Elementary flux modes in a nutshell: properties, calculation and applications

Robust Optimal Metabolic Factories

Perhaps the most fundamental model in synthetic and systems biology for inferring pathways in metabolic reaction networks is a metabolic factory: a system of reactions that starts from a set of source compounds and produces a set of target molecules, while conserving or not depleting intermediate metabolites. Finding a shortest factory-that minimizes a sum of real-valued weights on its reactions to infer the most likely pathway-is NP-complete. The current state-of-the-art for shortest factories solves a mixed-integer linear program with a major drawback: it requires the user to set a critical parameter, where too large a value can make optimal solutions infeasible, while too small a value can yield degenerate solutions due to numerical error. We present the first robust algorithm for optimal factories that is both parameter-free (relieving the user from determining a parameter setting) and degeneracy-free (guaranteeing it finds an optimal nondegenerate solution). We also give for the first time a complete characterization of the graph-theoretic structure of shortest factories, that reveals an important class of degenerate solutions which was overlooked and potentially output by the prior state-of-the-art.We show degeneracy is precisely due to invalid stoichiometries in reactions, and provide an efficient algorithm for identifying all such misannotations in a metabolic network. In addition we settle the relationship between the two established pathway models of hyperpaths and factories by proving hyperpaths actually comprise a subclass of factories. Comprehensive experiments over all instances from the standard metabolic reaction databases in the literature demonstrate our parameter-free exact algorithm is fast in practice, quickly finding optimal factories in large real-world networks containing thousands of reactions. A preliminary implementation of our robust algorithm for shortest factories in a new tool called Freeia is available free for research use at http://freeia.cs.arizona.edu.

Review: Towards the next-generation models of the rumen microbiome for enhancing predictive power and guiding sustainable production strategies

The rumen ecosystem harbours a galaxy of microbes working in syntrophy to carry out a metabolic cascade of hydrolytic and fermentative reactions. This fermentation process allows ruminants to harvest nutrients from a wide range of feedstuff otherwise inaccessible to the host. The interconnection between the ruminant and its rumen microbiota shapes key animal phenotypes such as feed efficiency and methane emissions and suggests the potential of reducing methane emissions and enhancing feed conversion into animal products by manipulating the rumen microbiota. Whilst significant technological progress in omics techniques has increased our knowledge of the rumen microbiota and its genome (microbiome), translating omics knowledge into effective microbial manipulation strategies remains a great challenge. This challenge can be addressed by modelling approaches integrating causality principles and thus going beyond current correlation-based approaches applied to analyse rumen microbial genomic data. However, existing rumen models are not yet adapted to capitalise on microbial genomic information. This gap between the rumen microbiota available omics data and the way microbial metabolism is represented in the existing rumen models needs to be filled to enhance rumen understanding and produce better predictive models with capabilities for guiding nutritional strategies. To fill this gap, the integration of computational biology tools and mathematical modelling frameworks is needed to translate the information of the metabolic potential of the rumen microbes (inferred from their genomes) into a mathematical object. In this paper, we aim to discuss the potential use of two modelling approaches for the integration of microbial genomic information into dynamic models. The first modelling approach explores the theory of state observers to integrate microbial time series data into rumen fermentation models. The second approach is based on the genome-scale network reconstructions of rumen microbes. For a given microorganism, the network reconstruction produces a stoichiometry matrix of the metabolism. This matrix is the core of the so-called genome-scale metabolic models which can be exploited by a plethora of methods comprised within the constraint-based reconstruction and analysis approaches. We will discuss how these methods can be used to produce the next-generation models of the rumen microbiome.

Next-generation feedstocks methanol and ethylene glycol and their potential in industrial biotechnology

Microbial fermentation processes are expected to play an important role in reducing dependence on fossil-based raw materials for the production of everyday chemicals. In order to meet the growing demand for biotechnological products in the future, alternative carbon sources that do not compete with human nutrition must be exploited. The chemical conversion of the industrially emitted greenhouse gas CO2 into microbially utilizable platform chemicals such as methanol represents a sustainable strategy for the utilization of an abundant carbon source and has attracted enormous scientific interest in recent years. A relatively new approach is the microbial synthesis of products from the C2-compound ethylene glycol, which can also be synthesized from CO2 and non-edible biomass and, in addition, can be recovered from plastic waste. Here we summarize the main chemical routes for the synthesis of methanol and ethylene glycol from sustainable resources and give an overview of recent metabolic engineering work for establishing natural and synthetic microbial assimilation pathways. The different metabolic routes for C1 and C2 alcohol-dependent bioconversions were compared in terms of their theoretical maximum yields and their oxygen requirements for a wide range of value-added products. Assessment of the process engineering challenges for methanol and ethylene glycol-based fermentations underscores the theoretical advantages of new synthetic metabolic routes and advocates greater consideration of ethylene glycol, a C2 substrate that has received comparatively little attention to date.

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.

Speeding Up the Structural Analysis of Metabolic Network Models Using the Fredman-Khachiyan Algorithm B

The problem of computing the Elementary Flux Modes (EFMs) and Minimal Cut Sets (MCSs) of metabolic network is a fundamental one in metabolic networks. A key insight is that they can be understood as a dual pair of monotone Boolean functions (MBFs). Using this insight, this computation reduces to the question of generating from an oracle a dual pair of MBFs. If one of the two sets (functions) is known, then the other can be computed through a process known as dualization. Fredman and Khachiyan provided two algorithms, which they called simply A and B that can serve as an engine for oracle-based generation or dualization of MBFs. We look at efficiencies available in implementing their algorithm B, which we will refer to as FK-B. Like their algorithm A, FK-B certifies whether two given MBFs in the form of Conjunctive Normal Form and Disjunctive Normal Form are dual or not, and in case of not being dual it returns a conflicting assignment (CA), that is, an assignment that makes one of the given Boolean functions True and the other one False. The FK-B algorithm is a recursive algorithm that searches through the tree of assignments to find a CA. If it does not find any CA, it means that the given Boolean functions are dual. In this article, we propose six techniques applicable to the FK-B and hence to the dualization process. Although these techniques do not reduce the time complexity, they considerably reduce the running time in practice. We evaluate the proposed improvements by applying them to compute the MCSs from the EFMs in the 19 small- and medium-sized models from the BioModels database along with 4 models of biomass synthesis in Escherichia coli that were used in an earlier computational survey Haus et al. (2008).

