A Computational Framework to Study the Primary Lifecycle Metabolism of Arabidopsis thaliana

Stoichiometric Models of metabolism have proven valuable tools for increased understanding of metabolism and accuracy of synthetic biology interventions to achieve desirable phenotypes. Such models have been used in conjunction with optimization-based and have provided “snapshot” views of organism metabolism at specific stages of growth, generally at exponential growth. This approach has limitations in that metabolic history of the modeled system cannot be studied. The inability to study the complete metabolic history has limited stoichiometric metabolic modeling only to the static investigations of an inherently dynamic process. In this work, we have sought to address this limitation by introducing an optimization-based computational framework and applying to a stoichiometric model of the model plant Arabidopsis thaliana of four linked sub-models of leaf, root, seed, and stem tissues which models the core carbon metabolism through the lifecycle of arabidopsis (named as p-ath780). Uniquely, this framework and model considers diurnal metabolism, changes in tissue mass, carbohydrate storage, and loss of plant mass to senescence and seed dispersal. p-ath780 provide “snapshots” of core-carbon metabolism at one hour intervals of growth, in order to show the evolution of metabolism and whole-plant growth across the lifecycle of a single representative plant. Further, it can simulate important growth stages including seed germination, leaf development, flower production, and silique ripening. The computational framework has shown broad agreement with published experimental data in tissue mass yield, maintenance cost, senescence cost, and whole-plant growth checkpoints. Having focused on core-carbon metabolism, it serves as a scaffold for lifecycle models of other plant systems, to further increase the sophistication of in silico metabolic modeling, and to increase the range of hypotheses which can be investigated in silico. As an example, we have investigated the effect of alternate growth objectives on this plant over the lifecycle. Author Summary In an attempt to study the evolution of metabolism across the lifecycle of plants, in this work we have created an optimization-based framework for the in silico modeling of plant metabolism across the lifecycle of a model plant. We then applied this framework to four core-carbon tissue-level (namely, leaf, root, seed, and stem) stoichiometric models of the model plant species Arabidopsis thaliana, and further informed this framework with a wide array of published in vivo data to increase model and framework accuracy. Unique to the p-ath780 model, comparted to other models of plant metabolism, is the simultaneous considerations of diurnal metabolism, carbohydrate storage, changes in tissue mass (including losses), and changes in metabolism with respect to plant growth stage. This provides a more complete picture of plant metabolism and allows for a wider array of future studies of plant metabolism, particularly since we have only modeled the core carbon metabolism of A. thaliana, allowing this work to serve as a framework for studies of other plant systems.

The use of synthetic biology for the engineering of uni-and multi-cellular organisms to enhance history. These limitations have been inconsequential for single-cell systems in that laboratory 1 0 0 apparatuses have held single-cell cultures at an exponential growth state; therefore, the 1 0 1 "snapshot" approach has given good approximation of metabolism in these steady-state systems. In contrast, multi-cellular organisms, such as plants, will have passed through multiple and 1 0 3 distinct stages of growth throughout its lifecycle [24], and the organism cannot be held at a insignificant compared to biomass (e.g. be an order or magnitude or more different) and to 3 2 8 investigate the different effects of weight factors. The first row (green) of Table 1  vivo arabidopsis data which has been used as targets and verification of the p-ath780 model. The growth as carbon used elsewhere is diverted to the seed tissue. This alternate objective function 3 3 9 has no effect when the plant does not have seed tissue present. Photonic efficiency for the leaf  acid storage objective at a moderate weight value (values enumerated in Table 1). As with other as with other investigations of the seed fatty acid objective, the plant growth is stunted when the 3 5 2 seed tissue is present. In summary, the p-ath780 model is robust to small and moderate photonic efficiency objectives, and results in continuously changeable growth levels to 3 5 5 metabolite production objectives. In the current work, a multi-tissue core metabolism stoichiometric model, including leaf, root, an FBA-based optimization framework ( Figure 1). This framework has been embedded in a to the presence or absence of light, the transition to different growth stages, and the gain or loss of tissues (such as seed). This model has incorporated a wide variety of data which has not been availability of usable light, and biomass-based plant maintenance (as opposed to ATP-based).

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The tissue models taken together with these literature-based constraints has been named the p- agreement with experimental data, particularly with respect to whole plant mass at certain 3 7 0 growth milestones and lifecycle tissue yields. The design-build-test cycle used to develop and tune p-ath780, shown in Figure 3, has been 3 7 3 implemented. As a result, in the final p-ath780 model, in silico predictions compared well to in 3 7 4 vivo data, particularly plant, leaf, seed, and stem masses, with the exception of biomass yield.

