Unraveling the complexity of flux regulation: a new method demonstrated for nutrient starvation in Saccharomyces cerevisiae

KinMod database: a tool for investigating metabolic regulation

The ability of current kinetic models to simulate the phenotypic behaviour of cells is limited since cell metabolism is regulated at different levels including enzyme regulation. The small molecule regulation network (SMRN) enables cells to respond rapidly to environmental fluctuations by controlling the activity of enzymes in metabolic pathways. However, SMRN is not as well studied relative to metabolic networks. The main contributor to the lack of knowledge on this regulatory system is the sparsity of experimental data and the absence of a standard framework for representing available information. In this paper, we introduce the KinMod database that encompasses more than 2 million data points on the metabolism and metabolic regulation network of 9814 organisms KinMod database employs a hierarchical data structure to: (i) signify relationships between kinetic information obtained through in-vitro experiments and proteins, with an emphasis on SMRN, (ii) provide a thorough insight into available kinetic parameters and missing experimental measurements of this regulatory network and (iii) facilitate machine learning approaches for parameter estimation and accurate kinetic model construction by providing a homogeneous list of linked omics data. The hierarchical ontology of the KinMod database allows flexible exploration of data attributes and investigation of metabolic relationships within- and cross-species. Identifying missing experimental values suggests additional experiments required for kinetic parameter estimation. Linking multi-omics data and providing data on SMRN encourages the development of novel machine learning techniques for predicting missing kinetic parameters and promotes accurate kinetic model construction of cells metabolism by providing a comprehensive list of available kinetic measurements. To illustrate the value of KinMod data, we develop six analyses to visualize associations between data classes belonging to separate sections of the metabolism. Through these analyses, we demonstrate that the KinMod database provides a unique framework for biologists and engineers to retrieve, evaluate and compare the functional metabolism of species, including the regulatory network, and discover the extent of available and missing experimental values of the metabolic regulation.

Database URL: https://lmse.utoronto.ca/kinmod/KINMOD.sql.gz

INTEGRATE: Model-based multi-omics data integration to characterize multi-level metabolic regulation

Metabolism is directly and indirectly fine-tuned by a complex web of interacting regulatory mechanisms that fall into two major classes. On the one hand, the expression level of the catalyzing enzyme sets the maximal theoretical flux level (i.e., the net rate of the reaction) for each enzyme-controlled reaction. On the other hand, metabolic regulation controls the metabolic flux through the interactions of metabolites (substrates, cofactors, allosteric modulators) with the responsible enzyme. High-throughput data, such as metabolomics and transcriptomics data, if analyzed separately, do not accurately characterize the hierarchical regulation of metabolism outlined above. They must be integrated to disassemble the interdependence between different regulatory layers controlling metabolism. To this aim, we propose INTEGRATE, a computational pipeline that integrates metabolomics and transcriptomics data, using constraint-based stoichiometric metabolic models as a scaffold. We compute differential reaction expression from transcriptomics data and use constraint-based modeling to predict if the differential expression of metabolic enzymes directly originates differences in metabolic fluxes. In parallel, we use metabolomics to predict how differences in substrate availability translate into differences in metabolic fluxes. We discriminate fluxes regulated at the metabolic and/or gene expression level by intersecting these two output datasets. We demonstrate the pipeline using a set of immortalized normal and cancer breast cell lines. In a clinical setting, knowing the regulatory level at which a given metabolic reaction is controlled will be valuable to inform targeted, truly personalized therapies in cancer patients.

Global coordination of metabolic pathways in Escherichia coli by active and passive regulation

Microorganisms adjust metabolic activity to cope with diverse environments. While many studies have provided insights into how individual pathways are regulated, the mechanisms that give rise to coordinated metabolic responses are poorly understood. Here, we identify the regulatory mechanisms that coordinate catabolism and anabolism in Escherichia coli. Integrating protein, metabolite, and flux changes in genetically implemented catabolic or anabolic limitations, we show that combined global and local mechanisms coordinate the response to metabolic limitations. To allocate proteomic resources between catabolism and anabolism, E. coli uses a simple global gene regulatory program. Surprisingly, this program is largely implemented by a single transcription factor, Crp, which directly activates the expression of catabolic enzymes and indirectly reduces the expression of anabolic enzymes by passively sequestering cellular resources needed for their synthesis. However, metabolic fluxes are not controlled by this regulatory program alone; instead, fluxes are adjusted mostly through passive changes in the local metabolite concentrations. These mechanisms constitute a simple but effective global regulatory program that coarsely partitions resources between different parts of metabolism while ensuring robust coordination of individual metabolic reactions.

Hierarchical and Dynamic Regulation of Defense-Responsive Specialized Metabolism by WRKY and MYB Transcription Factors

The plant kingdom produces hundreds of thousands of specialized bioactive metabolites, some with pharmaceutical and biotechnological importance. Their biosynthesis and function have been studied for decades, but comparatively less is known about how transcription factors with overlapping functions and contrasting regulatory activities coordinately control the dynamics and output of plant specialized metabolism. Here, we performed temporal studies on pathogen-infected intact host plants with perturbed transcription factors. We identified WRKY33 as the condition-dependent master regulator and MYB51 as the dual functional regulator in a hierarchical gene network likely responsible for the gene expression dynamics and metabolic fluxes in the camalexin and 4-hydroxy-indole-3-carbonylnitrile (4OH-ICN) pathways. This network may have also facilitated the regulatory capture of the newly evolved 4OH-ICN pathway in Arabidopsis thaliana by the more-conserved transcription factor MYB51. It has long been held that the plasticity of plant specialized metabolism and the canalization of development should be differently regulated; our findings imply a common hierarchical regulatory architecture orchestrated by transcription factors for specialized metabolism and development, making it an attractive target for metabolic engineering.

Quantifying Dynamic Regulation in Metabolic Pathways with Nonparametric Flux Inference

One of the central tasks in systems biology is to understand how cells regulate their metabolism. Hierarchical regulation analysis is a powerful tool to study this regulation at the metabolic, gene-expression, and signaling levels. It has been widely applied to study steady-state regulation, but analysis of the metabolic dynamics remains challenging because it is difficult to measure time-dependent metabolic flux. Here, we develop a nonparametric method that uses Gaussian processes to accurately infer the dynamics of a metabolic pathway based only on metabolite measurements; from this, we then go on to obtain a dynamical view of the hierarchical regulation processes invoked over time to control the activity in a pathway. Our approach allows us to use hierarchical regulation analysis in a dynamic setting but without the need for explicitly time-dependent flux measurements.

