Complete enumeration of elementary flux modes through scalable demand-based subnetwork definition

Logic programming-based Minimal Cut Sets reveal consortium-level therapeutic targets for chronic wound infections

Minimal Cut Sets (MCSs) identify sets of reactions which, when removed from a metabolic network, disable certain cellular functions. The traditional search for MCSs within genome-scale metabolic models (GSMMs) targets cellular growth, identifies reaction sets resulting in a lethal phenotype if disrupted, and retrieves a list of corresponding gene, mRNA, or enzyme targets. Using the dual link between MCSs and Elementary Flux Modes (EFMs), our logic programming-based tool aspefm was able to compute MCSs of any size from GSMMs in acceptable run times. The tool demonstrated better performance when computing large-sized MCSs than the mixed-integer linear programming methods. We applied the new MCSs methodology to a medically-relevant consortium model of two cross-feeding bacteria, Staphylococcus aureus and Pseudomonas aeruginosa. aspefm constraints were used to bias the computation of MCSs toward exchanged metabolites that could complement lethal phenotypes in individual species. We found that interspecies metabolite exchanges could play an essential role in rescuing single-species growth, for instance inosine could complement lethal reaction knock-outs in the purine synthesis, glycolysis, and pentose phosphate pathways of both bacteria. Finally, MCSs were used to derive a list of promising enzyme targets for consortium-level therapeutic applications that cannot be circumvented via interspecies metabolite exchange.

A Markov constraint to uniquely identify elementary flux mode weights in unimolecular metabolic networks

Elementary flux modes (EFMs) are minimal, steady state pathways characterizing a flux network. Fundamentally, all steady state fluxes in a network are decomposable into a linear combination of EFMs. While there is typically no unique set of EFM weights that reconstructs these fluxes, several optimization-based methods have been proposed to constrain the solution space by enforcing some notion of parsimony. However, it has long been recognized that optimization-based approaches may fail to uniquely identify EFM weights and return different feasible solutions across objective functions and solvers. Here we show that, for flux networks only involving single molecule transformations, these problems can be avoided by imposing a Markovian constraint on EFM weights. Our Markovian constraint guarantees a unique solution to the flux decomposition problem, and that solution is arguably more biophysically plausible than other solutions. We describe an algorithm for computing Markovian EFM weights via steady state analysis of a certain discrete-time Markov chain, based on the flux network, which we call the cycle-history Markov chain. We demonstrate our method with a differential analysis of EFM activity in a lipid metabolic network comparing healthy and Alzheimer's disease patients. Our method is the first to uniquely decompose steady state fluxes into EFM weights for any unimolecular metabolic network.

Combining Kinetic and Constraint-Based Modelling to Better Understand Metabolism Dynamics

To understand the phenotypic capabilities of organisms, it is useful to characterise cellular metabolism through the analysis of its pathways. Dynamic mathematical modelling of metabolic networks is of high interest as it provides the time evolution of the metabolic components. However, it also has limitations, such as the necessary mechanistic details and kinetic parameters are not always available. On the other hand, large metabolic networks exhibit a complex topological structure which can be studied rather efficiently in their stationary regime by constraint-based methods. These methods produce useful predictions on pathway operations. In this review, we present both modelling techniques and we show how they bring complementary views of metabolism. In particular, we show on a simple example how both approaches can be used in conjunction to shed some light on the dynamics of metabolic networks.

Boosting Biomass Quantity and Quality by Improved Mixotrophic Culture of the Diatom Phaeodactylum tricornutum

Diatoms are photoautotrophic unicellular algae and are among the most abundant, adaptable, and diverse marine phytoplankton. They are extremely interesting not only for their ecological role but also as potential feedstocks for sustainable biofuels and high-value commodities such as omega fatty acids, because of their capacity to accumulate lipids. However, the cultivation of microalgae on an industrial scale requires higher cell densities and lipid accumulation than those found in nature to make the process economically viable. One of the known ways to induce lipid accumulation in Phaeodactylum tricornutum is nitrogen deprivation, which comes at the expense of growth inhibition and lower cell density. Thus, alternative ways need to be explored to enhance the lipid production as well as biomass density to make them sustainable at industrial scale. In this study, we have used experimental and metabolic modeling approaches to optimize the media composition, in terms of elemental composition, organic and inorganic carbon sources, and light intensity, that boost both biomass quality and quantity of P. tricornutum. Eventually, the optimized conditions were scaled-up to 2 L photobioreactors, where a better system control (temperature, pH, light, aeration/mixing) allowed a further improvement of the biomass capacity of P. tricornutum to 12 g/L.

