Peroxiredoxins play central roles in the detoxification of reactive oxygen species and have been ... more Peroxiredoxins play central roles in the detoxification of reactive oxygen species and have been modelled across multiple organisms using a variety of kinetic methods. However, the peroxiredoxin dimer-to-decamer transition has been underappreciated in these studies despite the 100-fold difference in activity between these forms. This is due to the lack of available kinetics and theoretical framework for modelling this process. Using published isothermal titration calorimetry data, we obtained association and dissociation rate constants of 93.0 µM-4·s-1 and 102 s-1, respectively, for the dimer-decamer transition of human PRDX1. We developed an approach that greatly reduces the number of reactions and species needed to model the peroxiredoxin decamer oxidation cycle. Using these data, we simulated horse radish peroxidase competition and NADPH-oxidation linked assays and found that the dimer-decamer transition had an inhibition-like effect on peroxidase activity. Further, we incorporat...
The thioredoxin system plays a central role in intracellular redox regulation and its dysregulati... more The thioredoxin system plays a central role in intracellular redox regulation and its dysregulation is associated with a number of pathologies. However, the connectivity within this system poses a significant challenge for quantification and consequently several disparate measures have been used to characterize the system. For in vitro studies, the thioredoxin system flux has been measured by NADPH oxidation while the thioredoxin redox state has been used to estimate the activity of the system in vivo. The connection between these measures has been obscure although substrate saturation in the thioredoxin system results from the saturation of the thioredoxin redox cycle. We used computational modeling and in vitro kinetic assays to clarify the relationship between flux and the current in vivo measures of the thioredoxin system together with a novel measure, the thioredoxin redox charge (reduced thioredoxin/total thioredoxin). Our results revealed that the thioredoxin redox potential and redox charge closely tracked flux perturbations showing that these indices could be used as surrogate measures of the flux in vivo and, provide a mechanistic explanation for the previously observed correlations between thioredoxin oxidation and certain pathologies. While we found no significant difference in the linear correlations obtained for the thioredoxin redox potential and redox charge with the flux, the redox charge may be preferred because it is bounded between zero and one and can be determined over a wider range of conditions allowing for quantitative flux comparisons between cell types and conditions.
Dimethylallyl diphosphate (DMADP) and isopentenyl diphosphate (IDP) serves as the universal C5 pr... more Dimethylallyl diphosphate (DMADP) and isopentenyl diphosphate (IDP) serves as the universal C5 precursors of isoprenoid biosynthesis in plants. These compounds are formed by the last step of the 2-C-methyl-D-erythritol 4-phosphate (MEP) pathway, catalyzed by (E)-4-hydroxy-3-methylbut-2-en-1-yl diphosphate reductase (HDR). In this study, we investigated the major HDR isoforms of two woody plant species, Norway spruce (Picea abies) and gray poplar (Populus × canescens), to determine how they regulate isoprenoid formation. Since each of these species has a distinct profile of isoprenoid compounds, they may require different proportions of DMADP and IDP with proportionally more IDP being needed to make larger isoprenoids. Norway spruce contained two major HDR isoforms differing in their occurrence and biochemical characteristics. PaHDR1 produced relatively more IDP than PaHDR2 and it encoding gene was expressed constitutively in leaves, likely serving to form substrate for production of...
Since the previous recommendations for a metabolic control analysis terminology and symbolism [1]... more Since the previous recommendations for a metabolic control analysis terminology and symbolism [1] were made, the field has developed considerably, creating an urgent need for reconsideration and revision. In these recommendations we try to cope with the new complexities brought to light by the analysis of ‘non-ideal’ pathways, aiming to retain both the simplicity and the flexibility needed for use in both mathematical and biological contexts, i.e., allowing reference to both numbered and named conversion steps, variables and parameters. Our goal is to use a minimum number of terms and symbols, but yet to produce a system that allows application of metabolic control analysis to any system at any level of aggregation.
