Formulation,construction and analysis of kinetic models of metabolism: A review of modelling frameworks

Kinetic models are critical to predict the dynamic behaviour of metabolic networks. Mechanistic kinetic models for large networks remain uncommon due to the difficulty of fitting their parameters. Recent modelling frameworks promise new ways to overcome this obstacle while retaining predictive capabilities. In this review, we present an overview of the relevant mathematical frameworks for kinetic formulation, construction and analysis. Starting with kinetic formalisms, we next review statistical methods for parameter inference, as well as recent computational frameworks applied to the construction and analysis of kinetic models. Finally, we discuss opportunities and limitations hindering the development of larger kinetic reconstructions.     

Towards kinetic modeling of genome-scale metabolic networks without sacrificing stoichiometric,thermodynamic and physiological constraints

Mathematical modeling is an essential tool for the comprehensive understanding of cell metabolism and its interactions with the environmental and process conditions. Recent developments in the construction and analysis of stoichiometric models made it possible to define limits on steady-state metabolic behavior using flux balance analysis. However, detailed information on enzyme kinetics and enzyme regulation is needed to formulate kinetic models that can accurately capture the dynamic metabolic responses. The use of mechanistic enzyme kinetics is a difficult task due to uncertainty in the kinetic properties of enzymes. Therefore, the majority of recent works considered only mass action kinetics for reactions in metabolic networks. Herein, we applied the optimization and risk analysis of complex living entities (ORACLE) framework and constructed a large-scale mechanistic kinetic model of optimally grown Escherichia coli. We investigated the complex interplay between stoichiometry, thermodynamics, and kinetics in determining the flexibility and capabilities of metabolism. Our results indicate that enzyme saturation is a necessary consideration in modeling metabolic networks and it extends the feasible ranges of metabolic fluxes and metabolite concentrations. Our results further suggest that enzymes in metabolic networks have evolved to function at different saturation states to ensure greater flexibility and robustness of cellular metabolism.     

Preliminary studies about novel strategies to reverse chemoresistance to adriamycin regarding glutathione metabolism,peroxisomal and extraperoxisomal hydroperoxide and valproic acid metabolic pathways

Summary— The present work was aimed at defining novel strategies to reverse chemoresistance to anticancer drugs, especially by interfering with cellular glutathione metabolism, peroxisomal and/or extraperoxisomal hydroperoxide metabolic pathways. Preliminary results are presented about molecules we demonstrated to be capable of interfering with hydrogen peroxide metabolism in cells. Prior to describing these molecules, a short overview of glutathione and free radical metabolic pathways is presented as well as a rapid presentation of the characteristics of chemo-sensitivity and -resistance towards the anticancer drug adriamycin, with special emphasis on hydrogen peroxide metabolism. The strategies currently developed to reverse chemoresistance are further presented. in subsequent sections, our own strategy to achieve inhibition of hydrogen peroxide breakdown and stimulation of peroxisomal hydrogen peroxide production is illustrated on the basis of molecular modelling studies and biochemical investigations on extraperoxisomal and peroxisomal metabolic pathways. Preliminary studies on cultured cells have been initiated. The perspective for future studies is presented as well as other possible models of chemoresistance as target for the design of hydrogen peroxide metabolism-interfering pharmacomolecules.     

Metabolic modeling of Saccharomyces cerevisiae using the optimal control of homeostasis: a cybernetic model definition

A model is presented to describe the observed behavior of microorganisms that aim at metabolic homeostasis while growing and adapting to their environment in an optimal way. The cellular metabolism is seen as a network with a multiple controller system with both feedback and feedforward control, i.e., a model based on a dynamic optimal metabolic control. The dynamic network consists of aggregated pathways, each having a control setpoint for the metabolic states at a given growth rate. This set of strategies of the cell forms a true cybernetic model with a minimal number of assumptions. The cellular strategies and constraints were derived from metabolic flux analysis using an identified, biochemically relevant, stoichiometry matrix derived from experimental data on the cellular composition of continuous cultures of Saccharomyces cerevisiae. Based on these data a cybernetic model was developed to study its dynamic behavior. The growth rate of the cell is determined by the structural compounds and fluxes of compounds related to central metabolism. In contrast to many other cybernetic models, the minimal model does not consist of any assumed internal kinetic parameters or interactions. This necessitates the use of a stepwise integration with an optimization of the fluxes at every time interval. Some examples of the behavior of this model are given with respect to steady states and pulse responses. This model is very suitable for describing semiquantitatively dynamics of global cellular metabolism and may form a useful framework for including structured and more detailed kinetic models.     