Unlocking Elementary Conversion Modes: ecmtool Unveils All Capabilities of Metabolic Networks

The metabolic capabilities of cells determine their biotechnological potential, fitness in ecosystems, pathogenic threat levels, and function in multicellular organisms. Their comprehensive experimental characterization is generally not feasible, particularly for unculturable organisms. In principle, the full range of metabolic capabilities can be computed from an organism's annotated genome using metabolic network reconstruction. However, current computational methods cannot deal with genome-scale metabolic networks. Part of the problem is that these methods aim to enumerate all metabolic pathways, while computation of all (elementally balanced) conversions between nutrients and products would suffice. Indeed, the elementary conversion modes (ECMs, defined by Urbanczik and Wagner) capture the full metabolic capabilities of a network, but the use of ECMs has not been accessible until now. We explain and extend the theory of ECMs, implement their enumeration in ecmtool, and illustrate their applicability. This work contributes to the elucidation of the full metabolic footprint of any cell.

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Elementary conversion modes (ECMs) specify all metabolic capabilities of any organism

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Ecmtool computes all ECMs from a reconstructed metabolic network

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ECM enumeration enables metabolic characterization of larger networks than ever

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Focusing on ECMs between relevant metabolites even enables genome-scale enumeration

Understanding the metabolic capabilities of cells is of profound importance. Microbial metabolism shapes global cycles of elements and cleans polluted soils. Human and pathogen metabolism affects our health. Recent advances allow for automatic reconstruction of reaction networks for any organism, which is already used in synthetic biology, (food) microbiology, and agriculture to compute optimal yields from resources to products. However, computational tools are limited to optimal states or subnetworks, leaving many capabilities of organisms hidden. Our program, ecmtool, creates a blueprint of any organism's metabolic functionalities, drastically improving insights obtained from genome sequences. Ecmtool may become essential in exploratory research, especially for studying cells that are not culturable in laboratory conditions. Ideally, elementary conversion mode enumeration will someday be a standard step after metabolic network reconstruction, achieving the metabolic characterization of all known organisms.

Answer Set Programming for Computing Constraints-Based Elementary Flux Modes: Application to Escherichia coli Core Metabolism

Elementary Flux Modes (EFMs) provide a rigorous basis to systematically characterize the steady state, cellular phenotypes, as well as metabolic network robustness and fragility. However, the number of EFMs typically grows exponentially with the size of the metabolic network, leading to excessive computational demands, and unfortunately, a large fraction of these EFMs are not biologically feasible due to system constraints. This combinatorial explosion often prevents the complete analysis of genome-scale metabolic models. Traditionally, EFMs are computed by the double description method, an efficient algorithm based on matrix calculation; however, only a few constraints can be integrated into this computation. They must be monotonic with regard to the set inclusion of the supports; otherwise, they must be treated in post-processing and thus do not save computational time. We present aspefm, a hybrid computational tool based on Answer Set Programming (ASP) and Linear Programming (LP) that permits the computation of EFMs while implementing many different types of constraints. We apply our methodology to the Escherichia coli core model, which contains 226×106 EFMs. In considering transcriptional and environmental regulation, thermodynamic constraints, and resource usage considerations, the solution space is reduced to 1118 EFMs that can be computed directly with aspefm. The solution set, for E. coli growth on O2 gradients spanning fully aerobic to anaerobic, can be further reduced to four optimal EFMs using post-processing and Pareto front analysis.

Boosting the extraction of elementary flux modes in genome-scale metabolic networks using the linear programming approach

MOTIVATION

Elementary flux modes (EFMs) are a key tool for analyzing genome-scale metabolic networks, and several methods have been proposed to compute them. Among them, those based on solving linear programming (LP) problems are known to be very efficient if the main interest lies in computing large enough sets of EFMs.

RESULTS

Here, we propose a new method called EFM-Ta that boosts the efficiency rate by analyzing the information provided by the LP solver. We base our method on a further study of the final tableau of the simplex method. By performing additional elementary steps and avoiding trivial solutions consisting of two cycles, we obtain many more EFMs for each LP problem posed, improving the efficiency rate of previously proposed methods by more than one order of magnitude.

AVAILABILITY AND IMPLEMENTATION

Software is freely available at https://github.com/biogacop/Boost_LP_EFM.

