A quantitative comparison of Calvin-Benson cycle models

Enhancing control systems of higher plant culture chambers via multilevel structural mechanistic modelling

Modelling higher plant growth is of strategic interest for modern agriculture as well as for the development of bioregenerative life support systems for space applications, where crop growth is expected to play an essential role. The capability of constraint-based metabolic models to cope the diel dynamics of plants growth is integrated into a multilevel modelling approach including mass and energy transfer and enzyme kinetics. Lactuca sativa is used as an exemplary crop to validate, with experimental data, the approach presented as well as to design a novel model-based predictive control strategy embedding metabolic information. The proposed modelling strategy predicts with high accuracy the dynamics of gas exchange and the distribution of fluxes in the metabolic network whereas the control architecture presented can be useful to manage higher plants chambers and open new ways of merging metabolome and control algorithms.

Relative flux trade-offs and optimization of metabolic network functionalities

Trade-offs between traits are present across different levels of biological systems and ultimately reflect constraints imposed by physicochemical laws and the structure of underlying biochemical networks. Yet, mechanistic explanation of how trade-offs between molecular traits arise and how they relate to optimization of fitness-related traits remains elusive. Here, we introduce the concept of relative flux trade-offs and propose a constraint-based approach, termed FluTOr, to identify metabolic reactions whose fluxes are in relative trade-off with respect to an optimized fitness-related cellular task, like growth. We then employed FluTOr to identify relative flux trade-offs in the genome-scale metabolic networks of Escherichia coli, Saccharomyces cerevisiae, and Arabidopsis thaliana. For the metabolic models of E. coli and S. cerevisiae we showed that: (i) the identified relative flux trade-offs depend on the carbon source used and that (ii) reactions that participated in relative trade-offs in both species were implicated in cofactor biosynthesis. In contrast to the two microorganisms, the relative flux trade-offs for the metabolic model of A. thaliana did not depend on the available nitrogen sources, reflecting the differences in the underlying metabolic network as well as the considered environments. Lastly, the established connection between relative flux trade-offs allowed us to identify overexpression targets that can be used to optimize fitness-related traits. Altogether, our computational approach and findings demonstrate how relative flux trade-offs can shape optimization of metabolic tasks, important in biotechnological applications.

Probing Light-Dependent Regulation of the Calvin Cycle Using a Multi-Omics Approach

Photoautotrophic microorganisms are increasingly explored for the conversion of atmospheric carbon dioxide into biomass and valuable products. The Calvin-Benson-Bassham (CBB) cycle is the primary metabolic pathway for net CO₂ fixation within oxygenic photosynthetic organisms. The cyanobacteria, Synechocystis sp. PCC 6803, is a model organism for the study of photosynthesis and a platform for many metabolic engineering efforts. The CBB cycle is regulated by complex mechanisms including enzymatic abundance, intracellular metabolite concentrations, energetic cofactors and post-translational enzymatic modifications that depend on the external conditions such as the intensity and quality of light. However, the extent to which each of these mechanisms play a role under different light intensities remains unclear. In this work, we conducted non-targeted proteomics in tandem with isotopically non-stationary metabolic flux analysis (INST-MFA) at four different light intensities to determine the extent to which fluxes within the CBB cycle are controlled by enzymatic abundance. The correlation between specific enzyme abundances and their corresponding reaction fluxes is examined, revealing several enzymes with uncorrelated enzyme abundance and their corresponding flux, suggesting flux regulation by mechanisms other than enzyme abundance. Additionally, the kinetics of ¹³C labeling of CBB cycle intermediates and estimated inactive pool sizes varied significantly as a function of light intensity suggesting the presence of metabolite channeling, an additional method of flux regulation. These results highlight the importance of the diverse methods of regulation of CBB enzyme activity as a function of light intensity, and highlights the importance of considering these effects in future kinetic models.

