A simulation-free constrained regression approach for flux estimation in isotopically nonstationary metabolic flux analysis with applications in microalgae.

Introduction: Flux phenotypes from different organisms and growth conditions allow better understanding of differential metabolic networks functions. Fluxes of metabolic reactions represent the integrated outcome of transcription, translation, and post-translational modifications, and directly affect growth and fitness. However, fluxes of intracellular metabolic reactions cannot be directly measured, but are estimated via metabolic flux analysis (MFA) that integrates data on isotope labeling patterns of metabolites with metabolic models. While the application of metabolomics technologies in photosynthetic organisms have resulted in unprecedented data from 13CO2-labeling experiments, the bottleneck in flux estimation remains the application of isotopically nonstationary MFA (INST-MFA). INST-MFA entails fitting a (large) system of coupled ordinary differential equations, with metabolite pools and reaction fluxes as parameters. Here, we focus on the Calvin-Benson cycle (CBC) as a key pathway for carbon fixation in photosynthesizing organisms and ask if approaches other than classical INST-MFA can provide reliable estimation of fluxes for reactions comprising this pathway. Methods: First, we show that flux estimation with the labeling patterns of all CBC intermediates can be formulated as a single constrained regression problem, avoiding the need for repeated simulation of time-resolved labeling patterns. Results: We then compare the flux estimates of the simulation-free constrained regression approach with those obtained from the classical INST-MFA based on labeling patterns of metabolites from the microalgae Chlamydomonas reinhardtii, Chlorella sorokiniana and Chlorella ohadii under different growth conditions. Discussion: Our findings indicate that, in data-rich scenarios, simulation-free regression-based approaches provide a suitable alternative for flux estimation from classical INST-MFA since we observe a high qualitative agreement (rs=0.89) to predictions obtained from INCA, a state-of-the-art tool for INST-MFA.

The effective deficiency of biochemical networks.

The deficiency of a (bio)chemical reaction network can be conceptually interpreted as a measure of its ability to support exotic dynamical behavior and/or multistationarity. The classical definition of deficiency relates to the capacity of a network to permit variations of the complex formation rate vector at steady state, irrespective of the network kinetics. However, the deficiency is by definition completely insensitive to the fine details of the directionality of reactions as well as bounds on reaction fluxes. While the classical definition of deficiency can be readily applied in the analysis of unconstrained, weakly reversible networks, it only provides an upper bound in the cases where relevant constraints on reaction fluxes are imposed. Here we propose the concept of effective deficiency, which provides a more accurate assessment of the network's capacity to permit steady state variations at the complex level for constrained networks of any reversibility patterns. The effective deficiency relies on the concept of nonstoichiometric balanced complexes, which we have already shown to be present in real-world biochemical networks operating under flux constraints. Our results demonstrate that the effective deficiency of real-world biochemical networks is smaller than the classical deficiency, indicating the effects of reaction directionality and flux bounds on the variation of the complex formation rate vector at steady state.

The unraveling of balanced complexes in metabolic networks.

Balanced complexes in biochemical networks are at core of several theoretical and computational approaches that make statements about the properties of the steady states supported by the network. Recent computational approaches have employed balanced complexes to reduce metabolic networks, while ensuring preservation of particular steady-state properties; however, the underlying factors leading to the formation of balanced complexes have not been studied, yet. Here, we present a number of factorizations providing insights in mechanisms that lead to the origins of the corresponding balanced complexes. The proposed factorizations enable us to categorize balanced complexes into four distinct classes, each with specific origins and characteristics. They also provide the means to efficiently determine if a balanced complex in large-scale networks belongs to a particular class from the categorization. The results are obtained under very general conditions and irrespective of the network kinetics, rendering them broadly applicable across variety of network models. Application of the categorization shows that all classes of balanced complexes are present in large-scale metabolic models across all kingdoms of life, therefore paving the way to study their relevance with respect to different properties of steady states supported by these networks.

Light-independent regulation of algal photoprotection by CO2 availability.