CONTACT

fguil@um.es.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

EFMviz: A COBRA Toolbox extension to visualize Elementary Flux Modes in Genome-Scale Metabolic Models

Elementary Flux Modes (EFMs) are a tool for constraint-based modeling and metabolic network analysis. However, systematic and automated visualization of EFMs, capable of integrating various data types is still a challenge. In this study, we developed an extension for the widely adopted COBRA Toolbox, EFMviz, for analysis and graphical visualization of EFMs as networks of reactions, metabolites and genes. The analysis workflow offers a platform for EFM visualization to improve EFM interpretability by connecting COBRA toolbox with the network analysis and visualization software Cytoscape. The biological applicability of EFMviz is demonstrated in two use cases on medium (Escherichia coli, iAF1260) and large (human, Recon 2.2) genome-scale metabolic models. EFMviz is open-source and integrated into COBRA Toolbox. The analysis workflows used for the two use cases are detailed in the two tutorials provided with EFMviz along with the data used in this study.

Flux tope analysis: studying the coordination of reaction directions in metabolic networks

Motivation

Elementary flux mode (EFM) analysis allows an unbiased description of metabolic networks in terms of minimal pathways (involving a minimal set of reactions). To date, the enumeration of EFMs is impracticable in genome-scale metabolic models. In a complementary approach, we introduce the concept of a flux tope (FT), involving a maximal set of reactions (with fixed directions), which allows one to study the coordination of reaction directions in metabolic networks and opens a new way for EFM enumeration.

Results

A FT is a (nontrivial) subset of the flux cone specified by fixing the directions of all reversible reactions. In a consistent metabolic network (without unused reactions), every FT contains a 'maximal pathway', carrying flux in all reactions. This decomposition of the flux cone into FTs allows the enumeration of EFMs (of individual FTs) without increasing the problem dimension by reaction splitting. To develop a mathematical framework for FT analysis, we build on the concepts of sign vectors and hyperplane arrangements. Thereby, we observe that FT analysis can be applied also to flux optimization problems involving additional (inhomogeneous) linear constraints. For the enumeration of FTs, we adapt the reverse search algorithm and provide an efficient implementation. We demonstrate that (biomass-optimal) FTs can be enumerated in genome-scale metabolic models of B.cuenoti and E.coli, and we use FTs to enumerate EFMs in models of M.genitalium and B.cuenoti.

Availability and implementation

The source code is freely available at https://github.com/mpgerstl/FTA.

Supplementary information

Supplementary data are available at Bioinformatics online.

Investigating mixotrophic metabolism in the model diatom Phaeodactylum tricornutum

Diatoms are prominent marine microalgae, interesting not only from an ecological point of view, but also for their possible use in biotechnology applications. They can be cultivated in phototrophic conditions, using sunlight as the sole energy source. Some diatoms, however, can also grow in a mixotrophic mode, wherein both light and external reduced carbon contribute to biomass accumulation. In this study, we investigated the consequences of mixotrophy on the growth and metabolism of the pennate diatom Phaeodactylum tricornutum, using glycerol as the source of reduced carbon. Transcriptomics, metabolomics, metabolic modelling and physiological data combine to indicate that glycerol affects the central-carbon, carbon-storage and lipid metabolism of the diatom. In particular, provision of glycerol mimics typical responses of nitrogen limitation on lipid metabolism at the level of triacylglycerol accumulation and fatty acid composition. The presence of glycerol, despite provoking features reminiscent of nutrient limitation, neither diminishes photosynthetic activity nor cell growth, revealing essential aspects of the metabolic flexibility of these microalgae and suggesting possible biotechnological applications of mixotrophy.This article is part of the themed issue 'The peculiar carbon metabolism in diatoms'.

Sequential computation of elementary modes and minimal cut sets in genome-scale metabolic networks using alternate integer linear programming

Motivation

Elementary (flux) modes (EMs) have served as a valuable tool for investigating structural and functional properties of metabolic networks. Identification of the full set of EMs in genome-scale networks remains challenging due to combinatorial explosion of EMs in complex networks. It is often, however, that only a small subset of relevant EMs needs to be known, for which optimization-based sequential computation is a useful alternative. Most of the currently available methods along this line are based on the iterative use of mixed integer linear programming (MILP), the effectiveness of which significantly deteriorates as the number of iterations builds up. To alleviate the computational burden associated with the MILP implementation, we here present a novel optimization algorithm termed alternate integer linear programming (AILP).

Results

Our algorithm was designed to iteratively solve a pair of integer programming (IP) and linear programming (LP) to compute EMs in a sequential manner. In each step, the IP identifies a minimal subset of reactions, the deletion of which disables all previously identified EMs. Thus, a subsequent LP solution subject to this reaction deletion constraint becomes a distinct EM. In cases where no feasible LP solution is available, IP-derived reaction deletion sets represent minimal cut sets (MCSs). Despite the additional computation of MCSs, AILP achieved significant time reduction in computing EMs by orders of magnitude. The proposed AILP algorithm not only offers a computational advantage in the EM analysis of genome-scale networks, but also improves the understanding of the linkage between EMs and MCSs.