Temperature-dependent regulation of electron transport and ATP synthesis in chloroplasts in vitro and in silico

The significance of temperature-dependent regulation of photosynthetic apparatus (PSA) is determined by the fact that plant temperature changes with environmental temperature. In this work, we present a brief overview of temperature-dependent regulation of photosynthetic processes in class B chloroplasts (thylakoids) and analyze these processes using a computer model that takes into account the key stages of electron and proton transport coupled to ATP synthesis. The rate constants of partial reactions were parametrized on the basis of experimental temperature dependences of partial photosynthetic processes: (1) photosystem II (PSII) turnover and plastoquinone (PQ) reduction, (2) the plastoquinol (PQH₂) oxidation by the cytochrome (Cyt) b₆f complex, (3) the ATP synthase activity, and (4) the proton leak from the thylakoid lumen. We consider that PQH₂ oxidation is the rate-limiting step in the intersystem electron transport. The parametrization of the rate constants of these processes is based on earlier experimental data demonstrating strong correlations between the functional and structural properties of thylakoid membranes that were probed with the lipid-soluble spin labels embedded into the membranes. Within the framework of our model, we could adequately describe a number of experimental temperature dependences of photosynthetic reactions in thylakoids. Computer modeling of electron and proton transport coupled to ATP synthesis supports the notion that PQH₂ oxidation by the Cyt b₆f complex and proton pumping into the lumen are the basic temperature-dependent processes that determine the overall electron flux from PSII to molecular oxygen and the net ATP synthesis upon variations of temperature. The model describes two branches of the temperature dependence of the post-illumination reduction of [Formula: see text] characterized by different activation energies (about 60 and ≤ 3.5 kJ mol^-1). The model predicts the bell-like temperature dependence of ATP formation, which arises from the balance of several factors: (1) the thermo-induced acceleration of electron transport through the Cyt b₆f complex, (2) deactivation of PSII photochemistry at sufficiently high temperatures, and (3) acceleration of the passive proton outflow from the thylakoid lumen bypassing the ATP synthase complex. The model describes the temperature dependence of experimentally measured parameter P/2e, determined as the ratio between the rates of ATP synthesis and pseudocyclic electron transport (H₂O → PSII → PSI → O₂).

A cyanobacterial photorespiratory bypass model to enhance photosynthesis by rerouting photorespiratory pathway in C3 plants

Plants employ photosynthesis to produce sugars for supporting their growth. During photosynthesis, an enzyme Ribulose 1,5 bisphosphate carboxylase/oxygenase (Rubisco) combines its substrate Ribulose 1,5 bisphosphate (RuBP) with CO2 to produce phosphoglycerate (PGA). Alongside, Rubisco also takes up O2 and produce 2-phosphoglycolate (2-PG), a toxic compound broken down into PGA through photorespiration. Photorespiration is not only a resource-demanding process but also results in CO2 loss which affects photosynthetic efficiency in C3 plants. Here, we propose to circumvent photorespiration by adopting the cyanobacterial glycolate decarboxylation pathway into C3 plants. For that, we have integrated the cyanobacterial glycolate decarboxylation pathway into a kinetic model of C3 photosynthetic pathway to evaluate its impact on photosynthesis and photorespiration. Our results show that the cyanobacterial glycolate decarboxylation bypass model exhibits a 10% increase in net photosynthetic rate (A) in comparison with C3 model. Moreover, an increased supply of intercellular CO2 (Ci) from the bypass resulted in a 54.8% increase in PGA while reducing photorespiratory intermediates including glycolate (- 49%) and serine (- 32%). The bypass model, at default conditions, also elucidated a decline in phosphate-based metabolites including RuBP (- 61.3%). The C3 model at elevated level of inorganic phosphate (Pi), exhibited a significant change in RuBP (+ 355%) and PGA (- 98%) which is attributable to the low availability of Ci. Whereas, at elevated Pi, the bypass model exhibited an increase of 73.1% and 33.9% in PGA and RuBP, respectively. Therefore, we deduce a synergistic effect of elevation in CO2 and Pi pool on photosynthesis. We also evaluated the integrative action of CO2, Pi, and Rubisco carboxylation activity (Vcmax) on A and observed that their simultaneous increase raised A by 26%, in the bypass model. Taken together, the study potentiates engineering of cyanobacterial decarboxylation pathway in C3 plants to bypass photorespiration thereby increasing the overall efficiency of photosynthesis.

Characterization of maximal enzyme catalytic rates in central metabolism of Arabidopsis thaliana