High-level behaviour of metabolic systems results from the properties of, and interactions betwee... more High-level behaviour of metabolic systems results from the properties of, and interactions between, numerous molecular components. Reaching a complete understanding of metabolic behaviour based on the system's components is therefore a difficult task. This problem can be tackled by constructing and subsequently analysing kinetic models of metabolic pathways since such models aim to capture all the relevant properties of the system components and their interactions. Symbolic control analysis is a framework for analysing pathway models in order to reach a mechanistic understanding of their behaviour. By providing algebraic expressions for the sensitivities of system properties, such as metabolic flux or steadystate concentrations, in terms of the properties of individual reactions it allows one to trace the high level behaviour back to these low level components. Here we apply this method to a model of pyruvate branch metabolism in Lactococcus lactis in order to explain a previously observed negative flux response towards an increase in substrate concentration. With this method we are able to show, first, that the sensitivity of flux towards changes in reaction rates (represented by flux control coefficients) is determined by the individual metabolic branches of the pathway, and second, how the sensitivities of individual reaction rates towards their substrates (represented by elasticity coefficients) contribute to this flux control. We also quantify the contributions of enzyme binding and mass-action to enzyme elasticity separately, which allows for an even finer-grained understanding of flux control. These analytical tools allow us to analyse the control properties of a metabolic model and to arrive at a mechanistic understanding of the quantitative contributions of each of the enzymes to this control. Our analysis provides an example of the descriptive power of the general principles of symbolic control analysis.
The sugarcane stalk, besides being the main structural component of the plant, is also the major ... more The sugarcane stalk, besides being the main structural component of the plant, is also the major storage organ for carbohydrates. Previous studies have modelled the sucrose accumulation pathway in the internodal storage parenchyma of sugarcane using kinetic models cast as systems of ordinary differential equations. To address the shortcomings of these models, which did not include subcellular compartmentation or spatial information, the present study extends the original models within an advection–diffusion–reaction framework, requiring the use of partial differential equations to model sucrose metabolism coupled to phloem translocation. We propose a kinetic model of a coupled reaction network where species can be involved in chemical reactions and/or be transported over long distances in a fluid medium by advection or diffusion. Darcy’s law is used to model fluid flow and allows a simplified, phenomenological approach to be applied to translocation in the phloem. Similarly, generic...
Systems biology has experienced dramatic growth in the number, size, and complexity of computatio... more Systems biology has experienced dramatic growth in the number, size, and complexity of computational models. To reproduce simulation results and reuse models, researchers must exchange unambiguous model descriptions. We review the latest edition of the Systems Biology Markup Language (SBML), a format designed for this purpose. A community of modelers and software authors developed SBML Level 3 over the past decade. Its modular form consists of a core suited to representing reaction-based models and packages that extend the core with features suited to other model types including constraintbased models, reaction-diffusion models, logical network models, and rule-based models. The format leverages two decades of SBML and a rich software ecosystem that transformed how systems biologists build and interact with models. More recently, the rise of multiscale models of whole cells and organs, and new data sources such as single-cell measurements and live imaging, has precipitated new ways of integrating data with models. We provide our perspectives on the challenges presented by these developments and how SBML Level provides the foundation needed to support this evolution. 3
High-level behaviour of metabolic systems results from the properties of, and interactions betwee... more High-level behaviour of metabolic systems results from the properties of, and interactions between, numerous molecular components. Reaching a complete understanding of metabolic behaviour based on the system's components is therefore a difficult task. This problem can be tackled by constructing and subsequently analysing kinetic models of metabolic pathways since such models aim to capture all the relevant properties of the system components and their interactions. Symbolic control analysis is a framework for analysing pathway models in order to reach a mechanistic understanding of their behaviour. By providing algebraic expressions for the sensitivities of system properties, such as metabolic flux or steady-state concentrations, in terms of the properties of individual reactions it allows one to trace the high level behaviour back to these low level components. Here we apply this method to a model of pyruvate branch metabolism in Lactococcus lactis in order to explain a previously observed negative flux response towards an increase in substrate concentration. With this method we are able to show, first, that the sensitivity of flux towards changes in reaction rates (represented by flux control coefficients) is determined by the individual metabolic branches of the pathway, and second, how the sensitivities of individual reaction rates towards their substrates (represented by elasticity coefficients) contribute to this flux control. We also quantify the contributions of enzyme binding and mass-action to enzyme elasticity separately, which allows for an even finer-grained understanding of flux control. These analytical tools allow us to analyse the control properties of a metabolic model and to arrive at a mechanistic understanding of the quantitative contributions of each of the enzymes to this control. Our analysis provides an example of the descriptive power of the general principles of symbolic control analysis.
