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Plantaricin 423 is produced by Lactobacillus plantarum 423 using the pla biosynthetic operon located on the 8188 bp plasmid, pPLA4. As with many class IIa bacteriocin operons, the pla operon encodes biosynthetic genes (plaA: precursor peptide, plaB: immunity, plaC: accessory and plaD: ABC transporter) but does not encode local regulatory genes. Little is known about the regulatory mechanisms involved in the expression of the apparently regulationless class IIa bacteriocins such as plantaricin 423. In this study, phylogenetic analysis of class IIa immunity proteins indicated that at least three distinct clades exist, which were then used to subgroup the class IIa operons. It became evident that the absence of classical quorum sensing genes on mobile bacteriocin encoding elements is a predisposition of the subgroup which includes plantaricin 423, pediocin AcH/PA-1, divercin V41, enterocin A, leucocin-A and -B, mesentericin Y105 and sakacin G. Further analysis of the subgroup suggested that the regulation of these class IIa operons may be linked to transition metal homeostasis in the host. By using a fluorescent promoter-reporter system in Lactobacillus plantarum 423, transcriptional regulation of plantaricin 423 was shown to be upregulated in response to manganese privation. IMPORTANCE Lactic acid bacteria hold huge industrial application and economic value, especially bacteriocinogenic strains which further aids in the exclusion of specific foodborne pathogens. Since bacteriocinogenic strains are sought after it is equally important to understand the mechanism of bacteriocin regulation. This is currently an understudied aspect of class IIa operons. Our research suggests the existence of a previously undescribed mode of class IIa bacteriocin regulation, whereby bacteriocin expression is linked to management of the producer's transition metal homeostasis. This delocalized metalloregulatory model may fundamentally affect the selection of culture conditions for bacteriocin expression and change our understanding of class IIa bacteriocin gene transfer dynamics in a given microbiome.

The glycine conjugation pathway in humans is involved in the metabolism of natural substrates and the detoxification of xenobiotics. The interactions between the various substrates in this pathway and their competition for the pathway enzymes are currently unknown. The pathway consists of a mitochondrial xenobiotic/medium-chain fatty acid: coenzyme A (CoA) ligase (ACSM2B) and glycine N-acyltransferase (GLYAT). The catalytic mechanism and substrate specificity of both of these enzymes have not been thoroughly characterised. In this study, the level of evolutionary conservation of GLYAT missense variants and haplotypes were analysed. From these data, haplotype variants were selected (156Asn &gt, Ser, [17Ser &gt, Thr,156Asn &gt, Ser] and [156Asn &gt, Ser,199Arg &gt, Cys]) in order to characterise the kinetic mechanism of the enzyme over a wide range of substrate concentrations. The 156Asn &gt, Ser haplotype has the highest frequency and the highest relative enzyme activity in all populations studied, and hence was used as the reference in this study. Cooperative substrate binding was observed, and the kinetic data were fitted to a two-substrate Hill equation. The coding region of the GLYAT gene was found to be highly conserved and the rare 156Asn &gt, Cys variant negatively affected the relative enzyme activity. Even though the 156Asn &gt, Cys variant had a higher affinity for benzoyl-CoA (s0.5,benz = 61.2 µM), kcat was reduced to 9.8% of the most abundant haplotype 156Asn &gt, Ser (s0.5,benz = 96.6 µM), while the activity of 17Ser &gt, Ser (s0.5,benz = 118 µM) was 73% of 156Asn &gt, Ser. The in vitro kinetic analyses of the effect of the 156Asn &gt, Cys variant on human GLYAT enzyme activity indicated that individuals with this haplotype might have a decreased ability to metabolise benzoate when compared to individuals with the 156Asn &gt, Ser variant. Furthermore, the accumulation of acyl-CoA intermediates can inhibit ACSM2B leading to a reduction in mitochondrial energy production.

The glycine conjugation pathway in humans is involved in the metabolism of natural substrates and the detoxification of xenobiotics. The interactions between the various substrates in this pathway and their competition for the pathway enzymes are currently unknown. The pathway consists of a mitochondrial xenobiotic/medium-chain fatty acid: coenzyme A (CoA) ligase (ACSM2B) and glycine N-acyltransferase (GLYAT). The catalytic mechanism and substrate specificity of both of these enzymes have not been thoroughly characterised. In this study, the level of evolutionary conservation of GLYAT missense variants and haplotypes were analysed. From these data, haplotype variants were selected (156Asn > Ser, [17Ser > Thr,156Asn > Ser] and [156Asn > Ser,199Arg > Cys]) in order to characterise the kinetic mechanism of the enzyme over a wide range of substrate concentrations. The 156Asn > Ser haplotype has the highest frequency and the highest relative enzyme activity in all populations studied, and hence was used as the reference in this study. Cooperative substrate binding was observed, and the kinetic data were fitted to a two-substrate Hill equation. The coding region of the GLYAT gene was found to be highly conserved and the rare 156Asn > Ser,199Arg > Cys variant negatively affected the relative enzyme activity. Even though the 156Asn > Ser,199Arg > Cys variant had a higher affinity for benzoyl-CoA (s0.5,benz = 61.2 µM), kcat was reduced to 9.8% of the most abundant haplotype 156Asn > Ser (s0.5,benz = 96.6 µM), while the activity of 17Ser > Thr,156Asn > Ser (s0.5,benz = 118 µM) was 73% of 156Asn > Ser. The in vitro kinetic analyses of the effect of the 156Asn > Ser,199Arg > Cys variant on human GLYAT enzyme activity indicated that individuals with this haplotype might have a decreased ability to metabolise benzoate when compared to individuals with the 156Asn > Ser variant. Furthermore, the accumulation of acyl-CoA intermediates can inhibit ACSM2B leading to a reduction in mitochondrial energy production.