Systems Biology - A Guide for Understanding and Developing Improved Strains of Lactic Acid Bacteria

Lactic Acid Bacteria (LAB) are extensively employed in the production of various fermented foods, due to their safe status, ability to affect texture and flavor and finally due to the beneficial effect they have on shelf-life. More recently, LAB have also gained interest as production hosts for various useful compounds, particularly compounds with sensitive applications, such as food ingredients and therapeutics. As for all industrial microorganisms, it is important to have a good understanding of the physiology and metabolism of LAB in order to fully exploit their potential, and for this purpose, many systems biology approaches are available. Systems metabolic engineering, an approach that combines optimization of metabolic enzymes/pathways at the systems level, synthetic biology as well as in silico model simulation, has been used to build microbial cell factories for production of biofuels, food ingredients and biochemicals. When developing LAB for use in foods, genetic engineering is in general not an accepted approach. An alternative is to screen mutant libraries for candidates with desirable traits using high-throughput screening technologies or to use adaptive laboratory evolution to select for mutants with special properties. In both cases, by using omics data and data-driven technologies to scrutinize these, it is possible to find the underlying cause for the desired attributes of such mutants. This review aims to describe how systems biology tools can be used for obtaining both engineered as well as non-engineered LAB with novel and desired properties.

Transcriptional regulation of the genes involved in protein metabolism and processing in Saccharomyces cerevisiae

Topological analysis of large networks, which focus on a specific biological process or on related biological processes, where functional coherence exists among the interacting members, may provide a wealth of insight into cellular functionality. This work presents an unbiased systems approach to analyze genetic, transcriptional regulatory and physical interaction networks of yeast genes possessing such functional coherence to gain novel biological insight. The present analysis identified only a few transcriptional regulators amongst a large gene cohort associated with the protein metabolism and processing in yeast. These transcription factors are not functionally required for the maintenance of these tasks in growing cells. Rather, they are involved in rewiring gene transcription in response to such major challenges as starvation, hypoxia, DNA damage, heat shock or the accumulation of unfolded proteins. Indeed, only a subset of these proteins were captured empirically in the nuclear-enriched fraction of non-stressed yeast cells, suggesting that the transcriptional regulation of protein metabolism and processing in yeast is primarily concerned with maintaining cellular robustness in the face of threat by either internal or external stressors.

Metabolic flexibility of a prospective bioremediator: Desulfitobacterium hafniense Y51 challenged in chemostats

Desulfitobacterium hafniense Y51 has been widely used in investigations of perchloroethylene (PCE) biodegradation, but limited information exists on its other physiological capabilities. We investigated how D. hafniense Y51 confronts the debilitating limitations of not having enough electron donor (lactate), or electron acceptor (fumarate) during cultivation in chemostats. The residual concentrations of the substrates supplied in excess were much lower than expected. Transcriptomics, proteomics and fluxomics were integrated to investigate how this phenomenon was regulated. Through diverse regulation at both transcriptional and translational levels, strain Y51 turned to fermenting the excess lactate and disproportionating the excess fumarate under fumarate- and lactate-limiting conditions respectively. Genes and proteins related to the utilization of a variety of alternative electron donors and acceptors absent from the medium were induced, apparently involving the Wood-Ljungdahl pathway. Through this metabolic flexibility, D. hafniense Y51 may be able to switch between different metabolic capabilities under limiting conditions.

Control of pancreatic β-cell bioenergetics

The canonical model of glucose-stimulated insulin secretion (GSIS) by pancreatic β-cells predicts a glucose-induced rise in the cytosolic ATP/ADP ratio. Such bioenergetic sensitivity to metabolic fuel is unusual as it implies that ATP flux is governed, to a significant extent, by ATP supply, while it is predominantly demand-driven in other cell types. Metabolic control is generally shared between different processes, but potential control of ATP consumption over β-cell bioenergetics has been largely ignored to date. The present paper offers a brief overview of experimental evidence that demonstrates ATP flux control by glucose-fuelled oxidative phosphorylation. Based on old and new data, it is argued that ATP supply does not hold exclusive control over ATP flux, but shares it with ATP demand, and that the distribution of control is flexible. Quantification of the bioenergetic control distribution will be important from basic and clinical perspectives, but precise measurement of the cytosolic ATP/ADP ratio is complicated by adenine nucleotide compartmentalisation. Metabolic control analysis of β-cell bioenergetics will likely clarify the mechanisms by which glucose and fatty acids amplify and potentiate GSIS, respectively. Moreover, such analysis may offer hints as to how ATP flux control shifts from ATP supply to ATP demand during the development of type 2 diabetes, and why prolonged sulfonylurea treatment causes β-cell deterioration.

Beyond topology: coevolution of structure and flux in metabolic networks

Interactions between the structure of a metabolic network and its functional properties underlie its evolutionary diversification, but the mechanism by which such interactions arise remains elusive. Particularly unclear is whether metabolic fluxes that determine the concentrations of compounds produced by a metabolic network, are causally linked to a network's structure or emerge independently of it. A direct empirical study of populations where both structural and functional properties vary among individuals' metabolic networks is required to establish whether changes in structure affect the distribution of metabolic flux. In a population of house finches (Haemorhous mexicanus), we reconstructed full carotenoid metabolic networks for 442 individuals and uncovered 11 structural variants of this network with different compounds and reactions. We examined the consequences of this structural diversity for the concentrations of plumage-bound carotenoids produced by flux in these networks. We found that concentrations of metabolically derived, but not dietary carotenoids, depended on network structure. Flux was partitioned similarly among compounds in individuals of the same network structure: within each network, compound concentrations were closely correlated. The highest among-individual variation in flux occurred in networks with the strongest among-compound correlations, suggesting that changes in the magnitude, but not the distribution of flux, underlie individual differences in compound concentrations on a static network structure. These findings indicate that the distribution of flux in carotenoid metabolism closely follows network structure. Thus, evolutionary diversification and local adaptations in carotenoid metabolism may depend more on the gain or loss of enzymatic reactions than on changes in flux within a network structure.