This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY
This paper is dedicated to the memory of Prof Prieur du Plessis, whose help in conceiving and set... more This paper is dedicated to the memory of Prof Prieur du Plessis, whose help in conceiving and setting up this analysis has been invaluable.
Archives of Biochemistry and Biophysics, Feb 1, 2020
The thioredoxin system plays a central role in intracellular redox regulation and its dysregulati... more The thioredoxin system plays a central role in intracellular redox regulation and its dysregulation is associated with a number of pathologies. However, the connectivity within this system poses a significant challenge for quantification and consequently several disparate measures have been used to characterize the system. For in vitro studies, the thioredoxin system flux has been measured by NADPH oxidation while the thioredoxin redox state has been used to estimate the activity of the system in vivo. The connection between these measures has been obscure although substrate saturation in the thioredoxin system results from the saturation of the thioredoxin redox cycle. We used computational modeling and in vitro kinetic assays to clarify the relationship between flux and the current in vivo measures of the thioredoxin system together with a novel measure, the thioredoxin redox charge (reduced thioredoxin/total thioredoxin). Our results revealed that the thioredoxin redox potential and redox charge closely tracked flux perturbations showing that these indices could be used as surrogate measures of the flux in vivo and, provide a mechanistic explanation for the previously observed correlations between thioredoxin oxidation and certain pathologies. While we found no significant difference in the linear correlations obtained for the thioredoxin redox potential and redox charge with the flux, the redox charge may be preferred because it is bounded between zero and one and can be determined over a wider range of conditions allowing for quantitative flux comparisons between cell types and conditions.
Dimethylallyl diphosphate (DMADP) and isopentenyl diphosphate (IDP) serves as the universal C 5 p... more Dimethylallyl diphosphate (DMADP) and isopentenyl diphosphate (IDP) serves as the universal C 5 precursors of isoprenoid biosynthesis in plants. These compounds are formed by the last step of the 2-C-methyl-D-erythritol 4-phosphate (MEP) pathway, catalyzed by (E)-4-hydroxy-3-methylbut-2-en-1-yl diphosphate reductase (HDR). In this study, we investigated the major HDR isoforms of two woody plant species, Norway spruce (Picea abies) and gray poplar (Populus × canescens), to determine how they regulate isoprenoid formation. Since each of these species has a distinct profile of isoprenoid compounds, they may require different proportions of DMADP and IDP with proportionally more IDP being needed to make larger isoprenoids. Norway spruce contained two major HDR isoforms differing in their occurrence and biochemical characteristics. PaHDR1 produced relatively more IDP than PaHDR2 and it encoding gene was expressed constitutively in leaves, likely serving to form substrate for production of carotenoids, chlorophylls, and other primary isoprenoids derived from a C 20 precursor. On the other hand, Norway spruce PaHDR2 produced relatively more DMADP than PaHDR1 and its encoding gene was expressed in leaves, stems, and roots, both constitutively and after induction with the defense hormone methyl jasmonate. This second HDR enzyme likely forms a substrate for the specialized monoterpene (C 10), sesquiterpene (C 15), and diterpene (C 20) metabolites of spruce oleoresin. Gray poplar contained only one dominant isoform (named PcHDR2) that produced relatively more DMADP and the gene of which was expressed in all organs. In leaves, where the requirement for IDP is high to make the major carotenoid and chlorophyll isoprenoids derived from C 20 precursors, excess DMADP may accumulate, which could explain the high rate of isoprene (C 5) emission. Our results provide new insights into the biosynthesis of isoprenoids in woody plants under conditions of differentially regulated biosynthesis of the precursors IDP and DMADP.
