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.

Bicarbonate-rich fluid secretion predicted by a computational model of guinea-pig pancreatic duct epithelium.

KEY POINTS: The ductal system of the pancreas secretes large volumes of alkaline fluid containing HCO3- concentrations as high as 140 mm during hormonal stimulation. A computational model has been constructed to explore the underlying ion transport mechanisms. Parameters were estimated by fitting the model to experimental data from guinea-pig pancreatic ducts. The model was readily able to secrete 140 mm HCO3- . Its capacity to do so was not dependent upon special properties of the cystic fibrosis transmembrane conductance regulator (CFTR) anion channels and solute carrier family 26 member A6 (SLC26A6) anion exchangers. We conclude that the main requirement for secreting high HCO3- concentrations is to minimize the secretion of Cl- ions. These findings help to clarify the mechanism responsible for pancreatic HCO3- secretion, a vital process that prevents the formation of protein plugs and viscous mucus in the ducts, which could otherwise lead to pancreatic disease. ABSTRACT: A computational model of guinea-pig pancreatic duct epithelium was developed to determine the transport mechanism by which HCO3- ions are secreted at concentrations in excess of 140 mm. Parameters defining the contributions of the individual ion channels and transporters were estimated by least-squares fitting of the model predictions to experimental data obtained from isolated ducts and intact pancreas under a range of experimental conditions. The effects of cAMP-stimulated secretion were well replicated by increasing the activities of the basolateral Na+ -HCO3- cotransporter (NBC1) and apical Cl- /HCO3- exchanger (solute carrier family 26 member A6; SLC26A6), increasing the basolateral K+ permeability and apical Cl- and HCO3- permeabilities (CFTR), and reducing the activity of the basolateral Cl- /HCO3- exchanger (anion exchanger 2; AE2). Under these conditions, the model secreted ∼140 mm HCO3- at a rate of ∼3 nl min-1  mm-2 , which is consistent with experimental observations. Alternative 1:2 and 1:1 stoichiometries for Cl- /HCO3- exchange via SLC26A6 at the apical membrane were able to support a HCO3- -rich secretion. Raising the HCO3- /Cl- permeability ratio of CFTR from 0.4 to 1.0 had little impact upon either the secreted HCO3- concentration or the volume flow. However, modelling showed that a reduction in basolateral AE2 activity by ∼80% was essential in minimizing the intracellular Cl- concentration following cAMP stimulation and thereby maximizing the secreted HCO3- concentration. The addition of a basolateral Na+ -K+ -2Cl- cotransporter (NKCC1), assumed to be present in rat and mouse ducts, raised intracellular Cl- and resulted in a lower secreted HCO3- concentration, as is characteristic of those species. We conclude therefore that minimizing the driving force for Cl- secretion is the main requirement for secreting 140 mm HCO3- .

A mathematical model of the colon crypt capturing compositional dynamic interactions between cell types.

Models of the development and early progression of colorectal cancer are based upon understanding the cycle of stem cell turnover, proliferation, differentiation and death. Existing crypt compartmental models feature a linear pathway of cell types, with little regulatory mechanism. Previous work has shown that there are perturbations in the enteroendocrine cell population of macroscopically normal crypts, a compartment not included in existing models. We show that existing models do not adequately recapitulate the dynamics of cell fate pathways in the crypt. We report the progressive development, iterative testing and fitting of a developed compartmental model with additional cell types, and which includes feedback mechanisms and cross-regulatory mechanisms between cell types. The fitting of the model to existing data sets suggests a need to invoke cross-talk between cell types as a feature of colon crypt cycle models.

Modelling acidosis and the cell cycle in multicellular tumour spheroids.

A partial differential equation model is developed to understand the effect that nutrient and acidosis have on the distribution of proliferating and quiescent cells and dead cell material (necrotic and apoptotic) within a multicellular tumour spheroid. The rates of cell quiescence and necrosis depend upon the local nutrient and acid concentrations and quiescent cells are assumed to consume less nutrient and produce less acid than proliferating cells. Analysis of the differences in nutrient consumption and acid production by quiescent and proliferating cells shows low nutrient levels do not necessarily lead to increased acid concentration via anaerobic metabolism. Rather, it is the balance between proliferating and quiescent cells within the tumour which is important; decreased nutrient levels lead to more quiescent cells, which produce less acid than proliferating cells. We examine this effect via a sensitivity analysis which also includes a quantification of the effect that nutrient and acid concentrations have on the rates of cell quiescence and necrosis.