Availability and Implementation

The software is implemented in Matlab, and is provided as supplementary information .

Contact

hyunseob.song@pnnl.gov.

Supplementary information

Supplementary data are available at Bioinformatics online.

Designing Optimized Production Hosts by Metabolic Modeling

Many of the complex and expensive production steps in the chemical industry are readily available in living cells. In order to overcome the metabolic limits of these cells, the optimal genetic intervention strategies can be computed by the use of metabolic modeling. Elementary flux mode analysis (EFMA) is an ideal tool for this task, as it does not require defining a cellular objective function. We present two EFMA-based methods to optimize production hosts: (1) the standard approach that can only be used for small and medium scale metabolic networks and (2) the advanced dual system approach that can be utilized to directly compute intervention strategies in a genome-scale metabolic model.

Reconstruction of the microalga Nannochloropsis salina genome-scale metabolic model with applications to lipid production

Background

Nannochloropsis salina (= Eustigmatophyceae) is a marine microalga which has become a biotechnological target because of its high capacity to produce polyunsaturated fatty acids and triacylglycerols. It has been used as a source of biofuel, pigments and food supplements, like Omega 3. Only some Nannochloropsis species have been sequenced, but none of them benefit from a genome-scale metabolic model (GSMM), able to predict its metabolic capabilities.

Results

We present iNS934, the first GSMM for N. salina, including 2345 reactions, 934 genes and an exhaustive description of lipid and nitrogen metabolism. iNS934 has a 90% of accuracy when making simple growth/no-growth predictions and has a 15% error rate in predicting growth rates in different experimental conditions. Moreover, iNS934 allowed us to propose 82 different knockout strategies for strain optimization of triacylglycerols.

Conclusions

iNS934 provides a powerful tool for metabolic improvement, allowing predictions and simulations of N. salina metabolism under different media and genetic conditions. It also provides a systemic view of N. salina metabolism, potentially guiding research and providing context to -omics data.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-017-0441-1) contains supplementary material, which is available to authorized users.

Growth-coupled overproduction is feasible for almost all metabolites in five major production organisms

Computational modelling of metabolic networks has become an established procedure in the metabolic engineering of production strains. One key principle that is frequently used to guide the rational design of microbial cell factories is the stoichiometric coupling of growth and product synthesis, which makes production of the desired compound obligatory for growth. Here we show that the coupling of growth and production is feasible under appropriate conditions for almost all metabolites in genome-scale metabolic models of five major production organisms. These organisms comprise eukaryotes and prokaryotes as well as heterotrophic and photoautotrophic organisms, which shows that growth coupling as a strain design principle has a wide applicability. The feasibility of coupling is proven by calculating appropriate reaction knockouts, which enforce the coupling behaviour. The study presented here is the most comprehensive computational investigation of growth-coupled production so far and its results are of fundamental importance for rational metabolic engineering.

A systems-wide understanding of photosynthetic acclimation in algae and higher plants

The ability of phototrophs to colonise different environments relies on robust protection against oxidative stress, a critical requirement for the successful evolutionary transition from water to land. Photosynthetic organisms have developed numerous strategies to adapt their photosynthetic apparatus to changing light conditions in order to optimise their photosynthetic yield, which is crucial for life on Earth to exist. Photosynthetic acclimation is an excellent example of the complexity of biological systems, where highly diverse processes, ranging from electron excitation over protein protonation to enzymatic processes coupling ion gradients with biosynthetic activity, interact on drastically different timescales from picoseconds to hours. Efficient functioning of the photosynthetic apparatus and its protection is paramount for efficient downstream processes, including metabolism and growth. Modern experimental techniques can be successfully integrated with theoretical and mathematical models to promote our understanding of underlying mechanisms and principles. This review aims to provide a retrospective analysis of multidisciplinary photosynthetic acclimation research carried out by members of the Marie Curie Initial Training Project, AccliPhot, placing the results in a wider context. The review also highlights the applicability of photosynthetic organisms for industry, particularly with regards to the cultivation of microalgae. It intends to demonstrate how theoretical concepts can successfully complement experimental studies broadening our knowledge of common principles in acclimation processes in photosynthetic organisms, as well as in the field of applied microalgal biotechnology.

