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

Enzyme economy in metabolic networks

Metabolic systems are governed by a compromise between metabolic benefit and enzyme cost. This hypothesis and its consequences can be studied by kinetic models in which enzyme profiles are chosen by optimality principles. In enzyme-optimal states, active enzymes must provide benefits: a higher enzyme level must provide a metabolic benefit to justify the additional enzyme cost. This entails general relations between metabolic fluxes, reaction elasticities, and enzyme costs, the laws of metabolic economics. The laws can be formulated using economic potentials and loads, state variables that quantify how metabolites, reactions, and enzymes affect the metabolic performance in a steady state. Economic balance equations link them to fluxes, reaction elasticities, and enzyme levels locally in the network. Economically feasible fluxes must be free of futile cycles and must lead from lower to higher economic potentials, just like thermodynamics makes them lead from higher to lower chemical potentials. Metabolic economics provides algebraic conditions for economical fluxes, which are independent of the underlying kinetic models. It justifies and extends the principle of minimal fluxes and shows how to construct kinetic models in enzyme-optimal states, where all enzymes have a positive influence on the metabolic performance

Metabolic network percolation quantifies biosynthetic capabilities across the human oral microbiome

The biosynthetic capabilities of microbes underlie their growth and interactions, playing a prominent role in microbial community structure. For large, diverse microbial communities, prediction of these capabilities is limited by uncertainty about metabolic functions and environmental conditions. To address this challenge, we propose a probabilistic method, inspired by percolation theory, to computationally quantify how robustly a genome-derived metabolic network produces a given set of metabolites under an ensemble of variable environments. We used this method to compile an atlas of predicted biosynthetic capabilities for 97 metabolites across 456 human oral microbes. This atlas captures taxonomically-related trends in biomass composition, and makes it possible to estimate inter-microbial metabolic distances that correlate with microbial co-occurrences. We also found a distinct cluster of fastidious/uncultivated taxa, including several Saccharibacteria (TM7) species, characterized by their abundant metabolic deficiencies. By embracing uncertainty, our approach can be broadly applied to understanding metabolic interactions in complex microbial ecosystems.T32GM008764 - NIGMS NIH HHS; T32 GM008764 - NIGMS NIH HHS; R01 DE024468 - NIDCR NIH HHS; R01 GM121950 - NIGMS NIH HHS; DE-SC0012627 - Biological and Environmental Research; RGP0020/2016 - Human Frontier Science Program; NSFOCE-BSF 1635070 - National Science Foundation; HR0011-15-C-0091 - Defense Advanced Research Projects Agency; R37DE016937 - NIDCR NIH HHS; R37 DE016937 - NIDCR NIH HHS; R01GM121950 - NIGMS NIH HHS; R01DE024468 - NIDCR NIH HHS; 1457695 - National Science FoundationPublished versio

The interdependence between environment and metabolism in microbes and their ecosystems

Microbes are ubiquitous in virtually all habitats on Earth and affect human life in multiple ways, from the health-balancing role of the human microbiome, to the involvement of microbial communities in the global nitrogen and carbon cycles. The capacity of microbes to survive and grow in diverse environments relates directly to their ability to utilize available resources, be they from other microbes or from the environment itself. Hence, understanding how the environment shapes the metabolic functionality of individual microbes and complex communities constitutes an important area of research. In the first part of my thesis work, I explored how environmental nutrient composition and intracellular transcriptional regulation data can be integrated to provide insight into the temporal metabolic behavior of a bacterium through the use of genome-scale stoichiometric modeling approaches (Flux Balance Analysis). Thus I developed the method of Temporal Expression-based Analysis of Metabolism (TEAM), and applied it to Shewanella oneidensis, a bacterium studied for its important bioenergy and bioremediation applications. I found that TEAM improves on previous models' predictions of S. oneidensis metabolic fluxes, and recovers the overflow metabolism that has been seen experimentally. This study demonstrated the value of incorporating environmental context and transcriptional data for the prediction of time-dependent metabolic behavior. In the second part of my work, I extended the exploration of microbial metabolism from single species to complex communities in order to understand the robustness of metabolic functions. Specifically, I implemented novel mathematical analyses of metagenomic sequencing data to ask how functional stability of microbial communities could ensue despite large taxonomic variability. Upon representing in matrix form the metabolic capabilities of all genera found in 202 available metabolic ecosystem datasets, I compared the different communities with each other and with various randomized analogues. My results reveal new connections between the abundance of an organism in the community and the functions that it encodes. Furthermore, I found that genus abundances govern the metabolic robustness of a community more than the distribution of genetically encoded functions among the community members, suggesting that communities rely largely on ecological interactions to regulate their overall functionality

