A hierarchy of metabolite exchanges in metabolic models of microbial species and communities

The metabolic network of an organism can be analyzed as a constraint-based model. This analysis can be biased, optimizing an objective such as growth rate, or unbiased, aiming to describe the full feasible space of metabolic fluxes through pathway analysis or random flux sampling. In particular, pathway analysis can decompose the flux space into fundamental and formally defined metabolic pathways. Unbiased methods scale poorly with network size due to combinatorial explosion, but a promising approach to improve scalability is to focus on metabolic subnetworks, e.g., cells' metabolite exchanges with each other and the environment, rather than the full metabolic networks. Here, we applied pathway enumeration and flux sampling to metabolite exchanges in microbial species and a microbial community, using models ranging from central carbon metabolism to genome-scale and focusing on pathway definitions that allow direct targeting of subnetworks such as metabolite exchanges (elementary conversion modes, elementary flux patterns, and minimal pathways). Enumerating growth-supporting metabolite exchanges, we found that metabolite exchanges from different pathway definitions were related through a hierarchy, and we show that this hierarchical relationship between pathways holds for metabolic networks and subnetworks more generally. Metabolite exchange frequencies, defined as the fraction of pathways in which each metabolite was exchanged, were similar across pathway definitions, with a few specific exchanges explaining large differences in pathway counts. This indicates that biological interpretation of predicted metabolite exchanges is robust to the choice of pathway definition, and it suggests strategies for more scalable pathway analysis. Our results also signal wider biological implications, facilitating detailed and interpretable analysis of metabolite exchanges and other subnetworks in fields such as metabolic engineering and synthetic biology.

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.

Genome-scale and pathway engineering for the sustainable aviation fuel precursor isoprenol production in Pseudomonas putida

Sustainable aviation fuel (SAF) will significantly impact global warming in the aviation sector, and important SAF targets are emerging. Isoprenol is a precursor for a promising SAF compound DMCO (1,4-dimethylcyclooctane) and has been produced in several engineered microorganisms. Recently, Pseudomonas putida has gained interest as a future host for isoprenol bioproduction as it can utilize carbon sources from inexpensive plant biomass. Here, we engineer metabolically versatile host P. putida for isoprenol production. We employ two computational modeling approaches (Bilevel optimization and Constrained Minimal Cut Sets) to predict gene knockout targets and optimize the "IPP-bypass" pathway in P. putida to maximize isoprenol production. Altogether, the highest isoprenol production titer from P. putida was achieved at 3.5 g/L under fed-batch conditions. This combination of computational modeling and strain engineering on P. putida for an advanced biofuels production has vital significance in enabling a bioproduction process that can use renewable carbon streams.

Costs of ribosomal RNA stabilization affect ribosome composition at maximum growth rate

Ribosomes are key to cellular self-fabrication and limit growth rate. While most enzymes are proteins, ribosomes consist of 1/3 protein and 2/3 ribonucleic acid (RNA) (in E. coli).Here, we develop a mechanistic model of a self-fabricating cell, validated across diverse growth conditions. Through resource balance analysis (RBA), we explore the variation in maximum growth rate with ribosome composition, assuming constant kinetic parameters.Our model highlights the importance of RNA instability. If we neglect it, RNA synthesis is always cheaper than protein synthesis, leading to an RNA-only ribosome at maximum growth rate. Upon accounting for RNA turnover, we find that a mixed ribosome composed of RNA and proteins maximizes growth rate. To account for RNA turnover, we explore two scenarios regarding the activity of RNases. In (a) degradation is proportional to RNA content. In (b) ribosomal proteins cooperatively mitigate RNA instability by protecting it from misfolding and subsequent degradation. In both cases, higher protein content elevates protein synthesis costs and simultaneously lowers RNA turnover expenses, resulting in mixed RNA-protein ribosomes. Only scenario (b) aligns qualitatively with experimental data across varied growth conditions.Our research provides fresh insights into ribosome biogenesis and evolution, paving the way for understanding protein-rich ribosomes in archaea and mitochondria.