Kinetic and regulatory aspects of the function of the alternative oxidase in plant respiration

The kinetic modelling of the respiratory network in plant mitochondria is discussed, with emphasis on the importance of the choice of boundary conditions, and of modelling of both quinol-oxidising and quinone-reducing pathways. This allows quantitative understanding of the interplay between the different pathways, and of the functioning of the plant respiratory network in terms of the kinetic properties of its component parts. The effects of activation of especially succinate dehydrogenase and the cyanide-insensitive alternative oxidase are discussed. Phenomena, such as respiratory control ratios depending on the substrate, shortcomings of the Bahr and Bonner model for electron distribution between the oxidases and reversed respiratory control, are explained. The relation to metabolic control analysis of the respiratory network is discussed in terms of top-down analysis.     

Elementary mode analysis: a useful metabolic pathway analysis tool for characterizing cellular metabolism

Elementary mode analysis is a useful metabolic pathway analysis tool to identify the structure of a metabolic network that links the cellular phenotype to the corresponding genotype. The analysis can decompose the intricate metabolic network comprised of highly interconnected reactions into uniquely organized pathways. These pathways consisting of a minimal set of enzymes that can support steady state operation of cellular metabolism represent independent cellular physiological states. Such pathway definition provides a rigorous basis to systematically characterize cellular phenotypes, metabolic network regulation, robustness, and fragility that facilitate understanding of cell physiology and implementation of metabolic engineering strategies. This mini-review aims to overview the development and application of elementary mode analysis as a metabolic pathway analysis tool in studying cell physiology and as a basis of metabolic engineering.     

Expanding Metabolic Capabilities Using Novel Pathway Designs: Computational Tools and Case Studies

Design and selection of efficient metabolic pathways is critical for the success of metabolic engineering endeavors. Convenient pathways should not only produce the target metabolite in high yields but also are required to be thermodynamically feasible under production conditions, and to prefer efficient enzymes. To support the design and selection of such pathways, different computational approaches have been proposed for exploring the feasible pathway space under many of the above constraints. In this review, an overview of recent constraint‐based optimization frameworks for metabolic pathway prediction, as well as relevant pathway engineering case studies that highlight the importance of rational metabolic designs is presented. Despite the availability and suitability of in silico design tools for metabolic pathway engineering, scarce—although increasing—application of computational outcomes is found. Finally, challenges and limitations hindering the broad adoption and successful application of these tools in metabolic engineering projects are discussed.     

A systems biology approach for the analysis of carbohydrate dynamics during acclimation to low temperature in Arabidopsis thaliana

Low temperature is an important environmental factor affecting the performance and distribution of plants. During the so-called process of cold acclimation, many plants are able to develop low-temperature tolerance, associated with the reprogramming of a large part of their metabolism. In this study, we present a systems biology approach based on mathematical modelling to determine interactions between the reprogramming of central carbohydrate metabolism and the development of freezing tolerance in two accessions of Arabidopsis thaliana. Different regulation strategies were observed for (a) photosynthesis, (b) soluble carbohydrate metabolism and (c) enzyme activities of central metabolite interconversions. Metabolism of the storage compound starch was found to be independent of accession-specific reprogramming of soluble sugar metabolism in the cold. Mathematical modelling and simulation of cold-induced metabolic reprogramming indicated major differences in the rates of interconversion between the pools of hexoses and sucrose, as well as the rate of assimilate export to sink organs. A comprehensive overview of interconversion rates is presented, from which accession-specific regulation strategies during exposure to low temperature can be derived. We propose this concept as a tool for predicting metabolic engineering strategies to optimize plant freezing tolerance. We confirm that a significant improvement in freezing tolerance in plants involves multiple regulatory instances in sucrose metabolism, and provide evidence for a pivotal role of sucrose-hexose interconversion in increasing the cold acclimation output.     