Quantifying biosynthetic network robustness across the human oral microbiome

Metabolic interactions, such as cross-feeding, play a prominent role in microbial communitystructure. For example, they may underlie the ubiquity of uncultivated microorganisms. We investigated this phenomenon in the human oral microbiome, by analyzing microbial metabolic networks derived from sequenced genomes. Specifically, we devised a probabilistic biosynthetic network robustness metric that describes the chance that an organism could produce a given metabolite, and used it to assemble a comprehensive atlas of biosynthetic capabilities for 88 metabolites across 456 human oral microbiome strains. A cluster of organisms characterized by reduced biosynthetic capabilities stood out within this atlas. This cluster included several uncultivated taxa and three recently co-cultured Saccharibacteria (TM7) phylum species. Comparison across strains also allowed us to systematically identify specific putative metabolic interdependences between organisms. Our method, which provides a new way of converting annotated genomes into metabolic predictions, is easily extendible to other microbial communities and metabolic products.https://www.biorxiv.org/content/10.1101/392621v1First author draf

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

Modelling and multiobjective optimization for simulation of cyanobacterial metabolism

The present thesis is devoted to the development of models and algorithms to improve metabolic simulations of cyanobacterial metabolism. Cyanobacteria are photosynthetic bacteria of great biotechnological interest to the development of sustainable bio-based manufacturing processes. For this purpose, it is fundamental to understand metabolic behaviour of these organisms, and constraint-based metabolic modelling techniques offer a platform for analysis and assessment of cell's metabolic functionality. Reliable simulations are needed to enhance the applicability of the results, and this is the main goal of this thesis. This dissertation has been structured in three parts. The first part is devoted to introduce needed fundamentals of the disciplines that are combined in this work: metabolic modelling, cyanobacterial metabolism and multi-objective optimisation. In the second part the reconstruction and update of metabolic models of two cyanobacterial strains is addressed. These models are then used to perform metabolic simulations with the application of the classic Flux Balance Analysis (FBA) methodology. The studies conducted in this part are useful to illustrate the uses and applications of metabolic simulations for the analysis of living organisms. And at the same time they serve to identify important limitations of classic simulation techniques based on mono-objective linear optimisation that motivate the search of new strategies. Finally, in the third part a novel approach is defined based on the application of multi-objective optimisation procedures to metabolic modelling. Main steps in the definition of multi-objective problem and the description of an optimisation algorithm that ensure the applicability of the obtained results, as well as the multi-criteria analysis of the solutions are covered. The resulting tool allows the definition of non-linear objective functions and constraints, as well as the analysis of multiple Pareto-optimal solutions. It avoids some of the main drawbacks of classic methodologies, leading to more flexible simulations and more realistic results. Overall this thesis contributes to the advance in the study of cyanobacterial metabolism by means of definition of models and strategies that improve plasticity and predictive capacities of metabolic simulations.La presente tesis está dedicada al desarrollo de modelos y algoritmos para mejorar las simulaciones metabólicas de cianobacterias. Las cianobacterias son bacterias fotosintéticas de gran interés biotecnológico para el desarrollo de bioprocesos productivos sostenibles. Para este propósito, es fundamental entender el comportamiento metabólico de estos organismos, y el modelado metabólico basado en restricciones ofrece una plataforma para el análisis y la evaluación de las funcionalidades metabólicas de las células. Se necesitan simulaciones fidedignas para aumentar la aplicabilidad de los resultados, y este es el objetivo principal de esta tesis. Esta disertación se ha estructurado en tres partes. La primera parte está