From metagenomes to metabolism: Systematically assessing the metabolic flux feasibilities for "Candidatus Accumulibacter" species during anaerobic substrate uptake

With the rapid growing availability of metagenome assembled genomes (MAGs) and associated metabolic models, the identification of metabolic potential in individual community members has become possible. However, the field still lacks an unbiassed systematic evaluation of the generated metagenomic information to uncover not only metabolic potential, but also feasibilities of these models under specific environmental conditions. In this study, we present a systematic analysis of the metabolic potential in species of "Candidatus Accumulibacter", a group of polyphosphate-accumulating organisms (PAOs). We constructed a metabolic model of the central carbon metabolism and compared the metabolic potential among available MAGs for "Ca. Accumulibacter" species. By combining Elementary Flux Modes Analysis (EFMA) with max-min driving force (MDF) optimization, we obtained all possible flux distributions of the metabolic network and calculated their individual thermodynamic feasibility. Our findings reveal significant variations in the metabolic potential among "Ca. Accumulibacter" MAGs, particularly in the presence of anaplerotic reactions. EFMA revealed 700 unique flux distributions in the complete metabolic model that enable the anaerobic uptake of acetate and its conversion into polyhydroxyalkanoates (PHAs), a well-known phenotype of "Ca. Accumulibacter". However, thermodynamic constraints narrowed down this solution space to 146 models that were stoichiometrically and thermodynamically feasible (MDF > 0 kJ/mol), of which only 8 were strongly feasible (MDF > 7 kJ/mol). Notably, several novel flux distributions for the metabolic model were identified, suggesting putative, yet unreported, functions within the PAO communities. Overall, this work provides valuable insights into the metabolic variability among "Ca. Accumulibacter" species and redefines the anaerobic metabolic potential in the context of phosphate removal. More generally, the integrated workflow presented in this paper can be applied to any metabolic model obtained from a MAG generated from microbial communities to objectively narrow the expected phenotypes from community members.

neo4jsbml: import systems biology markup language data into the graph database Neo4j

Systems Biology Markup Language (SBML) has emerged as a standard for representing biological models, facilitating model sharing and interoperability. It stores many types of data and complex relationships, complicating data management and analysis. Traditional database management systems struggle to effectively capture these complex networks of interactions within biological systems. Graph-oriented databases perform well in managing interactions between different entities. We present neo4jsbml, a new solution that bridges the gap between the Systems Biology Markup Language data and the Neo4j database, for storing, querying and analyzing data. The Systems Biology Markup Language organizes biological entities in a hierarchical structure, reflecting their interdependencies. The inherent graphical structure represents these hierarchical relationships, offering a natural and efficient means of navigating and exploring the model's components. Neo4j is an excellent solution for handling this type of data. By representing entities as nodes and their relationships as edges, Cypher, Neo4j's query language, efficiently traverses this type of graph representing complex biological networks. We have developed neo4jsbml, a Python library for importing Systems Biology Markup Language data into a Neo4j database using a user-defined schema. By leveraging Neo4j's graphical database technology, exploration of complex biological networks becomes intuitive and information retrieval efficient. Neo4jsbml is a tool designed to import Systems Biology Markup Language data into a Neo4j database. Only the desired data is loaded into the Neo4j database. neo4jsbml is user-friendly and can become a useful new companion for visualizing and analyzing metabolic models through the Neo4j graphical database. neo4jsbml is open source software and available at https://github.com/brsynth/neo4jsbml.

Control Theory and Systems Biology: Potential Applications in Neurodegeneration and Search for Therapeutic Targets

Control theory, a well-established discipline in engineering and mathematics, has found novel applications in systems biology. This interdisciplinary approach leverages the principles of feedback control and regulation to gain insights into the complex dynamics of cellular and molecular networks underlying chronic diseases, including neurodegeneration. By modeling and analyzing these intricate systems, control theory provides a framework to understand the pathophysiology and identify potential therapeutic targets. Therefore, this review examines the most widely used control methods in conjunction with genomic-scale metabolic models in the steady state of the multi-omics type. According to our research, this approach involves integrating experimental data, mathematical modeling, and computational analyses to simulate and control complex biological systems. In this review, we find that the most significant application of this methodology is associated with cancer, leaving a lack of knowledge in neurodegenerative models. However, this methodology, mainly associated with the Minimal Dominant Set (MDS), has provided a starting point for identifying therapeutic targets for drug development and personalized treatment strategies, paving the way for more effective therapies.

Maximizing microbial bioproduction from sustainable carbon sources using iterative systems engineering

Maximizing the production of heterologous biomolecules is a complex problem that can be addressed with a systems-level understanding of cellular metabolism and regulation. Specifically, growth-coupling approaches can increase product titers and yields and also enhance production rates. However, implementing these methods for non-canonical carbon streams is challenging due to gaps in metabolic models. Over four design-build-test-learn cycles, we rewire Pseudomonas putida KT2440 for growth-coupled production of indigoidine from para-coumarate. We explore 4,114 potential growth-coupling solutions and refine one design through laboratory evolution and ensemble data-driven methods. The final growth-coupled strain produces 7.3 g/L indigoidine at 77% maximum theoretical yield in para-coumarate minimal medium. The iterative use of growth-coupling designs and functional genomics with experimental validation was highly effective and agnostic to specific hosts, carbon streams, and final products and thus generalizable across many systems.