From elementary flux modes to elementary flux vectors: Metabolic pathway analysis with arbitrary linear flux constraints

Elementary flux modes (EFMs) emerged as a formal concept to describe metabolic pathways and have become an established tool for constraint-based modeling and metabolic network analysis. EFMs are characteristic (support-minimal) vectors of the flux cone that contains all feasible steady-state flux vectors of a given metabolic network. EFMs account for (homogeneous) linear constraints arising from reaction irreversibilities and the assumption of steady state; however, other (inhomogeneous) linear constraints, such as minimal and maximal reaction rates frequently used by other constraint-based techniques (such as flux balance analysis [FBA]), cannot be directly integrated. These additional constraints further restrict the space of feasible flux vectors and turn the flux cone into a general flux polyhedron in which the concept of EFMs is not directly applicable anymore. For this reason, there has been a conceptual gap between EFM-based (pathway) analysis methods and linear optimization (FBA) techniques, as they operate on different geometric objects. One approach to overcome these limitations was proposed ten years ago and is based on the concept of elementary flux vectors (EFVs). Only recently has the community started to recognize the potential of EFVs for metabolic network analysis. In fact, EFVs exactly represent the conceptual development required to generalize the idea of EFMs from flux cones to flux polyhedra. This work aims to present a concise theoretical and practical introduction to EFVs that is accessible to a broad audience. We highlight the close relationship between EFMs and EFVs and demonstrate that almost all applications of EFMs (in flux cones) are possible for EFVs (in flux polyhedra) as well. In fact, certain properties can only be studied with EFVs. Thus, we conclude that EFVs provide a powerful and unifying framework for constraint-based modeling of metabolic networks.

Algal Cell Factories: Approaches, Applications, and Potentials

With the advent of modern biotechnology, microorganisms from diverse lineages have been used to produce bio-based feedstocks and bioactive compounds. Many of these compounds are currently commodities of interest, in a variety of markets and their utility warrants investigation into improving their production through strain development. In this review, we address the issue of strain improvement in a group of organisms with strong potential to be productive “cell factories”: the photosynthetic microalgae. Microalgae are a diverse group of phytoplankton, involving polyphyletic lineage such as green algae and diatoms that are commonly used in the industry. The photosynthetic microalgae have been under intense investigation recently for their ability to produce commercial compounds using only light, CO₂, and basic nutrients. However, their strain improvement is still a relatively recent area of work that is under development. Importantly, it is only through appropriate engineering methods that we may see the full biotechnological potential of microalgae come to fruition. Thus, in this review, we address past and present endeavors towards the aim of creating productive algal cell factories and describe possible advantageous future directions for the field.

Modelling metabolism of the diatom Phaeodactylum tricornutum

Marine diatoms have potential as a biotechnological production platform, especially for lipid-derived products, including biofuels. Here we introduce some features of diatom metabolism, particularly with respect to photosynthesis, photorespiration and lipid synthesis and their differences relative to other photosynthetic eukaryotes. Since structural metabolic modelling of other photosynthetic organisms has been shown to be capable of representing their metabolic capabilities realistically, we briefly review the main approaches to this type of modelling. We then propose that genome-scale modelling of the diatom Phaeodactylum tricornutum, in response to varying light intensity, could uncover the novel aspects of the metabolic potential of this organism.

Exploring complex cellular phenotypes and model-guided strain design with a novel genome-scale metabolic model of Clostridium thermocellum DSM 1313 implementing an adjustable cellulosome

BACKGROUND

Clostridium thermocellum is a gram-positive thermophile that can directly convert lignocellulosic material into biofuels. The metabolism of C. thermocellum contains many branches and redundancies which limit biofuel production, and typical genetic techniques are time-consuming. Further, the genome sequence of a genetically tractable strain C. thermocellum DSM 1313 has been recently sequenced and annotated. Therefore, developing a comprehensive, predictive, genome-scale metabolic model of DSM 1313 is desired for elucidating its complex phenotypes and facilitating model-guided metabolic engineering.

RESULTS

We constructed a genome-scale metabolic model iAT601 for DSM 1313 using the KEGG database as a scaffold and an extensive literature review and bioinformatic analysis for model refinement. Next, we used several sets of experimental data to train the model, e.g., estimation of the ATP requirement for growth-associated maintenance (13.5 mmol ATP/g DCW/h) and cellulosome synthesis (57 mmol ATP/g cellulosome/h). Using our tuned model, we investigated the effect of cellodextrin lengths on cell yields, and could predict in silico experimentally observed differences in cell yield based on which cellodextrin species is assimilated. We further employed our tuned model to analyze the experimentally observed differences in fermentation profiles (i.e., the ethanol to acetate ratio) between cellobiose- and cellulose-grown cultures and infer regulatory mechanisms to explain the phenotypic differences. Finally, we used the model to design over 250 genetic modification strategies with the potential to optimize ethanol production, 6155 for hydrogen production, and 28 for isobutanol production.

