Regulation of gene expression in flux balance models of metabolism

Deciphering and designing microbial communities by genome-scale metabolic modelling

Microbial communities are shaped by the complex interactions among organisms and the environment. Genome-scale metabolic models (GEMs) can provide deeper insights into the complexity and ecological properties of various microbial communities, revealing their intricate interactions. Many researchers have modified GEMs for the microbial communities based on specific needs. Thus, GEMs need to be comprehensively summarized to better understand the trends in their development. In this review, we summarized the key developments in deciphering and designing microbial communities using different GEMs. A timeline of selected highlights in GEMs indicated that this area is evolving from the single-strain level to the microbial community level. Then, we outlined a framework for constructing GEMs of microbial communities. We also summarized the models and resources of static and dynamic community-level GEMs. We focused on the role of external environmental and intracellular resources in shaping the assembly of microbial communities. Finally, we discussed the key challenges and future directions of GEMs, focusing on the integration of GEMs with quorum sensing mechanisms, microbial ecology interactions, machine learning algorithms, and automatic modeling, all of which contribute to consortia-based applications in different fields.

Development and applications of genome-scale metabolic network models

The genome-scale metabolic network model is an effective tool for characterizing the gene-protein-response relationship in the entire metabolic pathway of an organism. By combining various algorithms, the genome-scale metabolic network model can effectively simulate the influence of a specific environment on the physiological state of cells, optimize the culture conditions of strains, and predict the targets of genetic modification to achieve targeted modification of strains. In this review, we summarize the whole process of model building, sort out the various tools that may be involved in the model building process, and explain the role of various algorithms in model analysis. In addition, we also summarized the application of GSMM in network characteristics, cell phenotypes, metabolic engineering, etc. Finally, we discuss the current challenges facing GSMM.

Metabolic reprogramming and signalling cross-talks in tumour-immune interaction: a system-level exploration

Tumour-immune microenvironment (TIME) is pivotal in tumour progression and immunoediting. Within TIME, immune cells undergo metabolic adjustments impacting nutrient supply and the anti-tumour immune response. Metabolic reprogramming emerges as a promising approach to revert the immune response towards a pro-inflammatory state and conquer tumour dominance. This study proposes immunomodulatory mechanisms based on metabolic reprogramming and employs the regulatory flux balance analysis modelling approach, which integrates signalling, metabolism and regulatory processes. For the first time, a comprehensive system-level model is constructed to capture signalling and metabolic cross-talks during tumour-immune interaction and regulatory constraints are incorporated by considering the time lag between them. The model analysis identifies novel features to enhance the immune response while suppressing tumour activity. Particularly, altering the exchange of succinate and oxaloacetate between glioma and macrophage enhances the pro-inflammatory response of immune cells. Inhibition of glutamate uptake in T-cells disrupts the antioxidant mechanism of glioma and reprograms metabolism. Metabolic reprogramming through adenosine monophosphate (AMP)-activated protein kinase (AMPK), coupled with glutamate uptake inhibition, was identified as the most impactful combination to restore T-cell function. A comprehensive understanding of metabolism and gene regulation represents a favourable approach to promote immune cell recovery from tumour dominance.

Flux Balance Analysis of Mammalian Cell Systems

Flux balance analysis (FBA) is a computational methodology to model and analyze the metabolic behavior of cells. In this chapter, we break down the key steps for formulating an FBA model and other FBA-derived methodologies in the context of mammalian cell biology, including strain design, developing cell line-specific models, and conducting flux sampling. We provide annotated COBRApy code for each step to show how it would work in practice.

From microbiome composition to functional engineering, one step at a time

SUMMARYCommunities of microorganisms (microbiota) are present in all habitats on Earth and are relevant for agriculture, health, and climate. Deciphering the mechanisms that determine microbiota dynamics and functioning within the context of their respective environments or hosts (the microbiomes) is crucially important. However, the sheer taxonomic, metabolic, functional, and spatial complexity of most microbiomes poses substantial challenges to advancing our knowledge of these mechanisms. While nucleic acid sequencing technologies can chart microbiota composition with high precision, we mostly lack information about the functional roles and interactions of each strain present in a given microbiome. This limits our ability to predict microbiome function in natural habitats and, in the case of dysfunction or dysbiosis, to redirect microbiomes onto stable paths. Here, we will discuss a systematic approach (dubbed the N+1/N-1 concept) to enable step-by-step dissection of microbiome assembly and functioning, as well as intervention procedures to introduce or eliminate one particular microbial strain at a time. The N+1/N-1 concept is informed by natural invasion events and selects culturable, genetically accessible microbes with well-annotated genomes to chart their proliferation or decline within defined synthetic and/or complex natural microbiota. This approach enables harnessing classical microbiological and diversity approaches, as well as omics tools and mathematical modeling to decipher the mechanisms underlying N+1/N-1 microbiota outcomes. Application of this concept further provides stepping stones and benchmarks for microbiome structure and function analyses and more complex microbiome intervention strategies.

Maximizing multi-reaction dependencies provides more accurate and precise predictions of intracellular fluxes than the principle of parsimony

Intracellular fluxes represent a joint outcome of cellular transcription and translation and reflect the availability and usage of nutrients from the environment. While approaches from the constraint-based metabolic framework can accurately predict cellular phenotypes, such as growth and exchange rates with the environment, accurate prediction of intracellular fluxes remains a pressing problem. Parsimonious flux balance analysis (pFBA) has become an approach of choice to predict intracellular fluxes by employing the principle of efficient usage of protein resources. Nevertheless, comparative analyses of intracellular flux predictions from pFBA against fluxes estimated from labeling experiments remain scarce. Here, we posited that steady-state flux distributions derived from the principle of maximizing multi-reaction dependencies are of improved accuracy and precision than those resulting from pFBA. To this end, we designed a constraint-based approach, termed complex-balanced FBA (cbFBA), to predict steady-state flux distributions that support the given specific growth rate and exchange fluxes. We showed that the steady-state flux distributions resulting from cbFBA in comparison to pFBA show better agreement with experimentally measured fluxes from 17 Escherichia coli strains and are more precise, due to the smaller space of alternative solutions. We also showed that the same principle holds in eukaryotes by comparing the predictions of pFBA and cbFBA against experimentally derived steady-state flux distributions from 26 knock-out mutants of Saccharomyces cerevisiae. Furthermore, our results showed that intracellular fluxes predicted by cbFBA provide better support for the principle of minimizing metabolic adjustment between mutants and wild types. Together, our findings point that other principles that consider the dynamics and coordination of steady states may govern the distribution of intracellular fluxes.

Monitoring and modelling the glutamine metabolic pathway: a review and future perspectives

BACKGROUND

Analysis of the glutamine metabolic pathway has taken a special place in metabolomics research in recent years, given its important role in cell biosynthesis and bioenergetics across several disorders, especially in cancer cell survival. The science of metabolomics addresses the intricate intracellular metabolic network by exploring and understanding how cells function and respond to external or internal perturbations to identify potential therapeutic targets. However, despite recent advances in metabolomics, monitoring the kinetics of a metabolic pathway in a living cell in situ, real-time and holistically remains a significant challenge.