Nonhierarchical Flux Regulation Exposes the Fitness Burden Associated with Lactate Production in Synechocystis sp. PCC6803

Cyanobacteria are mostly engineered to be sustainable cell-factories by genetic manipulations alone. Here, by modulating the concentration of allosteric effectors, we focus on increasing product formation without further burdening the cells with increased expression of enzymes. Resorting to a novel 96-well microplate cultivation system for cyanobacteria, and using lactate-producing strains of Synechocystis PCC6803 expressing different l-lactate dehydrogenases (LDH), we titrated the effect of 2,5-anhydro-mannitol supplementation. The latter acts in cells as a nonmetabolizable analogue of fructose 1,6-bisphosphate, a known allosteric regulator of one of the tested LDHs. In this strain (SAA023), we achieved over 2-fold increase of lactate productivity. Furthermore, we observed that as carbon is increasingly deviated during growth toward product formation, there is an increased fixation rate in the population of spontaneous mutants harboring an impaired production pathway. This is a challenge in the development of green cell factories, which may be countered by the incorporation in biotechnological processes of strategies such as the one pioneered here.

Systems Biology of Metabolism

Metabolism is highly complex and involves thousands of different connected reactions; it is therefore necessary to use mathematical models for holistic studies. The use of mathematical models in biology is referred to as systems biology. In this review, the principles of systems biology are described, and two different types of mathematical models used for studying metabolism are discussed: kinetic models and genome-scale metabolic models. The use of different omics technologies, including transcriptomics, proteomics, metabolomics, and fluxomics, for studying metabolism is presented. Finally, the application of systems biology for analyzing global regulatory structures, engineering the metabolism of cell factories, and analyzing human diseases is discussed.

Metabolic regulation is sufficient for global and robust coordination of glucose uptake, catabolism, energy production and growth in Escherichia coli

The metabolism of microorganisms is regulated through two main mechanisms: changes of enzyme capacities as a consequence of gene expression modulation (“hierarchical control”) and changes of enzyme activities through metabolite-enzyme interactions. An increasing body of evidence indicates that hierarchical control is insufficient to explain metabolic behaviors, but the system-wide impact of metabolic regulation remains largely uncharacterized. To clarify its role, we developed and validated a detailed kinetic model of Escherichia coli central metabolism that links growth to environment. Metabolic control analyses confirm that the control is widely distributed across the network and highlight strong interconnections between all the pathways. Exploration of the model solution space reveals that several robust properties emerge from metabolic regulation, from the molecular level (e.g. homeostasis of total metabolite pool) to the overall cellular physiology (e.g. coordination of carbon uptake, catabolism, energy and redox production, and growth), while allowing a large degree of flexibility at most individual metabolic steps. These properties have important physiological implications for E. coli and significantly expand the self-regulating capacities of its metabolism.

Metabolism is a fundamental biochemical process that enables cells to operate and grow by converting nutrients into ‘building blocks’ and energy. Metabolism happens through the work of enzymes, which are encoded by genes. Thus, genes and their regulation are often thought of controlling metabolism, somewhat at the top of a hierarchical control system. However, an increasing body of evidence indicates that metabolism plays an active role in the control of its own operation via a dense network of metabolite-enzyme interactions. The system-wide role of metabolic regulation is hard to dissect and so far remains largely uncharacterized. To better understand its role, we constructed a detailed kinetic model of the carbon and energy metabolism of the bacterium Escherichia coli, a model organism in Systems and Synthetic biology. Model simulations indicate that kinetic considerations of metabolism alone can explain data from hundreds of experiments, without needing to invoke regulation of gene expression. In particular, metabolic regulation is sufficient to coordinate carbon utilization, redox and energy production, and growth, while maintaining local flexibility at individual metabolic steps. These findings indicate that the self-regulating capacities of E. coli metabolism are far more significant than previously expected, and improve our understanding on how cells work.

Metabolic modelling in a dynamic evolutionary framework predicts adaptive diversification of bacteria in a long-term evolution experiment

BACKGROUND

Predicting adaptive trajectories is a major goal of evolutionary biology and useful for practical applications. Systems biology has enabled the development of genome-scale metabolic models. However, analysing these models via flux balance analysis (FBA) cannot predict many evolutionary outcomes including adaptive diversification, whereby an ancestral lineage diverges to fill multiple niches. Here we combine in silico evolution with FBA and apply this modelling framework, evoFBA, to a long-term evolution experiment with Escherichia coli.

RESULTS

Simulations predicted the adaptive diversification that occurred in one experimental population and generated hypotheses about the mechanisms that promoted coexistence of the diverged lineages. We experimentally tested and, on balance, verified these mechanisms, showing that diversification involved niche construction and character displacement through differential nutrient uptake and altered metabolic regulation.

CONCLUSION

The evoFBA framework represents a promising new way to model biochemical evolution, one that can generate testable predictions about evolutionary and ecosystem-level outcomes.

The Landscape of Evolution: Reconciling Structural and Dynamic Properties of Metabolic Networks in Adaptive Diversifications

The network of the interactions among genes, proteins, and metabolites delineates a range of potential phenotypic diversifications in a lineage, and realized phenotypic changes are the result of differences in the dynamics of the expression of the elements and interactions in this deterministic network. Regulatory mechanisms, such as hormones, mediate the relationship between the structural and dynamic properties of networks by determining how and when the elements are expressed and form a functional unit or state. Changes in regulatory mechanisms lead to variable expression of functional states of a network within and among generations. Functional properties of network elements, and the magnitude and direction of evolutionary change they determine, depend on their location within a network. Here, we examine the relationship between network structure and the dynamic mechanisms that regulate flux through a metabolic network. We review the mechanisms that control metabolic flux in enzymatic reactions and examine structural properties of the network locations that are targets of flux control. We aim to establish a predictive framework to test the contributions of structural and dynamic properties of deterministic networks to evolutionary diversifications.

Synthetic biology and regulatory networks: where metabolic systems biology meets control engineering

Metabolic pathways can be engineered to maximize the synthesis of various products of interest. With the advent of computational systems biology, this endeavour is usually carried out through in silico theoretical studies with the aim to guide and complement further in vitro and in vivo experimental efforts. Clearly, what counts is the result in vivo, not only in terms of maximal productivity but also robustness against environmental perturbations. Engineering an organism towards an increased production flux, however, often compromises that robustness. In this contribution, we review and investigate how various analytical approaches used in metabolic engineering and synthetic biology are related to concepts developed by systems and control engineering. While trade-offs between production optimality and cellular robustness have already been studied diagnostically and statically, the dynamics also matter. Integration of the dynamic design aspects of control engineering with the more diagnostic aspects of metabolic, hierarchical control and regulation analysis is leading to the new, conceptual and operational framework required for the design of robust and productive dynamic pathways.