Mechanistic modelling of cancer: some reflections from software engineering and philosophy of science.

There is a growing interest in mathematical mechanistic modelling as a promising strategy for understanding tumour progression. This approach is accompanied by a methodological change of making research, in which models help to actively generate hypotheses instead of waiting for general principles to become apparent once sufficient data are accumulated. This paper applies recent research from philosophy of science to uncover three important problems of mechanistic modelling which may compromise its mainstream application, namely: the dilemma of formal and informal descriptions, the need to express degrees of confidence and the need of an argumentation framework. We report experience and research on similar problems from software engineering and provide evidence that the solutions adopted there can be transferred to the biological domain. We hope this paper can provoke new opportunities for further and profitable interdisciplinary research in the field.

Why does yeast ferment? A flux balance analysis study.

Advances in biological techniques have led to the availability of genome-scale metabolic reconstructions for yeast. The size and complexity of such networks impose limits on what types of analyses one can perform. Constraint-based modelling overcomes some of these restrictions by using physicochemical constraints to describe the potential behaviour of an organism. FBA (flux balance analysis) highlights flux patterns through a network that serves to achieve a particular objective and requires a minimal amount of data to make quantitative inferences about network behaviour. Even though FBA is a powerful tool for system predictions, its general formulation sometimes results in unrealistic flux patterns. A typical example is fermentation in yeast: ethanol is produced during aerobic growth in excess glucose, but this pattern is not present in a typical FBA solution. In the present paper, we examine the issue of yeast fermentation against respiration during growth. We have studied a number of hypotheses from the modelling perspective, and novel formulations of the FBA approach have been tested. By making the observation that more respiration requires the synthesis of more mitochondria, an energy cost related to mitochondrial synthesis is added to the FBA formulation. Results, although still approximate, are closer to experimental observations than earlier FBA analyses, at least on the issue of fermentation.

Why are (the best) women so good at chess? Participation rates and gender differences in intellectual domains.

A popular explanation for the small number of women at the top level of intellectually demanding activities from chess to science appeals to biological differences in the intellectual abilities of men and women. An alternative explanation is that the extreme values in a large sample are likely to be greater than those in a small one. Although the performance of the 100 best German male chess players is better than that of the 100 best German women, we show that 96 per cent of the observed difference would be expected given the much greater number of men who play chess. There is little left for biological or cultural explanations to account for. In science, where there are many more male than female participants, this statistical sampling explanation, rather than differences in intellectual ability, may also be the main reason why women are under-represented at the top end.

Flux balance analysis: a geometric perspective.

Advances in the field of bioinformatics have led to reconstruction of genome-scale networks for a number of key organisms. The application of physicochemical constraints to these stoichiometric networks allows researchers, through methods such as flux balance analysis, to highlight key sets of reactions necessary to achieve particular objectives. The key benefits of constraint-based analysis lie in the minimal knowledge required to infer systemic properties. However, network degeneracy leads to a large number of flux distributions that satisfy any objective; moreover, these distributions may be dominated by biologically irrelevant internal cycles. By examining the geometry underlying the problem, we define two methods for finding a unique solution within the space of all possible flux distributions; such a solution contains no internal cycles, and is representative of the space as a whole. The first method draws on typical geometric knowledge, but cannot be applied to large networks because of the high computational complexity of the problem. Thus a second method, an iteration of linear programs which scales easily to the genome scale, is defined. The algorithm is run on four recent genome-scale models, and unique flux solutions are found. The algorithm set out here will allow researchers in flux balance analysis to exchange typical solutions to their models in a reproducible format. Moreover, having found a single solution, statistical analyses such as correlations may be performed.

Capturing the essence of a metabolic network: a flux balance analysis approach.