AIM

This review paper explores the range of analytical approaches for monitoring metabolic pathways, as well as physicochemical modeling techniques, with a focus on glutamine metabolism. We discuss the advantages and disadvantages of each method and explore the potential of label-free Raman microspectroscopy, in conjunction with kinetic modeling, to enable real-time and in situ monitoring of the cellular kinetics of the glutamine metabolic pathway.

KEY SCIENTIFIC CONCEPTS

Given its important role in cell metabolism, the ability to monitor and model the glutamine metabolic pathways are highlighted. Novel, label free approaches have the potential to revolutionise metabolic biosensing, laying the foundation for a new paradigm in metabolomics research and addressing the challenges in monitoring metabolic pathways in living cells.

Functional decomposition of metabolism allows a system-level quantification of fluxes and protein allocation towards specific metabolic functions

Quantifying the contribution of individual molecular components to complex cellular processes is a grand challenge in systems biology. Here we establish a general theoretical framework (Functional Decomposition of Metabolism, FDM) to quantify the contribution of every metabolic reaction to metabolic functions, e.g. the synthesis of biomass building blocks. FDM allowed for a detailed quantification of the energy and biosynthesis budget for growing Escherichia coli cells. Surprisingly, the ATP generated during the biosynthesis of building blocks from glucose almost balances the demand from protein synthesis, the largest energy expenditure known for growing cells. This leaves the bulk of the energy generated by fermentation and respiration unaccounted for, thus challenging the common notion that energy is a key growth-limiting resource. Moreover, FDM together with proteomics enables the quantification of enzymes contributing towards each metabolic function, allowing for a first-principle formulation of a coarse-grained model of global protein allocation based on the structure of the metabolic network.

Metabolic function-based normalization improves transcriptome data-driven reduction of genome-scale metabolic models

Genome-scale metabolic models (GEMs) are extensively used to simulate cell metabolism and predict cell phenotypes. GEMs can also be tailored to generate context-specific GEMs, using omics data integration approaches. To date, many integration approaches have been developed, however, each with specific pros and cons; and none of these algorithms systematically outperforms the others. The key to successful implementation of such integration algorithms lies in the optimal selection of parameters, and thresholding is a crucial component in this process. To improve the predictive accuracy of context-specific models, we introduce a new integration framework that improves the ranking of related genes and homogenizes the expression values of those gene sets using single-sample Gene Set Enrichment Analysis (ssGSEA). In this study, we coupled ssGSEA with GIMME and validated the advantages of the proposed framework to predict the ethanol formation of yeast grown in the glucose-limited chemostats, and to simulate metabolic behaviors of yeast growth in four different carbon sources. This framework enhances the predictive accuracy of GIMME which we demonstrate for predicting the yeast physiology in nutrient-limited cultures.

A contribution of metabolic engineering to addressing medical problems: Metabolic flux analysis

Metabolic engineering has served as a systematic discipline for industrial biotechnology as it has offered systematic tools and methods for strain development and bioprocess optimization. Because these metabolic engineering tools and methods are concerned with the biological network of a cell with emphasis on metabolic network, they have also been applied to a range of medical problems where better understanding of metabolism has also been perceived to be important. Metabolic flux analysis (MFA) is a unique systematic approach initially developed in the metabolic engineering community, and has proved its usefulness and potential when addressing a range of medical problems. In this regard, this review discusses the contribution of MFA to addressing medical problems. For this, we i) provide overview of the milestones of MFA, ii) define two main branches of MFA, namely constraint-based reconstruction and analysis (COBRA) and isotope-based MFA (iMFA), and iii) present successful examples of their medical applications, including characterizing the metabolism of diseased cells and pathogens, and identifying effective drug targets. Finally, synergistic interactions between metabolic engineering and biomedical sciences are discussed with respect to MFA.

Flux balance analysis of metabolic networks for efficient engineering of microbial cell factories

Metabolic engineering principles have long been applied to explore the metabolic networks of complex microbial cell factories under a variety of environmental constraints for effective deployment of the microorganisms in the optimal production of biochemicals like biofuels, polymers, amino acids, recombinant proteins. One of the methodologies used for analyzing microbial metabolic networks is the Flux Balance Analysis (FBA), which employs applications of optimization techniques for forecasting biomass growth and metabolic flux distribution of industrially important products under specified environmental conditions. The in silico flux simulations are instrumental for designing the production-specific microbial cell factories. However, FBA has some inherent limitations. The present review emphasizes how the incorporation of additional kinetic, thermodynamic, expression and regulatory constraints and integration of omics data into the classical FBA platform improve the prediction accuracy of FBA. A programmed comparison of the simulated data with the experimental observations is presented for supporting the claim. The review further accounts for the successful implementation of classical FBA in biotechnological applications and identifies areas in which classical FBA fails to make correct predictions. The analysis of the predictive capabilities of the different FBA strategies presented here is expected to help researchers in finding new avenues in engineering highly efficient microbial metabolic pathways and identify the key metabolic bottlenecks during the process. Based on the appropriate metabolic network design, fermentation engineers will be able to effectively design the bioreactors and optimize large-scale biochemical production through suitable pathway modifications.

Metabolomics and modelling approaches for systems metabolic engineering

Metabolic engineering involves the manipulation of microbes to produce desirable compounds through genetic engineering or synthetic biology approaches. Metabolomics involves the quantitation of intracellular and extracellular metabolites, where mass spectrometry and nuclear magnetic resonance based analytical instrumentation are often used. Here, the experimental designs, sample preparations, metabolite quenching and extraction are essential to the quantitative metabolomics workflow. The resultant metabolomics data can then be used with computational modelling approaches, such as kinetic and constraint-based modelling, to better understand underlying mechanisms and bottlenecks in the synthesis of desired compounds, thereby accelerating research through systems metabolic engineering. Constraint-based models, such as genome scale models, have been used successfully to enhance the yield of desired compounds from engineered microbes, however, unlike kinetic or dynamic models, constraint-based models do not incorporate regulatory effects. Nevertheless, the lack of time-series metabolomic data generation has hindered the usefulness of dynamic models till today. In this review, we show that improvements in automation, dynamic real-time analysis and high throughput workflows can drive the generation of more quality data for dynamic models through time-series metabolomics data generation. Spatial metabolomics also has the potential to be used as a complementary approach to conventional metabolomics, as it provides information on the localization of metabolites. However, more effort must be undertaken to identify metabolites from spatial metabolomics data derived through imaging mass spectrometry, where machine learning approaches could prove useful. On the other hand, single-cell metabolomics has also seen rapid growth, where understanding cell-cell heterogeneity can provide more insights into efficient metabolic engineering of microbes. Moving forward, with potential improvements in automation, dynamic real-time analysis, high throughput workflows, and spatial metabolomics, more data can be produced and studied using machine learning algorithms, in conjunction with dynamic models, to generate qualitative and quantitative predictions to advance metabolic engineering efforts.