CONCLUSIONS

Our developed genome-scale model iAT601 is capable of accurately predicting complex cellular phenotypes under a variety of conditions and serves as a high-quality platform for model-guided strain design and metabolic engineering to produce industrial biofuels and chemicals of interest.

Genome-Scale Model Reveals Metabolic Basis of Biomass Partitioning in a Model Diatom

Diatoms are eukaryotic microalgae that contain genes from various sources, including bacteria and the secondary endosymbiotic host. Due to this unique combination of genes, diatoms are taxonomically and functionally distinct from other algae and vascular plants and confer novel metabolic capabilities. Based on the genome annotation, we performed a genome-scale metabolic network reconstruction for the marine diatom Phaeodactylum tricornutum. Due to their endosymbiotic origin, diatoms possess a complex chloroplast structure which complicates the prediction of subcellular protein localization. Based on previous work we implemented a pipeline that exploits a series of bioinformatics tools to predict protein localization. The manually curated reconstructed metabolic network iLB1027_lipid accounts for 1,027 genes associated with 4,456 reactions and 2,172 metabolites distributed across six compartments. To constrain the genome-scale model, we determined the organism specific biomass composition in terms of lipids, carbohydrates, and proteins using Fourier transform infrared spectrometry. Our simulations indicate the presence of a yet unknown glutamine-ornithine shunt that could be used to transfer reducing equivalents generated by photosynthesis to the mitochondria. The model reflects the known biochemical composition of P. tricornutum in defined culture conditions and enables metabolic engineering strategies to improve the use of P. tricornutum for biotechnological applications.

Which sets of elementary flux modes form thermodynamically feasible flux distributions?

Elementary flux modes (EFMs) are non-decomposable steady-state fluxes through metabolic networks. Every possible flux through a network can be described as a superposition of EFMs. The definition of EFMs is based on the stoichiometry of the network, and it has been shown previously that not all EFMs are thermodynamically feasible. These infeasible EFMs cannot contribute to a biologically meaningful flux distribution. In this work, we show that a set of thermodynamically feasible EFMs need not be thermodynamically consistent. We use first principles of thermodynamics to define the feasibility of a flux distribution and present a method to compute the largest thermodynamically consistent sets (LTCSs) of EFMs. An LTCS contains the maximum number of EFMs that can be combined to form a thermodynamically feasible flux distribution. As a case study we analyze all LTCSs found in Escherichia coli when grown on glucose and show that only one LTCS shows the required phenotypical properties. Using our method, we find that in our E. coli model < 10% of all EFMs are thermodynamically relevant.

In Silico Constraint-Based Strain Optimization Methods: the Quest for Optimal Cell Factories

Shifting from chemical to biotechnological processes is one of the cornerstones of 21st century industry. The production of a great range of chemicals via biotechnological means is a key challenge on the way toward a bio-based economy. However, this shift is occurring at a pace slower than initially expected. The development of efficient cell factories that allow for competitive production yields is of paramount importance for this leap to happen. Constraint-based models of metabolism, together with in silico strain design algorithms, promise to reveal insights into the best genetic design strategies, a step further toward achieving that goal. In this work, a thorough analysis of the main in silico constraint-based strain design strategies and algorithms is presented, their application in real-world case studies is analyzed, and a path for the future is discussed.

Rational design of efficient modular cells

The modular cell design principle is formulated to devise modular (chassis) cells. These cells can be assembled with exchangeable production modules in a plug-and-play fashion to build microbial cell factories for efficient combinatorial biosynthesis of novel molecules, requiring minimal iterative strain optimization steps. A modular cell is designed to be auxotrophic, containing core metabolic pathways that are necessary but insufficient to support cell growth and maintenance. To be functional, it must tightly couple with an exchangeable production module containing auxiliary metabolic pathways that not only complement cell growth but also enhance production of targeted molecules. We developed a MODCELL (modular cell) framework based on metabolic pathway analysis to implement the modular cell design principle. MODCELL identifies genetic modifications and requirements to construct modular cell candidates and their associated exchangeable production modules. By defining the degree of similarity and coupling metrics, MODCELL can evaluate which exchangeable production module(s) can be tightly coupled with a modular cell candidate. We first demonstrated how MODCELL works in a step-by-step manner for example metabolic networks, and then applied it to design modular Escherichia coli cells for efficient combinatorial biosynthesis of five alcohols (ethanol, propanol, isopropanol, butanol and isobutanol) and five butyrate esters (ethyl butyrate, propyl butyrate, isopropyl butyrate, butyl butyrate and isobutyl butyrate) from pentose sugars (arabinose and xylose) and hexose sugars (glucose, mannose, and galactose) under anaerobic conditions. We identified three modular cells, MODCELL1, MODCELL2 and MODCELL3, that can couple well with Group 1 of modules (ethanol, isobutanol, butanol, ethyl butyrate, isobutyl butyrate, butyl butyrate), Group 2 (isopropanol, isopropyl butyrate), and Group 3 (propanol, isopropanol), respectively. We validated the design of MODCELL1 for anaerobic production of ethanol, butanol, and ethyl butyrate using experimental data available in literature.