Extracting functionally accurate context-specific models of Atlantic salmon metabolism

Constraint-based models (CBMs) are used to study metabolic network structure and function in organisms ranging from microbes to multicellular eukaryotes. Published CBMs are usually generic rather than context-specific, meaning that they do not capture differences in reaction activities, which, in turn, determine metabolic capabilities, between cell types, tissues, environments, or other conditions. Only a subset of a CBM's metabolic reactions and capabilities are likely to be active in any given context, and several methods have therefore been developed to extract context-specific models from generic CBMs through integration of omics data. We tested the ability of six model extraction methods (MEMs) to create functionally accurate context-specific models of Atlantic salmon using a generic CBM (SALARECON) and liver transcriptomics data from contexts differing in water salinity (life stage) and dietary lipids. Three MEMs (iMAT, INIT, and GIMME) outperformed the others in terms of functional accuracy, which we defined as the extracted models' ability to perform context-specific metabolic tasks inferred directly from the data, and one MEM (GIMME) was faster than the others. Context-specific versions of SALARECON consistently outperformed the generic version, showing that context-specific modeling better captures salmon metabolism. Thus, we demonstrate that results from human studies also hold for a non-mammalian animal and major livestock species.

Nutrition or nature: using elementary flux modes to disentangle the complex forces shaping prokaryote pan-genomes

BACKGROUND

Microbial pan-genomes are shaped by a complex combination of stochastic and deterministic forces. Even closely related genomes exhibit extensive variation in their gene content. Understanding what drives this variation requires exploring the interactions of gene products with each other and with the organism's external environment. However, to date, conceptual models of pan-genome dynamics often represent genes as independent units and provide limited information about their mechanistic interactions.

RESULTS

We simulated the stochastic process of gene-loss using the pooled genome-scale metabolic reaction networks of 46 taxonomically diverse bacterial and archaeal families as proxies for their pan-genomes. The frequency by which reactions are retained in functional networks when stochastic gene loss is simulated in diverse environments allowed us to disentangle the metabolic reactions whose presence depends on the metabolite composition of the external environment (constrained by "nutrition") from those that are independent of the environment (constrained by "nature"). By comparing the frequency of reactions from the first group with their observed frequencies in bacterial and archaeal families, we predicted the metabolic niches that shaped the genomic composition of these lineages. Moreover, we found that the lineages that were shaped by a more diverse metabolic niche also occur in more diverse biomes as assessed by global environmental sequencing datasets.

CONCLUSION

We introduce a computational framework for analyzing and interpreting pan-reactomes that provides novel insights into the ecological and evolutionary drivers of pan-genome dynamics.

Elementary vectors and autocatalytic sets for resource allocation in next-generation models of cellular growth

Traditional (genome-scale) metabolic models of cellular growth involve an approximate biomass “reaction”, which specifies biomass composition in terms of precursor metabolites (such as amino acids and nucleotides). On the one hand, biomass composition is often not known exactly and may vary drastically between conditions and strains. On the other hand, the predictions of computational models crucially depend on biomass. Also elementary flux modes (EFMs), which generate the flux cone, depend on the biomass reaction. To better understand cellular phenotypes across growth conditions, we introduce and analyze new classes of elementary vectors for comprehensive (next-generation) metabolic models, involving explicit synthesis reactions for all macromolecules. Elementary growth modes (EGMs) are given by stoichiometry and generate the growth cone. Unlike EFMs, they are not support-minimal, in general, but cannot be decomposed “without cancellations”. In models with additional (capacity) constraints, elementary growth vectors (EGVs) generate a growth polyhedron and depend also on growth rate. However, EGMs/EGVs do not depend on the biomass composition. In fact, they cover all possible biomass compositions and can be seen as unbiased versions of elementary flux modes/vectors (EFMs/EFVs) used in traditional models. To relate the new concepts to other branches of theory, we consider autocatalytic sets of reactions. Further, we illustrate our results in a small model of a self-fabricating cell, involving glucose and ammonium uptake, amino acid and lipid synthesis, and the expression of all enzymes and the ribosome itself. In particular, we study the variation of biomass composition as a function of growth rate. In agreement with experimental data, low nitrogen uptake correlates with high carbon (lipid) storage.

Next-generation, genome-scale metabolic models allow to study the reallocation of cellular resources upon changing environmental conditions, by not only modeling flux distributions, but also expression profiles of the catalyzing proteome. In particular, they do no longer assume a fixed biomass composition. Methods to identify optimal solutions in such comprehensive models exist, however, an unbiased understanding of all feasible allocations is missing so far. Here we develop new concepts, called elementary growth modes and vectors, that provide a generalized definition of minimal pathways, thereby extending classical elementary flux modes (used in traditional models with a fixed biomass composition). The new concepts provide an understanding of all possible flux distributions and of all possible biomass compositions. In other words, elementary growth modes and vectors are the unique functional units in any comprehensive model of cellular growth. As an example, we show that lipid accumulation upon nitrogen starvation is a consequence of resource allocation and does not require active regulation. Our work puts current approaches on a theoretical basis and allows to seamlessly transfer existing workflows (e.g. for the design of cell factories) to next-generation metabolic models.

Elucidating Plant-Microbe-Environment Interactions Through Omics-Enabled Metabolic Modelling Using Synthetic Communities

With a growing world population and increasing frequency of climate disturbance events, we are in dire need of methods to improve plant productivity, resilience, and resistance to both abiotic and biotic stressors, both for agriculture and conservation efforts. Microorganisms play an essential role in supporting plant growth, environmental response, and susceptibility to disease. However, understanding the specific mechanisms by which microbes interact with each other and with plants to influence plant phenotypes is a major challenge due to the complexity of natural communities, simultaneous competition and cooperation effects, signalling interactions, and environmental impacts. Synthetic communities are a major asset in reducing the complexity of these systems by simplifying to dominant components and isolating specific variables for controlled experiments, yet there still remains a large gap in our understanding of plant microbiome interactions. This perspectives article presents a brief review discussing ways in which metabolic modelling can be used in combination with synthetic communities to continue progress toward understanding the complexity of plant-microbe-environment interactions. We highlight the utility of metabolic models as applied to a community setting, identify different applications for both flux balance and elementary flux mode simulation approaches, emphasize the importance of ecological theory in guiding data interpretation, and provide ideas for how the integration of metabolic modelling techniques with big data may bridge the gap between simplified synthetic communities and the complexity of natural plant-microbe systems.