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 reversible Hill equations are used to model biochemical reaction rates. Numerical solutions to this formulation are demonstrated with time-course analysis of a simplified model of sucrose accumulation. The model shows sucrose accumulation in the vacuoles of stalk parenchyma cells, and is moreover able to demonstrate the upregulation of photosynthesis in response to a change in sink demand. The model presented is able to capture the spatio-temporal evolution of the system from a set of initial conditions by combining phloem flow, diffusion, transport of metabolites between compartments and biochemical enzyme-catalysed reactions in a rigorous, quantitative framework that can form the basis for future modelling and experimental design.

The accompanying paper (Uys et al., in silico Plants, 2021: diab013) presented a core model of sucrose accumulation within the advection–diffusion–reaction framework, which is able to capture the spatio-temporal evolution of the system from a set of initial conditions. This paper presents a sensitivity analysis of this model. Because this is a non-steady-state model based on partial differential equations, we performed the sensitivity analysis using two approaches from engineering. The Morris method is based on a one-at-a-time design, perturbing parameters individually and calculating the influence on model output in terms of elementary effects. Fourier amplitude sensitivity test (FAST) is a global sensitivity analysis method, where all parameters are perturbed simultaneously, oscillating at different frequencies, enabling the calculation of the contribution of each parameter through Fourier analysis. Overall, both methods gave similar results. Perturbations in reactions tended to have a large influence on their own rate, as well as on directly connected metabolites. Sensitivities varied both with the time of the simulation and the position along the sugarcane stalk. Our results suggest that vacuolar sucrose concentrations are most sensitive to vacuolar invertase in the centre of the stalk, but that phloem unloading and vacuolar sucrose uptake also contribute, especially towards the stalk edges. Sucrose in the phloem was most sensitive to phloem loading at the nodes, but most sensitive to phloem unloading in the middle of the internodes. Sink concentrations of sucrose in the symplast were most sensitive to phloem unloading in the middle of the internodes, but at the nodes cytosolic invertase had the greatest effect.

The methylerythritol 4-phosphate (MEP) pathway of isoprenoid biosynthesis produces chlorophyll side chains and compounds that function in resistance to abiotic stresses, including carotenoids, and isoprene. Thus we investigated the effects of moderate and severe drought on MEP pathway function in the conifer Picea glauca, a boreal species at risk under global warming trends. Although moderate drought treatment reduced the photosynthetic rate by over 70%, metabolic flux through the MEP pathway was reduced by only 37%. The activity of the putative rate-limiting step, 1-deoxy-D-xylulose-5-phosphate synthase (DXS), was also reduced by about 50%, supporting the key role of this enzyme in regulating pathway metabolic flux. However, under severe drought, as flux declined below detectable levels, DXS activity showed no significant decrease, indicating a much-reduced role in controlling flux under these conditions. Both MEP pathway intermediates and the MEP pathway product isoprene incorporate administered 13CO2 to high levels (75-85%) under well-watered control conditions indicating a close connection to photosynthesis. However, this incorporation declined precipitously under drought, demonstrating exploitation of alternative carbon sources. Despite the reductions in MEP pathway flux and intermediate pools, there was no detectable decline in most major MEP pathway products under drought (except for violaxanthin under moderate and severe stress and isoprene under severe stress) suggesting that the pathway is somehow buffered against this stress. The resilience of the MEP pathway under drought may be a consequence of the importance of the metabolites formed under these conditions.

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 constraint‐based 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 3 provides the foundation needed to support this evolution., Over the past two decades, scientists from different fields have been developing SBML, a standard format for encoding computational models in biology and medicine. This article summarizes recent progress and gives perspectives on emerging challenges.

Bottom-up systems biology entails the construction of kinetic models of cellular pathways by collecting kinetic information on the pathway components (e.g., enzymes) and collating this into a kinetic model, based for example on ordinary differential equations. This requires integration and data transfer between a variety of tools, ranging from data acquisition in kinetics experiments, to fitting and parameter estimation, to model construction, evaluation and validation. Here, we present a workflow that uses the Python programming language, specifically the modules from the SciPy stack, to facilitate this task. Starting from raw kinetics data, acquired either from spectrophotometric assays with microtitre plates or from Nuclear Magnetic Resonance (NMR) spectroscopy time-courses, we demonstrate the fitting and construction of a kinetic model using scientific Python tools. The analysis takes place in a Jupyter notebook, which keeps all information related to a particular experiment together in one place and thus serves as an e-labbook, enhancing reproducibility and traceability. The Python programming language serves as an ideal foundation for this framework because it is powerful yet relatively easy to learn for the non-programmer, has a large library of scientific routines and active user community, is open-source and extensible, and many computational systems biology software tools are written in Python or have a Python Application Programming Interface (API). Our workflow thus enables investigators to focus on the scientific problem at hand rather than worrying about data integration between disparate platforms.

Summary Thioredoxin, glutaredoxin, and peroxiredoxin systems (collectively called redoxins) play critical roles in a large number of redox-sensitive cellular processes. These systems are linked to each other by coupled redox cycles and by common reaction intermediates into a larger network. Previous results from a realistic computational model of the Escherichia coli thioredoxin system developed in our group have revealed several modes of kinetic regulation in the system. Amongst others, the coupling of the thioredoxin and peroxiredoxin redox cycles was shown to exhibit the potential for ultrasensitive changes in the thioredoxin concentration and the flux through other thioredoxin-dependent processes in response to changes in the thioredoxin reductase level. Here, we analyse the basis for this ultrasensitive response using kinetic modelling and metabolic control analysis and derive quantitative conditions that must be fulfilled for ultrasensitivity to occur.