Availability of plant-specific enzyme kinetic data is scarce, limiting the predictive power of metabolic models and precluding identification of genetic factors of enzyme properties. Enzyme kinetic data are measured in vitro, often under non-physiological conditions, and conclusions elicited from modeling warrant caution. Here we estimate maximal in vivo catalytic rates for 168 plant enzymes, including photosystems I and II, cytochrome-b6f complex, ATP-citrate synthase, sucrose-phosphate synthase as well as enzymes from amino acid synthesis with previously undocumented enzyme kinetic data in BRENDA. The estimations are obtained by integrating condition-specific quantitative proteomics data, maximal rates of selected enzymes, growth measurements from Arabidopsis thaliana rosette with and fluxes through canonical pathways in a constraint-based model of leaf metabolism. In comparison to findings in Escherichia coli, we demonstrate weaker concordance between the plant-specific in vitro and in vivo enzyme catalytic rates due to a low degree of enzyme saturation. This is supported by the finding that concentrations of nicotinamide adenine dinucleotide (phosphate), adenosine triphosphate and uridine triphosphate, calculated based on our maximal in vivo catalytic rates, and available quantitative metabolomics data are below reported KM values and, therefore, indicate undersaturation of respective enzymes. Our findings show that genome-wide profiling of enzyme kinetic properties is feasible in plants, paving the way for understanding resource allocation.

An adjustable algal chloroplast plug-and-play model for genome-scale metabolic models

The chloroplast is a central part of plant cells, as this is the organelle where the photosynthesis, fixation of inorganic carbon, and other key functions related to fatty acid synthesis and amino acid synthesis occur. Since this organelle should be an integral part of any genome-scale metabolic model for a microalgae or a higher plant, it is of great interest to generate a detailed and standardized chloroplast model. Additionally, we see the need for a novel type of sub-model template, or organelle model, which could be incorporated into a larger, less specific genome-scale metabolic model, while allowing for minor differences between chloroplast-containing organisms. The result of this work is the very first standardized chloroplast model, iGR774, consisting of 788 reactions, 764 metabolites, and 774 genes. The model is currently able to run in three different modes, mimicking the chloroplast metabolism of three photosynthetic microalgae-Nannochloropsis gaditana, Chlamydomonas reinhardtii and Phaeodactylum tricornutum. In addition to developing the chloroplast metabolic network reconstruction, we have developed multiple software tools for working with this novel type of sub-model in the COBRA Toolbox for MATLAB, including tools for connecting the chloroplast model to a genome-scale metabolic reconstruction in need of a chloroplast, for switching the model between running in different organism modes, and for expanding it by introducing more reactions either related to one of the current organisms included in the model, or to a new organism.

Inference of chemical reaction networks based on concentration profiles using an optimization framework

Understanding the structure of reaction networks along with the underlying kinetics that lead to particular concentration readouts of the participating components is the first step toward optimization and control of (bio-)chemical processes. Yet, solutions to the problem of inferring the structure of reaction networks, i.e., characterizing the stoichiometry of the participating reactions provided concentration profiles of the participating components, remain elusive. Here, we present an approach to infer the stoichiometric subspace of a chemical reaction network from steady-state concentration data profiles obtained from a continuous isothermal reactor. The subsequent problem of finding reactions consistent with the observed subspace is cast as a series of mixed-integer linear programs whose solution generates potential reaction vectors together with a measure of their likelihood. We demonstrate the efficiency and applicability of the proposed approach using data obtained from synthetic reaction networks and from a well-established biological model for the Calvin-Benson cycle. Furthermore, we investigate the effect of missing information, in the form of unmeasured species or insufficient diversity within the data set, on the ability to accurately reconstruct the network reactions. The proposed framework is, in principle, applicable to many other reaction systems, thus providing future extensions to understanding reaction networks guiding chemical reactors and complex biological mixtures.

Relationship between irradiance and levels of Calvin-Benson cycle and other intermediates in the model eudicot Arabidopsis and the model monocot rice

Metabolite profiles provide a top-down overview of the balance between the reactions in a pathway. We compared Calvin-Benson cycle (CBC) intermediate profiles in different conditions in Arabidopsis (Arabidopsis thaliana) and rice (Oryza sativa) to learn which features of CBC regulation differ and which are shared between these model eudicot and monocot C3 species. Principal component analysis revealed that CBC intermediate profiles follow different trajectories in Arabidopsis and rice as irradiance increases. The balance between subprocesses or reactions differed, with 3-phosphoglycerate reduction being favoured in Arabidopsis and ribulose 1,5-bisphosphate regeneration in rice, and sedoheptulose-1,7-bisphosphatase being favoured in Arabidopsis compared with fructose-1,6-bisphosphatase in rice. Photosynthesis rates rose in parallel with ribulose 1,5-bisphosphate levels in Arabidopsis, but not in rice. Nevertheless, some responses were shared between Arabidopsis and rice. Fructose 1,6-bisphosphate and sedoheptulose-1,7-bisphosphate were high or peaked at very low irradiance in both species. Incomplete activation of fructose-1,6-bisphosphatase and sedoheptulose-1,7-bisphosphatase may prevent wasteful futile cycles in low irradiance. End-product synthesis is inhibited and high levels of CBC intermediates are maintained in low light or in low CO2 in both species. This may improve photosynthetic efficiency in fluctuating irradiance, and facilitate rapid CBC flux to support photorespiration and energy dissipation in low CO2.