OUP accepted manuscript

Motivation

A factory in a metabolic network specifies how to produce target molecules from source compounds through biochemical reactions, properly accounting for reaction stoichiometry to conserve or not deplete intermediate metabolites. While finding factories is a fundamental problem in systems biology, available methods do not consider the number of reactions used, nor address negative regulation.

Methods

We introduce the new problem of finding optimal factories that use the fewest reactions, for the first time incorporating both first- and second-order negative regulation. We model this problem with directed hypergraphs, prove it is NP-complete, solve it via mixed-integer linear programming, and accommodate second-order negative regulation by an iterative approach that generates next-best factories.

Results

This optimization-based approach is remarkably fast in practice, typically finding optimal factories in a few seconds, even for metabolic networks involving tens of thousands of reactions and metabolites, as demonstrated through comprehensive experiments across all instances from standard reaction databases.

Availability and implementation

Source code for an implementation of our new method for optimal factories with negative regulation in a new tool called Odinn, together with all datasets, is available free for non-commercial use at http://odinn.cs.arizona.edu.

Novel computational and experimental approaches for investigating the thermodynamics of metabolic networks

Thermodynamic analysis of metabolic networks has emerged as a useful new tool for pathway design and metabolic engineering. Understanding the relationship between the thermodynamic driving force of biochemical reactions and metabolic flux has generated new insights regarding the design principles of microbial carbon metabolism. This review summarizes the various lessons that can be obtained from the thermodynamic analysis of metabolic pathways, illustrates concepts of computational thermodynamic tools, and highlights recent applications of thermodynamic analysis to pathway design in industrially relevant microbes.

Recombinant protein production in Pichia pastoris: From transcriptionally redesigned strains to bioprocess optimization and metabolic modelling

Pichia pastoris is one of the most widely used host for the production of recombinant proteins. Expression systems that rely mostly on promoters from genes encoding alcohol oxidase 1 or glyceraldehyde-3-phosphate dehydrogenase have been developed together with related bioreactor operation strategies based on carbon sources such as methanol, glycerol, or glucose. Although, these processes are relatively efficient and easy to use, there have been notable improvements over the last twenty years to better control gene expression from these promoters and their engineered variants. Methanol-free and more efficient protein production platforms have been developed by engineering promoters and transcription factors. The production window of P. pastoris has been also extended by using alternative feedstocks including ethanol, lactic acid, mannitol, sorbitol, sucrose, xylose, gluconate, formate, or rhamnose. Herein, the specific aspects that are emerging as key parameters for recombinant protein synthesis are discussed. For this purpose, a holistic approach has been considered to scrutinize protein production processes from strain design to bioprocess optimization, particularly focusing on promoter engineering, transcriptional circuitry redesign. This review also considers the optimization of bioprocess based on alternative carbon sources and derived co-feeding strategies. Optimization strategies for recombinant protein synthesis through metabolic modelling are also discussed.

EFMlrs: a Python package for elementary flux mode enumeration via lexicographic reverse search

Background

Elementary flux mode (EFM) analysis is a well-established, yet computationally challenging approach to characterize metabolic networks. Standard algorithms require huge amounts of memory and lack scalability which limits their application to single servers and consequently limits a comprehensive analysis to medium-scale networks. Recently, Avis et al. developed mplrs—a parallel version of the lexicographic reverse search (lrs) algorithm, which, in principle, enables an EFM analysis on high-performance computing environments (Avis and Jordan. mplrs: a scalable parallel vertex/facet enumeration code. arXiv:1511.06487, 2017). Here we test its applicability for EFM enumeration.

Results

We developed EFMlrs, a Python package that gives users access to the enumeration capabilities of mplrs. EFMlrs uses COBRApy to process metabolic models from sbml files, performs loss-free compressions of the stoichiometric matrix, and generates suitable inputs for mplrs as well as efmtool, providing support not only for our proposed new method for EFM enumeration but also for already established tools. By leveraging COBRApy, EFMlrs also allows the application of additional reaction boundaries and seamlessly integrates into existing workflows.

Conclusion

We show that due to mplrs’s properties, the algorithm is perfectly suited for high-performance computing (HPC) and thus offers new possibilities for the unbiased analysis of substantially larger metabolic models via EFM analyses. EFMlrs is an open-source program that comes together with a designated workflow and can be easily installed via pip.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12859-021-04417-9.

Exact Boolean Abstraction of Linear Equation Systems

We study the problem of how to compute the boolean abstraction of the solution set of a linear equation system over the positive reals. We call a linear equation system ϕ exact for the boolean abstraction if the abstract interpretation of ϕ over the structure of booleans is equal to the boolean abstraction of the solution set of ϕ over the positive reals. Abstract interpretation over the booleans is thus complete for the boolean abstraction when restricted to exact linear equation systems, while it is not complete more generally. We present a new rewriting algorithm that makes linear equation systems exact for the boolean abstraction while preserving the solutions over the positive reals. The rewriting algorithm is based on the elementary modes of the linear equation system. The computation of the elementary modes may require exponential time in the worst case, but is often feasible in practice with freely available tools. For exact linear equation systems, we can compute the boolean abstraction by finite domain constraint programming. This yields a solution of the initial problem that is often feasible in practice. Our exact rewriting algorithm has two further applications. Firstly, it can be used to compute the sign abstraction of linear equation systems over the reals, as needed for analyzing function programs with linear arithmetics. Secondly, it can be applied to compute the difference abstraction of a linear equation system as used in change prediction algorithms for flux networks in systems biology.

How to Tackle Underdeterminacy in Metabolic Flux Analysis? A Tutorial and Critical Review

Metabolic flux analysis is often (not to say almost always) faced with system underdeterminacy. Indeed, the linear algebraic system formed by the steady-state mass balance equations around the intracellular metabolites and the equality constraints related to the measurements of extracellular fluxes do not define a unique solution for the distribution of intracellular fluxes, but instead a set of solutions belonging to a convex polytope. Various methods have been proposed to tackle this underdeterminacy, including flux pathway analysis, flux balance analysis, flux variability analysis and sampling. These approaches are reviewed in this article and a toy example supports the discussion with illustrative numerical results.