Solving the Differential Biochemical Jacobian from Metabolomics Covariance Data

High-throughput molecular analysis has become an integral part in organismal systems biology. In contrast, due to a missing systematic linkage of the data with functional and predictive theoretical models of the underlying metabolic network the understanding of the resulting complex data sets is lacking far behind. Here, we present a biomathematical method addressing this problem by using metabolomics data for the inverse calculation of a biochemical Jacobian matrix, thereby linking computer-based genome-scale metabolic reconstruction and in vivo metabolic dynamics. The incongruity of metabolome coverage by typical metabolite profiling approaches and genome-scale metabolic reconstruction was solved by the design of superpathways to define a metabolic interaction matrix. A differential biochemical Jacobian was calculated using an approach which links this metabolic interaction matrix and the covariance of metabolomics data satisfying a Lyapunov equation. The predictions of the differential Jacobian from real metabolomic data were found to be correct by testing the corresponding enzymatic activities. Moreover it is demonstrated that the predictions of the biochemical Jacobian matrix allow for the design of parameter optimization strategies for ODE-based kinetic models of the system. The presented concept combines dynamic modelling strategies with large-scale steady state profiling approaches without the explicit knowledge of individual kinetic parameters. In summary, the presented strategy allows for the identification of regulatory key processes in the biochemical network directly from metabolomics data and is a fundamental achievement for the functional interpretation of metabolomics data.     

Metabolic control analysis of Aspergillus niger L-arabinose catabolism

A mathematical model of the L-arabinose/D-xylose catabolic pathway of Aspergillus niger was constructed based on the kinetic properties of the enzymes. For this purpose L-arabinose reductase, L-arabitol dehydrogenase and D-xylose reductase were purified using dye-affinity chromatography, and their kinetic properties were characterized. For the other enzymes of the pathway the kinetic data were available from the literature. The metabolic model was used to analyze flux and metabolite concentration control of the L-arabinose catabolic pathway. The model demonstrated that flux control does not reside at the enzyme following the intermediate with the highest concentration, L-arabitol, but is distributed over the first three steps in the pathway, preceding and following L-arabitol. Flux control appeared to be strongly dependent on the intracellular L-arabinose concentration. At 5 mM intracellular L-arabinose, a level that resulted in realistic intermediate concentrations in the model, flux control coefficients for L-arabinose reductase, L-arabitol dehydrogenase and L-xylulose reductase were 0.68, 0.17 and 0.14, respectively. The analysis can be used as a guide to identify targets for metabolic engineering aiming at either flux or metabolite level optimization of the L-arabinose catabolic pathway of A. niger. Faster L-arabinose utilization may enhance utilization of readily available organic waste containing hemicelluloses to be converted into industrially interesting metabolites or valuable enzymes or proteins.     

Rhizobacteria with nematicide aptitude: enzymes and compounds associated

The use of rhizobacteria to control plant parasitic nematodes has been widely studied. Currently, the research focuses on bacteria-nematode interactions that can mitigate this complex microbiome in agriculture. Various enzymes, toxins and metabolic by-products from rhizobacteria antagonize plant parasitic nematodes, and many different modes of action have been proposed. Hydrolytic enzymes, primarily proteases, collagenases and chitinases, have been related to the nematicide effect in rhizobacteria, proving to be an important factor involved in the degradation of different chemical constituents of nematodes at distinct developmental stages. Exuded metabolites may also alter the nematode-plant recognition process or create a hostile environment for nematodes in the rhizosphere. Specific bacteria strains responsible for the production of toxins, such as Cry proteins, are one of the strategies used by rhizobacteria. Characterization of the rhizobacteria mode of action could strengthen the development of commercial products to control populations of plant parasitic nematodes. This review aims to provide an overview of different enzymes and compounds produced by rhizobacteria related to the process of antagonism to plant-parasitic nematodes.     