Photosynthetic algae have evolved mechanisms to cope with suboptimal light and CO2 conditions. When light energy exceeds CO2 fixation capacity, Chlamydomonas reinhardtii activates photoprotection, mediated by LHCSR1/3 and PSBS, and the CO2 Concentrating Mechanism (CCM). How light and CO2 signals converge to regulate these processes remains unclear. Here, we show that excess light activates photoprotection- and CCM-related genes by altering intracellular CO2 concentrations and that depletion of CO2 drives these responses, even in total darkness. High CO2 levels, derived from respiration or impaired photosynthetic fixation, repress LHCSR3/CCM genes while stabilizing the LHCSR1 protein. Finally, we show that the CCM regulator CIA5 also regulates photoprotection, controlling LHCSR3 and PSBS transcript accumulation while inhibiting LHCSR1 protein accumulation. This work has allowed us to dissect the effect of CO2 and light on CCM and photoprotection, demonstrating that light often indirectly affects these processes by impacting intracellular CO2 levels.

The hidden simplicity of metabolic networks is revealed by multireaction dependencies.

Understanding the complexity of metabolic networks has implications for manipulation of their functions. The complexity of metabolic networks can be characterized by identifying multireaction dependencies that are challenging to determine due to the sheer number of combinations to consider. Here, we propose the concept of concordant complexes that captures multireaction dependencies and can be efficiently determined from the algebraic structure and operational constraints of metabolic networks. The concordant complexes imply the existence of concordance modules based on which the apparent complexity of 12 metabolic networks of organisms from all kingdoms of life can be reduced by at least 78%. A comparative analysis against an ensemble of randomized metabolic networks shows that the metabolic network of Escherichia coli contains fewer concordance modules and is, therefore, more tightly coordinated than expected by chance. Together, our findings demonstrate that metabolic networks are considerably simpler than what can be perceived from their structure alone.

Carbon flux through photosynthesis and central carbon metabolism show distinct patterns between algae, C3 and C4 plants.

Photosynthesis-related pathways are regarded as a promising avenue for crop improvement. Whilst empirical studies have shown that photosynthetic efficiency is higher in microalgae than in C3 or C4 crops, the underlying reasons remain unclear. Using a tailor-made microfluidics labelling system to supply 13CO2 at steady state, we investigated in vivo labelling kinetics in intermediates of the Calvin Benson cycle and sugar, starch, organic acid and amino acid synthesis pathways, and in protein and lipids, in Chlamydomonas reinhardtii, Chlorella sorokiniana and Chlorella ohadii, which is the fastest growing green alga on record. We estimated flux patterns in these algae and compared them with published and new data from C3 and C4 plants. Our analyses identify distinct flux patterns supporting faster growth in photosynthetic cells, with some of the algae exhibiting faster ribulose 1,5-bisphosphate regeneration and increased fluxes through the lower glycolysis and anaplerotic pathways towards the tricarboxylic acid cycle, amino acid synthesis and lipid synthesis than in higher plants.

A structural property for reduction of biochemical networks.

Large-scale biochemical models are of increasing sizes due to the consideration of interacting organisms and tissues. Model reduction approaches that preserve the flux phenotypes can simplify the analysis and predictions of steady-state metabolic phenotypes. However, existing approaches either restrict functionality of reduced models or do not lead to significant decreases in the number of modelled metabolites. Here, we introduce an approach for model reduction based on the structural property of balancing of complexes that preserves the steady-state fluxes supported by the network and can be efficiently determined at genome scale. Using two large-scale mass-action kinetic models of Escherichia coli, we show that our approach results in a substantial reduction of 99% of metabolites. Applications to genome-scale metabolic models across kingdoms of life result in up to 55% and 85% reduction in the number of metabolites when arbitrary and mass-action kinetics is assumed, respectively. We also show that predictions of the specific growth rate from the reduced models match those based on the original models. Since steady-state flux phenotypes from the original model are preserved in the reduced, the approach paves the way for analysing other metabolic phenotypes in large-scale biochemical networks.

Characterization of effects of genetic variants via genome-scale metabolic modelling.