Modelling Cell Metabolism: A Review on Constraint-Based Steady-State and Kinetic Approaches

Studying cell metabolism serves a plethora of objectives such as the enhancement of bioprocess performance, and advancement in the understanding of cell biology, of drug target discovery, and in metabolic therapy. Remarkable successes in these fields emerged from heuristics approaches, for instance, with the introduction of effective strategies for genetic modifications, drug developments and optimization of bioprocess management. However, heuristics approaches have showed significant shortcomings, such as to describe regulation of metabolic pathways and to extrapolate experimental conditions. In the specific case of bioprocess management, such shortcomings limit their capacity to increase product quality, while maintaining desirable productivity and reproducibility levels. For instance, since heuristics approaches are not capable of prediction of the cellular functions under varying experimental conditions, they may lead to sub-optimal processes. Also, such approaches used for bioprocess control often fail in regulating a process under unexpected variations of external conditions. Therefore, methodologies inspired by the systematic mathematical formulation of cell metabolism have been used to address such drawbacks and achieve robust reproducible results. Mathematical modelling approaches are effective for both the characterization of the cell physiology, and the estimation of metabolic pathways utilization, thus allowing to characterize a cell population metabolic behavior. In this article, we present a review on methodology used and promising mathematical modelling approaches, focusing primarily to investigate metabolic events and regulation. Proceeding from a topological representation of the metabolic networks, we first present the metabolic modelling approaches that investigate cell metabolism at steady state, complying to the constraints imposed by mass conservation law and thermodynamics of reactions reversibility. Constraint-based models (CBMs) are reviewed highlighting the set of assumed optimality functions for reaction pathways. We explore models simulating cell growth dynamics, by expanding flux balance models developed at steady state. Then, discussing a change of metabolic modelling paradigm, we describe dynamic kinetic models that are based on the mathematical representation of the mechanistic description of nonlinear enzyme activities. In such approaches metabolic pathway regulations are considered explicitly as a function of the activity of other components of metabolic networks and possibly far from the metabolic steady state. We have also assessed the significance of metabolic model parameterization in kinetic models, summarizing a standard parameter estimation procedure frequently employed in kinetic metabolic modelling literature. Finally, some optimization practices used for the parameter estimation are reviewed.

Opportunities at the Interface of Network Science and Metabolic Modeling

Metabolism plays a central role in cell physiology because it provides the molecular machinery for growth. At the genome-scale, metabolism is made up of thousands of reactions interacting with one another. Untangling this complexity is key to understand how cells respond to genetic, environmental, or therapeutic perturbations. Here we discuss the roles of two complementary strategies for the analysis of genome-scale metabolic models: Flux Balance Analysis (FBA) and network science. While FBA estimates metabolic flux on the basis of an optimization principle, network approaches reveal emergent properties of the global metabolic connectivity. We highlight how the integration of both approaches promises to deliver insights on the structure and function of metabolic systems with wide-ranging implications in discovery science, precision medicine and industrial biotechnology.

Physicochemical and metabolic constraints for thermodynamics-based stoichiometric modelling under mesophilic growth conditions

Metabolic engineering in the post-genomic era is characterised by the development of new methods for metabolomics and fluxomics, supported by the integration of genetic engineering tools and mathematical modelling. Particularly, constraint-based stoichiometric models have been widely studied: (i) flux balance analysis (FBA) (in silico), and (ii) metabolic flux analysis (MFA) (in vivo). Recent studies have enabled the incorporation of thermodynamics and metabolomics data to improve the predictive capabilities of these approaches. However, an in-depth comparison and evaluation of these methods is lacking. This study presents a thorough analysis of two different in silico methods tested against experimental data (metabolomics and ¹³C-MFA) for the mesophile Escherichia coli. In particular, a modified version of the recently published matTFA toolbox was created, providing a broader range of physicochemical parameters. Validating against experimental data allowed the determination of the best physicochemical parameters to perform the TFA (Thermodynamics-based Flux Analysis). An analysis of flux pattern changes in the central carbon metabolism between ¹³C-MFA and TFA highlighted the limited capabilities of both approaches for elucidating the anaplerotic fluxes. In addition, a method based on centrality measures was suggested to identify important metabolites that (if quantified) would allow to further constrain the TFA. Finally, this study emphasised the need for standardisation in the fluxomics community: novel approaches are frequently released but a thorough comparison with currently accepted methods is not always performed.

Biotechnology has benefitted from the development of high throughput methods characterising living systems at different levels (e.g. concerning genes or proteins), allowing the industrial production of chemical commodities. Recently, focus has been placed on determining reaction rates (or metabolic fluxes) in the metabolic network of certain microorganisms, in order to identify bottlenecks hindering their exploitation. Two main approaches are commonly used, termed metabolic flux analysis (MFA) and flux balance analysis (FBA), based on measuring and estimating fluxes, respectively. While the influence of thermodynamics in living systems was accepted several decades ago, its application to study biochemical networks has only recently been enabled. In this sense, a multitude of different approaches constraining well-established modelling methods with thermodynamics has been suggested. However, physicochemical parameters are generally not properly adjusted to the experimental conditions, which might affect their predictive capabilities. In this study, we have explored the reliability of currently available tools by investigating the impact of varying said parameters in the simulation of metabolic fluxes and metabolite concentration values. Additionally, our in-depth analysis allowed us to highlight limitations and potential solutions that should be considered in future studies.

