Topological data analysis reveals a core gene expression backbone that defines form and function across flowering plants.

Since they emerged approximately 125 million years ago, flowering plants have evolved to dominate the terrestrial landscape and survive in the most inhospitable environments on earth. At their core, these adaptations have been shaped by changes in numerous, interconnected pathways and genes that collectively give rise to emergent biological phenomena. Linking gene expression to morphological outcomes remains a grand challenge in biology, and new approaches are needed to begin to address this gap. Here, we implemented topological data analysis (TDA) to summarize the high dimensionality and noisiness of gene expression data using lens functions that delineate plant tissue and stress responses. Using this framework, we created a topological representation of the shape of gene expression across plant evolution, development, and environment for the phylogenetically diverse flowering plants. The TDA-based Mapper graphs form a well-defined gradient of tissues from leaves to seeds, or from healthy to stressed samples, depending on the lens function. This suggests that there are distinct and conserved expression patterns across angiosperms that delineate different tissue types or responses to biotic and abiotic stresses. Genes that correlate with the tissue lens function are enriched in central processes such as photosynthetic, growth and development, housekeeping, or stress responses. Together, our results highlight the power of TDA for analyzing complex biological data and reveal a core expression backbone that defines plant form and function.

Reaction-diffusion modeling provides insights into biophysical carbon-concentrating mechanisms in land plants.

Carbon-concentrating mechanisms (CCMs) have evolved numerous times in photosynthetic organisms. They elevate the concentration of CO2 around the carbon-fixing enzyme rubisco, thereby increasing CO2 assimilatory flux and reducing photorespiration. Biophysical CCMs, like the pyrenoid-based CCM (PCCM) of Chlamydomonas reinhardtii or carboxysome systems of cyanobacteria, are common in aquatic photosynthetic microbes, but in land plants appear only among the hornworts. To predict the likely efficiency of biophysical CCMs in C3 plants, we used spatially resolved reaction-diffusion models to predict rubisco saturation and light use efficiency. We found that the energy efficiency of adding individual CCM components to a C3 land plant is highly dependent on the permeability of lipid membranes to CO2, with values in the range reported in the literature that are higher than those used in previous modeling studies resulting in low light use efficiency. Adding a complete PCCM into the leaf cells of a C3 land plant was predicted to boost net CO2 fixation, but at higher energetic costs than those incurred by photorespiratory losses without a CCM. Two notable exceptions were when substomatal CO2 levels are as low as those found in land plants that already use biochemical CCMs and when gas exchange is limited, such as with hornworts, making the use of a biophysical CCM necessary to achieve net positive CO2 fixation under atmospheric CO2 levels. This provides an explanation for the uniqueness of hornworts' CCM among land plants and the evolution of pyrenoids multiple times.

Reimport of carbon from cytosolic and vacuolar sugar pools into the Calvin-Benson cycle explains photosynthesis labeling anomalies.

SignificancePhotosynthesis metabolites are quickly labeled when 13CO2 is fed to leaves, but the time course of labeling reveals additional contributing processes involved in the metabolic dynamics of photosynthesis. The existence of three such processes is demonstrated, and a metabolic flux model is developed to explore and characterize them. The model is consistent with a slow return of carbon from cytosolic and vacuolar sugars into the Calvin-Benson cycle through the oxidative pentose phosphate pathway. Our results provide insight into how carbon assimilation is integrated into the metabolic network of photosynthetic cells with implications for global carbon fluxes.

Accurate flux predictions using tissue-specific gene expression in plant metabolic modeling.

