Multiscale Metabolic Modeling: Dynamic Flux Balance Analysis on a Whole-Plant Scale

Plant metabolism is characterized by a unique complexity on the cellular, tissue, and organ levels. On a whole-plant scale, changing source and sink relations accompanying plant development add another level of complexity to metabolism. With the aim of achieving a spatiotemporal resolution of source-sink interactions in crop plant metabolism, a multiscale metabolic modeling (MMM) approach was applied that integrates static organ-specific models with a whole-plant dynamic model. Allowing for a dynamic flux balance analysis on a whole-plant scale, the MMM approach was used to decipher the metabolic behavior of source and sink organs during the generative phase of the barley (Hordeum vulgare) plant. It reveals a sink-to-source shift of the barley stem caused by the senescence-related decrease in leaf source capacity, which is not sufficient to meet the nutrient requirements of sink organs such as the growing seed. The MMM platform represents a novel approach for the in silico analysis of metabolism on a whole-plant level, allowing for a systemic, spatiotemporally resolved understanding of metabolic processes involved in carbon partitioning, thus providing a novel tool for studying yield stability and crop improvement.Plants are of vital significance as a source of food (Grusak and DellaPenna, 1999; Rogalski and Carrer, 2011), feed (Lu et al., 2011), energy (Tilman et al., 2006; Parmar et al., 2011), and feedstocks for the chemical industry (Metzger and Bornscheuer, 2006; Kinghorn et al., 2011). Given the close connection between plant metabolism and the usability of plant products, there is a growing interest in understanding and predicting the behavior and regulation of plant metabolic processes. In order to increase crop quality and yield, there is a need for methods guiding the rational redesign of the plant metabolic network (Schwender, 2009).Mathematical modeling of plant metabolism offers new approaches to understand, predict, and modify complex plant metabolic processes. In plant research, the issue of metabolic modeling is constantly gaining attention, and different modeling approaches applied to plant metabolism exist, ranging from highly detailed quantitative to less complex qualitative approaches (for review, see Giersch, 2000; Morgan and Rhodes, 2002; Poolman et al., 2004; Rios-Estepa and Lange, 2007).A widely used modeling approach is flux balance analysis (FBA), which allows the prediction of metabolic capabilities and steady-state fluxes under different environmental and genetic backgrounds using (non)linear optimization (Orth et al., 2010). Assuming steady-state conditions, FBA has the advantage of not requiring the knowledge of kinetic parameters and, therefore, can be applied to model detailed, large-scale systems. In recent years, the FBA approach has been applied to several different plant species, such as maize (Zea mays; Dal’Molin et al., 2010; Saha et al., 2011), barley (Hordeum vulgare; Grafahrend-Belau et al., 2009b; Melkus et al., 2011; Rolletschek et al., 2011), rice (Oryza sativa; Lakshmanan et al., 2013), Arabidopsis (Arabidopsis thaliana; Poolman et al., 2009; de Oliveira Dal’Molin et al., 2010; Radrich et al., 2010; Williams et al., 2010; Mintz-Oron et al., 2012; Cheung et al., 2013), and rapeseed (Brassica napus; Hay and Schwender, 2011a, 2011b; Pilalis et al., 2011), as well as algae (Boyle and Morgan, 2009; Cogne et al., 2011; Dal’Molin et al., 2011) and photoautotrophic bacteria (Knoop et al., 2010; Montagud et al., 2010; Boyle and Morgan, 2011). These models have been used to study different aspects of metabolism, including the prediction of optimal metabolic yields and energy efficiencies (Dal’Molin et al., 2010; Boyle and Morgan, 2011), changes in flux under different environmental and genetic backgrounds (Grafahrend-Belau et al., 2009b; Dal’Molin et al., 2010; Melkus et al., 2011), and nonintuitive metabolic pathways that merit subsequent experimental investigations (Poolman et al., 2009; Knoop et al., 2010; Rolletschek et al., 2011). Although FBA of plant metabolic models was shown to be capable of reproducing experimentally determined flux distributions (Williams et al., 2010; Hay and Schwender, 2011b) and generating new insights into metabolic behavior, capacities, and efficiencies (Sweetlove and Ratcliffe, 2011), challenges remain to advance the utility and predictive power of the models.Given that many plant metabolic functions are based on interactions between different subcellular compartments, cell types, tissues, and organs, the reconstruction of organ-specific models and the integration of these models into interacting multiorgan and/or whole-plant models is a prerequisite to get insight into complex plant metabolic processes organized on a whole-plant scale (e.g. source-sink interactions). Almost all FBA models of plant metabolism are restricted to one cell type (Boyle and Morgan, 2009; Knoop et al., 2010; Montagud et al., 2010; Cogne et al., 2011; Dal’Molin et al., 2011), one tissue or one organ (Grafahrend-Belau et al., 2009b; Hay and Schwender, 2011a, 2011b; Pilalis et al., 2011; Mintz-Oron et al., 2012), and only one model exists taking into account the interaction between two cell types by specifying the interaction between mesophyll and bundle sheath cells in C4 photosynthesis (Dal’Molin et al., 2010). So far, no model representing metabolism at the whole-plant scale exists.Considering whole-plant metabolism raises the problem of taking into account temporal and environmental changes in metabolism during plant development and growth. Although classical static FBA is unable to predict the dynamics of metabolic processes, as the network analysis is based on steady-state solutions, time-dependent processes can be taken into account by extending the classical static FBA to a dynamic flux balance analysis (dFBA), as proposed by Mahadevan et al. (2002). The static (SOA) and dynamic optimization approaches introduced in this work provide a framework for analyzing the transience of metabolism by integrating kinetic expressions to dynamically constrain exchange fluxes. Due to the requirement of knowing or estimating a large number of kinetic parameters, so far dFBA has only been applied to a plant metabolic model once, to study the photosynthetic metabolism in the chloroplasts of C3 plants by a simplified model of five biochemical reactions (Luo et al., 2009). Integrating a dynamic model into a static FBA model is an alternative approach to perform dFBA.In this study, a multiscale metabolic modeling (MMM) approach was applied with the aim of achieving a spatiotemporal resolution of cereal crop plant metabolism. To provide a framework for the in silico analysis of the metabolic dynamics of barley on a whole-plant scale, the MMM approach integrates a static multiorgan FBA model and a dynamic whole-plant multiscale functional plant model (FPM) to perform dFBA. The performance of the novel whole-plant MMM approach was tested by studying source-sink interactions during the seed developmental phase of barley plants.