MERRIN: MEtabolic regulation rule INference from time series data

MOTIVATION

Many techniques have been developed to infer Boolean regulations from a prior knowledge network (PKN) and experimental data. Existing methods are able to reverse-engineer Boolean regulations for transcriptional and signaling networks, but they fail to infer regulations that control metabolic networks.

RESULTS

We present a novel approach to infer Boolean rules for metabolic regulation from time-series data and a PKN. Our method is based on a combination of answer set programming and linear programming. By solving both combinatorial and linear arithmetic constraints, we generate candidate Boolean regulations that can reproduce the given data when coupled to the metabolic network. We evaluate our approach on a core regulated metabolic network and show how the quality of the predictions depends on the available kinetic, fluxomics or transcriptomics time-series data.

AVAILABILITY AND IMPLEMENTATION

Software available at https://github.com/bioasp/merrin.

SUPPLEMENTARY INFORMATION

Supplementary data are available at https://doi.org/10.5281/zenodo.6670164.

Metabolic pathway design for growth-associated phenylalanine production using synthetically designed mutualism

Combination of growth-associated pathway engineering based on flux balance analysis (FBA) and adaptive laboratory evolution (ALE) is a powerful approach to enhance the production of useful compounds. However, the feasibility of such growth-associated pathway designs depends on the type of target compound. In the present study, FBA predicted a set of gene deletions (pykA, pykF, ppc, zwf, and adhE) that leads to growth-associated phenylalanine production in Escherichia coli. The knockout strain is theoretically enforced to produce phenylalanine only at high growth yields, and could not be applied to the ALE experiment because of a severe growth defect. To overcome this challenge, we propose a novel approach for ALE based on mutualistic co-culture for coupling growth and production, regardless of the growth rate. We designed a synthetic mutualism of a phenylalanine-producing leucine-auxotrophic strain (KF strain) and a leucine-producing phenylalanine-auxotrophic strain (KL strain) and performed an ALE experiment for approximately 160 generations. The evolved KF strain (KF-E strain) grew in a synthetic medium (with glucose as the main carbon source) supplemented with leucine, while severe growth defects were observed in the parental KF strain. The phenylalanine yield of the KF-E strain was 2.3 times higher than that of the KF strain.

Genome-scale metabolic network models: from first-generation to next-generation

Over the last two decades, thousands of genome-scale metabolic network models (GSMMs) have been constructed. These GSMMs have been widely applied in various fields, ranging from network interaction analysis, to cell phenotype prediction. However, due to the lack of constraints, the prediction accuracy of first-generation GSMMs was limited. To overcome these limitations, the next-generation GSMMs were developed by integrating omics data, adding constrain condition, integrating different biological models, and constructing whole-cell models. Here, we review recent advances of GSMMs from the first generation to the next generation. Then, we discuss the major application of GSMMs in industrial biotechnology, such as predicting phenotypes and guiding metabolic engineering. In addition, human health applications, including understanding biological mechanisms, discovering biomarkers and drug targets, are also summarized. Finally, we address the challenges and propose new trend of GSMMs. KEY POINTS: •This mini-review updates the literature on almost all published GSMMs since 1999. •Detailed insights into the development of the first- and next-generation GSMMs. •The application of GSMMs is summarized, and the prospects of integrating machine learning are emphasized.

Multi-scale model suggests the trade-off between protein and ATP demand as a driver of metabolic changes during yeast replicative ageing

The accumulation of protein damage is one of the major drivers of replicative ageing, describing a cell’s reduced ability to reproduce over time even under optimal conditions. Reactive oxygen and nitrogen species are precursors of protein damage and therefore tightly linked to ageing. At the same time, they are an inevitable by-product of the cell’s metabolism. Cells are able to sense high levels of reactive oxygen and nitrogen species and can subsequently adapt their metabolism through gene regulation to slow down damage accumulation. However, the older or damaged a cell is the less flexibility it has to allocate enzymes across the metabolic network, forcing further adaptions in the metabolism. To investigate changes in the metabolism during replicative ageing, we developed an multi-scale mathematical model using budding yeast as a model organism. The model consists of three interconnected modules: a Boolean model of the signalling network, an enzyme-constrained flux balance model of the central carbon metabolism and a dynamic model of growth and protein damage accumulation with discrete cell divisions. The model can explain known features of replicative ageing, like average lifespan and increase in generation time during successive division, in yeast wildtype cells by a decreasing pool of functional enzymes and an increasing energy demand for maintenance. We further used the model to identify three consecutive metabolic phases, that a cell can undergo during its life, and their influence on the replicative potential, and proposed an intervention span for lifespan control.

Mathematical models to study the biology of pathogens and the infectious diseases they cause

Mathematical models have many applications in infectious diseases: epidemiologists use them to forecast outbreaks and design containment strategies; systems biologists use them to study complex processes sustaining pathogens, from the metabolic networks empowering microbial cells to ecological networks in the microbiome that protects its host. Here, we (1) review important models relevant to infectious diseases, (2) draw parallels among models ranging widely in scale. We end by discussing a minimal set of information for a model to promote its use by others and to enable predictions that help us better fight pathogens and the diseases they cause.

Hybrid modelling of biological systems: current progress and future prospects

Integrated modelling of biological systems is becoming a necessity for constructing models containing the major biochemical processes of such systems in order to obtain a holistic understanding of their dynamics and to elucidate emergent behaviours. Hybrid modelling methods are crucial to achieve integrated modelling of biological systems. This paper reviews currently popular hybrid modelling methods, developed for systems biology, mainly revealing why they are proposed, how they are formed from single modelling formalisms and how to simulate them. By doing this, we identify future research requirements regarding hybrid approaches for further promoting integrated modelling of biological systems.

Quantitative prediction of conditional vulnerabilities in regulatory and metabolic networks using PRIME

The ability of Mycobacterium tuberculosis (Mtb) to adopt heterogeneous physiological states underlies its success in evading the immune system and tolerating antibiotic killing. Drug tolerant phenotypes are a major reason why the tuberculosis (TB) mortality rate is so high, with over 1.8 million deaths annually. To develop new TB therapeutics that better treat the infection (faster and more completely), a systems-level approach is needed to reveal the complexity of network-based adaptations of Mtb. Here, we report a new predictive model called PRIME (Phenotype of Regulatory influences Integrated with Metabolism and Environment) to uncover environment-specific vulnerabilities within the regulatory and metabolic networks of Mtb. Through extensive performance evaluations using genome-wide fitness screens, we demonstrate that PRIME makes mechanistically accurate predictions of context-specific vulnerabilities within the integrated regulatory and metabolic networks of Mtb, accurately rank-ordering targets for potentiating treatment with frontline drugs.