As genome-scale metabolic reconstructions emerge, tools to manage their size and complexity will be increasingly important. Flux balance analysis (FBA) is a constraint-based approach widely used to study the metabolic capabilities of cellular or subcellular systems. FBA problems are highly underdetermined and many different phenotypes can satisfy any set of constraints through which the metabolic system is represented. Two of the main concerns in FBA are exploring the space of solutions for a given metabolic network and finding a specific phenotype which is representative for a given task such as maximal growth rate. Here, we introduce a recursive algorithm suitable for overcoming both of these concerns. The method proposed is able to find the alternate optimal patterns of active reactions of an FBA problem and identify the minimal subnetwork able to perform a specific task as optimally as the whole. Our method represents an alternative to and an extension of other approaches conceived for exploring the space of solutions of an FBA problem. It may also be particularly helpful in defining a scaffold of reactions upon which to build up a dynamic model, when the important pathways of the system have not yet been well-defined.

Tumour glycolysis: the many faces of HIF.

We present a model for tumour metabolism that incorporates both microenvironmental (extracellular) and oncogenic (intracellular) influences. We explore the effects of the interaction between the hypoxic microenvironment and intracellular signalling on the glycolytic response of tumour tissue, finding that the glycolytic state is dependent on a delicately balanced interplay between the cellular hypoxic response, mediated by hypoxia-inducible factor-1alpha (HIF-1alpha), and growth-factor signalling cascades, which are frequently mutated in cancers. Our findings demonstrate the importance of considering both environmental and intracellular regulation when interpreting tumour metabolism for diagnostic or prognostic purposes. To illustrate this, we demonstrate the potential impact of this multi-factorial regulation on the kinetics of radiolabelled glucose analogues, used in positron emission tomography (PET).

Mathematical modelling of tumour acidity.

Acid-mediated tumour invasion is receiving increasing experimental and clinical attention. Previous models proposed to describe this phenomenon failed to capture key properties of the system, such as the existence of the benign steady state, or predicted incorrectly the size of the inter-tissue gap. Here we show that taking proper account of quiescence ameliorates these drawbacks as well as revealing novel behaviour. The simplicity of the model allows us to fully identify the key parameters controlling different aspects of behaviour.

Something from nothing: bridging the gap between constraint-based and kinetic modelling.

Two divergent modelling methodologies have been adopted to increase our understanding of metabolism and its regulation. Constraint-based modelling highlights the optimal path through a stoichiometric network within certain physicochemical constraints. Such an approach requires minimal biological data to make quantitative inferences about network behaviour; however, constraint-based modelling is unable to give an insight into cellular substrate concentrations. In contrast, kinetic modelling aims to characterize fully the mechanics of each enzymatic reaction. This approach suffers because parameterizing mechanistic models is both costly and time-consuming. In this paper, we outline a method for developing a kinetic model for a metabolic network, based solely on the knowledge of reaction stoichiometries. Fluxes through the system, estimated by flux balance analysis, are allowed to vary dynamically according to linlog kinetics. Elasticities are estimated from stoichiometric considerations. When compared to a popular branched model of yeast glycolysis, we observe an excellent agreement between the real and approximate models, despite the absence of (and indeed the requirement for) experimental data for kinetic constants. Moreover, using this particular methodology affords us analytical forms for steady state determination, stability analyses and studies of dynamical behaviour.

Recon 2.2: from reconstruction to model of human metabolism.