Redox signaling is now recognized as an important regulatory mechanism for a number of cellular processes including the antioxidant response, phosphokinase signal transduction and redox metabolism. While there has been considerable progress in identifying the cellular machinery involved in redox signaling, quantitative measures of redox signals have been lacking, limiting efforts aimed at understanding and comparing redox signaling under normoxic and pathogenic conditions. Here we have outlined some of the accepted principles for redox signaling, including the description of hydrogen peroxide as a signaling molecule and the role of kinetics in conferring specificity to these signaling events. Based on these principles, we then develop a working definition for redox signaling and review a number of quantitative methods that have been employed to describe signaling in other systems. Using computational modeling and published data, we show how time- and concentration- dependent analyses, in particular, could be used to quantitatively describe redox signaling and therefore provide important insights into the functional organization of redox networks. Finally, we consider some of the key challenges with implementing these methods.

A key component of enzyme function experiments is reporting of considerable metadata, to allow other researchers to replicate, interpret properly or use fully the results. This paper evaluates the completeness of enzyme function data reporting for reproducibility. We present a detailed examination of 11 recent papers (and their supplementary material) from two leading journals. We found that in every paper we were not able to collect some critical information necessary to reproduce the enzyme function findings. Study of 100 papers used by the SABIO-RK database confirmed some of the most common omissions: concentration of enzyme or its substrates, identity of counter-ions in buffers. A computer system should be better at preventing such omissions, helping secure the scientific record. Many of the omissions found would be trapped by the currently available version of STRENDA DB.

STRENDA DB, freely available at http://www.strenda-db.org, is an online validation and storage system for functional enzyme data that aims at being integrated into the publication practices of the scientific community and into the publication processes of journals. It provides a simple-to-use web submission tool and searchable database allowing the sharing, comparison and accurate reporting of enzyme kinetics data. The submission tool incorporates the STandards for Reporting ENzymology DAta (STRENDA), Guidelines which specify minimum information requested in the reporting of enzyme function data, including kinetic parameter values and full experimental conditions under which they were acquired. STRENDA DB checks the manuscript data entered by the author for compliance with the STRENDA Guidelines. If data is submitted prior to or during the publication process, the submission tool aids the author of a manuscript in the submission of kinetic parameters, ensuring that all required data and metadata are supplied. Data sets compliant with the Guidelines are assigned a STRENDA Registry Number and registered a Direct Object Identifier (DOI), which provides a perennial and resolvable identifier for each dataset. The data will normally be publicly available in STRENDA DB only after the corresponding article has been peer-reviewed and published in a journal. Data can also be submitted after publication. By promoting the practice of simultaneously submitting articles to journals and kinetics data to STRENDA DB, reviewers of journal articles as well as authors and consumers of data will benefit from the availability of standardised data in multiple ways.

Several enzymes have been described that undergo both allosteric and covalent regulation, but, to date, there exists no succinct kinetic description that is able to account for both of these mechanisms of regulation. Muscle glycogen synthase, an enzyme implicated in the pathogenesis of several metabolic diseases, is activated by glucose 6-phosphate and inhibited by ATP and phosphorylation at multiple sites. A kinetic description of glycogen synthase could provide insight into the relative importance of these modifiers. In the present study we show, using non-linear parameter optimization with robust weight estimation, that a Monod–Wyman–Changeux model in which phosphorylation favours the inactive T conformation provides a satisfactory description of muscle glycogen synthase kinetics. The best-fit model suggests that glucose 6-phosphate and ATP compete for the same allosteric site, but that ATP also competes with the substrate UDP-glucose for the active site. The novelty of our approach lies in treating covalent modification as equivalent to allosteric modification. Using the obtained rate equation, the relationship between enzyme activity and phosphorylation state is explored and shown to agree with experimental results. The methodology we propose could also be applied to other enzymes that undergo both allosteric and covalent modification.

The 2-C-methylerythritol 4-phosphate (MEP) pathway supplies precursors for plastidial isoprenoid biosynthesis including carotenoids, redox cofactor side chains, and biogenic volatile organic compounds. We examined the first enzyme of this pathway, 1-deoxyxylulose 5-phosphate synthase (DXS), using metabolic control analysis. Multiple Arabidopsis (Arabidopsis thaliana) lines presenting a range of DXS activities were dynamically labeled with 13CO2 in an illuminated, climate-controlled, gas exchange cuvette. Carbon was rapidly assimilated into MEP pathway intermediates, but not into the mevalonate pathway. A flux control coefficient of 0.82 was calculated for DXS by correlating absolute flux to enzyme activity under photosynthetic steady-state conditions, indicating that DXS is the major controlling enzyme of the MEP pathway. DXS manipulation also revealed a second pool of a downstream metabolite, 2-C-methylerythritol-2,4-cyclodiphosphate (MEcDP), metabolically isolated from the MEP pathway. DXS overexpression led to a 3- to 4-fold increase in MEcDP pool size but to a 2-fold drop in maximal labeling. The existence of this pool was supported by residual MEcDP levels detected in dark-adapted transgenic plants. Both pools of MEcDP are closely modulated by DXS activity, as shown by the fact that the concentration control coefficient of DXS was twice as high for MEcDP (0.74) as for 1-deoxyxylulose 5-phosphate (0.35) or dimethylallyl diphosphate (0.34). Despite the high flux control coefficient for DXS, its overexpression led to only modest increases in isoprenoid end products and in the photosynthetic rate. Diversion of flux via MEcDP may partly explain these findings and suggests new opportunities to engineer the MEP pathway., This work was supported by a Ramón y Cajal contract from the Spanish Ministry of Science and Innovation (contract no. RYC–2010–05759 to M.A.P.), a research fellowship from the Deutsche Forschungsgemeinschaft (PH 179/1–1 to M.A.P.), and a Max Planck Society-Fraunhofer Society Cooperation (to L.P.W. and J.G.).