A metabolic modeling platform for the computation of microbial ecosystems in time and space (COMETS)

Genome-scale stoichiometric modeling of metabolism has become a standard systems biology tool for modeling cellular physiology and growth. Extensions of this approach are emerging as a valuable avenue for predicting, understanding and designing microbial communities. Computation of microbial ecosystems in time and space (COMETS) extends dynamic flux balance analysis to generate simulations of multiple microbial species in molecularly complex and spatially structured environments. Here we describe how to best use and apply the most recent version of COMETS, which incorporates a more accurate biophysical model of microbial biomass expansion upon growth, evolutionary dynamics and extracellular enzyme activity modules. In addition to a command-line option, COMETS includes user-friendly Python and MATLAB interfaces compatible with the well-established COBRA models and methods, as well as comprehensive documentation and tutorials. This protocol provides a detailed guideline for installing, testing and applying COMETS to different scenarios, generating simulations that take from a few minutes to several days to run, with broad applicability to microbial communities across biomes and scales.

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

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

Next-Generation Genome-Scale Metabolic Modeling through Integration of Regulatory Mechanisms

Genome-scale metabolic models (GEMs) are powerful tools for understanding metabolism from a systems-level perspective. However, GEMs in their most basic form fail to account for cellular regulation. A diverse set of mechanisms regulate cellular metabolism, enabling organisms to respond to a wide range of conditions. This limitation of GEMs has prompted the development of new methods to integrate regulatory mechanisms, thereby enhancing the predictive capabilities and broadening the scope of GEMs. Here, we cover integrative models encompassing six types of regulatory mechanisms: transcriptional regulatory networks (TRNs), post-translational modifications (PTMs), epigenetics, protein-protein interactions and protein stability (PPIs/PS), allostery, and signaling networks. We discuss 22 integrative GEM modeling methods and how these have been used to simulate metabolic regulation during normal and pathological conditions. While these advances have been remarkable, there remains a need for comprehensive and widespread integration of regulatory constraints into GEMs. We conclude by discussing challenges in constructing GEMs with regulation and highlight areas that need to be addressed for the successful modeling of metabolic regulation. Next-generation integrative GEMs that incorporate multiple regulatory mechanisms and their crosstalk will be invaluable for discovering cell-type and disease-specific metabolic control mechanisms.

Genome-Scale Metabolic Models and Machine Learning Reveal Genetic Determinants of Antibiotic Resistance in Escherichia coli and Unravel the Underlying Metabolic Adaptation Mechanisms

Antimicrobial resistance (AMR) is becoming one of the largest threats to public health worldwide, with the opportunistic pathogen Escherichia coli playing a major role in the AMR global health crisis. Unravelling the complex interplay between drug resistance and metabolic rewiring is key to understand the ability of bacteria to adapt to new treatments and to the development of new effective solutions to combat resistant infections. We developed a computational pipeline that combines machine learning with genome-scale metabolic models (GSMs) to elucidate the systemic relationships between genetic determinants of resistance and metabolism beyond annotated drug resistance genes. Our approach was used to identify genetic determinants of 12 AMR profiles for the opportunistic pathogenic bacterium E. coli. Then, to interpret the large number of identified genetic determinants, we applied a constraint-based approach using the GSM to predict the effects of genetic changes on growth, metabolite yields, and reaction fluxes. Our computational platform leads to multiple results. First, our approach corroborates 225 known AMR-conferring genes, 35 of which are known for the specific antibiotic. Second, integration with the GSM predicted 20 top-ranked genetic determinants (including accA, metK, fabD, fabG, murG, lptG, mraY, folP, and glmM) essential for growth, while a further 17 top-ranked genetic determinants linked AMR to auxotrophic behavior. Third, clusters of AMR-conferring genes affecting similar metabolic processes are revealed, which strongly suggested that metabolic adaptations in cell wall, energy, iron and nucleotide metabolism are associated with AMR. The computational solution can be used to study other human and animal pathogens.

IMPORTANCEEscherichia coli is a major public health concern given its increasing level of antibiotic resistance worldwide and extraordinary capacity to acquire and spread resistance via horizontal gene transfer with surrounding species and via mutations in its existing genome. E. coli also exhibits a large amount of metabolic pathway redundancy, which promotes resistance via metabolic adaptability. In this study, we developed a computational approach that integrates machine learning with metabolic modeling to understand the correlation between AMR and metabolic adaptation mechanisms in this model bacterium. Using our approach, we identified AMR genetic determinants associated with cell wall modifications for increased permeability, virulence factor manipulation of host immunity, reduction of oxidative stress toxicity, and changes to energy metabolism. Unravelling the complex interplay between antibiotic resistance and metabolic rewiring may open new opportunities to understand the ability of E. coli, and potentially of other human and animal pathogens, to adapt to new treatments.

Undisclosed, unmet and neglected challenges in multi-omics studies

Multi-omics approaches have become a reality in both large genomics projects and small laboratories. However, the multi-omics research community still faces a number of issues that have either not been sufficiently discussed or for which current solutions are still limited. In this Perspective, we elaborate on these limitations and suggest points of attention for future research. We finally discuss new opportunities and challenges brought to the field by the rapid development of single-cell high-throughput molecular technologies.

Transcriptome integrated metabolic modeling of carbon assimilation underlying storage root development in cassava

The existing genome-scale metabolic model of carbon metabolism in cassava storage roots, rMeCBM, has proven particularly resourceful in exploring the metabolic basis for the phenotypic differences between high and low-yield cassava cultivars. However, experimental validation of predicted metabolic fluxes by carbon labeling is quite challenging. Here, we incorporated gene expression data of developing storage roots into the basic flux-balance model to minimize infeasible metabolic fluxes, denoted as rMeCBMx, thereby improving the plausibility of the simulation and predictive power. Three different conceptual algorithms, GIMME, E-Flux, and HPCOF were evaluated. The rMeCBMx-HPCOF model outperformed others in predicting carbon fluxes in the metabolism of storage roots and, in particular, was highly consistent with transcriptome of high-yield cultivars. The flux prediction was improved through the oxidative pentose phosphate pathway in cytosol, as has been reported in various studies on root metabolism, but hardly captured by simple FBA models. Moreover, the presence of fluxes through cytosolic glycolysis and alanine biosynthesis pathways were predicted with high consistency with gene expression levels. This study sheds light on the importance of prediction power in the modeling of complex plant metabolism. Integration of multi-omics data would further help mitigate the ill-posed problem of constraint-based modeling, allowing more realistic simulation.

History and Future Perspectives on the Discipline of Quantitative Systems Pharmacology Modeling and Its Applications

Mathematical biology and pharmacology models have a long and rich history in the fields of medicine and physiology, impacting our understanding of disease mechanisms and the development of novel therapeutics. With an increased focus on the pharmacology application of system models and the advances in data science spanning mechanistic and empirical approaches, there is a significant opportunity and promise to leverage these advancements to enhance the development and application of the systems pharmacology field. In this paper, we will review milestones in the evolution of mathematical biology and pharmacology models, highlight some of the gaps and challenges in developing and applying systems pharmacology models, and provide a vision for an integrated strategy that leverages advances in adjacent fields to overcome these challenges.