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The incongruity between in vivo and in silico biomass yield has likely resulted from the p-ath780 3 7 6 model only having included primary carbon metabolism, which in turn means that plant biomass has been built entirely from generally less metabolically expensive primary metabolites. This had 3 7 8 resulted in too efficient biomass production, hence the lower yield for the model. This discrepancy in biomass yield has served to highlight the large effect of secondary metabolism on made to the photonic efficiency objective, and is capable of some fine tuning with respect to 3 9 0 metabolite production objectives. The behavior of p-ath780 with respect to the linear photonic 3 9 1 efficiency objective function is due to multiple factors. First, as the partially photophobic case exists, this suggests that seed tissue is the most metabolically expensive tissue to create. This is 3 9 3 as expected because the seed tissue requires storage of high-energy molecules such as fatty acids, proteins, and sugars to feed its embryo when dispersed. Further, the rate of biomass production 3 9 5 for all tissues are linked in the optimization-based framework. Secondly, seed tissue has a target 3 9 6 fraction of overall plant mass which it must grow to for each hour interval of the flower 3 9 7 development stage. If seed tissue is too metabolically expensive to produce, relative to the cost to 3 9 8 uptake more light, it appears that the solution strategy then becomes to decrease the mass of highly-specific value of α at which the cost to the light needed to drive growth is balanced with the rate of production of new biomass, but this is an unsteady equilibrium which when the value 4 1 1 of α is slightly perturbed finds the new equilibrium at either extreme. Therefore, the value of α 4 1 2 might be imagined as a fulcrum between the two terms as illustrated in Figure 5. Figure  Restates the linear photonic efficiency objective function. B) Shows the theoretical balance 4 2 0 which might exist between light uptake and biomass production at some highly specific value of

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Overview of the reconstruction of core metabolic models of leaf, root, seed, and stem tissues.
The seed tissue model. The general workflow which has been used for the development of the 4 6 1 four core tissue models has been illustrated in Figure 3. We have developed the seed model first,

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Where I is the set of metabolites; J is the set of reactions; Micro is the set of micronutrients 5 3 5 (phosphate, ammonium, and sulfate) and is a subset of I; X is the set of amino acids which are accounted for by that tissue; and M tissue is the mass of the given tissue. The following subsections 5 4 5 will explain the constraints used in the FBA framework. ath780 has been to maximize the sum of the biomass production rates for all four tissues 5 4 9 according to the following equation (referred to as the default objective).
Where ‫ݖ‬ has been defined the objective function and is defined as the rate of having p-ath780 produce only the "cheapest" biomass, the growth rates of all four tissues have 6 4 0 been linked by a series of constraints which ensure that they grow at rates which maintain the 6 4 1 desired tissue mass ratios. The rate of biomass production determined by a SM is the exponential that all tissues do have biomass production (or loss) and that it is in an amount which will result 6 5 8 in tissue masses in the correct proportions. metabolism. This constraint just does that by forcing recovered metabolites into the biomass loss increases drastically as the flowering production stage finishes and the Silique Ripening phases growth curve in-line with in vivo evidence (see Table 1). to state mathematically and are therefore discussed here. Defining the usage of seed stores by the seedling. A seedling's source of carbon is primarily its 6 9 1 reserves of stored carbohydrates, proteins, and lipids. Namely, it has been shown that seeds have calculation. This quantity has then been scaled by plant mass to result in a mmol/gDW h 7 0 2 quantity, which is used to bound the uptake rates of seed store metabolites. As the leaf has  well, this has left approximately 11.0 ߤ g dry weight (DW) for the embryo. As information on the has been defined as the tissue mass fraction with respect to the total mass of the is defined as the change in tissue mass fraction with respect to seeding, and is defined as the initial mass fraction of each tissue. The gain in the seeding parameter has been 3 8 found in Supplemental File 22, and therefore will not be elaborated on here. The end result is 7 8 2 shown below for a given time point t.
Where, μ , θ , λ are parameters defined in equations (24), (26), and (28), The above system of nine where a solution has not been found via a CNS solver, a solution has been found using the why this method has been used (see Supplemental File 22).
After each partial step, the plant and tissues masses are updated for the next solution. These mass 8 0 7 step estimates are then combined using Heunn's rule for explicit third-order Runge-Kutta And the mass of each individual tissue is then updated as follows: supplemental files and lays out the file structure to use in conjunction with the p-ath780 model. 3. Gonzali S, Mazzucato A, Perata P. Purple as a tomato: towards high anthocyanin tomatoes.   8. Orth JD, Thiele I, Palsson BØ. What is flux balance analysis? Nat Biotechnol.  identifying gene knockout strategies for microbial strain optimization. Biotechnol Bioeng.