Minimizing enzyme mass to decompose flux distribution for identifying biologically relevant elementary flux modes

The flux distribution in metabolic network can be decomposed as non-negative linear combinations of elementary flux modes (EFMs). Identifying biologically relevant EFM combination by decomposing flux distribution in metabolic network is a useful method to study metabolisms in systems biology. However, the occurrence of biologically irrelevant EFMs hinders the application of such methods. In this paper, we introduce a novel method for identifying EFM combination by minimizing enzyme mass. Our proposed method, called EMMD (Enzyme Mass Minimization Decomposition), takes into consideration both thermodynamic and enzymatic constraints in stoichiometry metabolic models. By implementing EMMD, we can decompose the flux distributions in metabolic network to detect biologically relevant EFM combinations. We demonstrate the effectiveness of our method by applying it to the core Escherichia coli metabolic network and show that the optimal EFM combinations identified by EMMD are unique. Moreover, the optimal EFM combination identified by EMMD not only aligns more closely with experimental values in terms of estimated growth rate, but it also demonstrates more favorable thermodynamics. Finally, we investigated the growth of the core Escherichia coli metabolic network in Luria-Bertani medium containing different carbon sources, revealing the impact of various carbon sources on the growth rate of flux distribution. EMMD thus could be a promising complement to the existing flux decomposition tools.

Fast Substructure Search in Combinatorial Library Spaces

We present an efficient algorithm for substructure search in combinatorial libraries defined by synthons, i.e., substructures with connection points. Our method improves on existing approaches by introducing powerful heuristics and fast fingerprint screening to quickly eliminate branches of nonmatching combinations of synthons. With this, we achieve typical response times of a few seconds on a standard desktop computer for searches in large combinatorial libraries like the Enamine REAL Space. We published the Java source as part of the OpenChemLib under the BSD license, and we implemented tools to enable substructure search in custom combinatorial libraries.

Linear Response Theory of Evolved Metabolic Systems

Predicting cellular metabolic states is a central problem in biophysics. Conventional approaches, however, sensitively depend on the microscopic details of individual metabolic systems. In this Letter, we derived a universal linear relationship between the metabolic responses against nutrient conditions and metabolic inhibition, with the aid of a microeconomic theory. The relationship holds in arbitrary metabolic systems as long as the law of mass conservation stands, as supported by extensive numerical calculations. It offers quantitative predictions without prior knowledge of systems.

On the representativeness and stability of a set of EFMs

MOTIVATION

Elementary flux modes are a well-known tool for analyzing metabolic networks. The whole set of elementary flux modes (EFMs) cannot be computed in most genome-scale networks due to their large cardinality. Therefore, different methods have been proposed to compute a smaller subset of EFMs that can be used for studying the structure of the network. These latter methods pose the problem of studying the representativeness of the calculated subset. In this article, we present a methodology to tackle this problem.

RESULTS

We have introduced the concept of stability for a particular network parameter and its relation to the representativeness of the EFM extraction method studied. We have also defined several metrics to study and compare the EFM biases. We have applied these techniques to compare the relative behavior of previously proposed methods in two case studies. Furthermore, we have presented a new method for the EFM computation (PiEFM), which is more stable (less biased) than previous ones, has suitable representativeness measures, and exhibits better variability in the extracted EFMs.

AVAILABILITY AND IMPLEMENTATION

Software and additional material are freely available at https://github.com/biogacop/PiEFM.

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).

A universal dynamical metabolic model representing mixotrophic growth of Chlorella sp. on wastes

An emerging idea is to couple wastewater treatment and biofuel production using microalgae to achieve higher productivities and lower costs. This paper proposes a metabolic modeling of Chlorella sp. growing on fermentation wastes (blend of acetate, butyrate and other acids) in mixotrophic conditions, accounting also for the possible inhibitory substrates. This model extends previous works by modifying the metabolic network to include the consumption of glycerol and glucose by Chlorella sp., with the goal to test the addition of these substrates in order to overcome butyrate inhibition. The metabolic model was built using the DRUM framework and consists of 188 reactions and 173 metabolites. After a calibration phase, the model was successfully challenged with data from 122 experiments collected from scientific literature in autotrophic, heterotrophic and mixotrophic conditions. The optimal feeding strategy estimated with the model reduces the time to consume the volatile fatty acids from 16 days to 2 days. The high prediction capability of this model opens new routes for enhancing design and operation in waste valorization using microalgae.