MOTIVATION: The accurate prediction of complex phenotypes such as metabolic fluxes in living systems is a grand challenge for systems biology and central to efficiently identifying biotechnological interventions that can address pressing industrial needs. The application of gene expression data to improve the accuracy of metabolic flux predictions using mechanistic modeling methods such as flux balance analysis (FBA) has not been previously demonstrated in multi-tissue systems, despite their biotechnological importance. We hypothesized that a method for generating metabolic flux predictions informed by relative expression levels between tissues would improve prediction accuracy. RESULTS: Relative gene expression levels derived from multiple transcriptomic and proteomic datasets were integrated into FBA predictions of a multi-tissue, diel model of Arabidopsis thaliana's central metabolism. This integration dramatically improved the agreement of flux predictions with experimentally based flux maps from 13C metabolic flux analysis compared with a standard parsimonious FBA approach. Disagreement between FBA predictions and MFA flux maps was measured using weighted averaged percent error values, and for parsimonious FBA this was169%-180% for high light conditions and 94%-103% for low light conditions, depending on the gene expression dataset used. This fell to 10%-13% and 9%-11% upon incorporating expression data into the modeling process, which also substantially altered the predicted carbon and energy economy of the plant. AVAILABILITY AND IMPLEMENTATION: Code and data generated as part of this study are available from https://github.com/Gibberella/ArabidopsisGeneExpressionWeights.

Model validation and selection in metabolic flux analysis and flux balance analysis.

13C-Metabolic Flux Analysis (13C-MFA) and Flux Balance Analysis (FBA) are widely used to investigate the operation of biochemical networks in both biological and biotechnological research. Both methods use metabolic reaction network models of metabolism operating at steady state so that reaction rates (fluxes) and the levels of metabolic intermediates are constrained to be invariant. They provide estimated (MFA) or predicted (FBA) values of the fluxes through the network in vivo, which cannot be measured directly. These fluxes can shed light on basic biology and have been successfully used to inform metabolic engineering strategies. Several approaches have been taken to test the reliability of estimates and predictions from constraint-based methods and to compare alternative model architectures. Despite advances in other areas of the statistical evaluation of metabolic models, such as the quantification of flux estimate uncertainty, validation and model selection methods have been underappreciated and underexplored. We review the history and state-of-the-art in constraint-based metabolic model validation and model selection. Applications and limitations of the χ2 -test of goodness-of-fit, the most widely used quantitative validation and selection approach in 13C-MFA, are discussed, and complementary and alternative forms of validation and selection are proposed. A combined model validation and selection framework for 13C-MFA incorporating metabolite pool size information that leverages new developments in the field is presented and advocated for. Finally, we discuss how adopting robust validation and selection procedures can enhance confidence in constraint-based modeling as a whole and ultimately facilitate more widespread use of FBA in biotechnology.

Biophysical carbon concentrating mechanisms in land plants: insights from reaction-diffusion modeling.

Carbon Concentrating Mechanisms (CCMs) have evolved numerous times in photosynthetic organisms. They elevate the concentration of CO2 around the carbon-fixing enzyme rubisco, thereby increasing CO2 assimilatory flux and reducing photorespiration. Biophysical CCMs, like the pyrenoid-based CCM of Chlamydomonas reinhardtii or carboxysome systems of cyanobacteria, are common in aquatic photosynthetic microbes, but in land plants appear only among the hornworts. To predict the likely efficiency of biophysical CCMs in C3 plants, we used spatially resolved reaction-diffusion models to predict rubisco saturation and light use efficiency. We find that the energy efficiency of adding individual CCM components to a C3 land plant is highly dependent on the permeability of lipid membranes to CO2, with values in the range reported in the literature that are higher than used in previous modeling studies resulting in low light use efficiency. Adding a complete pyrenoid-based CCM into the leaf cells of a C3 land plant is predicted to boost net CO2 fixation, but at higher energetic costs than those incurred by photorespiratory losses without a CCM. Two notable exceptions are when substomatal CO2 levels are as low as those found in land plants that already employ biochemical CCMs and when gas exchange is limited such as with hornworts, making the use of a biophysical CCM necessary to achieve net positive CO2 fixation under atmospheric CO2 levels. This provides an explanation for the uniqueness of hornworts' CCM among land plants and evolution of pyrenoids multiple times.

Integrative teaching of metabolic modeling and flux analysis with interactive python modules.