Modeling the Contribution of Allosteric Regulation for Flux Control in the Central Carbon Metabolism of E. coli

Modeling cellular metabolism is fundamental for many biotechnological applications, including drug discovery and rational cell factory design. Central carbon metabolism (CCM) is particularly important as it provides the energy and precursors for other biological processes. However, the complex regulation of CCM pathways has still not been fully unraveled and recent studies have shown that CCM is mostly regulated at post-transcriptional levels. In order to better understand the role of allosteric regulation in controlling the metabolic phenotype, we expand the reconstruction of CCM in Escherichia coli with allosteric interactions obtained from relevant databases. This model is used to integrate multi-omics datasets and analyze the coordinated changes in enzyme, metabolite, and flux levels between multiple experimental conditions. We observe cases where allosteric interactions have a major contribution to the metabolic flux changes. Inspired by these results, we develop a constraint-based method (arFBA) for simulation of metabolic flux distributions that accounts for allosteric interactions. This method can be used for systematic prediction of potential allosteric regulation under the given experimental conditions based on experimental data. We show that arFBA allows predicting coordinated flux changes that would not be predicted without considering allosteric regulation. The results reveal the importance of key regulatory metabolites, such as fructose-1,6-bisphosphate, in controlling the metabolic flux. Accounting for allosteric interactions in metabolic reconstructions reveals a hidden topology in metabolic networks, improving our understanding of cellular metabolism and fostering the development of novel simulation methods that account for this type of regulation.

Context-Specific Metabolic Model Extraction Based on Regularized Least Squares Optimization

Genome-scale metabolic models have proven highly valuable in investigating cell physiology. Recent advances include the development of methods to extract context-specific models capable of describing metabolism under more specific scenarios (e.g., cell types). Yet, none of the existing computational approaches allows for a fully automated model extraction and determination of a flux distribution independent of user-defined parameters. Here we present RegrEx, a fully automated approach that relies solely on context-specific data and ℓ₁-norm regularization to extract a context-specific model and to provide a flux distribution that maximizes its correlation to data. Moreover, the publically available implementation of RegrEx was used to extract 11 context-specific human models using publicly available RNAseq expression profiles, Recon1 and also Recon2, the most recent human metabolic model. The comparison of the performance of RegrEx and its contending alternatives demonstrates that the proposed method extracts models for which both the structure, i.e., reactions included, and the flux distributions are in concordance with the employed data. These findings are supported by validation and comparison of method performance on additional data not used in context-specific model extraction. Therefore, our study sets the ground for applications of other regularization techniques in large-scale metabolic modeling.

How fast-growing bacteria robustly tune their ribosome concentration to approximate growth-rate maximization

Maximization of growth rate is an important fitness strategy for bacteria. Bacteria can achieve this by expressing proteins at optimal concentrations, such that resources are not wasted. This is exemplified for Escherichia coli by the increase of its ribosomal protein-fraction with growth rate, which precisely matches the increased protein synthesis demand. These findings and others have led to the hypothesis that E. coli aims to maximize its growth rate in environments that support growth. However, what kind of regulatory strategy is required for a robust, optimal adjustment of the ribosome concentration to the prevailing condition is still an open question. In the present study, we analyze the ppGpp-controlled mechanism of ribosome expression used by E. coli and show that this mechanism maintains the ribosomes saturated with its substrates. In this manner, overexpression of the highly abundant ribosomal proteins is prevented, and limited resources can be redirected to the synthesis of other growth-promoting enzymes. It turns out that the kinetic conditions for robust, optimal protein-partitioning, which are required for growth rate maximization across conditions, can be achieved with basic biochemical interactions. We show that inactive ribosomes are the most suitable ‘signal’ for tracking the intracellular nutritional state and for adjusting gene expression accordingly, as small deviations from optimal ribosome concentration cause a huge fractional change in ribosome inactivity. We expect to find this control logic implemented across fast-growing microbial species because growth rate maximization is a common selective pressure, ribosomes are typically highly abundant and thus costly, and the required control can be implemented by a small, simple network.

Elucidating the regulation of complex signalling systems in plant cells

The pollen tube represents a model system for the study of tip growth, and the root provides a valuable system to study gene and signalling networks in plants. In the present article, using the two systems as examples, we discuss how to elucidate the regulation of complex signalling systems in plant cells. First, we discuss how hormones and related genes in plant root development form a complex interacting network, and their activities are interdependent. Therefore their roles in root development must be analysed as an integrated system, and elucidation of the regulation of each component requires the adaptation of a novel modelling methodology: regulation analysis. Secondly, hydrodynamics, cell wall and ion dynamics are all important properties that regulate plant cell growth. We discuss how regulation analysis can be applied to study the regulation of hydrodynamics, cell wall and ion dynamics, using pollen tube growth as a model system. Finally, we discuss future prospects for elucidating the regulation of complex signalling systems in plant cells.

Dissecting the regulation of pollen tube growth by modeling the interplay of hydrodynamics, cell wall and ion dynamics

Hydrodynamics, cell wall and ion dynamics are all important properties that regulate pollen tube growth. Currently, the two main pollen tube growth models, the cell wall model and the hydrodynamic model do not appear to be reconcilable. Here we develop an integrative model for pollen tube growth and show that our model reproduces key experimental observations: (1) that the hypertonic condition leads to a much longer oscillatory period and that the hypotonic condition halves the oscillatory period; (2) that oscillations in turgor are experimentally undetectable; (3) that increasing the extracellular calcium concentration or decreasing the pH decreases the growth oscillatory amplitude; (4) that knockout of Raba4d, a member of the Rab family of small GTPase proteins, decreases pollen tube length after germination for 24 h. Using the model generated here, we reveal that (1) when cell wall extensibility is large, pollen tube may sustain growth at different volume changes and maintain relatively stable turgor; (2) turgor increases if cell wall extensibility decreases; (3) increasing turgor due to decrease in osmolarity in the media, although very small, increases volume change. However, increasing turgor due to decrease in cell wall extensibility decreases volume change. In this way regulation of pollen tube growth by turgor is context dependent. By changing the osmolarity in the media, the main regulatory points are extracellular osmolarity for water flow and turgor for the volume encompassed by the cell wall. However, if the viscosity of cell wall changes, the main regulatory points are turgor for water flow and wall extensibility for the volume encompassed by the cell wall. The novel methodology developed here reveals the underlying context-dependent regulatory principle of pollen tube growth.

