Mathematical modeling of plant metabolism-from reconstruction to prediction

Metabolomics: a systems biology approach for enhancing heat stress tolerance in plants

Comprehensive metabolomic investigations provide a large set of stress-related metabolites and metabolic pathways, advancing crops under heat stress conditions. Metabolomics-assisted breeding, including mQTL and mGWAS boosted our understanding of improving numerous quantitative traits under heat stress. During the past decade, metabolomics has emerged as a fascinating scientific field that includes documentation, evaluation of metabolites, and chemical methods for cell monitoring programs in numerous plant species. A comprehensive metabolome profiling allowed the investigator to handle the comprehensive data groups of metabolites and the equivalent metabolic pathways in an extraordinary manner. Metabolomics, together with transcriptomics, plays an influential role in discovering connections between stress and genes/metabolite, phenotyping, and biomarkers documentation. Further, it helps to decode several metabolic systems connected with heat stress (HS) tolerance in plants. Heat stress is a critical environmental factor that is globally affecting the growth and productivity of plants. Thus, there is an urgent need to exploit modern breeding and biotechnological tools like metabolomics to develop cultivars with improved HS tolerance. Several studies have reported that amino acids, carbohydrates, nitrogen metabolisms, etc. and metabolites involved in the biosynthesis and catalyzing actions play a game-changing role in HS response and help plants to cope with the HS. The use of metabolomics-assisted breeding (MAB) allows a well-organized transmission of higher yield and HS tolerance at the metabolome level with specific properties. Progressive metabolomics systematic techniques have accelerated metabolic profiling. Nonetheless, continuous developments in bioinformatics, statistical tools, and databases are allowing us to produce ever-progressing, comprehensive insights into the biochemical configuration of plants and by what means this is inclined by genetic and environmental cues. Currently, assimilating metabolomics with post-genomic platforms has allowed a significant division of genetic-phenotypic connotation in several plant species. This review highlights the potential of a state-of-the-art plant metabolomics approach for the improvement of crops under HS. The development of plants with specific properties using integrated omics (metabolomics and transcriptomics) and MAB can provide new directions for future research to enhance HS tolerance in plants to achieve a goal of "zero hunger".

Multiscale computational models can guide experimentation and targeted measurements for crop improvement

Computational models of plants have identified gaps in our understanding of biological systems, and have revealed ways to optimize cellular processes or organ-level architecture to increase productivity. Thus, computational models are learning tools that help direct experimentation and measurements. Models are simplifications of complex systems, and often simulate specific processes at single scales (e.g. temporal, spatial, organizational, etc.). Consequently, single-scale models are unable to capture the critical cross-scale interactions that result in emergent properties of the system. In this perspective article, we contend that to accurately predict how a plant will respond in an untested environment, it is necessary to integrate mathematical models across biological scales. Computationally mimicking the flow of biological information from the genome to the phenome is an important step in discovering new experimental strategies to improve crops. A key challenge is to connect models across biological, temporal and computational (e.g. CPU versus GPU) scales, and then to visualize and interpret integrated model outputs. We address this challenge by describing the efforts of the international Crops in silico consortium.

PlantSEED enables automated annotation and reconstruction of plant primary metabolism with improved compartmentalization and comparative consistency

Genome-scale metabolic reconstructions help us to understand and engineer metabolism. Next-generation sequencing technologies are delivering genomes and transcriptomes for an ever-widening range of plants. While such omic data can, in principle, be used to compare metabolic reconstructions in different species, organs and environmental conditions, these comparisons require a standardized framework for the reconstruction of metabolic networks from transcript data. We previously introduced PlantSEED as a framework covering primary metabolism for 10 species. We have now expanded PlantSEED to include 39 species and provide tools that enable automated annotation and metabolic reconstruction from transcriptome data. The algorithm for automated annotation in PlantSEED propagates annotations using a set of signature k-mers (short amino acid sequences characteristic of particular proteins) that identify metabolic enzymes with an accuracy of about 97%. PlantSEED reconstructions are built from a curated template that includes consistent compartmentalization for more than 100 primary metabolic subsystems. Together, the annotation and reconstruction algorithms produce reconstructions without gaps and with more accurate compartmentalization than existing resources. These tools are available via the PlantSEED web interface at http://modelseed.org, which enables users to upload, annotate and reconstruct from private transcript data and simulate metabolic activity under various conditions using flux balance analysis. We demonstrate the ability to compare these metabolic reconstructions with a case study involving growth on several nitrogen sources in roots of four species.

A Strategy for Functional Interpretation of Metabolomic Time Series Data in Context of Metabolic Network Information

The functional connection of experimental metabolic time series data with biochemical network information is an important, yet complex, issue in systems biology. Frequently, experimental analysis of diurnal, circadian, or developmental dynamics of metabolism results in a comprehensive and multidimensional data matrix comprising information about metabolite concentrations, protein levels, and/or enzyme activities. While, irrespective of the type of organism, the experimental high-throughput analysis of the transcriptome, proteome, and metabolome has become a common part of many systems biological studies, functional data integration in a biochemical and physiological context is still challenging. Here, an approach is presented which addresses the functional connection of experimental time series data with biochemical network information which can be inferred, for example, from a metabolic network reconstruction. Based on a time-continuous and variance-weighted regression analysis of experimental data, metabolic functions, i.e., first-order derivatives of metabolite concentrations, were related to time-dependent changes in other biochemically relevant metabolic functions, i.e., second-order derivatives of metabolite concentrations. This finally revealed time points of perturbed dependencies in metabolic functions indicating a modified biochemical interaction. The approach was validated using previously published experimental data on a diurnal time course of metabolite levels, enzyme activities, and metabolic flux simulations. To support and ease the presented approach of functional time series analysis, a graphical user interface including a test data set and a manual is provided which can be run within the numerical software environment Matlab®.