INTRODUCTION: The human genome-scale metabolic reconstruction details all known metabolic reactions occurring in humans, and thereby holds substantial promise for studying complex diseases and phenotypes. Capturing the whole human metabolic reconstruction is an on-going task and since the last community effort generated a consensus reconstruction, several updates have been developed. OBJECTIVES: We report a new consensus version, Recon 2.2, which integrates various alternative versions with significant additional updates. In addition to re-establishing a consensus reconstruction, further key objectives included providing more comprehensive annotation of metabolites and genes, ensuring full mass and charge balance in all reactions, and developing a model that correctly predicts ATP production on a range of carbon sources. METHODS: Recon 2.2 has been developed through a combination of manual curation and automated error checking. Specific and significant manual updates include a respecification of fatty acid metabolism, oxidative phosphorylation and a coupling of the electron transport chain to ATP synthase activity. All metabolites have definitive chemical formulae and charges specified, and these are used to ensure full mass and charge reaction balancing through an automated linear programming approach. Additionally, improved integration with transcriptomics and proteomics data has been facilitated with the updated curation of relationships between genes, proteins and reactions. RESULTS: Recon 2.2 now represents the most predictive model of human metabolism to date as demonstrated here. Extensive manual curation has increased the reconstruction size to 5324 metabolites, 7785 reactions and 1675 associated genes, which now are mapped to a single standard. The focus upon mass and charge balancing of all reactions, along with better representation of energy generation, has produced a flux model that correctly predicts ATP yield on different carbon sources. CONCLUSION: Through these updates we have achieved the most complete and best annotated consensus human metabolic reconstruction available, thereby increasing the ability of this resource to provide novel insights into normal and disease states in human. The model is freely available from the Biomodels database (http://identifiers.org/biomodels.db/MODEL1603150001).

Toward Community Standards and Software for Whole-Cell Modeling.

OBJECTIVE: Whole-cell (WC) modeling is a promising tool for biological research, bioengineering, and medicine. However, substantial work remains to create accurate comprehensive models of complex cells. METHODS: We organized the 2015 Whole-Cell Modeling Summer School to teach WC modeling and evaluate the need for new WC modeling standards and software by recoding a recently published WC model in the Systems Biology Markup Language. RESULTS: Our analysis revealed several challenges to representing WC models using the current standards. CONCLUSION: We, therefore, propose several new WC modeling standards, software, and databases. SIGNIFICANCE: We anticipate that these new standards and software will enable more comprehensive models.

A robust and efficient method for estimating enzyme complex abundance and metabolic flux from expression data.

A major theme in constraint-based modeling is unifying experimental data, such as biochemical information about the reactions that can occur in a system or the composition and localization of enzyme complexes, with high-throughput data including expression data, metabolomics, or DNA sequencing. The desired result is to increase predictive capability and improve our understanding of metabolism. The approach typically employed when only gene (or protein) intensities are available is the creation of tissue-specific models, which reduces the available reactions in an organism model, and does not provide an objective function for the estimation of fluxes. We develop a method, flux assignment with LAD (least absolute deviation) convex objectives and normalization (FALCON), that employs metabolic network reconstructions along with expression data to estimate fluxes. In order to use such a method, accurate measures of enzyme complex abundance are needed, so we first present an algorithm that addresses quantification of complex abundance. Our extensions to prior techniques include the capability to work with large models and significantly improved run-time performance even for smaller models, an improved analysis of enzyme complex formation, the ability to handle large enzyme complex rules that may incorporate multiple isoforms, and either maintained or significantly improved correlation with experimentally measured fluxes. FALCON has been implemented in MATLAB and ATS, and can be downloaded from: https://github.com/bbarker/FALCON. ATS is not required to compile the software, as intermediate C source code is available. FALCON requires use of the COBRA Toolbox, also implemented in MATLAB.

BioPreDyn-bench: a suite of benchmark problems for dynamic modelling in systems biology.

BACKGROUND: Dynamic modelling is one of the cornerstones of systems biology. Many research efforts are currently being invested in the development and exploitation of large-scale kinetic models. The associated problems of parameter estimation (model calibration) and optimal experimental design are particularly challenging. The community has already developed many methods and software packages which aim to facilitate these tasks. However, there is a lack of suitable benchmark problems which allow a fair and systematic evaluation and comparison of these contributions. RESULTS: Here we present BioPreDyn-bench, a set of challenging parameter estimation problems which aspire to serve as reference test cases in this area. This set comprises six problems including medium and large-scale kinetic models of the bacterium E. coli, baker's yeast S. cerevisiae, the vinegar fly D. melanogaster, Chinese Hamster Ovary cells, and a generic signal transduction network. The level of description includes metabolism, transcription, signal transduction, and development. For each problem we provide (i) a basic description and formulation, (ii) implementations ready-to-run in several formats, (iii) computational results obtained with specific solvers, (iv) a basic analysis and interpretation. CONCLUSIONS: This suite of benchmark problems can be readily used to evaluate and compare parameter estimation methods. Further, it can also be used to build test problems for sensitivity and identifiability analysis, model reduction and optimal experimental design methods. The suite, including codes and documentation, can be freely downloaded from the BioPreDyn-bench website, https://sites.google.com/site/biopredynbenchmarks/ .