Progestogens are widely used in contraception and in hormone therapy. Biochemical and molecular biological evidence suggests that progestogens differ widely in their affinities and transcriptional effects via different steroid receptors, and hence cannot be considered as a single class of compounds. Consistent with these observations, recent clinical evidence suggests that, despite their similar progestogenic actions, these differences underlie different side-effect profiles for cardiovascular disease and susceptibility to infectious diseases. However, choice of progestogen for maximal benefit and minimal side-effects is hampered by insufficient comparative clinical and molecular studies to understand their relative mechanisms of action, as well as their relative potencies for different assays and clinical effects. This review evaluates the usage, meaning and significance of the terms affinity, potency and efficacy in different models systems, with a view to improved understanding of their physiological and pharmacological significance. This article is part of a Special Issue entitled 'Menopause'.

Thioredoxin, glutaredoxin, and peroxiredoxin systems play critical roles in a large number of redox-sensitive cellular processes. These systems are linked to each other by coupled redox cycles and common reaction intermediates into a larger network. Given the scale and connectivity of this network, computational approaches are required to analyze its dynamics and organization.Theoretical advances, as well as new redox proteomic methods, have led to the development of both top-down and bottom-up systems biology approaches to analyze the these systems and the network as a whole. Top-down approaches have been based on modifications to the Nernst equation or on graph theoretical approaches, while bottom-up approaches have been based on kinetic or stoichiometric modeling techniques.This review will consider the rationale behind these approaches and focus on their advantages and limitations. Further, the review will discuss modeling standards to ensure model accuracy and availability.Top-down and bottom-up approaches have distinct strengths and limitations in describing cellular redoxin networks. The availability of methods to overcome these limitations, together with the adoption of common modeling standards, is expected to increase the pace of model-led discovery within the redox biology field.

Winery effluent is known to have a high chemical oxygen demand (COD) and a low pH. In this study, we extensively analysed effluent from two cellars and studied the temporal changes over the duration of a harvest and the duration of a year. We found that ethanol contributes approximately 85% to 90% of the COD of raw winery effluent, with acetic acid being the next significant contributor. The pH showed some dependence on the concentration of acetic acid. The concentration of sodium in the effluent is strongly dependent on the cleaning regime in place at the cellar, and the concentration of potassium has been shown to be linked to the spillage of juice, wine or lees. The data and correlations presented here could allow for an artificial effluent to be prepared easily for research purposes.

It is widely accepted that insufficient insulin-stimulated activation of muscle glycogen synthesis is one of the major components of non-insulin-dependent (type 2) diabetes mellitus. Glycogen synthase, a key enzyme in muscle glycogen synthesis, is extensively regulated, both allosterically (by glucose-6-phosphate, ATP, and others) and covalently (by phosphorylation). Although glycogen synthase has been a topic of intense study for more than 50 years, its kinetic characterization has been confounded by its large number of phosphorylation states. Questions remain regarding the function of glycogen synthase regulation and the relative importance of allosteric and covalent modification in fulfilling this function. In this review, we consider both earlier kinetic studies and more recent site-directed mutagenesis and crystal structure studies in a detailed qualitative discussion of the effects of regulation on the kinetics of glycogen synthase. We propose that both allosteric and covalent modification of glycogen synthase may be described by a Monod-Wyman-Changeux model in terms of apparent changes to L, the equilibrium constant for transition between the T and R conformers. As, with the exception of L, all parameters of this model are independent of the glycogen synthase phosphorylation state, the need to determine kinetic parameters for all possible states is eliminated; only the relationship between a particular state and L must be established. We conclude by suggesting that renewed efforts to characterize the relationship between phosphorylation and the kinetics of glycogen synthase are essential in order to obtain a better quantitative understanding of the function of glycogen synthesis regulation. The model we propose may prove useful in this regard.

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.

This paper provides a review of kinetic modelling of plant metabolic pathways as a tool for analysing their control and regulation. An overview of different modelling strategies is presented, starting with those approaches that only require a knowledge of the network stoichiometry; these are referred to as structural. Flux-balance analysis, metabolic flux analysis using isotope labelling, and elementary mode analysis are briefly mentioned as three representative examples. The main focus of this paper, however, is a discussion of kinetic modelling, which requires, in addition to the stoichiometry, a knowledge of the kinetic properties of the constituent pathway enzymes. The different types of kinetic modelling analysis, namely time-course simulation, steady-state analysis, and metabolic control analysis, are explained in some detail. An overview is presented of strategies for obtaining model parameters, as well as software tools available for simulation of such models. The kinetic modelling approach is exemplified with discussion of three models from the general plant physiology literature. With the aid of kinetic modelling it is possible to perform a control analysis of a plant metabolic system, to identify potential targets for biotechnological manipulation, as well as to ascertain the regulatory importance of different enzymes (including isoforms of the same enzyme) in a pathway. Finally, a framework is presented for extending metabolic models to the whole-plant scale by linking biochemical reactions with diffusion and advective flow through the phloem. Future challenges include explicit modelling of subcellular compartments, as well as the integration of kinetic models on the different levels of the cellular and organizational hierarchy.

Summary PySCeSToolbox is an extension to the Python Simulator for Cellular Systems (PySCeS) that includes tools for performing generalized supply–demand analysis, symbolic metabolic control analysis, and a framework for investigating the kinetic and thermodynamic aspects of enzyme-catalyzed reactions. Each tool addresses a different aspect of metabolic behaviour, control, and regulation; the tools complement each other and can be used in conjunction to better understand higher level system behaviour. Availability and implementation PySCeSToolbox is available on Linux, Mac OS X and Windows. It is licensed under the BSD 3-clause licence. Code, setup instructions and a link to documentation can be found at https://github.com/PySCeS/PyscesToolbox. Supplementary information Supplementary data are available at Bioinformatics online.