Contribution of network connectivity in determining the relationship between gene expression and metabolite concentration changes

One of the primary mechanisms through which a cell exerts control over its metabolic state is by modulating expression levels of its enzyme-coding genes. However, the changes at the level of enzyme expression allow only indirect control over metabolite levels, for two main reasons. First, at the level of individual reactions, metabolite levels are non-linearly dependent on enzyme abundances as per the reaction kinetics mechanisms. Secondly, specific metabolite pools are tightly interlinked with the rest of the metabolic network through their production and consumption reactions. While the role of reaction kinetics in metabolite concentration control is well studied at the level of individual reactions, the contribution of network connectivity has remained relatively unclear. Here we report a modeling framework that integrates both reaction kinetics and network connectivity constraints for describing the interplay between metabolite concentrations and mRNA levels. We used this framework to investigate correlations between the gene expression and the metabolite concentration changes in Saccharomyces cerevisiae during its metabolic cycle, as well as in response to three fundamentally different biological perturbations, namely gene knockout, nutrient shock and nutrient change. While the kinetic constraints applied at the level of individual reactions were found to be poor descriptors of the mRNA-metabolite relationship, their use in the context of the network enabled us to correlate changes in the expression of enzyme-coding genes to the alterations in metabolite levels. Our results highlight the key contribution of metabolic network connectivity in mediating cellular control over metabolite levels, and have implications towards bridging the gap between genotype and metabolic phenotype.

Generalized framework for context-specific metabolic model extraction methods

Genome-scale metabolic models (GEMs) are increasingly applied to investigate the physiology not only of simple prokaryotes, but also eukaryotes, such as plants, characterized with compartmentalized cells of multiple types. While genome-scale models aim at including the entirety of known metabolic reactions, mounting evidence has indicated that only a subset of these reactions is active in a given context, including: developmental stage, cell type, or environment. As a result, several methods have been proposed to reconstruct context-specific models from existing genome-scale models by integrating various types of high-throughput data. Here we present a mathematical framework that puts all existing methods under one umbrella and provides the means to better understand their functioning, highlight similarities and differences, and to help users in selecting a most suitable method for an application.

Transcriptional regulation is insufficient to explain substrate-induced flux changes in Bacillus subtilis

Regulation of enzyme expression is one key mechanism by which cells control their metabolic programs. In this work, a quantitative analysis of metabolism in a model bacterium under different conditions shows that expression alone cannot explain the majority of the observed metabolic changes.

Most enzymes are indeed highly expressed in conditions where they are more active.

Quantitatively, however, the observed changes in expression between conditions do not match the changes in activity for most enzymes.

A good quantitative match is only observed for enzymes involved in the TCA cycle.

Metabolomics reveals that increased substrate availability explains only a few instances of changes in activity.

One of the key ways in which microbes are thought to regulate their metabolism is by modulating the availability of enzymes through transcriptional regulation. However, the limited success of efforts to manipulate metabolic fluxes by rewiring the transcriptional network has cast doubt on the idea that transcript abundance controls metabolic fluxes. In this study, we investigate control of metabolic flux in the model bacterium Bacillus subtilis by quantifying fluxes, transcripts, and metabolites in eight metabolic states enforced by different environmental conditions. We find that most enzymes whose flux switches between on and off states, such as those involved in substrate uptake, exhibit large corresponding transcriptional changes. However, for the majority of enzymes in central metabolism, enzyme concentrations were insufficient to explain the observed fluxes—only for a number of reactions in the tricarboxylic acid cycle were enzyme changes approximately proportional to flux changes. Surprisingly, substrate changes revealed by metabolomics were also insufficient to explain observed fluxes, leaving a large role for allosteric regulation and enzyme modification in the control of metabolic fluxes.

(Im)Perfect robustness and adaptation of metabolic networks subject to metabolic and gene-expression regulation: marrying control engineering with metabolic control analysis

Background

Metabolic control analysis (MCA) and supply–demand theory have led to appreciable understanding of the systems properties of metabolic networks that are subject exclusively to metabolic regulation. Supply–demand theory has not yet considered gene-expression regulation explicitly whilst a variant of MCA, i.e. Hierarchical Control Analysis (HCA), has done so. Existing analyses based on control engineering approaches have not been very explicit about whether metabolic or gene-expression regulation would be involved, but designed different ways in which regulation could be organized, with the potential of causing adaptation to be perfect.

Results

This study integrates control engineering and classical MCA augmented with supply–demand theory and HCA. Because gene-expression regulation involves time integration, it is identified as a natural instantiation of the ‘integral control’ (or near integral control) known in control engineering. This study then focuses on robustness against and adaptation to perturbations of process activities in the network, which could result from environmental perturbations, mutations or slow noise. It is shown however that this type of ‘integral control’ should rarely be expected to lead to the ‘perfect adaptation’: although the gene-expression regulation increases the robustness of important metabolite concentrations, it rarely makes them infinitely robust. For perfect adaptation to occur, the protein degradation reactions should be zero order in the concentration of the protein, which may be rare biologically for cells growing steadily.

Conclusions

A proposed new framework integrating the methodologies of control engineering and metabolic and hierarchical control analysis, improves the understanding of biological systems that are regulated both metabolically and by gene expression. In particular, the new approach enables one to address the issue whether the intracellular biochemical networks that have been and are being identified by genomics and systems biology, correspond to the ‘perfect’ regulatory structures designed by control engineering vis-à-vis optimal functions such as robustness. To the extent that they are not, the analyses suggest how they may become so and this in turn should facilitate synthetic biology and metabolic engineering.

Energy and metabolism

Although firmly grounded in metabolic biochemistry, the study of energy metabolism has gone well beyond this discipline and become integrative and comparative as well as ecological and evolutionary in scope. At the cellular level, ATP is hydrolyzed by energy-expending processes and resynthesized by pathways in bioenergetics. A significant development in the study of bioenergetics is the realization that fluxes through pathways as well as metabolic rates in cells, tissues, organs, and whole organisms are "system properties." Therefore, studies of energy metabolism have become, increasingly, experiments in systems biology. A significant challenge continues to be the integration of phenomena over multiple levels of organization. Body mass and temperature are said to account for most of the variation in metabolic rates found in nature. A mechanistic foundation for the understanding of these patterns is outlined. It is emphasized that evolution, leading to adaptation to diverse lifestyles and environments, has resulted in a tremendous amount of deviation from popularly accepted scaling "rules." This is especially so in the deep sea which constitutes most of the biosphere.