Peroxiredoxins play central roles in the detoxification of reactive oxygen species and have been ... more Peroxiredoxins play central roles in the detoxification of reactive oxygen species and have been modelled across multiple organisms using a variety of kinetic methods. However, the peroxiredoxin dimer-to-decamer transition has been underappreciated in these studies despite the 100-fold difference in activity between these forms. This is due to the lack of available kinetics and theoretical framework for modelling this process. Using published isothermal titration calorimetry data, we obtained association and dissociation rate constants of 93.0 µM-4·s-1 and 102 s-1, respectively, for the dimer-decamer transition of human PRDX1. We developed an approach that greatly reduces the number of reactions and species needed to model the peroxiredoxin decamer oxidation cycle. Using these data, we simulated horse radish peroxidase competition and NADPH-oxidation linked assays and found that the dimer-decamer transition had an inhibition-like effect on peroxidase activity. Further, we incorporat...
The thioredoxin system plays a central role in intracellular redox regulation and its dysregulati... more The thioredoxin system plays a central role in intracellular redox regulation and its dysregulation is associated with a number of pathologies. However, the connectivity within this system poses a significant challenge for quantification and consequently several disparate measures have been used to characterize the system. For in vitro studies, the thioredoxin system flux has been measured by NADPH oxidation while the thioredoxin redox state has been used to estimate the activity of the system in vivo. The connection between these measures has been obscure although substrate saturation in the thioredoxin system results from the saturation of the thioredoxin redox cycle. We used computational modeling and in vitro kinetic assays to clarify the relationship between flux and the current in vivo measures of the thioredoxin system together with a novel measure, the thioredoxin redox charge (reduced thioredoxin/total thioredoxin). Our results revealed that the thioredoxin redox potential and redox charge closely tracked flux perturbations showing that these indices could be used as surrogate measures of the flux in vivo and, provide a mechanistic explanation for the previously observed correlations between thioredoxin oxidation and certain pathologies. While we found no significant difference in the linear correlations obtained for the thioredoxin redox potential and redox charge with the flux, the redox charge may be preferred because it is bounded between zero and one and can be determined over a wider range of conditions allowing for quantitative flux comparisons between cell types and conditions.
Dimethylallyl diphosphate (DMADP) and isopentenyl diphosphate (IDP) serves as the universal C5 pr... more Dimethylallyl diphosphate (DMADP) and isopentenyl diphosphate (IDP) serves as the universal C5 precursors of isoprenoid biosynthesis in plants. These compounds are formed by the last step of the 2-C-methyl-D-erythritol 4-phosphate (MEP) pathway, catalyzed by (E)-4-hydroxy-3-methylbut-2-en-1-yl diphosphate reductase (HDR). In this study, we investigated the major HDR isoforms of two woody plant species, Norway spruce (Picea abies) and gray poplar (Populus × canescens), to determine how they regulate isoprenoid formation. Since each of these species has a distinct profile of isoprenoid compounds, they may require different proportions of DMADP and IDP with proportionally more IDP being needed to make larger isoprenoids. Norway spruce contained two major HDR isoforms differing in their occurrence and biochemical characteristics. PaHDR1 produced relatively more IDP than PaHDR2 and it encoding gene was expressed constitutively in leaves, likely serving to form substrate for production of...
Since the previous recommendations for a metabolic control analysis terminology and symbolism [1]... more Since the previous recommendations for a metabolic control analysis terminology and symbolism [1] were made, the field has developed considerably, creating an urgent need for reconsideration and revision. In these recommendations we try to cope with the new complexities brought to light by the analysis of ‘non-ideal’ pathways, aiming to retain both the simplicity and the flexibility needed for use in both mathematical and biological contexts, i.e., allowing reference to both numbered and named conversion steps, variables and parameters. Our goal is to use a minimum number of terms and symbols, but yet to produce a system that allows application of metabolic control analysis to any system at any level of aggregation.