Modeling the metabolic dynamics at the genome-scale by optimized yield analysis

The hybrid cybernetic model (HCM) approach is a dynamic modeling framework that integrates enzyme synthesis and activity regulation. It has been widely applied in bioreaction engineering, particularly in the simulation of microbial growth in different mixtures of carbon sources. In a HCM, the metabolic network is decomposed into elementary flux modes (EFMs), whereby the network can be reduced into a few pathways by yield analysis. However, applying the HCM approach on conventional genome-scale metabolic models (GEMs) is still a challenge due to the high computational demands. Here, we present a HCM strategy that introduced an optimized yield analysis algorithm (opt-yield-FBA) to simulate metabolic dynamics at the genome-scale without the need for EFMs calculation. The opt-yield-FBA is a flux-balance analysis (FBA) based method that can calculate optimal yield solutions and yield space for GEM. With the opt-yield-FBA algorithm, the HCM strategy can be applied to get the yield spaces and avoid the computational burden of EFMs, and it can therefore be applied for developing dynamic models for genome-scale metabolic networks. Here, we illustrate the strategy by applying the concept to simulate the dynamics of microbial communities.

Fluxomics reveals cellular and molecular basis of increased renal ammoniagenesis

The kidney plays a critical role in excreting ammonia during metabolic acidosis and liver failure. The mechanisms behind this process have been poorly explored. The present study combines results of in vivo experiments of increased total ammoniagenesis with systems biology modeling, in which eight rats were fed an amino acid-rich diet (HD group) and eight a normal chow diet (AL group). We developed a method based on elementary mode analysis to study changes in amino acid flux occurring across the kidney in increased ammoniagenesis. Elementary modes represent minimal feasible metabolic paths in steady state. The model was used to predict amino acid fluxes in healthy and pre-hyperammonemic conditions, which were compared to experimental fluxes in rats. First, we found that total renal ammoniagenesis increased from 264 ± 68 to 612 ± 87 nmol (100 g body weight)^-1 min^-1 in the HD group (P = 0.021) and a concomitated upregulation of NKCC2 ammonia and other transporters in the kidney. In the kidney metabolic model, the best predictions were obtained with ammonia transport as an objective. Other objectives resulting in a fair correlation with the measured fluxes (correlation coefficient >0.5) were growth, protein uptake, urea excretion, and lysine and phenylalanine transport. These predictions were improved when specific gene expression data were considered in HD conditions, suggesting a role for the mitochondrial glycine pathway. Further studies are needed to determine if regulation through the mitochondrial glycine pathway and ammonia transporters can be modulated and how to use the kidney as a therapeutic target in hyperammonemia.

StrainDesign: a comprehensive Python package for computational design of metabolic networks

SUMMARY

Various constraint-based optimization approaches have been developed for the computational analysis and design of metabolic networks. Herein, we present StrainDesign, a comprehensive Python package that builds upon the COBRApy toolbox and integrates the most popular metabolic design algorithms, including nested strain optimization methods such as OptKnock, RobustKnock and OptCouple as well as the more general minimal cut sets approach. The optimization approaches are embedded in individual modules, which can also be combined for setting up more elaborate strain design problems. Advanced features, such as the efficient integration of GPR rules and the possibility to consider gene and reaction additions or regulatory interventions, have been generalized and are available for all modules. The package uses state-of-the-art preprocessing methods, supports multiple solvers and provides a number of enhanced tools for analyzing computed intervention strategies including 2D and 3D plots of user-selected metabolic fluxes or yields. Furthermore, a user-friendly interface for the StrainDesign package has been implemented in the GUI-based metabolic modeling software CNApy. StrainDesign provides thus a unique and rich framework for computational strain design in Python, uniting many algorithmic developments in the field and allowing modular extension in the future.

AVAILABILITY AND IMPLEMENTATION

The StrainDesign package can be retrieved from PyPi, Anaconda and GitHub (https://github.com/klamt-lab/straindesign) and is also part of the latest CNApy package.