Mathematical modelling of miRNA mediated BCR.ABL protein regulation in chronic myeloid leukaemia vis-a-vis therapeutic strategies

Chronic myeloid leukaemia (CML) is a clonal myeloproliferative disease resulting from an aberrant BCR.ABL gene and protein. To predict BCR.ABL protein abundance and phosphorylation in individual cells in a population of CML cells, we modelled BCR.ABL protein regulation through associated miRNAs using a systems approach. The model rationalizes the level of BCR.ABL protein heterogeneity in CML cells in correlation with the heterogeneous BCR.ABL mRNA levels. We also measured BCR.ABL mRNA and BCR.ABLp phosphorylation in individual cells. The experimental data were consistent with the modelling results, thereby partly validating the model. Provided it is tested further, the model may be used to support effective therapeutic strategies including the combined application of a tyrosine kinase inhibitor and miRNAs targeting BCR.ABL. It appears able to predict different effects of the two types of drug on cells with different expression levels and consequently different effects on the generation of resistance.

The ability of flux balance analysis to predict evolution of central metabolism scales with the initial distance to the optimum

The most powerful genome-scale framework to model metabolism, flux balance analysis (FBA), is an evolutionary optimality model. It hypothesizes selection upon a proposed optimality criterion in order to predict the set of internal fluxes that would maximize fitness. Here we present a direct test of the optimality assumption underlying FBA by comparing the central metabolic fluxes predicted by multiple criteria to changes measurable by a ¹³C-labeling method for experimentally-evolved strains. We considered datasets for three Escherichia coli evolution experiments that varied in their length, consistency of environment, and initial optimality. For ten populations that were evolved for 50,000 generations in glucose minimal medium, we observed modest changes in relative fluxes that led to small, but significant decreases in optimality and increased the distance to the predicted optimal flux distribution. In contrast, seven populations evolved on the poor substrate lactate for 900 generations collectively became more optimal and had flux distributions that moved toward predictions. For three pairs of central metabolic knockouts evolved on glucose for 600–800 generations, there was a balance between cases where optimality and flux patterns moved toward or away from FBA predictions. Despite this variation in predictability of changes in central metabolism, two generalities emerged. First, improved growth largely derived from evolved increases in the rate of substrate use. Second, FBA predictions bore out well for the two experiments initiated with ancestors with relatively sub-optimal yield, whereas those begun already quite optimal tended to move somewhat away from predictions. These findings suggest that the tradeoff between rate and yield is surprisingly modest. The observed positive correlation between rate and yield when adaptation initiated further from the optimum resulted in the ability of FBA to use stoichiometric constraints to predict the evolution of metabolism despite selection for rate.

The most common method of modeling genome-scale metabolism, flux balance analysis, involves using known stoichiometry to define feasible metabolic states and then choosing between these states by proposing that evolution has selected a metabolic flux that optimizes fitness. But does evolution optimize metabolism, and if so, what component of metabolism equates to fitness? We directly tested the underlying assumption of stoichiometric optimality by comparing predicted flux distributions with changes in fluxes that occurred following experimental evolution. Across three experiments ranging in length from a few hundred to fifty thousand generations, we found that substrate uptake – an input to the model – always increased, but supposed optimality criteria such as yield only increased sometimes. Despite this, there was a clear trend. Highly optimal ancestors evolved slightly lower yield in the course of increasing the overall rate, whereas more sub-optimal strains were able to increase both. These results suggest that flux balance analysis is capable of predicting either the initial metabolic behavior of strains or how they will evolve, but not both.

Relationships between metabolic fluxes and enzyme amino acid composition

Metabolic fluxes are a key parameter of metabolic pathways being closely related to the kinetic properties of enzymes and could be conditional on their sequence characteristics. This study examines possible relationships between the metabolic fluxes and the amino acid (AA) composition (AAC) for enzymes from the yeast Saccharomyces cerevisiae glycolysis pathway. Metabolic fluxes were quantified by the COPASI tool using the kinetic models of Hynne and Teusink at 25 mM, 50 mM, and 100 mM of external glucose or employing literature data for cognate kinetic or stoichiometric models. The enzyme sequences were taken from the UniProtKB, and the AAC computed by the ExPASy/ProtParam tool. Multiple linear regressions (89.07% < R2 adjusted < 91.82%; P<0.00001) were found between the values of metabolic fluxes and the selected sets of AA frequencies (5 to 7 for each model). Selected AA differed from the rest by their physicochemical and structural propensities, thus suggesting a distinctive contribution to the properties of enzymes, and hence the metabolic fluxes. The results provide evidence that metabolic fluxes of the yeast glycolysis pathway are closely related to the AAC of relevant enzymes and support the view that catalytic, binding and structural residues are interdependent to ensure the efficiency of biocatalysts.

Importance of understanding the main metabolic regulation in response to the specific pathway mutation for metabolic engineering of Escherichia coli

Recent metabolic engineering practice was briefly reviewed in particular for the useful metabolite production such as natural products and biofuel productions. With the emphasis on systems biology approach, the metabolic regulation of the main metabolic pathways in E. coli was discussed from the points of view of enzyme level (allosteric and phosphorylation/ dephosphorylation) regulation, and gene level (transcriptional) regulation. Then the effects of the specific pathway gene knockout such as pts, pgi, zwf, gnd, pyk, ppc, pckA, lpdA, pfl gene knockout on the metabolism in E. coli were overviewed from the systems biology point of view with possible application for strain improvement point.

Genome-level transcription data of Yersinia pestis analyzed with a new metabolic constraint-based approach

Background

Constraint-based computational approaches, such as flux balance analysis (FBA), have proven successful in modeling genome-level metabolic behavior for conditions where a set of simple cellular objectives can be clearly articulated. Recently, the necessity to expand the current range of constraint-based methods to incorporate high-throughput experimental data has been acknowledged by the proposal of several methods. However, these methods have rarely been used to address cellular metabolic responses to some relevant perturbations such as antimicrobial or temperature-induced stress. Here, we present a new method for combining gene-expression data with FBA (GX-FBA) that allows modeling of genome-level metabolic response to a broad range of environmental perturbations within a constraint-based framework. The method uses mRNA expression data to guide hierarchical regulation of cellular metabolism subject to the interconnectivity of the metabolic network.