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 fluxor 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 inLactococcus lactisin 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.Author summaryMetabolic networks are complex systems consisting of numerous individual molecular components. The properties of these components, together with their non-linear interactions, give rise to high-level observed behaviour of the system in which they reside. Therefore, in order to fully understand the behaviour of a metabolic system, one has to consider the properties of all of its components. The analysis of computer models that capture and represent these systems and their components simplifies this task by allowing for an easy way to isolate the effects of each individual component. In this paper we use the framework of symbolic control analysis to investigate the sensitivity of the rate of flow of matter through one of the branches in a particular metabolic pathway towards changes in the rates of individual reactions. Here we are able to quantify how certain chains of reactions, individual reactions, and even thermodynamic and kinetic aspects of individual reactions contribute to the overall sensitivity of the rate of matter-flow. Thus, we are able to trace the behaviour of the system as a whole in a mechanistic way to the properties of the individual molecular components.

In this contribution we resolve the long-standing dispute whether or not the Monod constant (KS), describing the overall affinity of an organism for its growth-limiting substrate, can be related to the affinity of the transporter for that substrate (KM). We show how this can be done via the control of the transporter on the specific growth rate; they are identical if the transport step has full control. The analysis leads to the counter-intuitive result that the affinity of an organism for its substrate is expected to be higher than the affinity of the enzyme that facilitates its transport. Experimentally, we show this indeed to be the case for the yeastSaccharomyces cerevisiae, for which we determined a KMvalue for glucose more than two times higher than the KSvalue in glucose-limited chemostat cultures. Moreover, we calculated that at glucose concentrations of 0.03 and 0.29 mM, the transport step controls the specific growth rate at 78 and 49 %, respectively.

We present the framework of generalised supply-demand analysis (SDA) of a kinetic model of a cellular system, which can be applied to networks of arbitrary complexity. By fixing the concentrations of each of the variable species in turn and varying them in a parameter scan, rate characteristics of supply-demand are constructed around each of these species. By inspecting the shapes of the rate characteristic patterns and comparing the flux-response coefficients of the supply and demand blocks with the elasticities of the enzymes that interact directly with the fixed metabolite, regulatory metabolites in the system can be identified and characterised. The analysis provides information on whether and where the system is functionally differentiated and which of its species are homeostatically buffered. The novelty in our proposed method lies in the fact that all metabolites are considered for SDA (hence the term "generalised"), which removes investigator bias. It supplies an entry point for the further analysis and detailed characterisation of large models of cellular systems, in which the choice of metabolite around which to perform a SDA is not always obvious.

Summary Three sucrose synthase (SuSy) (EC 2.4.1.13) forms were isolated from sugarcane leaf roll tissue. During anion exchange chromatography, one peak of activity (SuSyA) eluted during the wash step and the other peak (SuSyB) during the salt gradient phase at 180 mM KCl concentration. A third form of activity (SuSyC), which also eluted at 180 mM KCl, was also present in the leaf roll and replaced SuSyB depending on the season of the year. Substrate K m values, as well as sucrose breakdown/synthesis ratios, differed between these forms. For SuSyA, SuSyB, and SuSyC, respectively, K m values±SE (mM) were: 41.8±3.4, 109±23, and 35.9±2.3 for sucrose, 1.07±0.08, 0.214±0.039, and 0.00191±0.00019 for UDP, 6.62±1.55, 11.7±2.6, and 6.49±0.61 for fructose, and 3.59±0.37, 0.530±0.142, and 0.234±0.025 for UDP-glucose. Sucrose breakdown/synthesis ratios±SE were 0.0791±0.0199, 0.330±0.180, and 0.426±0.069 for SuSyA, SuSyB, and SuSyC, respectively. The ratio of the area of peak 1 (low breakdown/synthesis ratio) to the area of peak 2 (high breakdown/synthesis ratio) in sucrose accumulating tissue (internode 9) was 0.88, while in non-accumulating (leaf roll) tissue it was 14.5 at the same time of year. The molecular mass of the denatured subunits of all three forms was 94 kDa by SDS–PAGE. A polyclonal antiserum raised against SuSyB cross-reacted with all three forms on an immunoblot, but only SuSyA and SuSyB were immunoinactivated by this serum.

The kinetic data on sugarcane (Saccharum spp. hybrids) sucrose synthase (SuSy, UDP-glucose: D-fructose 2-alpha-D-glucosyltransferase, EC 2.4.1.13) are limited. We characterized kinetically a SuSy activity partially purified from sugarcane variety N19 leaf roll tissue. Primary plot analysis and product inhibition studies showed that a compulsory order ternary complex mechanism is followed, with UDP binding first and UDP-glucose dissociating last from the enzyme. Product inhibition studies showed that UDP-glucose is a competitive inhibitor with respect to UDP and a mixed inhibitor with respect to sucrose. Fructose is a mixed inhibitor with regard to both sucrose and UDP. Kinetic constants are as follows: Km values (mm, +/- SE) were, for sucrose, 35.9 +/- 2.3; for UDP, 0.00191 +/- 0.00019; for UDP-glucose, 0.234 +/- 0.025 and for fructose, 6.49 +/- 0.61. values were, for sucrose, 227 mm; for UDP, 0.086 mm; for UDP-glucose, 0.104; and for fructose, 2.23 mm. Replacing estimated kinetic parameters of SuSy in a kinetic model of sucrose accumulation with experimentally determined parameters of the partially purified isoform had significant effects on model outputs, with a 41% increase in sucrose concentration and 7.5-fold reduction in fructose the most notable. Of the metabolites included in the model, fructose concentration was most affected by changes in SuSy activity: doubling and halving of SuSy activity reduced and increased the steady-state fructose concentration by about 42 and 140%, respectively. It is concluded that different isoforms of SuSy could have significant differential effects on metabolite concentrations in vivo, therefore impacting on metabolic regulation.