Thermodynamic limitations of PHB production from formate and fructose in Cupriavidus necator

The chemolithotroph Cupriavidus necator H16 is known as a natural producer of the bioplastic-polymer PHB, as well as for its metabolic versatility to utilize different substrates, including formate as the sole carbon and energy source. Depending on the entry point of the substrate, this versatility requires adjustment of the thermodynamic landscape to maintain sufficiently high driving forces for biological processes. Here we employed a model of the core metabolism of C. necator H16 to analyze the thermodynamic driving forces and PHB yields from formate for different metabolic engineering strategies. For this, we enumerated elementary flux modes (EFMs) of the network and evaluated their PHB yields as well as thermodynamics via Max-min driving force (MDF) analysis and random sampling of driving forces. A heterologous ATP:citrate lyase reaction was predicted to increase driving force for producing acetyl-CoA. A heterologous phosphoketolase reaction was predicted to increase maximal PHB yields as well as driving forces. These enzymes were then verified experimentally to enhance PHB titers between 60 and 300% in select conditions. The EFM analysis also revealed that PHB production from formate may be limited by low driving forces through citrate lyase and aconitase, as well as cofactor balancing, and identified additional reactions associated with low and high PHB yield. Proteomics analysis of the engineered strains confirmed an increased abundance of aconitase and cofactor balancing. The findings of this study aid in understanding metabolic adaptation. Furthermore, the outlined approach will be useful in designing metabolic engineering strategies in other non-model bacteria.

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.

Simulating single-cell metabolism using a stochastic flux-balance analysis algorithm

Stochasticity from gene expression in single cells is known to drive metabolic heterogeneity at the level of cellular populations, which is understood to have important consequences for issues such as microbial drug tolerance and treatment of human diseases like cancer. Despite considerable advancements in profiling the genomes, transcriptomes, and proteomes of single cells, it remains difficult to experimentally characterize their metabolism at the genome scale. Computational methods could bridge this gap toward a systems understanding of single-cell biology. To address this challenge, we developed stochastic simulation algorithm with flux-balance analysis embedded (SSA-FBA), a computational framework for simulating the stochastic dynamics of the metabolism of individual cells using genome-scale metabolic models with experimental estimates of gene expression and enzymatic reaction rate parameters. SSA-FBA extends the constraint-based modeling formalism of metabolic network modeling to the single-cell regime, enabling simulation when experimentation is intractable. We also developed an efficient implementation of SSA-FBA that leverages the topology of embedded flux-balance analysis models to significantly reduce the computational cost of simulation. As a preliminary case study, we built a reduced single-cell model of Mycoplasma pneumoniae and used SSA-FBA to illustrate the role of stochasticity on the dynamics of metabolism at the single-cell level.

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.

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.

Probabilistic thermodynamic analysis of metabolic networks

MOTIVATION

Random sampling of metabolic fluxes can provide a comprehensive description of the capabilities of a metabolic network. However, current sampling approaches do not model thermodynamics explicitly, leading to inaccurate predictions of an organism's potential or actual metabolic operations.

RESULTS

We present a probabilistic framework combining thermodynamic quantities with steady-state flux constraints to analyze the properties of a metabolic network. It includes methods for probabilistic metabolic optimization and for joint sampling of thermodynamic and flux spaces. Applied to a model of Escherichia coli, we use the methods to reveal known and novel mechanisms of substrate channeling, and to accurately predict reaction directions and metabolite concentrations. Interestingly, predicted flux distributions are multimodal, leading to discrete hypotheses on E.coli's metabolic capabilities.

AVAILABILITY AND IMPLEMENTATION

Python and MATLAB packages available at https://gitlab.com/csb.ethz/pta.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Modeling coordinated enzymatic control of saccharification and fermentation by Clostridium thermocellum during consolidated bioprocessing of cellulose

Consolidated bioprocessing (CBP) of cellulose is a cost-effective route to produce valuable biochemicals by integrating saccharification, fermentation and cellulase synthesis in a single step. However, the lack of understanding of governing factors of interdependent saccharification and fermentation in CBP eludes reliable process optimization. Here, we propose a new framework that synergistically couples population balances (to simulate cellulose depolymerization) and cybernetic models (to model enzymatic regulation of fermentation) to enable improved understanding of CBP. The resulting framework, named the unified cybernetic-population balance model (UC-PBM), enables simulation of CBP driven by coordinated control of enzyme synthesis through closed-loop interactions. UC-PBM considers two key aspects in controlling CBP: (1) heterogeneity in cellulose properties and (2) cellular regulation of competing cell growth and cellulase secretion. In a case study on Clostridium thermocellum, UC-PBM not only provides a decent fit with various exometabolomic data, but also reveals that: (i) growth-decoupled cellulase-secreting pathways are only activated during famine conditions to promote the production of growth substrates, and (ii) starting cellulose concentration has a strong influence on the overall flux distribution. Equipped with mechanisms of cellulose degradation and fermentative regulations, UC-PBM is practical to explore phenotypic functions for primary evaluation of microorganisms' potential for metabolic engineering and optimal design of bioprocess.

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.

