Focus on Metabolism: A Method of Accounting for Enzyme Costs in Flux Balance Analysis Reveals Alternative Pathways and Metabolite Stores in an Illuminated Arabidopsis Leaf

Flux balance analysis of plant metabolism is an established method for predicting metabolic flux phenotypes and for exploring the way in which the plant metabolic network delivers specific outcomes in different cell types, tissues, and temporal phases. A recurring theme is the need to explore the flexibility of the network in meeting its objectives and, in particular, to establish the extent to which alternative pathways can contribute to achieving specific outcomes. Unfortunately, predictions from conventional flux balance analysis minimize the simultaneous operation of alternative pathways, but by introducing flux-weighting factors to allow for the variable intrinsic cost of supporting each flux, it is possible to activate different pathways in individual simulations and, thus, to explore alternative pathways by averaging thousands of simulations. This new method has been applied to a diel genome-scale model of Arabidopsis (Arabidopsis thaliana) leaf metabolism to explore the flexibility of the network in meeting the metabolic requirements of the leaf in the light. This identified alternative flux modes in the Calvin-Benson cycle revealed the potential for alternative transitory carbon stores in leaves and led to predictions about the light-dependent contribution of alternative electron flow pathways and futile cycles in energy rebalancing. Notable features of the analysis include the light-dependent tradeoff between the use of carbohydrates and four-carbon organic acids as transitory storage forms and the way in which multiple pathways for the consumption of ATP and NADPH can contribute to the balancing of the requirements of photosynthetic metabolism with the energy available from photon capture.Computational modeling of metabolism is increasingly used to analyze the complexity of plant metabolic networks and to understand system-level properties such as carbon use efficiency (Sweetlove and Ratcliffe, 2011; Nägele and Weckwerth, 2012; de Oliveira Dal’Molin and Nielsen, 2013; Kruger and Ratcliffe, 2015). Flux balance analysis (FBA), which is a method for predicting steady-state flux distributions using a stoichiometric model of the network, is particularly well suited to this task, because it can be applied to large-scale metabolic networks (Lewis et al., 2012). It is also computationally efficient, meaning that models of different cell types (de Oliveira Dal’Molin et al., 2010), different temporal phases (Cheung et al., 2014), and different tissues (Borisjuk et al., 2013; Grafahrend-Belau et al., 2013) can be combined.FBA can generate accurate predictions of plant metabolic fluxes (Williams et al., 2010; Hay and Schwender, 2011; Cheung et al., 2013), but the analysis is complicated by the presence of alternative pathways that share the same function within the network. For example, mitochondria and chloroplasts have several potential mechanisms for maintaining energetic homeostasis, including alternative electron flow pathways, metabolite shuttles for the transfer of reducing power or ATP, and uncoupling mechanisms (Millar et al., 2011; Taniguchi and Miyake, 2012). More generally, the distributed robustness of metabolic networks means that they have the inherent property of being able to achieve cellular objectives in different ways (Wagner, 2005). However, FBA does not automatically identify these alternative flux distributions, because the immediate output of the analysis is a single flux distribution that satisfies the constraints and objectives applied to the model. This has the effect of masking the potential contribution of alternative pathways, and to avoid this, it is necessary to extend the analysis in a way that will reveal them.The most commonly used approach to this problem is flux variability analysis (FVA), which defines the permissible flux ranges for each reaction in the optimal flux space (Mahadevan and Schilling, 2003). Another possibility is random sampling of the optimal flux space, using a uniform sampling algorithm that was originally introduced to characterize the entire feasible flux solution space (Price et al., 2004). While both approaches are useful for exploring the capability of the metabolic system in achieving the cellular objectives, they do not give any indication of which alternative optimal flux solutions are more likely to be found in vivo, and they do not generate flux distributions that represent the biological reality in which alternative pathways may be operating simultaneously.Here, we develop a methodology that permits alternative pathways to be explored efficiently and that allows the consequences of the simultaneous operation of alternative pathways on the rest of the metabolic network to be examined. Our approach emerged from a reconsideration of the use of flux minimization as the objective function. Minimization of the sum of the absolute flux values supported by all the reactions in the network is often used as an objective function in FBA on the principle that cells have evolved to minimize the costs for the synthesis of the enzymes and membrane transporters that support growth and cell maintenance (Holzhütter, 2004). However, no weighting is applied when calculating the sum of fluxes, so there is an implicit assumption that the machinery cost per unit of flux is the same for all reactions. This assumption is invalid in vivo, as enzymes vary in terms of their size, number of subunits, and catalytic capacity. Ideally, each reaction should be weighted by its enzyme machinery costs per unit of flux, but such information is not available for the majority of the reactions in large-/genome-scale metabolic models. Here, we develop a modeling method, cost-weighted FBA, that avoids the invalid assumption of equal costs and that allows the evaluation of alternative metabolic routes in a complex network. The method was used to demonstrate the flexibility of leaf metabolism in meeting the metabolic requirements of an Arabidopsis (Arabidopsis thaliana) leaf in the light. A genome-scale diel FBA model, in which the light and dark phases of the diel cycle were solved as a single optimization problem, was used for the analysis because this approach currently provides the most realistic constraints-based framework for modeling leaf metabolism (Cheung et al., 2014; de Oliveira Dal’Molin et al., 2015).