Playing off the curve - testing quantitative predictions of skill acquisition theories in development of chess performance.

Learning curves have been proposed as an adequate description of learning processes, no matter whether the processes manifest within minutes or across years. Different mechanisms underlying skill acquisition can lead to differences in the shape of learning curves. In the current study, we analyze the tournament performance data of 1383 chess players who begin competing at young age and play tournaments for at least 10 years. We analyze the performance development with the goal to test the adequacy of learning curves, and the skill acquisition theories they are based on, for describing and predicting expertise acquisition. On the one hand, we show that the skill acquisition theories implying a negative exponential learning curve do a better job in both describing early performance gains and predicting later trajectories of chess performance than those theories implying a power function learning curve. On the other hand, the learning curves of a large proportion of players show systematic qualitative deviations from the predictions of either type of skill acquisition theory. While skill acquisition theories predict larger performance gains in early years and smaller gains in later years, a substantial number of players begin to show substantial improvements with a delay of several years (and no improvement in the first years), deviations not fully accounted for by quantity of practice. The current work adds to the debate on how learning processes on a small time scale combine to large-scale changes.

Kinetic modeling of metabolic pathways: application to serine biosynthesis.

In this chapter, we describe the steps needed to create a kinetic model of a metabolic pathway using kinetic data from both experimental measurements and literature review. Our methodology is presented by using the example of serine biosynthesis in E. coli.

Version 6 of the consensus yeast metabolic network refines biochemical coverage and improves model performance.

Updates to maintain a state-of-the art reconstruction of the yeast metabolic network are essential to reflect our understanding of yeast metabolism and functional organization, to eliminate any inaccuracies identified in earlier iterations, to improve predictive accuracy and to continue to expand into novel subsystems to extend the comprehensiveness of the model. Here, we present version 6 of the consensus yeast metabolic network (Yeast 6) as an update to the community effort to computationally reconstruct the genome-scale metabolic network of Saccharomyces cerevisiae S288c. Yeast 6 comprises 1458 metabolites participating in 1888 reactions, which are annotated with 900 yeast genes encoding the catalyzing enzymes. Compared with Yeast 5, Yeast 6 demonstrates improved sensitivity, specificity and positive and negative predictive values for predicting gene essentiality in glucose-limited aerobic conditions when analyzed with flux balance analysis. Additionally, Yeast 6 improves the accuracy of predicting the likelihood that a mutation will cause auxotrophy. The network reconstruction is available as a Systems Biology Markup Language (SBML) file enriched with Minimium Information Requested in the Annotation of Biochemical Models (MIRIAM)-compliant annotations. Small- and macromolecules in the network are referenced to authoritative databases such as Uniprot or ChEBI. Molecules and reactions are also annotated with appropriate publications that contain supporting evidence. Yeast 6 is freely available at http://yeast.sf.net/ as three separate SBML files: a model using the SBML level 3 Flux Balance Constraint package, a model compatible with the MATLAB® COBRA Toolbox for backward compatibility and a reconstruction containing only reactions for which there is experimental evidence (without the non-biological reactions necessary for simulating growth). Database URL: http://yeast.sf.net/

Systematic construction of kinetic models from genome-scale metabolic networks.

The quantitative effects of environmental and genetic perturbations on metabolism can be studied in silico using kinetic models. We present a strategy for large-scale model construction based on a logical layering of data such as reaction fluxes, metabolite concentrations, and kinetic constants. The resulting models contain realistic standard rate laws and plausible parameters, adhere to the laws of thermodynamics, and reproduce a predefined steady state. These features have not been simultaneously achieved by previous workflows. We demonstrate the advantages and limitations of the workflow by translating the yeast consensus metabolic network into a kinetic model. Despite crudely selected data, the model shows realistic control behaviour, a stable dynamic, and realistic response to perturbations in extracellular glucose concentrations. The paper concludes by outlining how new data can continuously be fed into the workflow and how iterative model building can assist in directing experiments.