Recent advances in systems and synthetic biology approaches for developing novel cell-factories in non-conventional yeasts

Microbial bioproduction of chemicals, proteins, and primary metabolites from cheap carbon sources is currently an advancing area in industrial research. The model yeast, Saccharomyces cerevisiae, is a well-established biorefinery host that has been used extensively for commercial manufacturing of bioethanol from myriad carbon sources. However, its Crabtree-positive nature often limits the use of this organism for the biosynthesis of commercial molecules that do not belong in the fermentative pathway. To avoid extensive strain engineering of S. cerevisiae for the production of metabolites other than ethanol, non-conventional yeasts can be selected as hosts based on their natural capacity to produce desired commodity chemicals. Non-conventional yeasts like Kluyveromyces marxianus, K. lactis, Yarrowia lipolytica, Pichia pastoris, Scheffersomyces stipitis, Hansenula polymorpha, and Rhodotorula toruloides have been considered as potential industrial eukaryotic hosts owing to their desirable phenotypes such as thermotolerance, assimilation of a wide range of carbon sources, as well as ability to secrete high titers of protein and lipid. However, the advanced metabolic engineering efforts in these organisms are still lacking due to the limited availability of systems and synthetic biology methods like in silico models, well-characterised genetic parts, and optimized genome engineering tools. This review provides an insight into the recent advances and challenges of systems and synthetic biology as well as metabolic engineering endeavours towards the commercial usage of non-conventional yeasts. Particularly, the approaches in emerging non-conventional yeasts for the production of enzymes, therapeutic proteins, lipids, and metabolites for commercial applications are extensively discussed here. Various attempts to address current limitations in designing novel cell factories have been highlighted that include the advances in the fields of genome-scale metabolic model reconstruction, flux balance analysis, 'omics'-data integration into models, genome-editing toolkit development, and rewiring of cellular metabolisms for desired chemical production. Additionally, the understanding of metabolic networks using ¹³C-labelling experiments as well as the utilization of metabolomics in deciphering intracellular fluxes and reactions have also been discussed here. Application of cutting-edge nuclease-based genome editing platforms like CRISPR/Cas9, and its optimization towards efficient strain engineering in non-conventional yeasts have also been described. Additionally, the impact of the advances in promising non-conventional yeasts for efficient commercial molecule synthesis has been meticulously reviewed. In the future, a cohesive approach involving systems and synthetic biology will help in widening the horizon of the use of unexplored non-conventional yeast species towards industrial biotechnology.

Effective Biophysical Modeling of Cell Free Transcription and Translation Processes

Transcription and translation are at the heart of metabolism and signal transduction. In this study, we developed an effective biophysical modeling approach to simulate transcription and translation processes. The model, composed of coupled ordinary differential equations, was tested by comparing simulations of two cell free synthetic circuits with experimental measurements generated in this study. First, we considered a simple circuit in which sigma factor 70 induced the expression of green fluorescent protein. This relatively simple case was then followed by a more complex negative feedback circuit in which two control genes were coupled to the expression of a third reporter gene, green fluorescent protein. Many of the model parameters were estimated from previous biophysical studies in the literature, while the remaining unknown model parameters for each circuit were estimated by minimizing the difference between model simulations and messenger RNA (mRNA) and protein measurements generated in this study. In particular, either parameter estimates from published studies were used directly, or characteristic values found in the literature were used to establish feasible ranges for the parameter estimation problem. In order to perform a detailed analysis of the influence of individual model parameters on the expression dynamics of each circuit, global sensitivity analysis was used. Taken together, the effective biophysical modeling approach captured the expression dynamics, including the transcription dynamics, for the two synthetic cell free circuits. While, we considered only two circuits here, this approach could potentially be extended to simulate other genetic circuits in both cell free and whole cell biomolecular applications as the equations governing the regulatory control functions are modular and easily modifiable. The model code, parameters, and analysis scripts are available for download under an MIT software license from the Varnerlab GitHub repository.

Regulatory dynamic enzyme-cost flux balance analysis: A unifying framework for constraint-based modeling

Integrated modeling of metabolism and gene regulation continues to be a major challenge in computational biology. While there exist approaches like regulatory flux balance analysis (rFBA), dynamic flux balance analysis (dFBA), resource balance analysis (RBA) or dynamic enzyme-cost flux balance analysis (deFBA) extending classical flux balance analysis (FBA) in various directions, there have been no constraint-based methods so far that allow predicting the dynamics of metabolism taking into account both macromolecule production costs and regulatory events. In this paper, we introduce a new constraint-based modeling framework named regulatory dynamic enzyme-cost flux balance analysis (r-deFBA), which unifies dynamic modeling of metabolism, cellular resource allocation and transcriptional regulation in a hybrid discrete-continuous setting. With r-deFBA, we can predict discrete regulatory states together with the continuous dynamics of reaction fluxes, external substrates, enzymes, and regulatory proteins needed to achieve a cellular objective such as maximizing biomass over a time interval. The dynamic optimization problem underlying r-deFBA can be reformulated as a mixed-integer linear optimization problem, for which there exist efficient solvers.

A review of methods for the reconstruction and analysis of integrated genome-scale models of metabolism and regulation

The current survey aims to describe the main methodologies for extending the reconstruction and analysis of genome-scale metabolic models and phenotype simulation with Flux Balance Analysis mathematical frameworks, via the integration of Transcriptional Regulatory Networks and/or gene expression data. Although the surveyed methods are aimed at improving phenotype simulations obtained from these models, the perspective of reconstructing integrated genome-scale models of metabolism and gene expression for diverse prokaryotes is still an open challenge.

A biochemical network modeling of a whole-cell

All cellular processes can be ultimately understood in terms of respective fundamental biochemical interactions between molecules, which can be modeled as networks. Very often, these molecules are shared by more than one process, therefore interconnecting them. Despite this effect, cellular processes are usually described by separate networks with heterogeneous levels of detail, such as metabolic, protein-protein interaction, and transcription regulation networks. Aiming at obtaining a unified representation of cellular processes, we describe in this work an integrative framework that draws concepts from rule-based modeling. In order to probe the capabilities of the framework, we used an organism-specific database and genomic information to model the whole-cell biochemical network of the Mycoplasma genitalium organism. This modeling accounted for 15 cellular processes and resulted in a single component network, indicating that all processes are somehow interconnected. The topological analysis of the network showed structural consistency with biological networks in the literature. In order to validate the network, we estimated gene essentiality by simulating gene deletions and compared the results with experimental data available in the literature. We could classify 212 genes as essential, being 95% of them consistent with experimental results. Although we adopted a relatively simple organism as a case study, we suggest that the presented framework has the potential for paving the way to more integrated studies of whole organisms leading to a systemic analysis of cells on a broader scale. The modeling of other organisms using this framework could provide useful large-scale models for different fields of research such as bioengineering, network biology, and synthetic biology, and also provide novel tools for medical and industrial applications.