High-level behaviour of metabolic systems results from the properties of, and interactions betwee... more High-level behaviour of metabolic systems results from the properties of, and interactions between, numerous molecular components. Reaching a complete understanding of metabolic behaviour based on the system's components is therefore a difficult task. This problem can be tackled by constructing and subsequently analysing kinetic models of metabolic pathways since such models aim to capture all the relevant properties of the system components and their interactions. Symbolic control analysis is a framework for analysing pathway models in order to reach a mechanistic understanding of their behaviour. By providing algebraic expressions for the sensitivities of system properties, such as metabolic flux or steadystate concentrations, in terms of the properties of individual reactions it allows one to trace the high level behaviour back to these low level components. Here we apply this method to a model of pyruvate branch metabolism in Lactococcus lactis in order to explain a previously observed negative flux response towards an increase in substrate concentration. With this method we are able to show, first, that the sensitivity of flux towards changes in reaction rates (represented by flux control coefficients) is determined by the individual metabolic branches of the pathway, and second, how the sensitivities of individual reaction rates towards their substrates (represented by elasticity coefficients) contribute to this flux control. We also quantify the contributions of enzyme binding and mass-action to enzyme elasticity separately, which allows for an even finer-grained understanding of flux control. These analytical tools allow us to analyse the control properties of a metabolic model and to arrive at a mechanistic understanding of the quantitative contributions of each of the enzymes to this control. Our analysis provides an example of the descriptive power of the general principles of symbolic control analysis.
The sugarcane stalk, besides being the main structural component of the plant, is also the major ... more The sugarcane stalk, besides being the main structural component of the plant, is also the major storage organ for carbohydrates. Previous studies have modelled the sucrose accumulation pathway in the internodal storage parenchyma of sugarcane using kinetic models cast as systems of ordinary differential equations. To address the shortcomings of these models, which did not include subcellular compartmentation or spatial information, the present study extends the original models within an advection–diffusion–reaction framework, requiring the use of partial differential equations to model sucrose metabolism coupled to phloem translocation. We propose a kinetic model of a coupled reaction network where species can be involved in chemical reactions and/or be transported over long distances in a fluid medium by advection or diffusion. Darcy’s law is used to model fluid flow and allows a simplified, phenomenological approach to be applied to translocation in the phloem. Similarly, generic...
Systems biology has experienced dramatic growth in the number, size, and complexity of computatio... more Systems biology has experienced dramatic growth in the number, size, and complexity of computational models. To reproduce simulation results and reuse models, researchers must exchange unambiguous model descriptions. We review the latest edition of the Systems Biology Markup Language (SBML), a format designed for this purpose. A community of modelers and software authors developed SBML Level 3 over the past decade. Its modular form consists of a core suited to representing reaction-based models and packages that extend the core with features suited to other model types including constraintbased models, reaction-diffusion models, logical network models, and rule-based models. The format leverages two decades of SBML and a rich software ecosystem that transformed how systems biologists build and interact with models. More recently, the rise of multiscale models of whole cells and organs, and new data sources such as single-cell measurements and live imaging, has precipitated new ways of integrating data with models. We provide our perspectives on the challenges presented by these developments and how SBML Level provides the foundation needed to support this evolution. 3
High-level behaviour of metabolic systems results from the properties of, and interactions betwee... more High-level behaviour of metabolic systems results from the properties of, and interactions between, numerous molecular components. Reaching a complete understanding of metabolic behaviour based on the system's components is therefore a difficult task. This problem can be tackled by constructing and subsequently analysing kinetic models of metabolic pathways since such models aim to capture all the relevant properties of the system components and their interactions. Symbolic control analysis is a framework for analysing pathway models in order to reach a mechanistic understanding of their behaviour. By providing algebraic expressions for the sensitivities of system properties, such as metabolic flux or steady-state concentrations, in terms of the properties of individual reactions it allows one to trace the high level behaviour back to these low level components. Here we apply this method to a model of pyruvate branch metabolism in Lactococcus lactis in order to explain a previously observed negative flux response towards an increase in substrate concentration. With this method we are able to show, first, that the sensitivity of flux towards changes in reaction rates (represented by flux control coefficients) is determined by the individual metabolic branches of the pathway, and second, how the sensitivities of individual reaction rates towards their substrates (represented by elasticity coefficients) contribute to this flux control. We also quantify the contributions of enzyme binding and mass-action to enzyme elasticity separately, which allows for an even finer-grained understanding of flux control. These analytical tools allow us to analyse the control properties of a metabolic model and to arrive at a mechanistic understanding of the quantitative contributions of each of the enzymes to this control. Our analysis provides an example of the descriptive power of the general principles of symbolic control analysis.