Flux Coupling and the Objective Functions' Length in EFMs

Structural analysis of constraint-based metabolic network models attempts to find the network's properties by searching for subsets of suitable modes or Elementary Flux Modes (EFMs). One useful approach is based on Linear Program (LP) techniques, which introduce an objective function to convert the stoichiometric and thermodynamic constraints into a linear program (LP), using additional constraints to generate different nontrivial modes. This work introduces FLFS-FC (Fixed Length Function Sampling with Flux Coupling), a new approach to increase the efficiency of generation of large sets of different EFMs for the network. FLFS-FC is based on the importance of the length of the objective functions used in the associated LP problem and the imposition of additional negative constraints. Our proposal overrides some of the known drawbacks associated with the EFM extraction, such as the appearance of unfeasible problems or multiple repeated solutions arising from different LP problems.

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.

A system architecture for parallel analysis of flux-balanced metabolic pathways

Elementary flux mode (EFM) analysis is a well-studied method in constraint-based modeling of metabolic networks. In EFM analysis, a network is decomposed into minimal functional pathways based on the assumption of balanced metabolic fluxes. In this paper, a system architecture is proposed that approximately models the functionality of metabolic networks. The AND/OR graph model is used to represent the metabolic network and each processing element in the system emulates the functionality of a metabolite. The system is implemented on a graphics processing unit (GPU) as the hardware platform using CUDA environment. The proposed architecture takes advantage of the inherent parallelism in the network structure in terms of both pathway and metabolite traversal. The function of each element is defined such that it can find flux-balanced pathways. Pathways in both small and large metabolic networks are applied to the proposed architecture and the results are discussed.

MCS2: minimal coordinated supports for fast enumeration of minimal cut sets in metabolic networks

Motivation

Constraint-based modeling of metabolic networks helps researchers gain insight into the metabolic processes of many organisms, both prokaryotic and eukaryotic. Minimal cut sets (MCSs) are minimal sets of reactions whose inhibition blocks a target reaction in a metabolic network. Most approaches for finding the MCSs in constrained-based models require, either as an intermediate step or as a byproduct of the calculation, the computation of the set of elementary flux modes (EFMs), a convex basis for the valid flux vectors in the network. Recently, Ballerstein et al. proposed a method for computing the MCSs of a network without first computing its EFMs, by creating a dual network whose EFMs are a superset of the MCSs of the original network. However, their dual network is always larger than the original network and depends on the target reaction. Here we propose the construction of a different dual network, which is typically smaller than the original network and is independent of the target reaction, for the same purpose. We prove the correctness of our approach, minimal coordinated support (MCS²), and describe how it can be modified to compute the few smallest MCSs for a given target reaction.

Results

We compare MCS² to the method of Ballerstein et al. and two other existing methods. We show that MCS² succeeds in calculating the full set of MCSs in many models where other approaches cannot finish within a reasonable amount of time. Thus, in addition to its theoretical novelty, our approach provides a practical advantage over existing methods.

Availability and implementation

MCS² is freely available at https://github.com/RezaMash/MCS under the GNU 3.0 license.

Supplementary information

Supplementary data are available at Bioinformatics online.

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.

Dynamic Modeling of CHO Cell Metabolism Using the Hybrid Cybernetic Approach With a Novel Elementary Mode Analysis Strategy

Chinese hamster ovary (CHO) cell culture has a major importance on the production of biopharmaceuticals, including recombinant therapeutic proteins such as monoclonal antibodies (MAb). Mathematical modeling of biological systems can successfully assess metabolism complexity while providing logical and systematic methods for relevant genetic target and culture parameter identification toward cell growth and productivity improvements. Most modeling approaches on CHO cells have been performed under stationary constraints, and only a few dynamic models have been presented on simplified reaction sets, due to substantial overparameterization problems. The hybrid cybernetic modeling (HCM) approach has been recently used to describe the dynamic behavior by incorporating regulation between different metabolic states by elementary mode participation control, with sets of equations evaluated by objective functions. However, as metabolic networks evaluated are constructed toward a genomic scale, and cell compartmentalization is considered, identification of the active set becomes more difficult as EM number exponentially grows. Thus, the development of robust approaches for EM active set selection and analysis with smaller computational requirements is required to impulse the use of cybernetic modeling on larger up to genome-scale networks. In this report, a novel elementary mode selection strategy, based on a polar representation of the convex solution space is presented and coupled to a cybernetic approach to model the dynamic physiologic and metabolic behavior of CHO-S cell cultures. The proposed Polar Space Yield Analysis (PSYA) was compared to other reported elementary mode selection approaches derived from Common Metabolic Objective Analysis (CMOA) used in Flux Balance Analysis (FBA), Yield Space Analysis (YSA), and Lumped Yield Space Analysis (LYSA). For this purpose, exponential growth phase dynamic metabolic models were calculated using kinetic rate equations based on previously modeled growth parameters. Finally, complete culture dynamic metabolic flux models were constructed using the HCM approach with selected elementary mode sets. The yield space elementary mode- and the polar space elementary mode- hybrid cybernetic models presented the best fits and performances. Also, a flux reaction perturbation prediction approach based on the polar yield solution space resulted useful for metabolic network flux distribution capability analysis and identification of potential genetic modifications targets.