Results

We applied GX-FBA to a genome-scale model of metabolism in the gram negative bacterium Yersinia pestis and analyzed its metabolic response to (i) variations in temperature known to induce virulence, and (ii) antibiotic stress. Without imposition of any a priori behavioral constraints, our results show strong agreement with reported phenotypes. Our analyses also lead to novel insights into how Y. pestis uses metabolic adjustments to counter different forms of stress.

Conclusions

Comparisons of GX-FBA predicted metabolic states with fluxomic measurements and different reported post-stress phenotypes suggest that mass conservation constraints and network connectivity can be an effective representative of metabolic flux regulation in constraint-based models. We believe that our approach will be of aid in the in silico evaluation of cellular goals under different conditions and can be used for a variety of analyses such as identification of potential drug targets and their action.

Towards multiscale plant models: integrating cellular networks

One of the ambitions of 'crop systems biology' is to combine information from molecular biology with a broader view of plant development and growth. In the context of modeling, this calls for a multiscale perspective that focuses on the interplay between cellular and macroscopic studies. With this in mind, in this review we aim to draw attention to a panel of approaches that were developed in the context of systems biology and are used for analyzing and describing the behavior of cellular networks. Ultimately, insights obtained from these methods can be exploited to refine the description of plant processes, leading to integrated plant-cellular models.

Towards multiscale plant models: integrating cellular networks

One of the ambitions of 'crop systems biology' is to combine information from molecular biology with a broader view of plant development and growth. In the context of modeling, this calls for a multiscale perspective that focuses on the interplay between cellular and macroscopic studies. With this in mind, in this review we aim to draw attention to a panel of approaches that were developed in the context of systems biology and are used for analyzing and describing the behavior of cellular networks. Ultimately, insights obtained from these methods can be exploited to refine the description of plant processes, leading to integrated plant-cellular models.

What mRNA Abundances Can Tell us about Metabolism

Inferring decreased or increased metabolic functions from transcript profiles is at first sight a bold and speculative attempt because of the functional layers in between: proteins, enzymatic activities, and reaction fluxes. However, the growing interest in this field can easily be explained by two facts: the high quality of genome-scale metabolic network reconstructions and the highly developed technology to obtain genome-covering RNA profiles. Here, an overview of important algorithmic approaches is given by means of criteria by which published procedures can be classified. The frontiers of the methods are sketched and critical voices are being heard. Finally, an outlook for the prospects of the field is given.

Optimality principles in the regulation of metabolic networks

One of the challenging tasks in systems biology is to understand how molecular networks give rise to emergent functionality and whether universal design principles apply to molecular networks. To achieve this, the biophysical, evolutionary and physiological constraints that act on those networks need to be identified in addition to the characterisation of the molecular components and interactions. Then, the cellular "task" of the network-its function-should be identified. A network contributes to organismal fitness through its function. The premise is that the same functions are often implemented in different organisms by the same type of network; hence, the concept of design principles. In biology, due to the strong forces of selective pressure and natural selection, network functions can often be understood as the outcome of fitness optimisation. The hypothesis of fitness optimisation to understand the design of a network has proven to be a powerful strategy. Here, we outline the use of several optimisation principles applied to biological networks, with an emphasis on metabolic regulatory networks. We discuss the different objective functions and constraints that are considered and the kind of understanding that they provide.

Systems biology tools for toxicology

An important goal of toxicology is to understand and predict the adverse effects of drugs and other xenobiotics. For pharmaceuticals, such effects often emerge unexpectedly in man even when absent from trials in vitro and in animals. Although drugs and xenobiotics act on molecules, it is their perturbation of intracellular networks that matters. The tremendous complexity of these networks makes it difficult to understand the effects of xenobiotics on their ability to function. Because systems biology integrates data concerning molecules and their interactions into an understanding of network behaviour, it should be able to assist toxicology in this respect. This review identifies how in silico systems biology tools, such as kinetic modelling, and metabolic control, robustness and flux analyse, may indeed help understanding network-mediated toxicity. It also shows how these approaches function by implementing them vis-à-vis the glutathione network, which is important for the detoxification of reactive drug metabolites. The tools enable the appreciation of the steady state concept for the detoxification network and make it possible to simulate and then understand effects of perturbations of the macromolecules in the pathway that are counterintuitive. We review how a glutathione model has been used to explain the impact of perturbation of the pathway at various molecular sites, as would be the effect of single-nucleotide polymorphisms. We focus on how the mutations impact the levels of glutathione and of two candidate biomarkers of hepatic glutathione status. We conclude this review by sketching how the various systems biology tools may help in the various phases of drug development in the pharmaceutical industry.

A comparative transcriptomic, fluxomic and metabolomic analysis of the response of Saccharomyces cerevisiae to increases in NADPH oxidation

Background

Redox homeostasis is essential to sustain metabolism and growth. We recently reported that yeast cells meet a gradual increase in imposed NADPH demand by progressively increasing flux through the pentose phosphate (PP) and acetate pathways and by exchanging NADH for NADPH in the cytosol, via a transhydrogenase-like cycle. Here, we studied the mechanisms underlying this metabolic response, through a combination of gene expression profiling and analyses of extracellular and intracellular metabolites and ¹³ C-flux analysis.

Results

NADPH oxidation was increased by reducing acetoin to 2,3-butanediol in a strain overexpressing an engineered NADPH-dependent butanediol dehydrogenase cultured in the presence of acetoin. An increase in NADPH demand to 22 times the anabolic requirement for NADPH was accompanied by the intracellular accumulation of PP pathway metabolites consistent with an increase in flux through this pathway. Increases in NADPH demand were accompanied by the successive induction of several genes of the PP pathway. NADPH-consuming pathways, such as amino-acid biosynthesis, were upregulated as an indirect effect of the decrease in NADPH availability. Metabolomic analysis showed that the most extreme modification of NADPH demand resulted in an energetic problem. Our results also highlight the influence of redox status on aroma production.