This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY
This paper is dedicated to the memory of Prof Prieur du Plessis, whose help in conceiving and set... more This paper is dedicated to the memory of Prof Prieur du Plessis, whose help in conceiving and setting up this analysis has been invaluable.
Archives of Biochemistry and Biophysics, Feb 1, 2020
The thioredoxin system plays a central role in intracellular redox regulation and its dysregulati... more The thioredoxin system plays a central role in intracellular redox regulation and its dysregulation is associated with a number of pathologies. However, the connectivity within this system poses a significant challenge for quantification and consequently several disparate measures have been used to characterize the system. For in vitro studies, the thioredoxin system flux has been measured by NADPH oxidation while the thioredoxin redox state has been used to estimate the activity of the system in vivo. The connection between these measures has been obscure although substrate saturation in the thioredoxin system results from the saturation of the thioredoxin redox cycle. We used computational modeling and in vitro kinetic assays to clarify the relationship between flux and the current in vivo measures of the thioredoxin system together with a novel measure, the thioredoxin redox charge (reduced thioredoxin/total thioredoxin). Our results revealed that the thioredoxin redox potential and redox charge closely tracked flux perturbations showing that these indices could be used as surrogate measures of the flux in vivo and, provide a mechanistic explanation for the previously observed correlations between thioredoxin oxidation and certain pathologies. While we found no significant difference in the linear correlations obtained for the thioredoxin redox potential and redox charge with the flux, the redox charge may be preferred because it is bounded between zero and one and can be determined over a wider range of conditions allowing for quantitative flux comparisons between cell types and conditions.
Dimethylallyl diphosphate (DMADP) and isopentenyl diphosphate (IDP) serves as the universal C 5 p... more Dimethylallyl diphosphate (DMADP) and isopentenyl diphosphate (IDP) serves as the universal C 5 precursors of isoprenoid biosynthesis in plants. These compounds are formed by the last step of the 2-C-methyl-D-erythritol 4-phosphate (MEP) pathway, catalyzed by (E)-4-hydroxy-3-methylbut-2-en-1-yl diphosphate reductase (HDR). In this study, we investigated the major HDR isoforms of two woody plant species, Norway spruce (Picea abies) and gray poplar (Populus × canescens), to determine how they regulate isoprenoid formation. Since each of these species has a distinct profile of isoprenoid compounds, they may require different proportions of DMADP and IDP with proportionally more IDP being needed to make larger isoprenoids. Norway spruce contained two major HDR isoforms differing in their occurrence and biochemical characteristics. PaHDR1 produced relatively more IDP than PaHDR2 and it encoding gene was expressed constitutively in leaves, likely serving to form substrate for production of carotenoids, chlorophylls, and other primary isoprenoids derived from a C 20 precursor. On the other hand, Norway spruce PaHDR2 produced relatively more DMADP than PaHDR1 and its encoding gene was expressed in leaves, stems, and roots, both constitutively and after induction with the defense hormone methyl jasmonate. This second HDR enzyme likely forms a substrate for the specialized monoterpene (C 10), sesquiterpene (C 15), and diterpene (C 20) metabolites of spruce oleoresin. Gray poplar contained only one dominant isoform (named PcHDR2) that produced relatively more DMADP and the gene of which was expressed in all organs. In leaves, where the requirement for IDP is high to make the major carotenoid and chlorophyll isoprenoids derived from C 20 precursors, excess DMADP may accumulate, which could explain the high rate of isoprene (C 5) emission. Our results provide new insights into the biosynthesis of isoprenoids in woody plants under conditions of differentially regulated biosynthesis of the precursors IDP and DMADP.
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