Multiscale metabolic modeling of C4 plants: connecting nonlinear genome-scale models to leaf-scale metabolism in developing maize leaves

C4 plants, such as maize, concentrate carbon dioxide in a specialized compartment surrounding the veins of their leaves to improve the efficiency of carbon dioxide assimilation. Nonlinear relationships between carbon dioxide and oxygen levels and reaction rates are key to their physiology but cannot be handled with standard techniques of constraint-based metabolic modeling. We demonstrate that incorporating these relationships as constraints on reaction rates and solving the resulting nonlinear optimization problem yields realistic predictions of the response of C4 systems to environmental and biochemical perturbations. Using a new genome-scale reconstruction of maize metabolism, we build an 18000-reaction, nonlinearly constrained model describing mesophyll and bundle sheath cells in 15 segments of the developing maize leaf, interacting via metabolite exchange, and use RNA-seq and enzyme activity measurements to predict spatial variation in metabolic state by a novel method that optimizes correlation between fluxes and expression data. Though such correlations are known to be weak in general, here the predicted fluxes achieve high correlation with the data, successfully capture the experimentally observed base-to-tip transition between carbon-importing tissue and carbon-exporting tissue, and include a nonzero growth rate, in contrast to prior results from similar methods in other systems. We suggest that developmental gradients may be particularly suited to the inference of metabolic fluxes from expression data.Comment: 57 pages, 14 figures; submitted to PLoS Computational Biology; source code available at http://github.com/ebogart/fluxtools and http://github.com/ebogart/multiscale_c4_sourc

Maize plant and models.

<p>(a) Nine-day-old maize plant (image from [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0151722#pone.0151722.ref025" target="_blank">25</a>]). (b) Organization of the two-cell-type metabolic model, showing compartmentalization and exchanges across mesophyll and bundle sheath cell boundaries. (c) Combined 121-compartment model for leaf 3 at the developmental stage shown in (a). Fifteen identical copies of the model shown in (b) represent 1-cm segments from base to tip.</p

Source-sink transition along the leaf as predicted by optimizing the agreement between fluxes in the nonlinear model and RNA-seq data.

<p>Predicted fluxes are obtained by minimizing the objective function of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0151722#pone.0151722.e003" target="_blank">Eq 3</a>. (a) Predicted rates of exchange of carbon with the atmosphere and phloem along the leaf. (b) Experimental observation of the source-sink transition, reproduced from [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0151722#pone.0151722.ref025" target="_blank">25</a>]. Upper image, photograph of leaf 3; middle image, autoradiograph of leaf 3 after feeding ¹⁴CO₂ to leaf 2; lower image, autoradiograph of leaf 3 after feeding ¹⁴CO₂ to the tip of leaf 3. (c) Total biomass production in the best-fitting solution. In panels a and c, dotted lines indicate minimum and maximum predicted rates consistent with an objective function value no more than 0.1% greater than the optimal value. Here, the biomass composition is allowed to vary along the leaf; <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0151722#pone.0151722.s008" target="_blank">S8 Fig</a> shows corresponding results where the biomass composition is fixed.</p

CO₂ assimilation rates (<i>A</i>) predicted by the C4 photosynthesis model of [15], solid lines, and the present nonlinear genome-scale model (markers) maximizing CO₂ assimilation with equivalent parameters.

<p>The nonlinear model incorporates the mesophyll CO₂ level as a parameter through the constraints in Eqs <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0151722#pone.0151722.e008" target="_blank">5</a>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0151722#pone.0151722.e009" target="_blank">6</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0151722#pone.0151722.e007" target="_blank">7</a>. Left, <i>A</i> vs mesophyll CO₂ levels with varying PEPC levels (top to bottom, <i>v</i>_<i>p</i>,max = 110, 90, 70, 50, and 30 μmol m^-2 s^-1). Right, <i>A</i> vs total maximum activity of all bundle sheath decarboxylase enzymes (equivalent to the maximum PEP regeneration rate <i>V</i>_<i>pr</i> in [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0151722#pone.0151722.ref015" target="_blank">15</a>]) at varying Rubisco levels (top to bottom, <i>v</i>_<i>c</i>,max = 70, 60, 50, 40, and 30 μmol m^-2 s^-1). Other parameters as in Table 4.1 of [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0151722#pone.0151722.ref015" target="_blank">15</a>], except with nonphotorespiratory respiration rates <i>r</i>_<i>d</i> = <i>r</i>_<i>m</i> = 0.</p

Operation of the C4 system in the best-fitting solution, as determined by minimizing the objective function, Eq 3.

<p>(a) Rates of carboxylation by PEPC in the mesophyll and Rubisco in the mesophyll and bundle sheath. (b) Rates of CO₂ release by PEP carboxykinase and chloroplastic NADP-malic enzyme in the bundle sheath. (c) Transport of 3-phosphoglycerate and glyceraldehyde 3-phosphate from bundle sheath to mesophyll (or the reverse, where negative) and glyceraldehyde 3-phosphate dehydrogenation rate in the mesophyll chloroplast, showing the involvement of the mesophyll in the reductive steps of the Calvin cycle throughout the source region. (d) Oxygen and carbon dioxide levels in the bundle sheath. Straight lines show mesophyll levels. Throughout, dotted lines indicate minimum and maximum predicted values consistent with an objective function value no more than 0.1% greater than the optimal value.</p

DESC DC2 Data Release Note

In preparation for cosmological analyses of the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST), the LSST Dark Energy Science Collaboration (LSST DESC) has created a 300 deg$^2$ simulated survey as part of an effort called Data Challenge 2 (DC2). The DC2 simulated sky survey, in six optical bands with observations following a reference LSST observing cadence, was processed with the LSST Science Pipelines (19.0.0). In this Note, we describe the public data release of the resulting object catalogs for the coadded images of five years of simulated observations along with associated truth catalogs. We include a brief description of the major features of the available data sets. To enable convenient access to the data products, we have developed a web portal connected to Globus data services. We describe how to access the data and provide example Jupyter Notebooks in Python to aid first interactions with the data. We welcome feedback and questions about the data release via a GitHub repository

The LSST DESC DC2 Simulated Sky Survey

International audienceWe describe the simulated sky survey underlying the second data challenge (DC2) carried out in preparation for analysis of the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST) by the LSST Dark Energy Science Collaboration (LSST DESC). Significant connections across multiple science domains will be a hallmark of LSST; the DC2 program represents a unique modeling effort that stresses this interconnectivity in a way that has not been attempted before. This effort encompasses a full end-to-end approach: starting from a large N-body simulation, through setting up LSST-like observations including realistic cadences, through image simulations, and finally processing with Rubin’s LSST Science Pipelines. This last step ensures that we generate data products resembling those to be delivered by the Rubin Observatory as closely as is currently possible. The simulated DC2 sky survey covers six optical bands in a wide-fast-deep area of approximately 300 deg2, as well as a deep drilling field of approximately 1 deg2. We simulate 5 yr of the planned 10 yr survey. The DC2 sky survey has multiple purposes. First, the LSST DESC working groups can use the data set to develop a range of DESC analysis pipelines to prepare for the advent of actual data. Second, it serves as a realistic test bed for the image processing software under development for LSST by the Rubin Observatory. In particular, simulated data provide a controlled way to investigate certain image-level systematic effects. Finally, the DC2 sky survey enables the exploration of new scientific ideas in both static and time domain cosmology