Genome-scale metabolic networks for model plants and crops in combination with approaches from the constraint-based modelling framework have been used to predict metabolic traits and design metabolic engineering strategies for their manipulation. With the advances in technologies to generate large-scale genotyping data from natural diversity panels and other populations, genome-wide association and genomic selection have emerged as statistical approaches to determine genetic variants associated with and predictive of traits. Here, we review recent advances in constraint-based approaches that integrate genetic variants in genome-scale metabolic models to characterize their effects on reaction fluxes. Since some of these approaches have been applied in organisms other than plants, we provide a critical assessment of their applicability particularly in crops. In addition, we further dissect the inferred effects of genetic variants with respect to reaction rate constants, abundances of enzymes, and concentrations of metabolites, as main determinants of reaction fluxes and relate them with their combined effects on complex traits, like growth. Through this systematic review, we also provide a roadmap for future research to increase the predictive power of statistical approaches by coupling them with mechanistic models of metabolism.

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.

Integrating molecular markers into metabolic models improves genomic selection for Arabidopsis growth.

The current trends of crop yield improvements are not expected to meet the projected rise in demand. Genomic selection uses molecular markers and machine learning to identify superior genotypes with improved traits, such as growth. Plant growth directly depends on rates of metabolic reactions which transform nutrients into the building blocks of biomass. Here, we predict growth of Arabidopsis thaliana accessions by employing genomic prediction of reaction rates estimated from accession-specific metabolic models. We demonstrate that, comparing to classical genomic selection on the available data sets for 67 accessions, our approach improves the prediction accuracy for growth within and across nitrogen environments by 32.6% and 51.4%, respectively, and from optimal nitrogen to low carbon environment by 50.4%. Therefore, integration of molecular markers into metabolic models offers an approach to predict traits directly related to metabolism, and its usefulness in breeding can be examined by gathering matching datasets in crops.

Cellular determinants of metabolite concentration ranges.

Cellular functions are shaped by reaction networks whose dynamics are determined by the concentrations of underlying components. However, cellular mechanisms ensuring that a component's concentration resides in a given range remain elusive. We present network properties which suffice to identify components whose concentration ranges can be efficiently computed in mass-action metabolic networks. We show that the derived ranges are in excellent agreement with simulations from a detailed kinetic metabolic model of Escherichia coli. We demonstrate that the approach can be used with genome-scale metabolic models to arrive at predictions concordant with measurements from Escherichia coli under different growth scenarios. By application to 14 genome-scale metabolic models from diverse species, our approach specifies the cellular determinants of concentration ranges that can be effectively employed to make predictions for a variety of biotechnological and medical applications.

Computational Approaches to Design and Test Plant Synthetic Metabolic Pathways.

Successfully designed and implemented plant-specific synthetic metabolic pathways hold promise to increase crop yield and nutritional value. Advances in synthetic biology have already demonstrated the capacity to design artificial biological pathways whose behavior can be predicted and controlled in microbial systems. However, the transfer of these advances to model plants and crops faces the lack of characterization of plant cellular pathways and increased complexity due to compartmentalization and multicellularity. Modern computational developments provide the means to test the feasibility of plant synthetic metabolic pathways despite gaps in the accumulated knowledge of plant metabolism. Here, we provide a succinct systematic review of optimization-based and retrobiosynthesis approaches that can be used to design and in silico test synthetic metabolic pathways in large-scale plant context-specific metabolic models. In addition, by surveying the existing case studies, we highlight the challenges that these approaches face when applied to plants. Emphasis is placed on understanding the effect that metabolic designs can have on native metabolism, particularly with respect to metabolite concentrations and thermodynamics of biochemical reactions. In addition, we discuss the computational developments that may help to transform the identified challenges into opportunities for plant synthetic biology.

Effects of microcompartmentation on flux distribution and metabolic pools in Chlamydomonas reinhardtii chloroplasts.

Cells and organelles are not homogeneous but include microcompartments that alter the spatiotemporal characteristics of cellular processes. The effects of microcompartmentation on metabolic pathways are however difficult to study experimentally. The pyrenoid is a microcompartment that is essential for a carbon concentrating mechanism (CCM) that improves the photosynthetic performance of eukaryotic algae. Using Chlamydomonas reinhardtii, we obtained experimental data on photosynthesis, metabolites, and proteins in CCM-induced and CCM-suppressed cells. We then employed a computational strategy to estimate how fluxes through the Calvin-Benson cycle are compartmented between the pyrenoid and the stroma. Our model predicts that ribulose-1,5-bisphosphate (RuBP), the substrate of Rubisco, and 3-phosphoglycerate (3PGA), its product, diffuse in and out of the pyrenoid, respectively, with higher fluxes in CCM-induced cells. It also indicates that there is no major diffusional barrier to metabolic flux between the pyrenoid and stroma. Our computational approach represents a stepping stone to understanding microcompartmentalized CCM in other organisms.