Kinetic modeling of the Calvin cycle identifies flux control and stable metabolomes in Synechocystis carbon fixation

Biological fixation of atmospheric CO2 via the Calvin-Benson-Bassham cycle has massive ecological impact and offers potential for industrial exploitation, either by improving carbon fixation in plants and autotrophic bacteria, or by installation into new hosts. A kinetic model of the Calvin-Benson-Bassham cycle embedded in the central carbon metabolism of the cyanobacterium Synechocystis sp. PCC 6803 was developed to investigate its stability and underlying control mechanisms. To reduce the uncertainty associated with a single parameter set, random sampling of the steady-state metabolite concentrations and the enzyme kinetic parameters was employed, resulting in millions of parameterized models which were analyzed for flux control and stability against perturbation. Our results show that the Calvin cycle had an overall high intrinsic stability, but a high concentration of ribulose 1,5-bisphosphate was associated with unstable states. Low substrate saturation and high product saturation of enzymes involved in highly interconnected reactions correlated with increased network stability. Flux control, that is the effect that a change in one reaction rate has on the other reactions in the network, was distributed and mostly exerted by energy supply (ATP), but also by cofactor supply (NADPH). Sedoheptulose 1,7-bisphosphatase/fructose 1,6-bisphosphatase, fructose-bisphosphate aldolase, and transketolase had a weak but positive effect on overall network flux, in agreement with published observations. The identified flux control and relationships between metabolite concentrations and system stability can guide metabolic engineering. The kinetic model structure and parameterizing framework can be expanded for analysis of metabolic systems beyond the Calvin cycle.

Using a Multi-compartmental Metabolic Model to Predict Carbon Allocation in Arabidopsis thaliana

The molecular mechanism of loading/unloading of sucrose into/from the phloem plays an important role in sucrose translocation among plant tissues. Perturbation of this mechanism results in growth phenotypes of a plant. In order to better understand the coupling of sucrose translocation with metabolic processes a multi-compartmental metabolic network of Arabidopsis thaliana was reconstructed and optimized with respect to biomass growth, both in light and in dark conditions. The model can be used to perform flux balance analysis of metabolic fluxes through the central carbon metabolism and catabolic and anabolic pathways. Balances and turnover of energy (ATP/ADP) and redox metabolites (NAD(P)H/NAD(P)) as well as proton concentrations in different compartments can be estimated. Importantly, the model can be used to quantify the translocation of sucrose from source to sink tissues through phloem in association with an integral balance of protons, which in turn is defined by the operational modes of the energy metabolism (light and dark conditions). This chapter describes how a multi-compartmental model to predict carbon allocation is constructed and used.

Next-generation strategies for understanding and influencing source-sink relations in crop plants

Whether plants are source or sink limited, that is, whether carbon assimilation or rather assimilate usage is ultimately responsible for crop yield, has been the subject of intense debate over several decades. Here we provide a short review of this debate before focusing on the use of transgenic intervention as a means to influence yield by modifying either source or sink function (or both). Given the relatively low success rates of strategies targeting single genes we highlight the success of multi-target transformations. The emergence of whole plant models and the potential impact that these will have in aiding yield improvement strategies are then discussed. We end by providing our perspective for next generation strategies for improving crop plants by means of manipulating their source-sink relations.

Stoichiometric Correlation Analysis: Principles of Metabolic Functionality from Metabolomics Data