Simulating the evolutionary trajectories of metabolic pathways for insect symbionts in the genus Sodalis

Insect-bacterial symbioses are ubiquitous, but there is still much to uncover about how these relationships establish, persist and evolve. The tsetse endosymbiont Sodalis glossinidius displays intriguing metabolic adaptations to its microenvironment, but the process by which this relationship evolved remains to be elucidated. The recent chance discovery of the free-living species of the genus Sodalis, Sodalis praecaptivus, provides a serendipitous starting point from which to investigate the evolution of this symbiosis. Here, we present a flux balance model for S. praecaptivus and empirically verify its predictions. Metabolic modelling is used in combination with a multi-objective evolutionary algorithm to explore the trajectories that S. glossinidius may have undertaken from this starting point after becoming internalized. The order in which key genes are lost is shown to influence the evolved populations, providing possible targets for future in vitro genetic manipulation. This method provides a detailed perspective on possible evolutionary trajectories for S. glossinidius in this fundamental process of evolutionary and ecological change.

Model Reduction for Kinetic Models of Biological Systems

High dimensionality continues to be a challenge in computational systems biology. The kinetic models of many phenomena of interest are high-dimensional and complex, resulting in large computational effort in the simulation. Model order reduction (MOR) is a mathematical technique that is used to reduce the computational complexity of high-dimensional systems by approximation with lower dimensional systems, while retaining the important information and properties of the full order system. Proper orthogonal decomposition (POD) is a method based on Galerkin projection that can be used for reducing the model order. POD is considered an optimal linear approach since it obtains the minimum squared distance between the original model and its reduced representation. However, POD may represent a restriction for nonlinear systems. By applying the POD method for nonlinear systems, the complexity to solve the nonlinear term still remains that of the full order model. To overcome the complexity for nonlinear terms in the dynamical system, an approach called the discrete empirical interpolation method (DEIM) can be used. In this paper, we discuss model reduction by POD and DEIM to reduce the order of kinetic models of biological systems and illustrate the approaches on some examples. Additional computational costs for setting up the reduced order system pay off for large-scale systems. In general, a reduced model should not be expected to yield good approximations if different initial conditions are used from that used to produce the reduced order model. We used the POD method of a kinetic model with different initial conditions to compute the reduced model. This reduced order model is able to predict the full order model for a variety of different initial conditions.

Global responses to oxytetracycline treatment in tetracycline-resistant Escherichia coli

We characterized the global transcriptome of Escherichia coli MG1655:: tetA grown in the presence of ½ MIC (14 mg/L) of OTC, and for comparison WT MG1655 strain grown with 1//2 MIC of OTC (0.25 mg/L OTC). 1646 genes changed expression significantly (FDR > 0.05) in the resistant strain, the majority of which (1246) were also regulated in WT strain. Genes involved in purine synthesis and ribosome structure and function were top-enriched among up-regulated genes, and anaerobic respiration, nitrate metabolism and aromatic amino acid biosynthesis genes among down-regulated genes. Blocking of the purine-synthesis- did not affect resistance phenotypes (MIC and growth rate with OTC), while blocking of protein synthesis using low concentrations of chloramphenicol or gentamicin, lowered MIC towards OTC. Metabolic-modeling, using a novel model for MG1655 and continuous weighing factor that reflected the degree of up or down regulation of genes encoding a reaction, identified 102 metabolic reactions with significant change in flux in MG1655:: tetA when grown in the presence of OTC compared to growth without OTC. These pathways could not have been predicted by simply analyzing functions of the up and down regulated genes, and thus this work has provided a novel method for identification of reactions which are essential in the adaptation to growth in the presence of antimicrobials.

LK-DFBA: a linear programming-based modeling strategy for capturing dynamics and metabolite-dependent regulation in metabolism

BACKGROUND

The systems-scale analysis of cellular metabolites, "metabolomics," provides data ideal for applications in metabolic engineering. However, many of the computational tools for strain design are built around Flux Balance Analysis (FBA), which makes assumptions that preclude direct integration of metabolomics data into the underlying models. Finding a way to retain the advantages of FBA's linear structure while relaxing some of its assumptions could allow us to account for metabolite levels and metabolite-dependent regulation in strain design tools built from FBA, improving the accuracy of predictions made by these tools. We designed, implemented, and characterized a modeling strategy based on Dynamic FBA (DFBA), called Linear Kinetics-Dynamic Flux Balance Analysis (LK-DFBA), to satisfy these specifications. Our strategy adds constraints describing the dynamics and regulation of metabolism that are strictly linear. We evaluated LK-DFBA against alternative modeling frameworks using simulated noisy data from a small in silico model and a larger model of central carbon metabolism in E. coli, and compared each framework's ability to recapitulate the original system.

RESULTS

In the smaller model, we found that we could use regression from a dynamic flux estimation (DFE) with an optional non-linear parameter optimization to reproduce metabolite concentration dynamic trends more effectively than an ordinary differential equation model with generalized mass action rate laws when tested under realistic data sampling frequency and noise levels. We observed detrimental effects across all tested modeling approaches when metabolite time course data were missing, but found these effects to be smaller for LK-DFBA in most cases. With the E. coli model, we produced qualitatively reasonable results with similar properties to the smaller model and explored two different parameterization structures that yield trade-offs in computation time and accuracy.

CONCLUSIONS

LK-DFBA allows for calculation of metabolite concentrations and considers metabolite-dependent regulation while still retaining many computational advantages of FBA. This provides the proof-of-principle for a new metabolic modeling framework with the potential to create genome-scale dynamic models and the potential to be applied in strain engineering tools that currently use FBA.

Formalizing Metabolic-Regulatory Networks by Hybrid Automata

Computational approaches in systems biology have become a powerful tool for understanding the fundamental mechanisms of cellular metabolism and regulation. However, the interplay between the regulatory and the metabolic system is still poorly understood. In particular, there is a need for formal mathematical frameworks that allow analyzing metabolism together with dynamic enzyme resources and regulatory events. Here, we introduce a metabolic-regulatory network model (MRN) that allows integrating metabolism with transcriptional regulation, macromolecule production and enzyme resources. Using this model, we show that the dynamic interplay between these different cellular processes can be formalized by a hybrid automaton, combining continuous dynamics and discrete control.

Bayesian Integrative Modeling of Genome-Scale Metabolic and Regulatory Networks

The integration of high-throughput data to build predictive computational models of cellular metabolism is a major challenge of systems biology. These models are needed to predict cellular responses to genetic and environmental perturbations. Typically, this response involves both metabolic regulations related to the kinetic properties of enzymes and a genetic regulation affecting their concentrations. Thus, the integration of the transcriptional regulatory information is required to improve the accuracy and predictive ability of metabolic models. Integrative modeling is of primary importance to guide the search for various applications such as discovering novel potential drug targets to develop efficient therapeutic strategies for various diseases. In this paper, we propose an integrative predictive model based on techniques combining semantic web, probabilistic modeling, and constraint-based modeling methods. We applied our approach to human cancer metabolism to predict in silico the growth response of specific cancer cells under approved drug effects. Our method has proven successful in predicting the biomass rates of human liver cancer cells under drug-induced transcriptional perturbations.