Environmental flexibility does not explain metabolic robustness

Cells show remarkable resilience against genetic and environmental perturbations. However, its evolutionary origin remains obscure. In order to leverage methods of systems biology for examining cellular robustness, a computationally accessible way of quantification is needed. Here, we present an unbiased metric of structural robustness in genome-scale metabolic models based on concepts prevalent in reliability engineering and fault analysis. The probability of failure (PoF) is defined as the (weighted) portion of all possible combinations of loss-of-function mutations that disable network functionality. It can be exactly determined if all essential reactions, synthetic lethal pairs of reactions, synthetic lethal triplets of reactions etc. are known. In theory, these minimal cut sets (MCSs) can be calculated for any network, but for large models the problem remains computationally intractable. Herein, we demonstrate that even at the genome scale only the lowest-cardinality MCSs are required to efficiently approximate the PoF with reasonable accuracy. Building on an improved theoretical understanding, we analysed the robustness of 489 E. coli, Shigella, Salmonella, and fungal genome-scale metabolic models (GSMMs). In contrast to the popular "congruence theory", which explains the origin of genetic robustness as a byproduct of selection for environmental flexibility, we found no correlation between network robustness and the diversity of growth-supporting environments. On the contrary, our analysis indicates that amino acid synthesis rather than carbon metabolism dominates metabolic robustness.

Software and Methods for Computational Flux Balance Analysis

As genetic engineering of organisms has grown easier and more precise, computational modeling of metabolic systems has played an increasingly important role in both guiding experimental interventions and in understanding the results of metabolic perturbations.

Metabolic Modelling as a Framework for Metabolomics Data Integration and Analysis

Metabolic networks are regulated to ensure the dynamic adaptation of biochemical reaction fluxes to maintain cell homeostasis and optimal metabolic fitness in response to endogenous and exogenous perturbations. To this end, metabolism is tightly controlled by dynamic and intricate regulatory mechanisms involving allostery, enzyme abundance and post-translational modifications. The study of the molecular entities involved in these complex mechanisms has been boosted by the advent of high-throughput technologies. The so-called omics enable the quantification of the different molecular entities at different system layers, connecting the genotype with the phenotype. Therefore, the study of the overall behavior of a metabolic network and the omics data integration and analysis must be approached from a holistic perspective. Due to the close relationship between metabolism and cellular phenotype, metabolic modelling has emerged as a valuable tool to decipher the underlying mechanisms governing cell phenotype. Constraint-based modelling and kinetic modelling are among the most widely used methods to study cell metabolism at different scales, ranging from cells to tissues and organisms. These approaches enable integrating metabolomic data, among others, to enhance model predictive capabilities. In this review, we describe the current state of the art in metabolic modelling and discuss future perspectives and current challenges in the field.

Key Challenges in Designing CHO Chassis Platforms

Following the success of and the high demand for recombinant protein-based therapeutics during the last 25 years, the pharmaceutical industry has invested significantly in the development of novel treatments based on biologics. Mammalian cells are the major production systems for these complex biopharmaceuticals, with Chinese hamster ovary (CHO) cell lines as the most important players. Over the years, various engineering strategies and modeling approaches have been used to improve microbial production platforms, such as bacteria and yeasts, as well as to create pre-optimized chassis host strains. However, the complexity of mammalian cells curtailed the optimization of these host cells by metabolic engineering. Most of the improvements of titer and productivity were achieved by media optimization and large-scale screening of producer clones. The advances made in recent years now open the door to again consider the potential application of systems biology approaches and metabolic engineering also to CHO. The availability of a reference genome sequence, genome-scale metabolic models and the growing number of various “omics” datasets can help overcome the complexity of CHO cells and support design strategies to boost their production performance. Modular design approaches applied to engineer industrially relevant cell lines have evolved to reduce the time and effort needed for the generation of new producer cells and to allow the achievement of desired product titers and quality. Nevertheless, important steps to enable the design of a chassis platform similar to those in use in the microbial world are still missing. In this review, we highlight the importance of mammalian cellular platforms for the production of biopharmaceuticals and compare them to microbial platforms, with an emphasis on describing novel approaches and discussing still open questions that need to be resolved to reach the objective of designing enhanced modular chassis CHO cell lines.

Metabolic Efficiency of Sugar Co-Metabolism and Phenol Degradation in Alicyclobacillus acidocaldarius for Improved Lignocellulose Processing

Substrate availability plays a key role in dictating metabolic strategies. Most microorganisms consume carbon/energy sources in a sequential, preferential order. The presented study investigates metabolic strategies of Alicyclobacillus acidocaldarius, a thermoacidophilic bacterium that has been shown to co-utilize glucose and xylose, as well as degrade phenolic compounds. An existing metabolic model was expanded to include phenol degradation and was analyzed with both metabolic pathway and constraint-based analysis methods. Elementary flux mode analysis was used in conjunction with resource allocation theory to investigate ecologically optimal metabolic pathways for different carbon substrate combinations. Additionally, a dynamic version of flux balance analysis was used to generate time-resolved simulations of growth on phenol and xylose. Results showed that availability of xylose along with glucose did not predict enhanced growth efficiency beyond that of glucose alone, but did predict some differences in pathway utilization and byproduct profiles. In contrast, addition of phenol as a co-substrate with xylose predicted lower growth efficiency. Dynamic simulations predicted co-consumption of xylose and phenol in a similar pattern as previously reported experiments. Altogether, this work serves as a case study for combining both elementary flux mode and flux balance analyses to probe unique metabolic features, and also demonstrates the versatility of A. acidocaldarius for lignocellulosic biomass processing applications.

Glycan Residues Balance Analysis - GReBA: A novel model for the N-linked glycosylation of IgG produced by CHO cells

The structure of N-linked glycosylation is a very important quality attribute for therapeutic monoclonal antibodies. Different carbon sources in cell culture media, such as mannose and galactose, have been reported to have different influences on the glycosylation patterns. Accurate prediction and control of the glycosylation profile are important for the process development of mammalian cell cultures. In this study, a mathematical model, that we named Glycan Residues Balance Analysis (GReBA), was developed based on the concept of Elementary Flux Mode (EFM), and used to predict the glycosylation profile for steady state cell cultures. Experiments were carried out in pseudo-perfusion cultivation of antibody producing Chinese Hamster Ovary (CHO) cells with various concentrations and combinations of glucose, mannose and galactose. Cultivation of CHO cells with mannose or the combinations of mannose and galactose resulted in decreased lactate and ammonium production, and more matured glycosylation patterns compared to the cultures with glucose. Furthermore, the growth rate and IgG productivity were similar in all the conditions. When the cells were cultured with galactose alone, lactate was fed as well to be used as complementary carbon source, leading to cell growth rate and IgG productivity comparable to feeding the other sugars. The data of the glycoprofiles were used for training the model, and then to simulate the glycosylation changes with varying the concentrations of mannose and galactose. In this study we showed that the GReBA model had a good predictive capacity of the N-linked glycosylation. The GReBA can be used as a guidance for development of glycoprotein cultivation processes.