Recent advances in metabolomics technologies have resulted in high-quality (time-resolved) metabolic profiles with an increasing coverage of metabolic pathways. These data profiles represent read-outs from often non-linear dynamics of metabolic networks. Yet, metabolic profiles have largely been explored with regression-based approaches that only capture linear relationships, rendering it difficult to determine the extent to which the data reflect the underlying reaction rates and their couplings. Here we propose an approach termed Stoichiometric Correlation Analysis (SCA) based on correlation between positive linear combinations of log-transformed metabolic profiles. The log-transformation is due to the evidence that metabolic networks can be modeled by mass action law and kinetics derived from it. Unlike the existing approaches which establish a relation between pairs of metabolites, SCA facilitates the discovery of higher-order dependence between more than two metabolites. By using a paradigmatic model of the tricarboxylic acid cycle we show that the higher-order dependence reflects the coupling of concentration of reactant complexes, capturing the subtle difference between the employed enzyme kinetics. Using time-resolved metabolic profiles from Arabidopsis thaliana and Escherichia coli, we show that SCA can be used to quantify the difference in coupling of reactant complexes, and hence, reaction rates, underlying the stringent response in these model organisms. By using SCA with data from natural variation of wild and domesticated wheat and tomato accession, we demonstrate that the domestication is accompanied by loss of such couplings, in these species. Therefore, application of SCA to metabolomics data from natural variation in wild and domesticated populations provides a mechanistic way to understanding domestication and its relation to metabolic networks.

Metabolic model of central carbon and energy metabolisms of growing Arabidopsis thaliana in relation to sucrose translocation

BACKGROUND

Sucrose translocation between plant tissues is crucial for growth, development and reproduction of plants. Systemic analysis of these metabolic and underlying regulatory processes allow a detailed understanding of carbon distribution within the plant and the formation of associated phenotypic traits. Sucrose translocation from 'source' tissues (e.g. mesophyll) to 'sink' tissues (e.g. root) is tightly bound to the proton gradient across the membranes. The plant sucrose transporters are grouped into efflux exporters (SWEET family) and proton-symport importers (SUC, STP families). To better understand regulation of sucrose export from source tissues and sucrose import into sink tissues, there is a need for a metabolic model that takes in account the tissue organisation of Arabidopsis thaliana with corresponding metabolic specificities of respective tissues in terms of sucrose and proton production/utilization. An ability of the model to operate under different light modes ('light' and 'dark') and correspondingly in different energy producing modes is particularly important in understanding regulatory modules.

RESULTS

Here, we describe a multi-compartmental model consisting of a mesophyll cell with plastid and mitochondrion, a phloem cell, as well as a root cell with mitochondrion. In this model, the phloem was considered as a non-growing transport compartment, the mesophyll compartment was considered as both autotrophic (growing on CO₂ under light) and heterotrophic (growing on starch in darkness), and the root was always considered as heterotrophic tissue dependent on sucrose supply from the mesophyll compartment. In total, the model includes 413 balanced compounds interconnected by 400 transformers. The structured metabolic model accounts for central carbon metabolism, photosynthesis, photorespiration, carbohydrate metabolism, energy and redox metabolisms, proton metabolism, biomass growth, nutrients uptake, proton gradient generation and sucrose translocation between tissues. Biochemical processes in the model were associated with gene-products (742 ORFs). Flux Balance Analysis (FBA) of the model resulted in balanced carbon, nitrogen, proton, energy and redox states under both light and dark conditions. The main H⁺-fluxes were reconstructed and their directions matched with proton-dependent sucrose translocation from 'source' to 'sink' under any light condition.

CONCLUSIONS

The model quantified the translocation of sucrose between plant tissues in association with an integral balance of protons, which in turn is defined by operational modes of the energy metabolism.

Current state and challenges for dynamic metabolic modeling

While the stoichiometry of metabolism is probably the best studied cellular level, the dynamics in metabolism can still not be well described, predicted and, thus, engineered. Unknowns in the metabolic flux behavior arise from kinetic interactions, especially allosteric control mechanisms. While the stoichiometry of enzymes is preserved in vitro, their activity and kinetic behavior differs from the in vivo situation. Next to this challenge, it is infeasible to test the interaction of each enzyme with each intracellular metabolite in vitro exhaustively. As a consequence, the whole interacting metabolome has to be studied in vivo to identify the relevant enzymes properties. In this review we discuss current approaches for in vivo perturbation experiments, that is, stimulus response experiments using different setups and quantitative analytical approaches, including dynamic carbon tracing. Next to reliable and informative data, advanced modeling approaches and computational tools are required to identify kinetic mechanisms and their parameters.

SBMLsqueezer 2: context-sensitive creation of kinetic equations in biochemical networks

BACKGROUND

The size and complexity of published biochemical network reconstructions are steadily increasing, expanding the potential scale of derived computational models. However, the construction of large biochemical network models is a laborious and error-prone task. Automated methods have simplified the network reconstruction process, but building kinetic models for these systems is still a manually intensive task. Appropriate kinetic equations, based upon reaction rate laws, must be constructed and parameterized for each reaction. The complex test-and-evaluation cycles that can be involved during kinetic model construction would thus benefit from automated methods for rate law assignment.