Advanced Modeling of Cellular Proliferation: Toward a Multi-scale Framework Coupling Cell Cycle to Metabolism by Integrating Logical and Constraint-Based Models

Biological functions require a coherent cross talk among multiple layers of regulation within the cell. Computational efforts that aim to understand how these layers are integrated across spatial, temporal, and functional scales represent a challenge in Systems Biology. We have developed a computational, multi-scale framework that couples cell cycle and metabolism networks in the budding yeast cell. Here we describe the methodology at the basis of this framework, which integrates on off-the-shelf logical (Boolean) models of a minimal yeast cell cycle with a constraint-based model of metabolism (i.e., the Yeast 7 metabolic network reconstruction). Models are implemented in Python code using the BooleanNet and COBRApy packages, respectively, and are connected through the Boolean logic. The methodology allows for incorporation of interaction data, and validation through -omics data. Furthermore, evolutionary strategies may be incorporated to explore regulatory structures underlying coherent cross talks among regulatory layers.

Connecting signaling and metabolic pathways in EGF receptor-mediated oncogenesis of glioblastoma

As malignant transformation requires synchronization of growth-driving signaling (S) and metabolic (M) pathways, defining cancer-specific S-M interconnected networks (SMINs) could lead to better understanding of oncogenic processes. In a systems-biology approach, we developed a mathematical model for SMINs in mutated EGF receptor (EGFRvIII) compared to wild-type EGF receptor (EGFRwt) expressing glioblastoma multiforme (GBM). Starting with experimentally validated human protein-protein interactome data for S-M pathways, and incorporating proteomic data for EGFRvIII and EGFRwt GBM cells and patient transcriptomic data, we designed a dynamic model for EGFR-driven GBM-specific information flow. Key nodes and paths identified by in silico perturbation were validated experimentally when inhibition of signaling pathway proteins altered expression of metabolic proteins as predicted by the model. This demonstrated capacity of the model to identify unknown connections between signaling and metabolic pathways, explain the robustness of oncogenic SMINs, predict drug escape, and assist identification of drug targets and the development of combination therapies.

Complex and highly dynamic interconnected networks allow cancer to take different routes and circumvent chemotherapy. Therefore, understanding these context-specific networks and their dynamics of molecular interactions driven by different oncogenic signaling and metabolic pathways is very much needed to predict drug targets and the effect of therapeutics. We incorporated high-throughput transcriptome and proteome data into mathematical models to deduce properties of cancer cells through systems biology approach. Here we report the development, testing and validation of an integrated systems biology model of information flow between signaling and metabolic pathways to understand the regulation of the interconnection between them in cancer. Our model efficiently identified unique connections and key nodes important in signaling-metabolic information flow. We predicted some potential novel targets before performing actual drug tests. We have successfully applied this model to identify the interconnections altered in the constitutive signaling of the mutated EGFR by comparing EGF-dependent and wild-type EGFR signaling in glioblastoma multiforme.

A Protocol for the Construction and Curation of Genome-Scale Integrated Metabolic and Regulatory Network Models

Genome-scale metabolic network models have been widely used over the last decade and have been shown to successfully predict the metabolic behavior of many organisms. Yet the complexity of metabolic regulation often limits the accuracy of these models. Integrative modeling approaches have recently been developed that combine metabolic and regulatory networks, thereby expanding the capabilities and accuracy of genome-scale modeling. This chapter provides a guide to reconstruct and curate such integrated network models. Specifically, this protocol describes the PROM (Probabilistic Regulation of Metabolism) and GEMINI (Gene Expression and Metabolism Integrated for Network Inference) approaches. PROM is an automated method for the construction of integrated metabolic and transcriptional regulatory network models, while the GEMINI approach curates the integrated network models using transcriptomics and phenomics data. GEMINI represents the first attempt at applying well-established curation tools that exist for metabolic networks to be applied for curating regulatory networks. The integrated network models generated by these approaches enable the mechanistic integration of diverse biological data and can identify novel strategies to engineer cellular metabolism.

Systems Biology Approaches Toward Understanding Primary Mitochondrial Diseases

Primary mitochondrial diseases form one of the most common and severe groups of genetic disease, with a birth prevalence of at least 1 in 5000. These disorders are multi-genic and multi-phenotypic (even within the same gene defect) and span the entire age range from prenatal to late adult onset. Mitochondrial disease typically affects one or multiple high-energy demanding organs, and is frequently fatal in early life. Unfortunately, to date there are no known curative therapies, mostly owing to the rarity and heterogeneity of individual mitochondrial diseases, leading to diagnostic odysseys and difficulties in clinical trial design. This review aims to discuss recent advances and challenges of systems approaches for the study of primary mitochondrial diseases. Although there has been an explosion in the generation of omics data, few studies have progressed toward the integration of multiple levels of omics. It is evident that the integration of different types of data to create a more complete representation of biology remains challenging, perhaps due to the scarcity of available integrative tools and the complexity inherent in their use. In addition, "bottom-up" systems approaches have been adopted for use in the iterative cycle of systems biology: from data generation to model prediction and validation. Primary mitochondrial diseases, owing to their complex nature, will most likely benefit from a multidisciplinary approach encompassing clinical, molecular and computational studies integrated together by systems biology to elucidate underlying pathomechanisms for better diagnostics and therapeutic discovery. Just as next generation sequencing has rapidly increased diagnostic rates from approximately 5% up to 60% over two decades, more recent advancing technologies are encouraging; the generation of multi-omics, the integration of multiple types of data, and the ability to predict perturbations will, ultimately, be translated into improved patient care.

DynamicME: dynamic simulation and refinement of integrated models of metabolism and protein expression

BACKGROUND

Genome-scale models of metabolism and macromolecular expression (ME models) enable systems-level computation of proteome allocation coupled to metabolic phenotype.

RESULTS

We develop DynamicME, an algorithm enabling time-course simulation of cell metabolism and protein expression. DynamicME correctly predicted the substrate utilization hierarchy on a mixed carbon substrate medium. We also found good agreement between predicted and measured time-course expression profiles. ME models involve considerably more parameters than metabolic models (M models). We thus generate an ensemble of models (each model having its rate constants perturbed), and then analyze the models by identifying archetypal time-course metabolite concentration profiles. Furthermore, we use a metaheuristic optimization method to calibrate ME model parameters using time-course measurements such as from a (fed-) batch culture. Finally, we show that constraints on protein concentration dynamics ("inertia") alter the metabolic response to environmental fluctuations, including increased substrate-level phosphorylation and lowered oxidative phosphorylation.

CONCLUSIONS

Overall, DynamicME provides a novel method for understanding proteome allocation and metabolism under complex and transient environments, and to utilize time-course cell culture data for model-based interpretation or model refinement.