The modeling of rates of biochemical reactions-fluxes-in metabolic networks is widely used for both basic biological research and biotechnological applications. A number of different modeling methods have been developed to estimate and predict fluxes, including kinetic and constraint-based (Metabolic Flux Analysis and flux balance analysis) approaches. Although different resources exist for teaching these methods individually, to-date no resources have been developed to teach these approaches in an integrative way that equips learners with an understanding of each modeling paradigm, how they relate to one another, and the information that can be gleaned from each. We have developed a series of modeling simulations in Python to teach kinetic modeling, metabolic control analysis, 13C-metabolic flux analysis, and flux balance analysis. These simulations are presented in a series of interactive notebooks with guided lesson plans and associated lecture notes. Learners assimilate key principles using models of simple metabolic networks by running simulations, generating and using data, and making and validating predictions about the effects of modifying model parameters. We used these simulations as the hands-on computer laboratory component of a four-day metabolic modeling workshop and participant survey results showed improvements in learners' self-assessed competence and confidence in understanding and applying metabolic modeling techniques after having attended the workshop. The resources provided can be incorporated in their entirety or individually into courses and workshops on bioengineering and metabolic modeling at the undergraduate, graduate, or postgraduate level.

Model Validation and Selection in Metabolic Flux Analysis and Flux Balance Analysis.

13C-Metabolic Flux Analysis (13C-MFA) and Flux Balance Analysis (FBA) are widely used to investigate the operation of biochemical networks in both biological and biotechnological research. Both of these methods use metabolic reaction network models of metabolism operating at steady state, so that reaction rates (fluxes) and the levels of metabolic intermediates are constrained to be invariant. They provide estimated (MFA) or predicted (FBA) values of the fluxes through the network in vivo, which cannot be measured directly. A number of approaches have been taken to test the reliability of estimates and predictions from constraint-based methods and to decide on and/or discriminate between alternative model architectures. Despite advances in other areas of the statistical evaluation of metabolic models, validation and model selection methods have been underappreciated and underexplored. We review the history and state-of-the-art in constraint-based metabolic model validation and model selection. Applications and limitations of the χ2-test of goodness-of-fit, the most widely used quantitative validation and selection approach in 13C-MFA, are discussed, and complementary and alternative forms of validation and selection are proposed. A combined model validation and selection framework for 13C-MFA incorporating metabolite pool size information that leverages new developments in the field is presented and advocated for. Finally, we discuss how the adoption of robust validation and selection procedures can enhance confidence in constraint-based modeling as a whole and ultimately facilitate more widespread use of FBA in biotechnology in particular.

Flux-Balance Analysis and Mobile CRISPRi-Guided Deletion of a Conditionally Essential Gene in Shewanella oneidensis MR-1.

Carbon-neutral production of valuable bioproducts is critical to sustainable development but remains limited by the slow engineering of photosynthetic organisms. Improving existing synthetic biology tools to engineer model organisms to fix carbon dioxide is one route to overcoming the limitations of photosynthetic organisms. In this work, we describe a pipeline that enabled the deletion of a conditionally essential gene from the Shewanella oneidensis MR-1 genome. S. oneidensis is a simple bacterial host that could be used for electricity-driven conversion of carbon dioxide in the future with further genetic engineering. We used Flux Balance Analysis (FBA) to model carbon and energy flows in central metabolism and assess the effects of single and double gene deletions. We modeled the growth of deletion strains under several alternative conditions to identify substrates that restore viability to an otherwise lethal gene knockout. These predictions were tested in vivo using a Mobile-CRISPRi gene knockdown system. The information learned from FBA and knockdown experiments informed our strategy for gene deletion, allowing us to successfully delete an "expected essential" gene, gpmA. FBA predicted, knockdown experiments supported, and deletion confirmed that the "essential" gene gpmA is not needed for survival, dependent on the medium used. Removal of gpmA is a first step toward driving electrode-powered CO2 fixation via RuBisCO. This work demonstrates the potential for broadening the scope of genetic engineering in S. oneidensis as a synthetic biology chassis. By combining computational analysis with a CRISPRi knockdown system in this way, one can systematically assess the impact of conditionally essential genes and use this knowledge to generate mutations previously thought unachievable.