Lipoxygenases – Structure and reaction mechanism

Lipid oxidation is a common metabolic reaction in all biological systems, appearing in developmentally regulated processes and as response to abiotic and biotic stresses. Products derived from lipid oxidation processes are collectively named oxylipins. Initial lipid oxidation may either occur by chemical reactions or is derived from the action of enzymes. In plants this reaction is mainly catalyzed by lipoxygenase (LOXs) enzymes and during recent years analysis of different plant LOXs revealed insights into their enzyme mechanism. This review aims at giving an overview of concepts explaining the catalytic mechanism of LOXs as well as the different regio- and stereo-specificities of these enzymes.     

Getting to the inside of cells using metabolic control analysis

Metabolic control analysis can relate control properties of an intact system to kinetic properties (elasticity coefficients) of the enzymes within that system. The method formulating the former as matrix inverse of the latter is elaborated here for the general case and founded in standard metabolic control theory. Then a method is developed that accomplishes the reverse: it is shown that a matrix containing all elasticity coefficients and information concerning the pathway structure equals the inverse of a matrix containing flux and concentration control coefficients. As a consequence, by measuring the control properties of an intact system, one is able to deduce its in situ pathway structure and enzyme kinetic properties: This solves the ever-present question of whether the kinetic properties of enzymes in their isolated state differ from those under the conditions prevailing in the cell.     

'Slave' metabolites and enzymes. A rapid way of delineating metabolic control.

Although control of fluxes and concentrations tends to be distributed rather than confined to a single rate-limiting enzyme, the extent of control can differ widely between enzymes in a metabolic network. In some cases, there are enzymes that lack control completely. This paper identifies one surprising origin of such lack of control: If, in a metabolic system, there is a metabolite that affects the catalytic rate of only one enzyme, the corresponding enzyme cannot control any metabolic variable other than the concentration of that metabolite. We call such enzymes 'slave enzymes', and the corresponding metabolites 'slave metabolites'. Implications of the existence of slave enzymes for the control properties of enzymes further down the metabolic pathway are discussed and examined for the glycolytic pathway of yeast. Inadvertent assumptions in metabolic models may cause the latter incorrectly to calculate absence of metabolic control. The phenomenon of slave enzymes may well be important in enhancing metabolic signal transduction.     

Identification of metabolic engineering targets for the enhancement of 1,4-butanediol production in recombinant E. coli using large-scale kinetic models

Rational metabolic engineering methods are increasingly employed in designing the commercially viable processes for the production of chemicals relevant to pharmaceutical, biotechnology, and food and beverage industries. With the growing availability of omics data and of methodologies capable to integrate the available data into models, mathematical modeling and computational analysis are becoming important in designing recombinant cellular organisms and optimizing cell performance with respect to desired criteria. In this contribution, we used the computational framework ORACLE (Optimization and Risk Analysis of Complex Living Entities) to analyze the physiology of recombinant Escherichia coli producing 1,4-butanediol (BDO) and to identify potential strategies for improved production of BDO. The framework allowed us to integrate data across multiple levels and to construct a population of large-scale kinetic models despite the lack of available information about kinetic properties of every enzyme in the metabolic pathways. We analyzed these models and we found that the enzymes that primarily control the fluxes leading to BDO production are part of central glycolysis, the lower branch of tricarboxylic acid (TCA) cycle and the novel BDO production route. Interestingly, among the enzymes between the glucose uptake and the BDO pathway, the enzymes belonging to the lower branch of TCA cycle have been identified as the most important for improving BDO production and yield. We also quantified the effects of changes of the target enzymes on other intracellular states like energy charge, cofactor levels, redox state, cellular growth, and byproduct formation. Independent earlier experiments on this strain confirmed that the computationally obtained conclusions are consistent with the experimentally tested designs, and the findings of the present studies can provide guidance for future work on strain improvement. Overall, these studies demonstrate the potential and effectiveness of ORACLE for the accelerated design of microbial cell factories.     

ScrumPy: metabolic modelling with Python

ScrumPy is a software package used for the definition and analysis of metabolic models. It is written using the Python programming language that is also used as a user interface. ScrumPy has features for both kinetic and structural modelling, but the emphasis is on structural modelling and those features of most relevance to analysis of large (genome-scale) models. The aim is at describing ScrumPy's functionality to readers with some knowledge of metabolic modelling, but implementation, programming and other computational details are omitted. ScrumPy is released under the Gnu Public Licence, and available for download from http://mudshark.brookes.ac.uk/ ScrumPy.