Evaluating the stoichiometric and energetic constraints of cyanobacterial diurnal growth

Cyanobacteria are an integral part of the Earth’s biogeochemical cycles and a promising resource for the synthesis of renewable bioproducts from atmospheric CO2. Growth and metabolism of cyanobacteria are inherently tied to the diurnal rhythm of light availability. As yet, however, insight into the stoichiometric and energetic constraints of cyanobacterial diurnal growth is limited. Here, we develop a computational platform to evaluate the optimality of diurnal phototrophic growth using a high-quality genome-scale metabolic reconstruction of the cyanobacterium Synechococcus elongatus PCC 7942. We formulate phototrophic growth as a self-consistent autocatalytic process and evaluate the resulting time-dependent resource allocation problem using constraint-based analysis. Based on a narrow and well defined set of parameters, our approach results in an ab initio prediction of growth properties over a full diurnal cycle. In particular, our approach allows us to study the optimality of metabolite partitioning during diurnal growth. The cyclic pattern of glycogen accumulation, an emergent property of the model, has timing characteristics that are shown to be a trade-off between conflicting cellular objectives. The approach presented here provides insight into the time-dependent resource allocation problem of phototrophic diurnal growth and may serve as a general framework to evaluate the optimality of metabolic strategies that evolved in photosynthetic organisms under diurnal conditions. ∗Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany †International Max Planck Research School for Computational Biology and Scientific Computing, Max-PlanckInstitut für molekulare Genetik, Ihnestraße 63-73, 14195 Berlin, Germany ‡Fachinstitut Theoretische Biologie (ITB), Institut für Biologie, Humboldt-Universität zu Berlin, Invalidenstraße 43, 10115 Berlin, Germany 1 ar X iv :1 61 0. 06 85 9v 2 [ qbi o. M N ] 2 4 O ct 2 01 6 Cyanobacterial photoautotrophic growth requires a highly coordinated distribution of cellular resources to different intracellular processes, including the de novo synthesis of proteins, ribosomes, lipids, as well as other cellular components. For unicellular organisms, the optimal allocation of limiting resources is a key determinant of evolutionary fitness in almost all environments. Owing to the importance of cellular resource allocation for understanding cellular trade-offs, as well as its importance for the effective design of synthetic properties, the cellular ’economy’ and its implication for bacterial growth laws have been studied extensively (Molenaar et al., 2009; Scott et al., 2010; Flamholz et al., 2013; Vázquez-Laslop and Mankin, 2014; Hui et al., 2015; Burnap, 2015; Weiße et al., 2015) – albeit almost exclusively for heterotrophic organisms under stationary environmental conditions. For photoautotrophic organisms, including cyanobacteria, growth-dependent resource allocation is further subject to diurnal light-dark (LD) cycles that partition cellular metabolism into distinct phases. Recent experimental results have demonstrated the relevance of time-specific synthesis for cellular growth (Diamond et al., 2015). Nonetheless the implications and consequences of growth in a diurnal environment on the cellular resource allocation problem are insufficiently understood, and computational approaches hitherto developed for heterotrophic growth are not straightforwardly applicable to phototrophic diurnal growth. Here, we propose a computational framework to evaluate the optimality of diurnal resource allocation for diurnal phototrophic growth. We are primarily interested in the stoichiometric and energetic constraints that shape the cellular ’protein economy’, that is, the relationship between the average growth rate and the relative partitioning of metabolic, photosynthetic, and ribosomal proteins during a full diurnal period. Beyond the established constraint-based reconstruction and analysis methodologies, we aim to obtain an ab initio prediction of emergent properties that arise from a narrow and well-defined set of assumptions and parameters about cyanobacterial diurnal growth – and to contrast these emergent properties with known and observed cellular behavior. To this end, we assemble and evaluate an auto-catalytic genomescale model of cyanobacterial growth, based on a high-quality metabolic reconstruction of the cyanobacterium Synechococcus elongatus PCC 7942. Our evaluation significantly improves upon a previous model of diurnal cyanobacterial growth (Rügen et al., 2015) and takes into account recent developments in constraint-based analysis (King et al., 2015; Henson, 2015). Our approach is closely related to resource balance analysis (RBA) (Goelzer et al., 2011), dynamic enzyme-cost flux balance analysis (deFBA) (Waldherr et al., 2015), as well as integrated metabolism and gene expression (ME) models (O’Brien et al., 2013), but explicitly accounts for diurnal phototrophic growth. Using Synechococcus elongatus PCC 7942 as a model system, our starting point is the observation that almost all cellular processes are dependent upon the presence of catalytic compounds, typically enzymes and other cellular macromolecules. Hence, a self-consistent description of cyanobacterial growth must take the synthesis of these macromolecules into account – and reflect the fact that the abundance of these macromolecules limits the capacity of cellular metabolism at all times. De novo synthesis of cellular macromolecules increases the metabolic capacity – the timing and amount of the respective synthesis reactions can therefore be described as a cellular resource allocation problem: What is the amount and temporal order of synthesis reactions to allow for maximal growth of a cyanobacterial cell in a diurnal environment? To evaluate the respective stoichiometric and energetic constraints, we only require knowledge about the stoichiometric composition, and the catalytic efficiency of macromolecules – quantities for which reasonable estimates are available. We therefore seek to evaluate the emergent properties of phototrophic diurnal growth, based on best a priori estimates of relevant parameters only. Our key results include (i) a prediction of the timing of intracellular synthesis reactions that is in good agreement with known facts about metabolite partitioning during diurnal growth, (ii) limits on