RESULTS

We present a high-throughput algorithm to automatically suggest and create suitable rate laws based upon reaction type according to several criteria. The criteria for choices made by the algorithm can be influenced in order to assign the desired type of rate law to each reaction. This algorithm is implemented in the software package SBMLsqueezer 2. In addition, this program contains an integrated connection to the kinetics database SABIO-RK to obtain experimentally-derived rate laws when desired.

CONCLUSIONS

The described approach fills a heretofore absent niche in workflows for large-scale biochemical kinetic model construction. In several applications the algorithm has already been demonstrated to be useful and scalable. SBMLsqueezer is platform independent and can be used as a stand-alone package, as an integrated plugin, or through a web interface, enabling flexible solutions and use-case scenarios.

Mathematical modelling of the diurnal regulation of the MEP pathway in Arabidopsis

Isoprenoid molecules are essential elements of plant metabolism. Many important plant isoprenoids, such as chlorophylls, carotenoids, tocopherols, prenylated quinones and hormones are synthesised in chloroplasts via the 2-C-methyl-d-erythritol 4-phosphate (MEP) pathway. Here we develop a mathematical model of diurnal regulation of the MEP pathway in Arabidopsis thaliana. We used both experimental and theoretical approaches to integrate mechanisms potentially involved in the diurnal control of the pathway. Our data show that flux through the MEP pathway is accelerated in light due to the photosynthesis-dependent supply of metabolic substrates of the pathway and the transcriptional regulation of key biosynthetic genes by the circadian clock. We also demonstrate that feedback regulation of both the activity and the abundance of the first enzyme of the MEP pathway (1-deoxy-D-xylulose 5-phosphate synthase, DXS) by pathway products stabilizes the flux against changes in substrate supply and adjusts the flux according to product demand under normal growth conditions. These data illustrate the central relevance of photosynthesis, the circadian clock and feedback control of DXS for the diurnal regulation of the MEP pathway.

Computer modeling of electron and proton transport in chloroplasts

Photosynthesis is one of the most important biological processes in biosphere, which provides production of organic substances from atmospheric CO2 and water at expense of solar energy. In this review, we contemplate computer models of oxygenic photosynthesis in the context of feedback regulation of photosynthetic electron transport in chloroplasts, the energy-transducing organelles of the plant cell. We start with a brief overview of electron and proton transport processes in chloroplasts coupled to ATP synthesis and consider basic regulatory mechanisms of oxygenic photosynthesis. General approaches to computer simulation of photosynthetic processes are considered, including the random walk models of plastoquinone diffusion in thylakoid membranes and deterministic approach to modeling electron transport in chloroplasts based on the mass action law. Then we focus on a kinetic model of oxygenic photosynthesis that includes key stages of the linear electron transport, alternative pathways of electron transfer around photosystem I (PSI), transmembrane proton transport and ATP synthesis in chloroplasts. This model includes different regulatory processes: pH-dependent control of the intersystem electron transport, down-regulation of photosystem II (PSII) activity (non-photochemical quenching), the light-induced activation of the Bassham-Benson-Calvin (BBC) cycle. The model correctly describes pH-dependent feedback control of electron transport in chloroplasts and adequately reproduces a variety of experimental data on induction events observed under different experimental conditions in intact chloroplasts (variations of CO2 and O2 concentrations in atmosphere), including a complex kinetics of P700 (primary electron donor in PSI) photooxidation, CO2 consumption in the BBC cycle, and photorespiration. Finally, we describe diffusion-controlled photosynthetic processes in chloroplasts within the framework of the model that takes into account complex architecture of chloroplasts and lateral heterogeneity of lamellar system of thylakoids. The lateral profiles of pH in the thylakoid lumen and in the narrow gap between grana thylakoids have been calculated under different metabolic conditions. Analyzing topological aspects of diffusion-controlled stages of electron and proton transport in chloroplasts, we conclude that along with the NPQ mechanism of attenuation of PSII activity and deceleration of PQH2 oxidation by the cytochrome b6f complex caused by the lumen acidification, the intersystem electron transport may be down-regulated due to the light-induced alkalization of the narrow partition between adjacent thylakoids of grana. The computer models of electron and proton transport described in this article may be integrated as appropriate modules into a comprehensive model of oxygenic photosynthesis.

Why measure enzyme activities in the era of systems biology?