A Method of Accounting for Enzyme Costs in Flux Balance Analysis Reveals Alternative Pathways and Metabolite Stores in an Illuminated Arabidopsis Leaf

Flux balance analysis of plant metabolism is an established method for predicting metabolic flux phenotypes and for exploring the way in which the plant metabolic network delivers specific outcomes in different cell types, tissues, and temporal phases. A recurring theme is the need to explore the flexibility of the network in meeting its objectives and, in particular, to establish the extent to which alternative pathways can contribute to achieving specific outcomes. Unfortunately, predictions from conventional flux balance analysis minimize the simultaneous operation of alternative pathways, but by introducing flux-weighting factors to allow for the variable intrinsic cost of supporting each flux, it is possible to activate different pathways in individual simulations and, thus, to explore alternative pathways by averaging thousands of simulations. This new method has been applied to a diel genome-scale model of Arabidopsis (Arabidopsis thaliana) leaf metabolism to explore the flexibility of the network in meeting the metabolic requirements of the leaf in the light. This identified alternative flux modes in the Calvin-Benson cycle revealed the potential for alternative transitory carbon stores in leaves and led to predictions about the light-dependent contribution of alternative electron flow pathways and futile cycles in energy rebalancing. Notable features of the analysis include the light-dependent tradeoff between the use of carbohydrates and four-carbon organic acids as transitory storage forms and the way in which multiple pathways for the consumption of ATP and NADPH can contribute to the balancing of the requirements of photosynthetic metabolism with the energy available from photon capture.

Solving the differential biochemical Jacobian from metabolomics covariance data

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

The low energy signaling network

Stress impacts negatively on plant growth and crop productivity, caicultural production worldwide. Throughout their life, plants are often confronted with multiple types of stress that affect overall cellular energy status and activate energy-saving responses. The resulting low energy syndrome (LES) includes transcriptional, translational, and metabolic reprogramming and is essential for stress adaptation. The conserved kinases sucrose-non-fermenting-1-related protein kinase-1 (SnRK1) and target of rapamycin (TOR) play central roles in the regulation of LES in response to stress conditions, affecting cellular processes and leading to growth arrest and metabolic reprogramming. We review the current understanding of how TOR and SnRK1 are involved in regulating the response of plants to low energy conditions. The central role in the regulation of cellular processes, the reprogramming of metabolism, and the phenotypic consequences of these two kinases will be discussed in light of current knowledge and potential future developments.

A workflow for mathematical modeling of subcellular metabolic pathways in leaf metabolism of Arabidopsis thaliana

During the last decade genome sequencing has experienced a rapid technological development resulting in numerous sequencing projects and applications in life science. In plant molecular biology, the availability of sequence data on whole genomes has enabled the reconstruction of metabolic networks. Enzymatic reactions are predicted by the sequence information. Pathways arise due to the participation of chemical compounds as substrates and products in these reactions. Although several of these comprehensive networks have been reconstructed for the genetic model plant Arabidopsis thaliana, the integration of experimental data is still challenging. Particularly the analysis of subcellular organization of plant cells limits the understanding of regulatory instances in these metabolic networks in vivo. In this study, we develop an approach for the functional integration of experimental high-throughput data into such large-scale networks. We present a subcellular metabolic network model comprising 524 metabolic intermediates and 548 metabolic interactions derived from a total of 2769 reactions. We demonstrate how to link the metabolite covariance matrix of different Arabidopsis thaliana accessions with the subcellular metabolic network model for the inverse calculation of the biochemical Jacobian, finally resulting in the calculation of a matrix which satisfies a Lyaponov equation. In this way, different strategies of metabolite compartmentation and involved reactions were identified in the accessions when exposed to low temperature.

Granger causality in integrated GC-MS and LC-MS metabolomics data reveals the interface of primary and secondary metabolism

Metabolomics has emerged as a key technique of modern life sciences in recent years. Two major techniques for metabolomics in the last 10 years are gas chromatography coupled to mass spectrometry (GC-MS) and liquid chromatography coupled to mass spectrometry (LC-MS). Each platform has a specific performance detecting subsets of metabolites. GC-MS in combination with derivatisation has a preference for small polar metabolites covering primary metabolism. In contrast, reversed phase LC-MS covers large hydrophobic metabolites predominant in secondary metabolism. Here, we present an integrative metabolomics platform providing a mean to reveal the interaction of primary and secondary metabolism in plants and other organisms. The strategy combines GC-MS and LC-MS analysis of the same sample, a novel alignment tool MetMAX and a statistical toolbox COVAIN for data integration and linkage of Granger Causality with metabolic modelling. For metabolic modelling we have implemented the combined GC-LC-MS metabolomics data covariance matrix and a stoichiometric matrix of the underlying biochemical reaction network. The changes in biochemical regulation are expressed as differential Jacobian matrices. Applying the Granger causality, a subset of secondary metabolites was detected with significant correlations to primary metabolites such as sugars and amino acids. These metabolic subsets were compiled into a stoichiometric matrix N. Using N the inverse calculation of a differential Jacobian J from metabolomics data was possible. Key points of regulation at the interface of primary and secondary metabolism were identified.