No comprehensive studies on the localization of sucrose synthase (SuSy, EC 2.4.1.13) in sugarcane internodes have been reported. The expression and localization of SuSy in young (internode 3) to mature (internode 9) internodes of sugarcane (Saccharum spp. hybrids) var. N19 was investigated. Enzyme activity in the top and bottom, as well as the peripheral and core parts of the internodes suggested that SuSy is present ubiquitously but that levels can differ significantly in different parts of the internodes and with maturity. This was also confirmed by immunohistochemistry, which showed that both vascular and storage parenchyma tissues contain SuSy in young and mature internodes. The ratio of sucrose breakdown to synthesis activity increased approximately 12-fold from an average of 0.12 in internode three to 1.4 in internode nine. This indicates that different forms of SuSy are present in young and mature internodes, or that the ratios of different isoforms differ between young and mature internodes. Immunoblotting showed that at least one form of SuSy present in young tissue was absent, or present below detection limits, in mature culm tissue.

We show how to incorporate the membrane potential and its effects on the kinetics of ion transport processes into kinetic models.

A numerical model of the LmrA multi-drug transport system of Lactococcus lactis is used to explore the possibility of distinguishing experimentally between two putative transport mechanisms, i.e., the vacuum-cleaner and the flippase mechanisms. This comparative model also serves as an example of numerical simulation with the scripting language Python and its scientific add-on Scipy.

Although metabolic control analysis (MCA) cannot be applied directly to microbial ecological systems because of mass conservation and stoichiometric constraints, we demonstrate here that Hierarchical Control Analysis (HCA) can be applied to such systems. We illustrate the approach for a particular ecosystem example of the biological synthesis of acetic acid from glucose, and uncover some surprising aspects to the control of this miniature ecosystem.

Experimental supply-demand analysis of yeast fermentative energy metabolism shows that control of the glycolytic flux is shared between supply and demand. In glucose limited chemostat cultures the supply block was modulated in a dilution rate change and demand block via a benzoic acid titration. Under these conditions the supply block had a flux control of 0.90 and the demand block a flux control of 0.10.

This paper shows how Python and Scipy can be used to simulate the time-dependent and steady-state behaviour of reaction networks, and introduces Pysces, a Python modelling toolkit.

The uptake of methyl alpha-D-glucopyranoside by the phosphoenolpyruvate-dependent phosphotransferase system of Salmonella typhimurium could be inhibited by prior incubation of the cells with glycerol. Inhibition was only observed for glycerol preincubation times longer than 45 s and required the preinduction of both the glucose and the glycerol-catabolizing systems. Larger extents of inhibition by glycerol correlated with higher intracellular levels of glycerol kinase when the glp regulon had been induced to different extents. Preincubation with lactate did not inhibit methyl alpha-D-glucopyranoside uptake significantly, although both lactate and glycerol were oxidized by the cells. The cellular free-energy state of the cells (intracellular [ATP]/[ADP] ratio) was virtually identical for lactate and glycerol preincubation, suggesting that the inhibition of phosphotransferase-mediated uptake was not a metabolic effect. In vitro, phosphotransferase activity was inhibited to a maximal extent of 32% upon titrating cell-free extracts with high concentrations of commercial glycerol kinase. The results show that uptake systems that have hitherto been regarded merely as targets of the phosphotransferase system component IIA(Glc) also have the capacity themselves to retroinhibit the phosphotransferase system flux, presumably by sequestration of the available IIA(Glc), provided that these systems are induced to appropriate levels.

It is shown that both the reversible Hill equation and a generalised, reversible Monod-Wyman-Changeux equation can give analogous regulatory behaviour when embedded in a model metabolic pathway.

The importance of kinetic modeling for understanding the control and regulation of complex metabolic networks is increasingly being recognized. Kinetic models encapsulate the available kinetic information of all the enzymes in a pathway, and then calculate the complex behavior that emerges from the interactions between these network components. Kinetic models are particularly useful because they can simulate untested scenarios and thus explore pathway behavior beyond the realm of what is experimentally available or currently feasible. Models can also suggest new experiments in a directed approach.This chapter provides a brief introduction to kinetic modeling and its application to plant metabolic pathways. A two-pronged strategy is followed: first, a method is presented for further analysis of existing published models, with references to the relevant databases housing such models and instructions on how to load the models into simulation software. Next, the requirements for and processes of constructing and validating a kinetic model from scratch are outlined. To conclude, potential applications of models are summarized.

The importance of kinetic modeling for understanding the control and regulation of complex metabolic networks is increasingly being recognized. Kinetic models encapsulate the available kinetic information of all the enzymes in a pathway, and then calculate the complex behavior that emerges from the interactions between these network components. Kinetic models are particularly useful because they can simulate untested scenarios and thus explore pathway behavior beyond the realm of what is experimentally available or currently feasible. Models can also suggest new experiments in a directed approach.This chapter provides a brief introduction to kinetic modeling and its application to plant metabolic pathways. A two-pronged strategy is followed: first, a method is presented for further analysis of existing published models, with references to the relevant databases housing such models and instructions on how to load the models into simulation software. Next, the requirements for and processes of constructing and validating a kinetic model from scratch are outlined. To conclude, potential applications of models are summarized.

Biosynthetic networks link to growth and reproduction processes through template-directed synthesis of macromolecules such as polynucleotides and polypeptides. No rate equation exists that captures this link in a way that it can effectively be incorporated into a single computational model of the overall process. This paper describes the derivation of such a generic steady-state rate equation for catalysed, template-directed polymerisation reactions with varying monomer stoichiometry and varying chain length. The derivation is based on a classical Michaelis–Menten mechanism with template binding and an arbitrary number of chain elongation steps that produce a polymer composed of an arbitrary number of monomer types. The rate equation only requires the identity of the first dimer in the polymer sequence; for the remainder only the monomer composition needs be known. Further simplification of a term in the denominator yielded an equation requiring no positional information at all, only the monomer composition of the polymer; this equation still gave an excellent estimate of the reaction rate provided that either the monomer concentrations are at least half-saturating, or the polymer is very long.