Seeing the wood for the trees: a forest of methods for optimization and omic-network integration in metabolic modelling

Metabolic modelling has entered a mature phase with dozens of methods and software implementations available to the practitioner and the theoretician. It is not easy for a modeller to be able to see the wood (or the forest) for the trees. Driven by this analogy, we here present a 'forest' of principal methods used for constraint-based modelling in systems biology. This provides a tree-based view of methods available to prospective modellers, also available in interactive version at http://modellingmetabolism.net, where it will be kept updated with new methods after the publication of the present manuscript. Our updated classification of existing methods and tools highlights the most promising in the different branches, with the aim to develop a vision of how existing methods could hybridize and become more complex. We then provide the first hands-on tutorial for multi-objective optimization of metabolic models in R. We finally discuss the implementation of multi-view machine learning approaches in poly-omic integration. Throughout this work, we demonstrate the optimization of trade-offs between multiple metabolic objectives, with a focus on omic data integration through machine learning. We anticipate that the combination of a survey, a perspective on multi-view machine learning and a step-by-step R tutorial should be of interest for both the beginner and the advanced user.

Genome-driven cell engineering review: in vivo and in silico metabolic and genome engineering

Producing 'designer cells' with specific functions is potentially feasible in the near future. Recent developments, including whole-cell models, genome design algorithms and gene editing tools, have advanced the possibility of combining biological research and mathematical modelling to further understand and better design cellular processes. In this review, we will explore computational and experimental approaches used for metabolic and genome design. We will highlight the relevance of modelling in this process, and challenges associated with the generation of quantitative predictions about cell behaviour as a whole: although many cellular processes are well understood at the subsystem level, it has proved a hugely complex task to integrate separate components together to model and study an entire cell. We explore these developments, highlighting where computational design algorithms compensate for missing cellular information and underlining where computational models can complement and reduce lab experimentation. We will examine issues and illuminate the next steps for genome engineering.

Computing Weakly Reversible Deficiency Zero Network Translations Using Elementary Flux Modes

We present a computational method for performing structural translation, which has been studied recently in the context of analyzing the steady states and dynamical behavior of mass-action systems derived from biochemical reaction networks. Our procedure involves solving a binary linear programming problem where the decision variables correspond to interactions between the reactions of the original network. We call the resulting network a reaction-to-reaction graph and formalize how such a construction relates to the original reaction network and the structural translation. We demonstrate the efficacy and efficiency of the algorithm by running it on 508 networks from the European Bioinformatics Institutes' BioModels database. We also summarize how this work can be incorporated into recently proposed algorithms for establishing mono- and multistationarity in biochemical reaction systems.

RedCom: A strategy for reduced metabolic modeling of complex microbial communities and its application for analyzing experimental datasets from anaerobic digestion

Constraint-based modeling (CBM) is increasingly used to analyze the metabolism of complex microbial communities involved in ecology, biomedicine, and various biotechnological processes. While CBM is an established framework for studying the metabolism of single species with linear stoichiometric models, CBM of communities with balanced growth is more complicated, not only due to the larger size of the multi-species metabolic network but also because of the bilinear nature of the resulting community models. Moreover, the solution space of these community models often contains biologically unrealistic solutions, which, even with model linearization and under application of certain objective functions, cannot easily be excluded. Here we present RedCom, a new approach to build reduced community models in which the metabolisms of the participating organisms are represented by net conversions computed from the respective single-species networks. By discarding (single-species) net conversions that violate a minimality criterion in the exchange fluxes, it is ensured that unrealistic solutions in the community model are excluded where a species altruistically synthesizes large amounts of byproducts (instead of biomass) to fulfill the requirements of other species. We employed the RedCom approach for modeling communities of up to nine organisms involved in typical degradation steps of anaerobic digestion in biogas plants. Compared to full (bilinear and linearized) community models, we found that the reduced community models obtained with RedCom are not only much smaller but allow, also in the largest model with nine species, extensive calculations required to fully characterize the solution space and to reveal key properties of communities with maximum methane yield and production rates. Furthermore, the predictive power of the reduced community models is significantly larger because they predict much smaller ranges of feasible community compositions and exchange fluxes still being consistent with measurements obtained from enrichment cultures. For an enrichment culture for growth on ethanol, we also used metaproteomic data to further constrain the solution space of the community models. Both model and proteomic data indicated a dominance of acetoclastic methanogens (Methanosarcinales) and Desulfovibrionales being the least abundant group in this microbial community.

Microbial communities are involved in many fundamental processes in nature, health and biotechnology. The elucidation of interdependencies between the involved players of microbial communities and how the interactions shape the composition, behavior and characteristic features of the consortium has become an important branch of microbiology research. Many communities are based on the exchange of metabolites between the species and constraint-based metabolic modeling has become an important approach for a formal description and quantitative analysis of these metabolic dependencies. However, the complexity of the models rises quickly with a growing number of organisms and the space of predicted feasible behaviors often includes unrealistic solutions. Here we present RedCom, a new approach to build reduced stoichiometric models of balanced microbial communities based on net conversions of the single-species models. We demonstrate the applicability of our RedCom approach by modeling communities of up to nine organisms involved in degradation steps of anaerobic digestion in biogas plants. As one of the first studies in this field, we compare simulation results from the community models with experimental data of laboratory-scale biogas reactors for growth on ethanol and glucose-cellulose media. The results also demonstrate a higher predictive power of the RedCom vs. the full models.

A portable structural analysis library for reaction networks

The topology of a reaction network can have a significant influence on the network's dynamical properties. Such influences can include constraints on network flows and concentration changes or more insidiously result in the emergence of feedback loops. These effects are due entirely to mass constraints imposed by the network configuration and are important considerations before any dynamical analysis is made. Most established simulation software tools usually carry out some kind of structural analysis of a network before any attempt is made at dynamic simulation. In this paper, we describe a portable software library, libStructural, that can carry out a variety of popular structural analyses that includes conservation analysis, flux dependency analysis and enumerating elementary modes. The library employs robust algorithms that allow it to be used on large networks with more than a two thousand nodes. The library accepts either a raw or fully labeled stoichiometry matrix or models written in SBML format. The software is written in standard C/C++ and comes with extensive on-line documentation and a test suite. The software is available for Windows, Mac OS X, and can be compiled easily on any Linux operating system. A language binding for Python is also available through the pip package manager making it simple to install on any standard Python distribution. The bulk of the source code is licensed under the open source BSD license with other parts using as either the MIT license or more simply public domain. All source is available on GitHub (https://github.com/sys-bio/Libstructural).