On the feasibility of growth-coupled product synthesis in microbial strains

Enforcing obligate coupling of growth with synthesis of a desired product has become a key principle for metabolic engineering of microbial production strains. Various methods from stoichiometric and constraint-based modeling have been developed to calculate intervention strategies by which a given microorganism can only grow if it synthesizes a desired compound as a mandatory by-product. However, growth-coupled synthesis is not necessarily feasible for every compound of a metabolic network and no rigorous criterion is currently known to test feasibility of coupled product and biomass formation (before searching for suitable intervention strategies). In this work, we show which properties a network must fulfill such that strain designs guaranteeing coupled biomass and product synthesis can exist at all. In networks without flux bounds, coupling is feasible if and only if an elementary mode exists that leads to formation of both biomass and product. Setting flux boundaries leads to more complicated inhomogeneous problems. Making use of the concept of elementary (flux) vectors, a generalization of elementary modes, a criterion for feasibility can also be derived for this situation. We applied our criteria to a metabolic model of Escherichia coli and determined for each metabolite, whether its net production can be coupled with biomass synthesis and calculated the maximal (guaranteed) coupling yield. The somewhat surprising result is that, under aerobic conditions, coupling is indeed possible for each carbon metabolite of the central metabolism. This also holds true for most metabolites under anaerobic conditions but consideration of ATP maintenance requirements implies infeasibility of coupling for certain compounds. On the other hand, ATP maintenance may also increase the maximal coupling yield for some metabolites. Overall, our work provides important insights and novel tools for a central problem of computational strain design.

Avoiding the Enumeration of Infeasible Elementary Flux Modes by Including Transcriptional Regulatory Rules in the Enumeration Process Saves Computational Costs

Despite the significant progress made in recent years, the computation of the complete set of elementary flux modes of large or even genome-scale metabolic networks is still impossible. We introduce a novel approach to speed up the calculation of elementary flux modes by including transcriptional regulatory information into the analysis of metabolic networks. Taking into account gene regulation dramatically reduces the solution space and allows the presented algorithm to constantly eliminate biologically infeasible modes at an early stage of the computation procedure. Thereby, computational costs, such as runtime, memory usage, and disk space, are extremely reduced. Moreover, we show that the application of transcriptional rules identifies non-trivial system-wide effects on metabolism. Using the presented algorithm pushes the size of metabolic networks that can be studied by elementary flux modes to new and much higher limits without the loss of predictive quality. This makes unbiased, system-wide predictions in large scale metabolic networks possible without resorting to any optimization principle.

Predicting genetic engineering targets with Elementary Flux Mode Analysis: a review of four current methods

Elementary flux modes (EFMs) are a well-established tool in metabolic modeling. EFMs are minimal, feasible, steady state pathways through a metabolic network. They are used in various approaches to predict targets for genetic interventions in order to increase production of a molecule of interest via a host cell. Here we give an introduction to the concept of EFMs, present an overview of four methods which use EFMs in order to predict engineering targets and lastly use a toy model and a small-scale metabolic model to demonstrate and compare the capabilities of these methods.

Metabolomics integrated elementary flux mode analysis in large metabolic networks

Elementary flux modes (EFMs) are non-decomposable steady-state pathways in metabolic networks. They characterize phenotypes, quantify robustness or identify engineering targets. An EFM analysis (EFMA) is currently restricted to medium-scale models, as the number of EFMs explodes with the network's size. However, many topologically feasible EFMs are biologically irrelevant. We present thermodynamic EFMA (tEFMA), which calculates only the small(er) subset of thermodynamically feasible EFMs. We integrate network embedded thermodynamics into EFMA and show that we can use the metabolome to identify and remove thermodynamically infeasible EFMs during an EFMA without losing biologically relevant EFMs. Calculating only the thermodynamically feasible EFMs strongly reduces memory consumption and program runtime, allowing the analysis of larger networks. We apply tEFMA to study the central carbon metabolism of E. coli and find that up to 80% of its EFMs are thermodynamically infeasible. Moreover, we identify glutamate dehydrogenase as a bottleneck, when E. coli is grown on glucose and explain its inactivity as a consequence of network embedded thermodynamics. We implemented tEFMA as a Java package which is available for download at https://github.com/mpgerstl/tEFMA.

