Improving the yield and efficiency of plants is an urgent goal of research, but it is difficult to understand the functioning and regulation of these complex traits by studying individual genes and phenotypes. Mathematical models are particularly useful in addressing multifactorial characteristics because they embody the relations of multiple system components and can predict the quantitative effect of changing these components. Here, I describe my collaborative work on integrating experimental data with models of nutrient fluxes in plant systems operating at three different biological scales: plant-microbe interactions, the central metabolism network, and within one biochemical pathway. First, we analyzed carbon-for-nitrogen exchange in the legume-rhizobia mutualism using a trade-based model. We found that classical symmetric interactions could not explain the observed nutrient exchange rates and ratios. Rather, the plant had more influence on these nutrient exchange parameters than the rhizobia and the plant’s influence rose as soil nitrogen became scarcer. This finding highlights the importance of environmental conditions for the functioning and evolution of mutualisms. To explore other ways in which experiments have been or could be integrated with mathematical models, we also wrote a synthesis review. In this review, we summarized mathematical approaches that could investigate the cellular, individual, population, and community scales of plant-microbe nutrient-exchange mutualisms. For each scale, we addressed the potentials of integration to investigate mutualism stability, and how resource availability and structured interactions influence these dynamics. Second, we used isotopic labeling based metabolic flux analysis to determine the routes and rates of fluxes through central metabolism in developing embryos of Camelina sativa—a promising oil seed crop. By quantifying the major decarboxylation fluxes, we discovered that the oxidative phase of the pentose phosphate pathway exhibited a very high flux that was tightly correlated with the carbon use efficiencies of C. sativa embryos grown under different light levels. Together, these results indicate that this decarboxylation flux contributed substantially to the embryos having low carbon use efficiency. To test how bioengineering can affect central metabolism, we also performed metabolic flux analysis on transgenic C. sativa that had been genetically engineered to accumulate greater quantities of medium-chain fatty acids. We found that principal component analysis could use metabolite label content measurements to distinguish between embryos with different backgrounds, but there was much less distinction between the lines when the net fluxes were used. However, the lines could be moderately separated with hierarchal clustering, which could cleanly separate the transgenic lines from the wild-type grown under the different light level. This shows that there are distinct metabolic differences between the transgenic lines that are not detected with principal component analysis, and that environmental variances can have a stronger effect on central metabolism than fatty acid bioengineering. Lastly, I describe our recent progress towards elucidating the network topology of triacylglycerol synthesis in C. sativa embryos. We developed potential network topologies as systems of first-order rate equations. The models were fit to 14C glyceryl time-course data of the label content in other lipid classes in the network. We compared how well the model explains the labeling data and found that the data was best explained by a network that included two active diacylglycerol pools that are successive precursor to triacylglycerol biosynthesis and the first diacylglyerol pool can exchange with the active phosphatidylcholine pool. In addition, we performed short-term 14C acetate labeling experiments to track how newly synthesized or recently elongated fatty acids are incorporated into the different lipid classes. We found evidence for a large phosphatidylcholine pool that is used for acyl editing and is separate from the pool used for de novo triacylglycerol synthesis Together, these endeavors demonstrate how models can be integrated with a broad range of data to address questions at ecological, organismal, and metabolic scales.
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