The effect of different cellular free-energy states on the uptake of methyl alpha-D-glucopyranoside, an analogue of glucose, by the Escherichia coli phosphoenolpyruvate:carbohydrate phosphotransferase system was investigated. The intracellular [ATP]/[ADP] ratio was varied by changing the expression of the atp operon, which codes for the H+-ATPase, or by adding an uncoupler of oxidative phosphorylation or an inhibitor of respiration. Corresponding initial phosphotransferase uptake rates were determined using an improved uptake assay that works with growing cells in steady state. The results show that the initial uptake rate was decreased under conditions of lowered intracellular [ATP]/[ADP] ratios, irrespective of which method was used to change the cellular energy state. When either the expression of the atp operon was changed or 2,4-dinitrophenol was added to wild-type cells, the relationship between initial phosphotransferase uptake rate and the logarithm of the [ATP]/[ADP] ratio was approximately linear. These results suggest that the cellular free-energy state, as reflected in the intracellular [ATPI]/[ADP] ratio, plays an important role in regulating the activity of the phosphotransferase system.

Glucocorticoid receptor (GR) levels vary between tissues and individuals and are altered by physiological and pharmacological effectors. However, the effects and implications of differences in GR concentration have not been fully elucidated. Using three statistically different GR concentrations in transiently transfected COS-1 cells, we demonstrate, using co-immunoprecipitation (CoIP) and fluorescent resonance energy transfer (FRET), that high levels of wild type GR (wtGR), but not of dimerization deficient GR (GRdim), display ligand-independent dimerization. Whole-cell saturation ligand-binding experiments furthermore establish that positive cooperative ligand-binding, with a concomitant increased ligand-binding affinity, is facilitated by ligand-independent dimerization at high concentrations of wtGR, but not GRdim. The down-stream consequences of ligand-independent dimerization at high concentrations of wtGR, but not GRdim, are shown to include basal priming of the system as witnessed by ligand-independent transactivation of both a GRE-containing promoter-reporter and the endogenous glucocorticoid (GC)-responsive gene, GILZ, as well as ligand-independent loading of GR onto the GILZ promoter. Pursuant to the basal priming of the system, addition of ligand results in a significantly greater modulation of transactivation potency than would be expected solely from the increase in ligand-binding affinity. Thus ligand-independent dimerization of the GR at high concentrations primes the system, through ligand-independent DNA loading and transactivation, which together with positive cooperative ligand-binding increases the potency of GR agonists and shifts the bio-character of partial GR agonists. Clearly GR-levels are a major factor in determining the sensitivity to GCs and a critical factor regulating transcriptional programs.

The living cell functions by virtue of an enormous number of different processes. It is one of the most difficult challenges of modern biology to elucidate how all those processes are coordinated quantitatively so as to lead to a viable system with optimal responses to various changes in the environment. The biochemical and biophysical processes of the living cell do not constitute a network with random connections. In this paper we shall discuss that cell function is organized in hierarchical substructures. We will briefly touch on the topics of (i) metabolic control and regulated gene expression, (ii) time dependent metabolism in intact yeast cells, and (iii) metabolite channelling.

Enzyme kinetics for systems biology should ideally yield information about the enzyme’s activity under in vivo conditions, including such reaction features as substrate cooperativity, reversibility and allostery, and be applicable to enzymatic reactions with multiple substrates. A large body of enzyme-kinetic data in the literature is based on the uni-substrate Michaelis-Menten equation, which makes unnatural assumptions about enzymatic reactions (e.g., irreversibility), and its application in systems biology models is therefore limited. To overcome this limitation, we have utilised NMR time-course data in a combined theoretical and experimental approach to parameterize the generic reversible Hill equation, which is capable of describing enzymatic reactions in terms of all the properties mentioned above and has fewer parameters than detailed mechanistic kinetic equations; these parameters are moreover defined operationally. Traditionally, enzyme kinetic data have been obtained from initial-rate studies, often using assays coupled to NAD(P)H-producing or NAD(P)H-consuming reactions. However, these assays are very labour-intensive, especially for detailed characterisation of multi-substrate reactions. We here present a cost-effective and relatively rapid method for obtaining enzyme-kinetic parameters from metabolite time-course data generated using NMR spectroscopy. The method requires fewer runs than traditional initial-rate studies and yields more information per experiment, as whole time-courses are analyzed and used for parameter fitting. Additionally, this approach allows real-time simultaneous quantification of all metabolites present in the assay system (including products and allosteric modifiers), which demonstrates the superiority of NMR over traditional spectrophotometric coupled enzyme assays. The methodology presented is applied to the elucidation of kinetic parameters for two coupled glycolytic enzymes from Escherichia coli (phosphoglucose isomerase and phosphofructokinase). 31P-NMR time-course data were collected by incubating cell extracts with substrates, products and modifiers at different initial concentrations. NMR kinetic data were subsequently processed using a custom software module written in the Python programming language, and globally fitted to appropriately modified Hill equations.

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.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.