Thermodynamic constraints for identifying elementary flux modes

Metabolic pathway analysis is a key method to study metabolism and the elementary flux modes (EFMs) is one major concept allowing one to analyze the network in terms of minimal pathways. Their practical use has been hampered by the combinatorial explosion of their number in large systems. The EFMs give the possible pathways at steady state, but the real pathways are limited by biological constraints. In this review, we display three different methods that integrate thermodynamic constraints in terms of Gibbs free energy in the EFMs computation.

A mathematical framework for yield (vs. rate) optimization in constraint-based modeling and applications in metabolic engineering

BACKGROUND

The optimization of metabolic rates (as linear objective functions) represents the methodical core of flux-balance analysis techniques which have become a standard tool for the study of genome-scale metabolic models. Besides (growth and synthesis) rates, metabolic yields are key parameters for the characterization of biochemical transformation processes, especially in the context of biotechnological applications. However, yields are ratios of rates, and hence the optimization of yields (as nonlinear objective functions) under arbitrary linear constraints is not possible with current flux-balance analysis techniques. Despite the fundamental importance of yields in constraint-based modeling, a comprehensive mathematical framework for yield optimization is still missing.

RESULTS

We present a mathematical theory that allows one to systematically compute and analyze yield-optimal solutions of metabolic models under arbitrary linear constraints. In particular, we formulate yield optimization as a linear-fractional program. For practical computations, we transform the linear-fractional yield optimization problem to a (higher-dimensional) linear problem. Its solutions determine the solutions of the original problem and can be used to predict yield-optimal flux distributions in genome-scale metabolic models. For the theoretical analysis, we consider the linear-fractional problem directly. Most importantly, we show that the yield-optimal solution set (like the rate-optimal solution set) is determined by (yield-optimal) elementary flux vectors of the underlying metabolic model. However, yield- and rate-optimal solutions may differ from each other, and hence optimal (biomass or product) yields are not necessarily obtained at solutions with optimal (growth or synthesis) rates. Moreover, we discuss phase planes/production envelopes and yield spaces, in particular, we prove that yield spaces are convex and provide algorithms for their computation. We illustrate our findings by a small example and demonstrate their relevance for metabolic engineering with realistic models of E. coli.

CONCLUSIONS

We develop a comprehensive mathematical framework for yield optimization in metabolic models. Our theory is particularly useful for the study and rational modification of cell factories designed under given yield and/or rate requirements.

Exploring the combinatorial space of complete pathways to chemicals

Computational pathway design tools often face the challenges of balancing the stoichiometry of co-metabolites and cofactors, and dealing with reaction rule utilization in a single workflow. To this end, we provide an overview of two complementary stoichiometry-based pathway design tools optStoic and novoStoic developed in our group to tackle these challenges. optStoic is designed to determine the stoichiometry of overall conversion first which optimizes a performance criterion (e.g. high carbon/energy efficiency) and ensures a comprehensive search of co-metabolites and cofactors. The procedure then identifies the minimum number of intervening reactions to connect the source and sink metabolites. We also further the pathway design procedure by expanding the search space to include both known and hypothetical reactions, represented by reaction rules, in a new tool termed novoStoic. Reaction rules are derived based on a mixed-integer linear programming (MILP) compatible reaction operator, which allow us to explore natural promiscuous enzymes, engineer candidate enzymes that are not already promiscuous as well as design de novo enzymes. The identified biochemical reaction rules then guide novoStoic to design routes that expand the currently known biotransformation space using a single MILP modeling procedure. We demonstrate the use of the two computational tools in pathway elucidation by designing novel synthetic routes for isobutanol.

Network Analyses in Plant Pathogens

Even in the age of big data in Biology, studying the connections between the biological processes and the molecular mechanisms behind them is a challenging task. Systems biology arose as a transversal discipline between biology, chemistry, computer science, mathematics, and physics to facilitate the elucidation of such connections. A scenario, where the application of systems biology constitutes a very powerful tool, is the study of interactions between hosts and pathogens using network approaches. Interactions between pathogenic bacteria and their hosts, both in agricultural and human health contexts are of great interest to researchers worldwide. Large amounts of data have been generated in the last few years within this area of research. However, studies have been relatively limited to simple interactions. This has left great amounts of data that remain to be utilized. Here, we review the main techniques in network analysis and their complementary experimental assays used to investigate bacterial-plant interactions. Other host-pathogen interactions are presented in those cases where few or no examples of plant pathogens exist. Furthermore, we present key results that have been obtained with these techniques and how these can help in the design of new strategies to control bacterial pathogens. The review comprises metabolic simulation, protein-protein interactions, regulatory control of gene expression, host-pathogen modeling, and genome evolution in bacteria. The aim of this review is to offer scientists working on plant-pathogen interactions basic concepts around network biology, as well as an array of techniques that will be useful for a better and more complete interpretation of their data.

A graph-based approach to analyze flux-balanced pathways in metabolic networks

An elementary flux mode (EFM) is a pathway with minimum set of reactions that are functional in steady-state constrained space. Due to the high computational complexity of calculating EFMs, different approaches have been proposed to find these flux-balanced pathways. In this paper, an approach to find a subset of EFMs is proposed based on a graph data model. The given metabolic network is mapped to the graph model and decisions for reaction inclusion can be made based on metabolites and their associated reactions. This notion makes the approach more convenient to categorize the output pathways. Implications of the proposed method on metabolic networks are discussed.

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.

Extended Metabolic Space Modeling

Determining the fraction of the chemical space that can be processed in vivo by using natural and synthetic biology devices is crucial for the development of advanced synthetic biology applications. The extended metabolic space is a coding system based on molecular signatures that enables the derivation of reaction rules for metabolic reactions and the enumeration of all possible substrates and products corresponding to the rules. The extended metabolic space expands capabilities for controlling the production, processing, sensing, and the release of specific molecules in chassis organisms.