Thermodynamic Approaches in Flux Analysis

Networks of reactions inside the cell are constrained by the laws of mass and energy balance. Constrained-based modelling (CBM) is the most used method to describe the mass balance of metabolic network. The main key concepts in CBM are stoichiometric analysis such as elementary flux mode analysis or flux balance analysis. Some of these methods have focused on adding thermodynamics constraints to eliminate non-physical fluxes or inconsistencies in the metabolic system. Here, we review the main different approaches and how they tackle the different class of problems.

Towards scaling elementary flux mode computation

While elementary flux mode (EFM) analysis is now recognized as a cornerstone computational technique for cellular pathway analysis and engineering, EFM application to genome-scale models remains computationally prohibitive. This article provides a review of aspects of EFM computation that elucidates bottlenecks in scaling EFM computation. First, algorithms for computing EFMs are reviewed. Next, the impact of redundant constraints, sensitivity to constraint ordering and network compression are evaluated. Then, the advantages and limitations of recent parallelization and GPU-based efforts are highlighted. The article then reviews alternative pathway analysis approaches that aim to reduce the EFM solution space. Despite advances in EFM computation, our review concludes that continued scaling of EFM computation is necessary to apply EFM to genome-scale models. Further, our review concludes that pathway analysis methods that target specific pathway properties can provide powerful alternatives to EFM analysis.

Metabolic engineering of Bacillus subtilis for production of para-aminobenzoic acid - unexpected importance of carbon source is an advantage for space application

High-strength polymers, such as aramid fibres, are important materials in space technology. To obtain these materials in remote locations, such as Mars, biological production is of interest. The aromatic polymer precursor para-aminobenzoic acid (pABA) can be derived from the shikimate pathway through metabolic engineering of Bacillus subtilis, an organism suited for space synthetic biology. Our engineering strategy included repair of the defective indole-3-glycerol phosphate synthase (trpC), knockout of one chorismate mutase isozyme (aroH) and overexpression of the aminodeoxychorismate synthase (pabAB) and aminodeoxychorismate lyase (pabC) from the bacteria Corynebacterium callunae and Xenorhabdus bovienii respectively. Further, a fusion-protein enzyme (pabABC) was created for channelling of the carbon flux. Using adaptive evolution, mutants of the production strain, able to metabolize xylose, were created, to explore and compare pABA production capacity from different carbon sources. Rather than the efficiency of the substrate or performance of the biochemical pathway, the product toxicity, which was strongly dependent on the pH, appeared to be the overall limiting factor. The highest titre achieved in shake flasks was 3.22 g l-1 with a carbon yield of 12.4% [C-mol/C-mol] from an amino sugar. This promises suitability of the system for in situ resource utilization (ISRU) in space biotechnology, where feedstocks that can be derived from cyanobacterial cell lysate play a role.

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.

Metabolic modeling and response surface analysis of an Escherichia coli strain engineered for shikimic acid production

Background

Classic metabolic engineering strategies often induce significant flux imbalances to microbial metabolism, causing undesirable outcomes such as suboptimal conversion of substrates to products. Several mathematical frameworks have been developed to understand the physiological and metabolic state of production strains and to identify genetic modification targets for improved bioproduct formation. In this work, a modeling approach was applied to describe the physiological behavior and the metabolic fluxes of a shikimic acid overproducing Escherichia coli strain lacking the major glucose transport system, grown on complex media.

Results

The obtained flux distributions indicate the presence of high fluxes through the pentose phosphate and Entner-Doudoroff pathways, which could limit the availability of erythrose-4-phosphate for shikimic acid production even with high flux redirection through the pentose phosphate pathway. In addition, highly active glyoxylate shunt fluxes and a pyruvate/acetate cycle are indicators of overflow glycolytic metabolism in the tested conditions. The analysis of the combined physiological and flux response surfaces, enabled zone allocation for different physiological outputs within variant substrate conditions. This information was then used for an improved fed-batch process designed to preserve the metabolic conditions that were found to enhance shikimic acid productivity. This resulted in a 40% increase in the shikimic acid titer (60 g/L) and 70% increase in volumetric productivity (2.45 gSA/L*h), while preserving yields, compared to the batch process.