Conclusions

Combined ¹³ C-flux, intracellular metabolite levels and microarrays analyses revealed that NADPH homeostasis, in response to a progressive increase in NADPH demand, was achieved by the regulation, at several levels, of the PP pathway. This pathway is principally under metabolic control, but regulation of the transcription of PP pathway genes can exert a stronger effect, by redirecting larger amounts of carbon to this pathway to satisfy the demand for NADPH. No coordinated response of genes involved in NADPH metabolism was observed, suggesting that yeast has no system for sensing NADPH/NADP⁺ ratio. Instead, the induction of NADPH-consuming amino-acid pathways in conditions of NADPH limitation may indirectly trigger the transcription of a set of PP pathway genes.

From steady-state to synchronized yeast glycolytic oscillations I: model construction

An existing detailed kinetic model for the steady-state behavior of yeast glycolysis was tested for its ability to simulate dynamic behavior. Using a small subset of experimental data, the original model was adapted by adjusting its parameter values in three optimization steps. Only small adaptations to the original model were required for realistic simulation of experimental data for limit-cycle oscillations. The greatest changes were required for parameter values for the phosphofructokinase reaction. The importance of ATP for the oscillatory mechanism and NAD(H) for inter-and intra-cellular communications and synchronization was evident in the optimization steps and simulation experiments. In an accompanying paper [du Preez F et al. (2012) FEBS J279, 2823-2836], we validate the model for a wide variety of experiments on oscillatory yeast cells. The results are important for re-use of detailed kinetic models in modular modeling approaches and for approaches such as that used in the Silicon Cell initiative.

DATABASE

The mathematical models described here have been submitted to the JWS Online Cellular Systems Modelling Database and can be accessed at http://jjj.biochem.sun.ac.za/database/dupreez/index.html.

From steady-state to synchronized yeast glycolytic oscillations II: model validation

In an accompanying paper [du Preez et al., (2012) FEBS J279, 2810-2822], we adapt an existing kinetic model for steady-state yeast glycolysis to simulate limit-cycle oscillations. Here we validate the model by testing its capacity to simulate a wide range of experiments on dynamics of yeast glycolysis. In addition to its description of the oscillations of glycolytic intermediates in intact cells and the rapid synchronization observed when mixing out-of-phase oscillatory cell populations (see accompanying paper), the model was able to predict the Hopf bifurcation diagram with glucose as the bifurcation parameter (and one of the bifurcation points with cyanide as the bifurcation parameter), the glucose- and acetaldehyde-driven forced oscillations, glucose and acetaldehyde quenching, and cell-free extract oscillations (including complex oscillations and mixed-mode oscillations). Thus, the model was compliant, at least qualitatively, with the majority of available experimental data for glycolytic oscillations in yeast. To our knowledge, this is the first time that a model for yeast glycolysis has been tested against such a wide variety of independent data sets.

DATABASE

The mathematical models described here have been submitted to the JWS Online Cellular Systems Modelling Database and can be accessed at http://jjj.biochem.sun.ac.za/database/dupreez/index.html.

Engineering of self-sustaining systems: substituting the yeast glucose transporter plus hexokinase for the Lactococcus lactis phosphotransferase system in a Lactococcus lactis network in silico

The success rate of introducing new functions into a living species is still rather unsatisfactory. Much of this is due to the very essence of the living state, i.e. its robustness towards perturbations. Living cells are bound to notice that metabolic engineering is being effected, through changes in metabolite concentrations. In this study, we asked whether one could engage in such engineering without changing metabolite concentrations. We have illustrated that, in silico, one can do so in principle. We have done this for the case of substituting the yeast glucose transporter plus hexokinase for the Lactococcus lactis phosphotransferase system, in an L. lactis network, this engineering is 'silent' in terms of metabolite concentrations and almost all fluxes.

Sustained glycolytic oscillations in individual isolated yeast cells

Yeast glycolytic oscillations have been studied since the 1950s in cell-free extracts and intact cells. For intact cells, sustained oscillations have so far only been observed at the population level, i.e. for synchronized cultures at high biomass concentrations. Using optical tweezers to position yeast cells in a microfluidic chamber, we were able to observe sustained oscillations in individual isolated cells. Using a detailed kinetic model for the cellular reactions, we simulated the heterogeneity in the response of the individual cells, assuming small differences in a single internal parameter. This is the first time that sustained limit-cycle oscillations have been demonstrated in isolated yeast cells.

DATABASE

The mathematical model described here has been submitted to the JWS Online Cellular Systems Modelling Database and can be accessed at http://jjj.biochem.sun.ac.za/database/gustavsson/index.html free of charge.

Isoenzyme expression changes in response to high temperature determine the metabolic regulation of increased glycolytic flux in yeast

Qualitative phenotypic changes are the integrated result of quantitative changes at multiple regulatory levels. To explain the temperature-induced increase of glycolytic flux in fermenting cultures of Saccharomyces cerevisiae, we quantified the contributions of changes in activity at many regulatory levels. We previously showed that a similar temperature increase in glucose-limited cultivations lead to a qualitative change from respiratory to fermentative metabolism, and this change was mainly regulated at the metabolic level. In contrast, in fermenting cells, a combination of different modes of regulation was observed. Regulation by changes in expression and the effect of temperature on enzyme activities contributed much to the increase in flux. Mass spectrometric quantification of glycolytic enzymes revealed that increased enzyme activity did not correlate with increased protein abundance, suggesting a large contribution of post-translational regulation to activity. Interestingly, the differences in the direct effect of temperature on enzyme kinetics can be explained by changes in the expression of the isoenzymes. Therefore, both the interaction of enzyme with its metabolic environment and the temperature dependence of activity are in turn regulated at the hierarchical level.

Global network reorganization during dynamic adaptations of Bacillus subtilis metabolism

Adaptation of cells to environmental changes requires dynamic interactions between metabolic and regulatory networks, but studies typically address only one or a few layers of regulation. For nutritional shifts between two preferred carbon sources of Bacillus subtilis, we combined statistical and model-based data analyses of dynamic transcript, protein, and metabolite abundances and promoter activities. Adaptation to malate was rapid and primarily controlled posttranscriptionally compared with the slow, mainly transcriptionally controlled adaptation to glucose that entailed nearly half of the known transcription regulation network. Interactions across multiple levels of regulation were involved in adaptive changes that could also be achieved by controlling single genes. Our analysis suggests that global trade-offs and evolutionary constraints provide incentives to favor complex control programs.