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.

Development of fungal cell factories for the production of secondary metabolites: Linking genomics and metabolism

The genomic era has revolutionized research on secondary metabolites and bioinformatics methods have in recent years revived the antibiotic discovery process after decades with only few new active molecules being identified. New computational tools are driven by genomics and metabolomics analysis, and enables rapid identification of novel secondary metabolites. To translate this increased discovery rate into industrial exploitation, it is necessary to integrate secondary metabolite pathways in the metabolic engineering process. In this review, we will describe the novel advances in discovery of secondary metabolites produced by filamentous fungi, highlight the utilization of genome-scale metabolic models (GEMs) in the design of fungal cell factories for the production of secondary metabolites and review strategies for optimizing secondary metabolite production through the construction of high yielding platform cell factories.

Towards stable kinetics of large metabolic networks: Nonequilibrium potential function approach

While the biochemistry of metabolism in many organisms is well studied, details of the metabolic dynamics are not fully explored yet. Acquiring adequate in vivo kinetic parameters experimentally has always been an obstacle. Unless the parameters of a vast number of enzyme-catalyzed reactions happened to fall into very special ranges, a kinetic model for a large metabolic network would fail to reach a steady state. In this work we show that a stable metabolic network can be systematically established via a biologically motivated regulatory process. The regulation is constructed in terms of a potential landscape description of stochastic and nongradient systems. The constructed process draws enzymatic parameters towards stable metabolism by reducing the change in the Lyapunov function tied to the stochastic fluctuations. Biologically it can be viewed as interplay between the flux balance and the spread of workloads on the network. Our approach allows further constraints such as thermodynamics and optimal efficiency. We choose the central metabolism of Methylobacterium extorquens AM1 as a case study to demonstrate the effectiveness of the approach. Growth efficiency on carbon conversion rate versus cell viability and futile cycles is investigated in depth.

Elementary Vectors and Conformal Sums in Polyhedral Geometry and their Relevance for Metabolic Pathway Analysis

A fundamental result in metabolic pathway analysis states that every flux mode can be decomposed into a sum of elementary modes. However, only a decomposition without cancelations is biochemically meaningful, since a reversible reaction cannot have different directions in the contributing elementary modes. This essential requirement has been largely overlooked by the metabolic pathway community. Indeed, every flux mode can be decomposed into elementary modes without cancelations. The result is an immediate consequence of a theorem by Rockafellar which states that every element of a linear subspace is a conformal sum (a sum without cancelations) of elementary vectors (support-minimal vectors). In this work, we extend the theorem, first to “subspace cones” and then to general polyhedral cones and polyhedra. Thereby, we refine Minkowski's and Carathéodory's theorems, two fundamental results in polyhedral geometry. We note that, in general, elementary vectors need not be support-minimal; in fact, they are conformally non-decomposable and form a unique minimal set of conformal generators. Our treatment is mathematically rigorous, but suitable for systems biologists, since we give self-contained proofs for our results and use concepts motivated by metabolic pathway analysis. In particular, we study cones defined by linear subspaces and nonnegativity conditions — like the flux cone — and use them to analyze general polyhedral cones and polyhedra. Finally, we review applications of elementary vectors and conformal sums in metabolic pathway analysis.

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.

Designing minimal microbial strains of desired functionality using a genetic algorithm

Background

The rational, in silico prediction of gene-knockouts to turn organisms into efficient cell factories is an essential and computationally challenging task in metabolic engineering. Elementary flux mode analysis in combination with constraint minimal cut sets is a particularly powerful method to identify optimal engineering targets, which will force an organism into the desired metabolic state. Given an engineering objective, it is theoretically possible, although computationally impractical, to find the best minimal intervention strategies.

Results

We developed a genetic algorithm (GA-MCS) to quickly find many (near) optimal intervention strategies while overcoming the above mentioned computational burden. We tested our algorithm on Escherichia coli metabolic networks of three different sizes to find intervention strategies satisfying three different engineering objectives.

Conclusions

We show that GA-MCS finds all practically relevant targets for any (non)-linear engineering objective. Our algorithm also found solutions comparable to previously published results. We show that for large networks optimal solutions are found within a fraction of the time used for a complete enumeration.

Editorial: Biotechnology Journal 10 year Anniversary - Thank you for your continued support

When we came to realize that Biotechnology Journal is 10 years "old" and she is no longer "young", we started to look back and look forward again. We would like to thank all of the editors, authors, reviewers, readers and partners for your continued support during the past ten years!

Designing overall stoichiometric conversions and intervening metabolic reactions

Existing computational tools for de novo metabolic pathway assembly, either based on mixed integer linear programming techniques or graph-search applications, generally only find linear pathways connecting the source to the target metabolite. The overall stoichiometry of conversion along with alternate co-reactant (or co-product) combinations is not part of the pathway design. Therefore, global carbon and energy efficiency is in essence fixed with no opportunities to identify more efficient routes for recycling carbon flux closer to the thermodynamic limit. Here, we introduce a two-stage computational procedure that both identifies the optimum overall stoichiometry (i.e., optStoic) and selects for (non-)native reactions (i.e., minRxn/minFlux) that maximize carbon, energy or price efficiency while satisfying thermodynamic feasibility requirements. Implementation for recent pathway design studies identified non-intuitive designs with improved efficiencies. Specifically, multiple alternatives for non-oxidative glycolysis are generated and non-intuitive ways of co-utilizing carbon dioxide with methanol are revealed for the production of C₂₊ metabolites with higher carbon efficiency.

Heading in the right direction: thermodynamics-based network analysis and pathway engineering

Thermodynamics-based network analysis through the introduction of thermodynamic constraints in metabolic models allows a deeper analysis of metabolism and guides pathway engineering. The number and the areas of applications of thermodynamics-based network analysis methods have been increasing in the last ten years. We review recent applications of these methods and we identify the areas that such analysis can contribute significantly, and the needs for future developments. We find that organisms with multiple compartments and extremophiles present challenges for modeling and thermodynamics-based flux analysis. The evolution of current and new methods must also address the issues of the multiple alternatives in flux directionalities and the uncertainties and partial information from analytical methods.