The present study reports the effect of high molecular weight bacterial fructan (levan) and glucan (reuteran) on growth and carbohydrate partitioning in transgenic sugarcane plants. These biopolymers are products of bacterial glycosyltransferases, enzymes that catalyze the polymerization of glucose or fructose residues from sucrose. Constructs, targeted to different subcellular compartments (cell wall and cytosol) and driven by the Cauliflower mosaic virus-35S: maize-ubiquitin promoter, were introduced into sugarcane by biolistic transformation. Polysaccharide accumulation severely affected growth of callus suspension cultures. Regeneration of embryonic callus tissue into plants proved problematic for cell wall-targeted lines. When targeted to the cytosol, only plants with relative low levels of biopolymer accumulation survived. In internodal stalk tissue that accumulate reuteran (max 0.03 mg/g FW), sucrose content (ca 60 mg/g FW) was not affected, while starch content (

In this communiqué, we discuss the use of the Arrhenius relationship to describe the temperature dependence of reacting biological systems, such as those treating wastewater. We also discuss the use of the modified Arrhenius function, and those instances where its applicability is limited. We show that the error when using the modified relationship is 7% at 30°C, 15% at 40°C and 25% at 50°C. We conclude that whilst the modified relationship is acceptable at lower temperatures, in those applications where higher temperatures are reached (above 25°C) the error with using the relationship may not be acceptable. We present an Arrhenius equation for use in biological systems, which is applicable for all temperature ranges.Keywords: kinetics, biological processes, Arrhenius equation

The living cell can be thought of as a collection of linked chemical factories, a molecular economy in which the principles of supply and demand obtain. Supply-demand analysis is a framework for exploring and gaining an understanding of metabolic regulation, both theoretically and experimentally, where regulatory performance is measured in terms of flux control and homeostatic maintenance of metabolite concentrations. It is based on a metabolic control analysis of a supply-demand system in steady state in which the degree of flux and concentration control by the supply and demand blocks is related to their local properties, which are quantified as the elasticities of supply and demand. These elasticities can be visualized as the slopes of the log-log rate characteristics of supply and demand. Rate characteristics not only provide insight about system behavior around the steady state but can also be expanded to provide a view of the behavior of the system over a wide range of concentrations of the metabolic intermediate that links the supply and the demand. The theoretical and experimental results of supply-demand analysis paint a picture of the regulatory design of metabolic systems that differs radically from what can be called the classical view of metabolic regulation, which generally explains the role of regulatory mechanisms only in terms of the supply, completely ignoring the demand. Supply-demand analysis has recently been generalized into a computational tool that can be used to study the regulatory behavior of kinetic models of metabolic systems up to genome-scale.

Background The thioredoxin system consisting of NADP(H), thioredoxin reductase and thioredoxin provides reducing equivalents to a large and diverse array of cellular processes. Despite a great deal of information on the kinetics of individual thioredoxin-dependent reactions, the kinetic regulation of this system as an integrated whole is not known. We address this by using kinetic modeling to identify and describe kinetic behavioral motifs found within the system. Results Analysis of a realistic computational model of the Escherichia coli thioredoxin system revealed several modes of kinetic regulation in the system. In keeping with published findings, the model showed that thioredoxin-dependent reactions were adaptable (i.e. changes to the thioredoxin system affected the kinetic profiles of these reactions). Further and in contrast to other systems-level descriptions, analysis of the model showed that apparently unrelated thioredoxin oxidation reactions can affect each other via their combined effects on the thioredoxin redox cycle. However, the scale of these effects depended on the kinetics of the individual thioredoxin oxidation reactions with some reactions more sensitive to changes in the thioredoxin cycle and others, such as the Tpx-dependent reduction of hydrogen peroxide, less sensitive to these changes. The coupling of the thioredoxin and Tpx redox cycles also allowed for ultrasensitive changes in the thioredoxin concentration in response to changes in the thioredoxin reductase concentration. We were able to describe the kinetic mechanisms underlying these behaviors precisely with analytical solutions and core models. Conclusions Using kinetic modeling we have revealed the logic that underlies the functional organization and kinetic behavior of the thioredoxin system. The thioredoxin redox cycle and associated reactions allows for a system that is adaptable, interconnected and able to display differential sensitivities to changes in this redox cycle. This work provides a theoretical, systems-biological basis for an experimental analysis of the thioredoxin system and its associated reactions.

The living cell can be thought of as a collection of linked chemical factories, a molecular economy in which the principles of supply and demand obtain. Supply–demand analysis is a framework for exploring and gaining an understanding of metabolic regulation, both theoretically and experimentally, where regulatory performance is measured in terms of flux control and homeostatic maintenance of metabolite concentrations. It is based on a metabolic control analysis of a supply–demand system in steady state in which the degree of flux and concentration control by the supply and demand blocks is related to their local properties, which are quantified as the elasticities of supply and demand. These elasticities can be visualized as the slopes of the log–log rate characteristics of supply and demand. Rate characteristics not only provide insight about system behavior around the steady state but can also be expanded to provide a view of the behavior of the system over a wide range of concentrations of the metabolic intermediate that links the supply and the demand. The theoretical and experimental results of supply–demand analysis paint a picture of the regulatory design of metabolic systems that differs radically from what can be called the classical view of metabolic regulation, which generally explains the role of regulatory mechanisms only in terms of the supply, completely ignoring the demand. Supply–demand analysis has recently been generalized into a computational tool that can be used to study the regulatory behavior of kinetic models of metabolic systems up to genome-scale.

This paper develops concepts for assessing and quantifying the regulation of the rate of an enzyme-catalyzed reaction. We show how generic reversible rate equations can be recast in two ways, one making the distance from equilibrium explicit, thereby allowing the distinction between kinetic and thermodynamic control of reaction rate, as well as near-equilibrium and far-from-equilibrium reactions. Recasting in the second form separates mass action from rate capacity and quantifies the degree to which intrinsic mass action contributes to reaction rate and how regulation of an enzyme-catalyzed reaction either enhances or counteracts this mass-action behavior. The contribution of enzyme binding to regulation is analyzed in detail for a number of enzyme-kinetic rate laws, including cooperative reactions.