Information about the abundance and biological activities of proteins is essential to reveal how genes affect phenotypes. Over the past decade, mass spectrometry (MS)-based proteomics has revolutionized the identification and quantification of proteins, and the detection of post-translational modifications. Interpretation of proteomics data depends on information about the biological activities of proteins, which has created a bottleneck in research. This review focuses on enzymes in central metabolism. We examine the methods used for measuring enzyme activities, and discuss how these methods provide information about the kinetic and regulatory properties of enzymes, their turnover, and how this information can be integrated into metabolic models. We also discuss how robotized assays could enable the genetic networks that control enzyme abundance to be analyzed.

Structural control of metabolic flux

Organisms have to continuously adapt to changing environmental conditions or undergo developmental transitions. To meet the accompanying change in metabolic demands, the molecular mechanisms of adaptation involve concerted interactions which ultimately induce a modification of the metabolic state, which is characterized by reaction fluxes and metabolite concentrations. These state transitions are the effect of simultaneously manipulating fluxes through several reactions. While metabolic control analysis has provided a powerful framework for elucidating the principles governing this orchestrated action to understand metabolic control, its applications are restricted by the limited availability of kinetic information. Here, we introduce structural metabolic control as a framework to examine individual reactions' potential to control metabolic functions, such as biomass production, based on structural modeling. The capability to carry out a metabolic function is determined using flux balance analysis (FBA). We examine structural metabolic control on the example of the central carbon metabolism of Escherichia coli by the recently introduced framework of functional centrality (FC). This framework is based on the Shapley value from cooperative game theory and FBA, and we demonstrate its superior ability to assign “share of control” to individual reactions with respect to metabolic functions and environmental conditions. A comparative analysis of various scenarios illustrates the usefulness of FC and its relations to other structural approaches pertaining to metabolic control. We propose a Monte Carlo algorithm to estimate FCs for large networks, based on the enumeration of elementary flux modes. We further give detailed biological interpretation of FCs for production of lactate and ATP under various respiratory conditions.

Insight into the functioning of metabolic control to meet changing demands is a first step in rational engineering of biological systems towards a desired behavior. Metabolic control analysis provides the means to examine the impact of change of reaction fluxes on a specific target flux based on kinetic modeling, but suffers from limitations of the kinetic approach. Here, we introduce and analyze structural metabolic control as a framework to overcome these limitations. We utilize functional centrality, a framework based on the Shapley value from cooperative game theory and flux balance analysis, to determine the contribution of individual reactions to the functions accomplished by a metabolic network. These contributions, in turn, depend on the control exerted on the remaining network. Functional centrality provides the mathematical means to gain further understanding of metabolic control. The potential applications range from facilitating strategies of rational strain design to drug target identification.

Optimization of photosynthesis by multiple metabolic pathways involving interorganelle interactions: resource sharing and ROS maintenance as the bases

The bioenergetic processes of photosynthesis and respiration are mutually beneficial. Their interaction extends to photorespiration, which is linked to optimize photosynthesis. The interplay of these three pathways is facilitated by two major phenomena: sharing of energy/metabolite resources and maintenance of optimal levels of reactive oxygen species (ROS). The resource sharing among different compartments of plant cells is based on the production/utilization of reducing equivalents (NADPH, NADH) and ATP as well as on the metabolite exchange. The responsibility of generating the cellular requirements of ATP and NAD(P)H is mostly by the chloroplasts and mitochondria. In turn, besides the chloroplasts, the mitochondria, cytosol and peroxisomes are common sinks for reduced equivalents. Transporters located in membranes ensure the coordinated movement of metabolites across the cellular compartments. The present review emphasizes the beneficial interactions among photosynthesis, dark respiration and photorespiration, in relation to metabolism of C, N and S. Since the bioenergetic reactions tend to generate ROS, the cells modulate chloroplast and mitochondrial reactions, so as to ensure that the ROS levels do not rise to toxic levels. The patterns of minimization of ROS production and scavenging of excess ROS in intracellular compartments are highlighted. Some of the emerging developments are pointed out, such as model plants, orientation/movement of organelles and metabolomics.

The systems biology simulation core algorithm

BACKGROUND

With the increasing availability of high dimensional time course data for metabolites, genes, and fluxes, the mathematical description of dynamical systems has become an essential aspect of research in systems biology. Models are often encoded in formats such as SBML, whose structure is very complex and difficult to evaluate due to many special cases.