Conclusions

The combination of dynamic metabolic modeling and experimental parameter response surfaces was a successful approach to understand and predict the behavior of a shikimic acid producing strain under variable substrate concentrations. Response surfaces were useful for allocating different physiological behavior zones with different preferential product outcomes. Both model sets provided information that could be applied to enhance shikimic acid production on an engineered shikimic acid overproducing Escherichia coli strain.

Electronic supplementary material

The online version of this article (10.1186/s12918-018-0632-4) contains supplementary material, which is available to authorized users.

Dynamic elementary mode modelling of non-steady state flux data

BACKGROUND

A novel framework is proposed to analyse metabolic fluxes in non-steady state conditions, based on the new concept of dynamic elementary mode (dynEM): an elementary mode activated partially depending on the time point of the experiment.

RESULTS

Two methods are introduced here: dynamic elementary mode analysis (dynEMA) and dynamic elementary mode regression discriminant analysis (dynEMR-DA). The former is an extension of the recently proposed principal elementary mode analysis (PEMA) method from steady state to non-steady state scenarios. The latter is a discriminant model that permits to identify which dynEMs behave strongly different depending on the experimental conditions. Two case studies of Saccharomyces cerevisiae, with fluxes derived from simulated and real concentration data sets, are presented to highlight the benefits of this dynamic modelling.

CONCLUSIONS

This methodology permits to analyse metabolic fluxes at early stages with the aim of i) creating reduced dynamic models of flux data, ii) combining many experiments in a single biologically meaningful model, and iii) identifying the metabolic pathways that drive the organism from one state to another when changing the environmental conditions.

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.

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.

Muconic Acid Production via Alternative Pathways and a Synthetic "Metabolic Funnel"

Muconic acid is a promising platform biochemical and precursor to adipic acid, which can be used to synthesize various plastics and polymers. In this study, the systematic construction and comparative evaluation of a modular network of non-natural pathways for muconic acid biosynthesis was investigated in Escherichia coli, including via three distinct and novel pathways proceeding via phenol as a common intermediate. However, poor recombinant activity and high promiscuity of phenol hydroxylase ultimately limited "phenol-dependent" muconic acid production. A fourth pathway proceeding via p-hydroxybenzoate, protocatechuate, and catechol was accordingly developed, though with muconic acid titers by this route reaching just 819 mg/L, its performance lagged behind that of the established, "3-dehydroshikimiate-derived" route. Finally, these two most promising pathways were coexpressed in parallel to create a synthetic "metabolic funnel" that, by enabling maximal net precursor assimilation and flux while preserving native chorismate biosynthesis, nearly doubled muconic acid production to up to >3.1 g/L at a glucose yield of 158 mg/g while introducing only a single auxotrophy. This generalizable, "funneling" strategy is expected to have broad applications in metabolic engineering for further enhancing production of muconic acid, as well as other important bioproducts of interest.

Toward Synthetic Biology Strategies for Adipic Acid Production: An in Silico Tool for Combined Thermodynamics and Stoichiometric Analysis of Metabolic Networks

Adipic acid, a nylon-6,6 precursor, has recently gained popularity in synthetic biology. Here, 16 different production routes to adipic acid were evaluated using a novel tool for network-embedded thermodynamic analysis of elementary flux modes. The tool distinguishes between thermodynamically feasible and infeasible modes under determined metabolite concentrations, allowing the thermodynamic feasibility of theoretical yields to be assessed. Further, patterns that always caused infeasible flux distributions were identified, which will aid the development of tailored strain design. A review of cellular efflux mechanisms revealed that significant accumulation of extracellular product is only possible if coupled with ATP hydrolysis. A stoichiometric analysis demonstrated that the maximum theoretical product carbon yield heavily depends on the metabolic route, ranging from 32 to 99% on glucose and/or palmitate in Escherichia coli and Saccharomyces cerevisiae metabolic models. Equally important, metabolite concentrations appeared to be thermodynamically restricted in several pathways. Consequently, the number of thermodynamically feasible flux distributions was reduced, in some cases even rendering whole pathways infeasible, highlighting the importance of pathway choice. Only routes based on the shikimate pathway were thermodynamically favorable over a large concentration and pH range. The low pH capability of S. cerevisiae shifted the thermodynamic equilibrium of some pathways toward product formation. One identified infeasible-pattern revealed that the reversibility of the mitochondrial malate dehydrogenase contradicted the current state of knowledge, which imposes a major restriction on the metabolism of S. cerevisiae. Finally, the evaluation of industrially relevant constraints revealed that two shikimate pathway-based routes in E. coli were the most robust.

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.