Genome-Scale Modeling of Photorespiratory Pathway Manipulation.

Quantifying the redistribution of metabolic reaction fluxes under experimental scenarios that affect the photorespiratory pathway can provide insights about the coupling of this pathway with other parts of metabolism. However, differential flux profiling on a genome-scale level remains the biggest challenge in modern systems biology. Here we present a protocol for applying a constraint-based approach, termed iReMet-Flux, that integrates data about relative metabolite levels in a stoichiometric metabolic model to predict differential fluxes at a genome-scale level under mild modeling assumptions. We demonstrate how iReMet-Flux can be employed to investigate the interplay between photorespiration and other pathways at a genome-scale level, and complements flux profiling methods based on radioactive tracer labeling.

A network property necessary for concentration robustness.

Maintenance of functionality of complex cellular networks and entire organisms exposed to environmental perturbations often depends on concentration robustness of the underlying components. Yet, the reasons and consequences of concentration robustness in large-scale cellular networks remain largely unknown. Here, we derive a necessary condition for concentration robustness based only on the structure of networks endowed with mass action kinetics. The structural condition can be used to design targeted experiments to study concentration robustness. We show that metabolites satisfying the necessary condition are present in metabolic networks from diverse species, suggesting prevalence of this property across kingdoms of life. We also demonstrate that our predictions about concentration robustness of energy-related metabolites are in line with experimental evidence from Escherichia coli. The necessary condition is applicable to mass action biological systems of arbitrary size, and will enable understanding the implications of concentration robustness in genetic engineering strategies and medical applications.

Observability of Plant Metabolic Networks Is Reflected in the Correlation of Metabolic Profiles.

Understanding whether the functionality of a biological system can be characterized by measuring few selected components is key to targeted phenotyping techniques in systems biology. Methods from observability theory have proven useful in identifying sensor components that have to be measured to obtain information about the entire system. Yet, the extent to which the data profiles reflect the role of components in the observability of the system remains unexplored. Here we first identify the sensor metabolites in the model plant Arabidopsis (Arabidopsis thaliana) by employing state-of-the-art genome-scale metabolic networks. By using metabolic data profiles from a set of seven environmental perturbations as well as from natural variability, we demonstrate that the data profiles of sensor metabolites are more correlated than those of nonsensor metabolites. This pattern was confirmed with in silico generated metabolic profiles from a medium-size kinetic model of plant central carbon metabolism. Altogether, due to the small number of identified sensors, our study implies that targeted metabolite analyses may provide the vast majority of relevant information about plant metabolic systems.

Photorespiratory Bypasses Lead to Increased Growth in Arabidopsis thaliana: Are Predictions Consistent with Experimental Evidence?

Arguably, the biggest challenge of modern plant systems biology lies in predicting the performance of plant species, and crops in particular, upon different intracellular and external perturbations. Recently, an increased growth of Arabidopsis thaliana plants was achieved by introducing two different photorespiratory bypasses via metabolic engineering. Here, we investigate the extent to which these findings match the predictions from constraint-based modeling. To determine the effect of the employed metabolic network model on the predictions, we perform a comparative analysis involving three state-of-the-art metabolic reconstructions of A. thaliana. In addition, we investigate three scenarios with respect to experimental findings on the ratios of the carboxylation and oxygenation reactions of Ribulose-1,5-bisphosphate carboxylase/oxygenase (RuBisCO). We demonstrate that the condition-dependent growth phenotypes of one of the engineered bypasses can be qualitatively reproduced by each reconstruction, particularly upon considering the additional constraints with respect to the ratio of fluxes for the RuBisCO reactions. Moreover, our results lend support for the hypothesis of a reduced photorespiration in the engineered plants, and indicate that specific changes in CO2 exchange as well as in the proxies for co-factor turnover are associated with the predicted growth increase in the engineered plants. We discuss our findings with respect to the structure of the used models, the modeling approaches taken, and the available experimental evidence. Our study sets the ground for investigating other strategies for increase of plant biomass by insertion of synthetic reactions.