dedicada a introducir los fundamentos necesarios de las disciplinas que se combinan en este trabajo: el modelado metabólico, el metabolismo de cianobacterias, y la optimización multiobjetivo. En la segunda parte, se encara la reconstrucción y la actualización de los modelos metabólicos de dos cepas de cianobacterias. Estos modelos se usan después para llevar a cabo simulaciones metabólicas con la aplicación de la metodología clásica Flux Balance Analysis (FBA). Los estudios realizados en esta parte son útiles para ilustrar los usos y aplicaciones de las simulaciones metabólicas para el análisis de los organismos vivos. Y al mismo tiempo sirven para identificar importantes limitaciones de las técnicas clásicas de simulación basadas en optimización lineal mono-objetivo que motivan la búsqueda de nuevas estrategias. Finalmente, en la tercera parte, se define una nueva aproximación basada en la aplicación al modelado metabólico de procedimientos de optimización multiobjetivo. Se cubren los principales pasos en la definición de un problema multiobjetivo y la descripción de un algoritmo de optimización que aseguren la aplicabilidad de los resultados obtenidos, así como el análisis multi-criterio de las soluciones. La herramienta resultante permite la definición de funciones objetivo y restricciones no lineales, así como el análisis de múltiples soluciones en el sentido de Pareto. Esta herramienta evita algunos de los principales inconvenientes de las metodologías clásicas, lo que lleva a obtener simulaciones más flexibles y resultados más realistas. En conjunto, esta tesis contribuye al avance en el estudio del metabolismo de cianobacterias por medio de la definición de modelos y estrategias que mejoran la plasticidad y las capacidades predictivas de las simulaciones metabólicas.La present tesi està dedicada al desenvolupament de models i algorismes per a millorar les simulacions metabòliques de cianobacteris. Els cianobacteris són bacteris fotosintètics de gran interés biotecnològic per al desenvolupament de bioprocessos productius sostenibles. Per a aquest propòsit, és fonamental entendre el comportament metabòlic d'aquests organismes, i el modelatge metabòlic basat en restriccions ofereix una plataforma per a l'anàlisi i l'avaluació de les funcionalitats metabòliques de les cèl·lules. Es necessiten simulacions fidedignes per a augmentar l'aplicabilitat dels resultats, i aquest és l'objectiu principal d'aquesta tesi. Aquesta dissertació s'ha estructurat en tres parts. La primera part està dedicada a introduir els fonaments necessaris de les disciplines que es combinen en aquest treball: el modelatge metabòlic, el metabolisme de cianobacteris i l'optimització multiobjectiu. En la segona part, s'adreça la reconstrucció i l'actualització dels models metabòlics de dos soques de cianobacteris. Aquests models s'empren després per a portar a terme simulacions metabòliques amb l'aplicació de la metodologia clàssica Flux Balance Analysis (FBA). Els estudis realitzats en aquesta part són útils per a il·lustrar els usos i aplicacions de les simulacions metabòliques per a l'anàlisi dels organismes vius. I al mateix temps serveixen per a identificar importants limitacions de les tècniques clàssiques de simulació basades en optimització lineal mono-objectiu que motiven la cerca de noves estratègies. Finalment, en la tercera part, es defineix una nova aproximació basada en l'aplicació al modelatge metabòlic de procediments d'optimització multiobjectiu. Es cobreixen els principals passos en la definició d'un problema multiobjectiu i la descripció d'un algorisme d'optimització que asseguren l'aplicabilitat dels resultats obtinguts, així com l'anàlisi multi-criteri de les solucions. La ferramenta resultant permet la definició de funcions objectiu i restriccions no lineals, així com l'anàlisi de múltiples solucions òptimes en el sentit de Pareto. Aquesta ferramenta evita alguns dels principals inconvenients de les metodologies clàssiques, el que porta a obtenir simulacions més flexibles i resultats més realistes. En conjunt, aquesta tesi contribueix a l'avanç en l'estudi del metabolisme de cianobacteris per mitjà de la definició de models i estratègies que milloren la plasticitat i les capacitats predictives de les simulacions metabòliques.Siurana Paula, M. (2017). Modelling and multiobjective optimization for simulation of cyanobacterial metabolism [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/9057