RESULTS

This article describes an efficient algorithm to solve SBML models that are interpreted in terms of ordinary differential equations. We begin our consideration with a formal representation of the mathematical form of the models and explain all parts of the algorithm in detail, including several preprocessing steps. We provide a flexible reference implementation as part of the Systems Biology Simulation Core Library, a community-driven project providing a large collection of numerical solvers and a sophisticated interface hierarchy for the definition of custom differential equation systems. To demonstrate the capabilities of the new algorithm, it has been tested with the entire SBML Test Suite and all models of BioModels Database.

CONCLUSIONS

The formal description of the mathematics behind the SBML format facilitates the implementation of the algorithm within specifically tailored programs. The reference implementation can be used as a simulation backend for Java™-based programs. Source code, binaries, and documentation can be freely obtained under the terms of the LGPL version 3 from http://simulation-core.sourceforge.net. Feature requests, bug reports, contributions, or any further discussion can be directed to the mailing list simulation-core-development@lists.sourceforge.net.

Comprehensive classification and perspective for modelling photorespiratory metabolism

Biological processes involved in photorespiratory and photosynthetic metabolism operate concurrently and affect the interplay between carbon and nitrogen assimilation reflected in plant growth. Experimental evidence has indicated that photorespiratory metabolism has a wide-ranging influence not only on other principal metabolic pathways but also on a multitude of signalling cascades. Therefore, accurate quantitative models of photorespiration can provide a means for predicting and in silico probing of plant behaviour at various levels of the system. We first present a comprehensive classification of current models of photorespiratory metabolism developed within the existing carbon-centric modelling paradigm. We then offer a perspective for modelling photorespiratory metabolism by considering the coupling of carbon and nitrogen metabolism in the context of compartmentalised, genome-scale metabolic models of C3 plants. In addition, we outline the challenges stemming from the need to consider plant metabolic and signalling pathways in assessing the still controversial role of photorespiration and to confront the devised models with the ever-increasing amounts of high-throughput data.

Systematic analysis of stability patterns in plant primary metabolism

Metabolic networks are characterized by complex interactions and regulatory mechanisms between many individual components. These interactions determine whether a steady state is stable to perturbations. Structural kinetic modeling (SKM) is a framework to analyze the stability of metabolic steady states that allows the study of the system Jacobian without requiring detailed knowledge about individual rate equations. Stability criteria can be derived by generating a large number of structural kinetic models (SK-models) with randomly sampled parameter sets and evaluating the resulting Jacobian matrices. Until now, SKM experiments applied univariate tests to detect the network components with the largest influence on stability. In this work, we present an extended SKM approach relying on supervised machine learning to detect patterns of enzyme-metabolite interactions that act together in an orchestrated manner to ensure stability. We demonstrate its application on a detailed SK-model of the Calvin-Benson cycle and connected pathways. The identified stability patterns are highly complex reflecting that changes in dynamic properties depend on concerted interactions between several network components. In total, we find more patterns that reliably ensure stability than patterns ensuring instability. This shows that the design of this system is strongly targeted towards maintaining stability. We also investigate the effect of allosteric regulators revealing that the tendency to stability is significantly increased by including experimentally determined regulatory mechanisms that have not yet been integrated into existing kinetic models.

Dynamic regulatory on/off minimization for biological systems under internal temporal perturbations

Background

Flux balance analysis (FBA) together with its extension, dynamic FBA, have proven instrumental for analyzing the robustness and dynamics of metabolic networks by employing only the stoichiometry of the included reactions coupled with adequately chosen objective function. In addition, under the assumption of minimization of metabolic adjustment, dynamic FBA has recently been employed to analyze the transition between metabolic states.

Results

Here, we propose a suite of novel methods for analyzing the dynamics of (internally perturbed) metabolic networks and for quantifying their robustness with limited knowledge of kinetic parameters. Following the biochemically meaningful premise that metabolite concentrations exhibit smooth temporal changes, the proposed methods rely on minimizing the significant fluctuations of metabolic profiles to predict the time-resolved metabolic state, characterized by both fluxes and concentrations. By conducting a comparative analysis with a kinetic model of the Calvin-Benson cycle and a model of plant carbohydrate metabolism, we demonstrate that the principle of regulatory on/off minimization coupled with dynamic FBA can accurately predict the changes in metabolic states.

Conclusions

Our methods outperform the existing dynamic FBA-based modeling alternatives, and could help in revealing the mechanisms for maintaining robustness of dynamic processes in metabolic networks over time.

Kinetic modelling of plant metabolic pathways

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.