tEFMA: computing thermodynamically feasible elementary flux modes in metabolic networks

: Elementary flux modes (EFMs) are important structural tools for the analysis of metabolic networks. It is known that many topologically feasible EFMs are biologically irrelevant. Therefore, tools are needed to find the relevant ones. We present thermodynamic tEFM analysis (tEFMA) which uses the cellular metabolome to avoid the enumeration of thermodynamically infeasible EFMs. Specifically, given a metabolic network and a not necessarily complete metabolome, tEFMA efficiently returns the full set of thermodynamically feasible EFMs consistent with the metabolome. Compared with standard approaches, tEFMA strongly reduces the memory consumption and the overall runtime. Thus tEFMA provides a new way to analyze unbiasedly hitherto inaccessible large-scale metabolic networks.

AVAILABILITY AND IMPLEMENTATION

https://github.com/mpgerstl/tEFMA CONTACT: : christian.jungreuthmayer@boku.ac.at or juergen.zanghellini@boku.ac.at

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Computational strategies for a system-level understanding of metabolism

Cell metabolism is the biochemical machinery that provides energy and building blocks to sustain life. Understanding its fine regulation is of pivotal relevance in several fields, from metabolic engineering applications to the treatment of metabolic disorders and cancer. Sophisticated computational approaches are needed to unravel the complexity of metabolism. To this aim, a plethora of methods have been developed, yet it is generally hard to identify which computational strategy is most suited for the investigation of a specific aspect of metabolism. This review provides an up-to-date description of the computational methods available for the analysis of metabolic pathways, discussing their main advantages and drawbacks. In particular, attention is devoted to the identification of the appropriate scale and level of accuracy in the reconstruction of metabolic networks, and to the inference of model structure and parameters, especially when dealing with a shortage of experimental measurements. The choice of the proper computational methods to derive in silico data is then addressed, including topological analyses, constraint-based modeling and simulation of the system dynamics. A description of some computational approaches to gain new biological knowledge or to formulate hypotheses is finally provided.

TreeEFM: calculating elementary flux modes using linear optimization in a tree-based algorithm

MOTIVATION

Elementary flux modes (EFMs) analysis constitutes a fundamental tool in systems biology. However, the efficient calculation of EFMs in genome-scale metabolic networks (GSMNs) is still a challenge. We present a novel algorithm that uses a linear programming-based tree search and efficiently enumerates a subset of EFMs in GSMNs.

RESULTS

Our approach is compared with the EFMEvolver approach, demonstrating a significant improvement in computation time. We also validate the usefulness of our new approach by studying the acetate overflow metabolism in the Escherichia coli bacteria. To do so, we computed 1 million EFMs for each energetic amino acid and then analysed the relevance of each energetic amino acid based on gene/protein expression data and the obtained EFMs. We found good agreement between previous experiments and the conclusions reached using EFMs. Finally, we also analysed the performance of our approach when applied to large GSMNs.

AVAILABILITY AND IMPLEMENTATION

The stand-alone software TreeEFM is implemented in C++ and interacts with the open-source linear solver COIN-OR Linear program Solver (CLP).

A depth-first search algorithm to compute elementary flux modes by linear programming

Background

The decomposition of complex metabolic networks into elementary flux modes (EFMs) provides a useful framework for exploring reaction interactions systematically. Generating a complete set of EFMs for large-scale models, however, is near impossible. Even for moderately-sized models (<400 reactions), existing approaches based on the Double Description method must iterate through a large number of combinatorial candidates, thus imposing an immense processor and memory demand.

Results

Based on an alternative elementarity test, we developed a depth-first search algorithm using linear programming (LP) to enumerate EFMs in an exhaustive fashion. Constraints can be introduced to directly generate a subset of EFMs satisfying the set of constraints. The depth-first search algorithm has a constant memory overhead. Using flux constraints, a large LP problem can be massively divided and parallelized into independent sub-jobs for deployment into computing clusters. Since the sub-jobs do not overlap, the approach scales to utilize all available computing nodes with minimal coordination overhead or memory limitations.

Conclusions

The speed of the algorithm was comparable to efmtool, a mainstream Double Description method, when enumerating all EFMs; the attrition power gained from performing flux feasibility tests offsets the increased computational demand of running an LP solver. Unlike the Double Description method, the algorithm enables accelerated enumeration of all EFMs satisfying a set of constraints.