Yeast Genome-Scale Metabolic Models for Simulating Genotype-Phenotype Relations

Understanding genotype-phenotype dependency is a universal aim for all life sciences. While the complete genotype-phenotype relations remain challenging to resolve, metabolic phenotypes are moving within the reach through genome-scale metabolic model simulations. Genome-scale metabolic models are available for commonly investigated yeasts, such as model eukaryote and domesticated fermentation species Saccharomyces cerevisiae, and automatic reconstruction methods facilitate obtaining models for any sequenced species. The models allow for investigating genotype-phenotype relations through simulations simultaneously considering the effects of nutrient availability, and redox and energy homeostasis in cells. Genome-scale models also offer frameworks for omics data integration to help to uncover how the translation of genotypes to the apparent phenotypes is regulated at different levels. In this chapter, we provide an overview of the yeast genome-scale metabolic models and the simulation approaches for using these models to interrogate genotype-phenotype relations. We review the methodological approaches according to the underlying biological reasoning in order to inspire formulating novel questions and applications that the genome-scale metabolic models could contribute to. Finally, we discuss current challenges and opportunities in the genome-scale metabolic model simulations.

In silico predicted transcriptional regulatory control of steroidogenesis in spawning female fathead minnows (Pimephales promelas)

Oocyte development and maturation (or oogenesis) in spawning female fish is mediated by interrelated transcriptional regulatory and steroidogenesis networks. This study integrates a transcriptional regulatory network (TRN) model of steroidogenic enzyme gene expressions with a flux balance analysis (FBA) model of steroidogenesis. The two models were functionally related. Output from the TRN model (as magnitude gene expression simulated using extreme pathway (ExPa) analysis) was used to re-constrain linear inequality bounds for reactions in the FBA model. This allowed TRN model predictions to impact the steroidogenesis FBA model. These two interrelated models were tested as follows: First, in silico targeted steroidogenic enzyme gene activations in the TRN model showed high co-regulation (67-83%) for genes involved with oocyte growth and development (cyp11a1, cyp17-17,20-lyase, 3β-HSD and cyp19a1a). Whereas, no or low co-regulation corresponded with genes concertedly involved with oocyte final maturation prior to spawning (cyp17-17α-hydroxylase (0%) and 20β-HSD (33%)). Analysis (using FBA) of accompanying steroidogenesis fluxes showed high overlap for enzymes involved with oocyte growth and development versus those involved with final maturation and spawning. Second, the TRN model was parameterized with in vivo changes in the presence/absence of transcription factors (TFs) during oogenesis in female fathead minnows (Pimephales promelas). Oogenesis stages studied included: PreVitellogenic-Vitellogenic, Vitellogenic-Mature, Mature-Ovulated and Ovulated-Atretic stages. Predictions of TRN genes active during oogenesis showed overall elevated expressions for most genes during early oocyte development (PreVitellogenic-Vitellogenic, Vitellogenic-Mature) and post-ovulation (Ovulated-Atretic). Whereas ovulation (Mature-Ovulated) showed highest expression for cyp17-17α-hydroxylase only. FBA showed steroid hormone productions to also follow trends concomitant with steroidogenic enzyme gene expressions. General trends predicted by in silico modeling were similar to those observed in vivo. The integrated computational framework presented was capable of mechanistically representing aspects of reproductive function in fish. This approach can be extended to study reproductive effects under exposure to adverse environmental or anthropogenic stressors.

A Review of Dynamic Modeling Approaches and Their Application in Computational Strain Optimization for Metabolic Engineering

Mathematical modeling is a key process to describe the behavior of biological networks. One of the most difficult challenges is to build models that allow quantitative predictions of the cells' states along time. Recently, this issue started to be tackled through novel in silico approaches, such as the reconstruction of dynamic models, the use of phenotype prediction methods, and pathway design via efficient strain optimization algorithms. The use of dynamic models, which include detailed kinetic information of the biological systems, potentially increases the scope of the applications and the accuracy of the phenotype predictions. New efforts in metabolic engineering aim at bridging the gap between this approach and other different paradigms of mathematical modeling, as constraint-based approaches. These strategies take advantage of the best features of each method, and deal with the most remarkable limitation—the lack of available experimental information—which affects the accuracy and feasibility of solutions. Parameter estimation helps to solve this problem, but adding more computational cost to the overall process. Moreover, the existing approaches include limitations such as their scalability, flexibility, convergence time of the simulations, among others. The aim is to establish a trade-off between the size of the model and the level of accuracy of the solutions. In this work, we review the state of the art of dynamic modeling and related methods used for metabolic engineering applications, including approaches based on hybrid modeling. We describe approaches developed to undertake issues regarding the mathematical formulation and the underlying optimization algorithms, and that address the phenotype prediction by including available kinetic rate laws of metabolic processes. Then, we discuss how these have been used and combined as the basis to build computational strain optimization methods for metabolic engineering purposes, how they lead to bi-level schemes that can be used in the industry, including a consideration of their limitations.

Genome-Scale, Constraint-Based Modeling of Nitrogen Oxide Fluxes during Coculture of Nitrosomonas europaea and Nitrobacter winogradskyi

Modern agriculture is sustained by application of inorganic nitrogen (N) fertilizer in the form of ammonium (NH₄⁺). Up to 60% of NH₄⁺-based fertilizer can be lost through leaching of nitrifier-derived nitrate (NO₃⁻), and through the emission of N oxide gases (i.e., nitric oxide [NO], N dioxide [NO₂], and nitrous oxide [N₂O] gases), the latter being a potent greenhouse gas. Our approach to modeling of nitrification suggests that both biotic and abiotic mechanisms function as important sources and sinks of N oxides during microaerobic conditions and that previous models might have underestimated gross NO production during nitrification.

Nitrification, the aerobic oxidation of ammonia to nitrate via nitrite, emits nitrogen (N) oxide gases (NO, NO₂, and N₂O), which are potentially hazardous compounds that contribute to global warming. To better understand the dynamics of nitrification-derived N oxide production, we conducted culturing experiments and used an integrative genome-scale, constraint-based approach to model N oxide gas sources and sinks during complete nitrification in an aerobic coculture of two model nitrifying bacteria, the ammonia-oxidizing bacterium Nitrosomonas europaea and the nitrite-oxidizing bacterium Nitrobacter winogradskyi. The model includes biotic genome-scale metabolic models (iFC578 and iFC579) for each nitrifier and abiotic N oxide reactions. Modeling suggested both biotic and abiotic reactions are important sources and sinks of N oxides, particularly under microaerobic conditions predicted to occur in coculture. In particular, integrative modeling suggested that previous models might have underestimated gross NO production during nitrification due to not taking into account its rapid oxidation in both aqueous and gas phases. The integrative model may be found at https://github.com/chaplenf/microBiome-v2.1.

IMPORTANCE Modern agriculture is sustained by application of inorganic nitrogen (N) fertilizer in the form of ammonium (NH₄⁺). Up to 60% of NH₄⁺-based fertilizer can be lost through leaching of nitrifier-derived nitrate (NO₃⁻), and through the emission of N oxide gases (i.e., nitric oxide [NO], N dioxide [NO₂], and nitrous oxide [N₂O] gases), the latter being a potent greenhouse gas. Our approach to modeling of nitrification suggests that both biotic and abiotic mechanisms function as important sources and sinks of N oxides during microaerobic conditions and that previous models might have underestimated gross NO production during nitrification.