growth to changes in metabolite pools

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.Published versio

Coupling metabolic footprinting and flux balance analysis to predict how single gene knockouts perturb microbial metabolism

Tese de mestrado. Biologia (Bioinformática e Biologia Computacional). Universidade de Lisboa, Faculdade de Ciências, 2012The model organisms Caenorhabditis elegans and E. coli form one of the simplest gut microbe host interaction models. Interventions in the microbe that increase the host longevity including inhibition of folate synthesis have been reported previously. To find novel single gene knockouts with an effect on lifespan, a screen of the Keio collection of E. coli was undertaken, and some of the genes found are directly involved in metabolism. The next step in those specific cases is to understand how these mutations perturb metabolism systematically, so that hypotheses can be generated. For that, I employed dynamic Flux Balance Analysis (dFBA), a constraint-based modeling technique capable of simulating the dynamics of metabolism in a batch culture and making predictions about changes in intracellular flux distribution. Since the specificities of the C. elegans lifespan experiments demand us to culture microbes in conditions differing from most of the published literature on E. coli physiology, novel data must be acquired to characterize and make dFBA simulations as realistic as possible. To do this exchange fluxes were measured using quantitative H NMR Time-Resolved Metabolic Footprinting. Furthermore, I also investigate the combination of TReF and dFBA as a tool in microbial metabolism studies. These approaches were tested by comparing wild type E. coli with one of the knockout strains found, ΔmetL, a knockout of the metL gene which encodes a byfunctional enzyme involved in aspartate and threonine metabolism. I found that the strain exhibits a slower growth rate than the wild type. Model simulation results revealed that reduced homoserine and methionine synthesis, as well as impaired sulfur and folate metabolism are the main effects of this knockout and the reasons for the growth deficiency. These results indicate that there are common mechanisms of the lifespan extension between ΔmetL and inhibition of folate biosynthesis and that the flux balance analysis/metabolic footprinting approach can help us understand the nature of these mechanisms.Os organismos modelo Caenorhabditis elegans e E. coli formam um dos modelos mais simples de interacções entre micróbio do tracto digestivo e hospedeiro. Intervenções no micróbio capazes de aumentar a longevidade do hospedeiro, incluindo inibição de síntese de folatos, foram reportadas previamente. Para encontrar novas delecções génicas do micróbio capazes de aumentar a longevidade do hospedeiro, a colecção Keio de deleções génicas de E. coli foi rastreada. Alguns dos genes encontrados participam em processos metabólicos, e nesses casos, o próximpo passo é perceber como as deleções perturbam o metabolismo sistémicamente, para gerar hipóteses. Para isso, utilizo dynamic Flux Balance Analysis (dFBA), uma técnica de modelação metabólica capaz de fazer previsões sobre alterações na distribuição intracelular de fluxos. As especificidades das experiências de tempo de vida em C.elegans obrigam-nos a trabalhar em condições diferentes das usadas na maioria da literatura publicada em fisiologia de E. coli, e para dar o máximo realismo às simulações de dFBA novos dados foram adquiridos, utilizando H NMR Time-Resolved Metabolic Footprinting para medir fluxos de troca de metabolitos entre microorganismo e meio de cultura. A combinação de TReF e dFBA como ferramenta de estudo do metabolism microbiano é também investigada. Estas abordagens foram testadas ao comparar E. coli wild-type com uma das estirpes encontradas no rastreio, ΔmetL, knockout do gene metL, que codifica um enzima bifunctional participante no metabolismo de aspartato e treonina, e que exibe uma taxa de crescimento reduzida comparativamente ao wild-type. Os resultados das simulações revelaram que os principais efeitos da deleção deste gene, e as razões para a menor taxa de crescimento observada, são a produção reduzida de homoserina e metionina e os efeitos que provoca no metabolismo de folatos e enxofre. Estes resultados indicam que há mecanismos comuns na extensão da longevidade causada por esta deleção e inibição de síntese de folatos, e que a combinação metabolic footprinting/flux balance analysis pode ajudar-nos a compreender a natureza desses mecanismos

Fundamental Principles in Bacterial Physiology - History, Recent progress, and the Future with Focus on Cell Size Control: A Review

Bacterial physiology is a branch of biology that aims to understand overarching principles of cellular reproduction. Many important issues in bacterial physiology are inherently quantitative, and major contributors to the field have often brought together tools and ways of thinking from multiple disciplines. This article presents a comprehensive overview of major ideas and approaches developed since the early 20th century for anyone who is interested in the fundamental problems in bacterial physiology. This article is divided into two parts. In the first part (Sections 1 to 3), we review the first `golden era' of bacterial physiology from the 1940s to early 1970s and provide a complete list of major references from that period. In the second part (Sections 4 to 7), we explain how the pioneering work from the first golden era has influenced various rediscoveries of general quantitative principles and significant further development in modern bacterial physiology. Specifically, Section 4 presents the history and current progress of the `adder' principle of cell size homeostasis. Section 5 discusses the implications of coarse-graining the cellular protein composition, and how the coarse-grained proteome `sectors' re-balance under different growth conditions. Section 6 focuses on physiological invariants, and explains how they are the key to understanding the coordination between growth and the cell cycle underlying cell size control in steady-state growth. Section 7 overviews how the temporal organization of all the internal processes enables balanced growth. In the final Section 8, we conclude by discussing the remaining challenges for the future in the field.Comment: Published in Reports on Progress in Physics. (https://doi.org/10.1088/1361-6633/aaa628) 96 pages, 48 figures, 7 boxes, 715 reference

Statistical mechanics for metabolic networks during steady-state growth

Which properties of metabolic networks can be derived solely from stoichiometric information about the network's constituent reactions? Predictive results have been obtained by Flux Balance Analysis (FBA), by postulating that cells set metabolic fluxes within the allowed stoichiometry so as to maximize their growth. Here, we generalize this framework to single cell level using maximum entropy models from statistical physics. We define and compute, for the core metabolism of Escherichia coli, a joint distribution over all fluxes that yields the experimentally observed growth rate. This solution, containing FBA as a limiting case, provides a better match to the measured fluxes in the wild type and several mutants. We find that E. coli metabolism is close to, but not at, the optimality assumed by FBA. Moreover, our model makes a wide range of predictions: (i) on flux variability, its regulation, and flux correlations across individual cells; (ii) on the relative importance of stoichiometric constraints vs. growth rate optimization; (iii) on quantitative scaling relations for singe-cell growth rate distributions. We validate these scaling predictions using data from individual bacterial cells grown in a microfluidic device at different sub-inhibitory antibiotic concentrations. Under mild dynamical assumptions, fluctuation-response relations further predict the autocorrelation timescale in growth data and growth rate adaptation times following an environmental perturbation.Comment: 12 pages, 4 figure