Elucidating temporal resource allocation and diurnal dynamics in phototrophic metabolism using conditional FBA

Development and applications of genome-scale metabolic network models

The genome-scale metabolic network model is an effective tool for characterizing the gene-protein-response relationship in the entire metabolic pathway of an organism. By combining various algorithms, the genome-scale metabolic network model can effectively simulate the influence of a specific environment on the physiological state of cells, optimize the culture conditions of strains, and predict the targets of genetic modification to achieve targeted modification of strains. In this review, we summarize the whole process of model building, sort out the various tools that may be involved in the model building process, and explain the role of various algorithms in model analysis. In addition, we also summarized the application of GSMM in network characteristics, cell phenotypes, metabolic engineering, etc. Finally, we discuss the current challenges facing GSMM.

Trade-offs between the instantaneous growth rate and long-term fitness: Consequences for microbial physiology and predictive computational models

Microbial systems biology has made enormous advances in relating microbial physiology to the underlying biochemistry and molecular biology. By meticulously studying model microorganisms, in particular Escherichia coli and Saccharomyces cerevisiae, increasingly comprehensive computational models predict metabolic fluxes, protein expression, and growth. The modeling rationale is that cells are constrained by a limited pool of resources that they allocate optimally to maximize fitness. As a consequence, the expression of particular proteins is at the expense of others, causing trade-offs between cellular objectives such as instantaneous growth, stress tolerance, and capacity to adapt to new environments. While current computational models are remarkably predictive for E. coli and S. cerevisiae when grown in laboratory environments, this may not hold for other growth conditions and other microorganisms. In this contribution, we therefore discuss the relationship between the instantaneous growth rate, limited resources, and long-term fitness. We discuss uses and limitations of current computational models, in particular for rapidly changing and adverse environments, and propose to classify microbial growth strategies based on Grimes's CSR framework.

Predicting the impact of temperature on metabolic fluxes using resource allocation modelling: Application to polyphosphate accumulating organisms

The understanding of microbial communities and the biological regulation of its members is crucial for implementation of novel technologies using microbial ecology. One poorly understood metabolic principle of microbial communities is resource allocation and biosynthesis. Resource allocation theory in polyphosphate accumulating organisms (PAOs) is limited as a result of their slow imposed growth rate (typical sludge retention times of at least 4 days) and limitations to quantify changes in biomass components over a 6 hours cycle (less than 10% of their growth). As a result, there is no direct evidence supporting that biosynthesis is an exclusive aerobic process in PAOs that alternate continuously between anaerobic and aerobic phases. Here, we apply resource allocation metabolic flux analysis to study the optimal phenotype of PAOs over a temperature range of 4 °C to 20 °C. The model applied in this research allowed to identify optimal metabolic strategies in a core metabolic model with limited constraints based on biological principles. The addition of a constraint limiting biomass synthesis to be an exclusive aerobic process changed the metabolic behaviour and improved the predictability of the model over the studied temperature range by closing the gap between prediction and experimental findings. The results validate the assumption of limited anaerobic biosynthesis in PAOs, specifically "Candidatus Accumulibacter" related species. Interestingly, the predicted growth yield was lower, suggesting that there are mechanistic barriers for anaerobic growth not yet understood nor reflected in the current models of PAOs. Moreover, we identified strategies of resource allocation applied by PAOs at different temperatures as a result of the decreased catalytic efficiencies of their biochemical reactions. Understanding resource allocation is paramount in the study of PAOs and their currently unknown complex metabolic regulation, and metabolic modelling based on biological first principles provides a useful tool to develop a mechanistic understanding.

Time-Optimal Adaptation in Metabolic Network Models

Analysis of metabolic models using constraint-based optimization has emerged as an important computational technique to elucidate and eventually predict cellular metabolism and growth. In this work, we introduce time-optimal adaptation (TOA), a new constraint-based modeling approach that allows us to evaluate the fastest possible adaptation to a pre-defined cellular state while fulfilling a given set of dynamic and static constraints. TOA falls into the mathematical problem class of time-optimal control problems, and, in its general form, can be broadly applied and thereby extends most existing constraint-based modeling frameworks. Specifically, we introduce a general mathematical framework that captures many existing constraint-based methods and define TOA within this framework. We then exemplify TOA using a coarse-grained self-replicator model and demonstrate that TOA allows us to explain several well-known experimental phenomena that are difficult to explore using existing constraint-based analysis methods. We show that TOA predicts accumulation of storage compounds in constant environments, as well as overshoot uptake metabolism after periods of nutrient scarcity. TOA shows that organisms with internal temporal degrees of freedom, such as storage, can in most environments outperform organisms with a static intracellular composition. Furthermore, TOA reveals that organisms adapted to better growth conditions than present in the environment (“optimists”) typically outperform organisms adapted to poorer growth conditions (“pessimists”).

Predicting Metabolic Adaptation Under Dynamic Substrate Conditions Using a Resource-Dependent Kinetic Model: A Case Study Using Saccharomyces cerevisiae

Exposed to changes in their environment, microorganisms will adapt their phenotype, including metabolism, to ensure survival. To understand the adaptation principles, resource allocation-based approaches were successfully applied to predict an optimal proteome allocation under (quasi) steady-state conditions. Nevertheless, for a general, dynamic environment, enzyme kinetics will have to be taken into account which was not included in the linear resource allocation models. To this end, a resource-dependent kinetic model was developed and applied to the model organism Saccharomyces cerevisiae by combining published kinetic models and calibrating the model parameters to published proteomics and fluxomics datasets. Using this approach, we were able to predict specific proteomes at different dilution rates under chemostat conditions. Interestingly, the approach suggests that the occurrence of aerobic fermentation (Crabtree effect) in S. cerevisiae is not caused by space limitation in the total proteome but rather an effect of constraints on the mitochondria. When exposing the approach to repetitive, dynamic substrate conditions, the proteome space was allocated differently. Less space was predicted to be available for non-essential enzymes (reserve space). This could indicate that the perceived “overcapacity” present in experimentally measured proteomes may very likely serve a purpose in increasing the robustness of a cell to dynamic conditions, especially an increase of proteome space for the growth reaction as well as of the trehalose cycle that was shown to be essential in providing robustness upon stronger substrate perturbations. The model predictions of proteome adaptation to dynamic conditions were additionally evaluated against respective experimentally measured proteomes, which highlighted the model’s ability to accurately predict major proteome adaptation trends. This proof of principle for the approach can be extended to production organisms and applied for both understanding metabolic adaptation and improving industrial process design.

A Practical Guide to Integrating Multimodal Machine Learning and Metabolic Modeling

Complex, distributed, and dynamic sets of clinical biomedical data are collectively referred to as multimodal clinical data. In order to accommodate the volume and heterogeneity of such diverse data types and aid in their interpretation when they are combined with a multi-scale predictive model, machine learning is a useful tool that can be wielded to deconstruct biological complexity and extract relevant outputs. Additionally, genome-scale metabolic models (GSMMs) are one of the main frameworks striving to bridge the gap between genotype and phenotype by incorporating prior biological knowledge into mechanistic models. Consequently, the utilization of GSMMs as a foundation for the integration of multi-omic data originating from different domains is a valuable pursuit towards refining predictions. In this chapter, we show how cancer multi-omic data can be analyzed via multimodal machine learning and metabolic modeling. Firstly, we focus on the merits of adopting an integrative systems biology led approach to biomedical data mining. Following this, we propose how constraint-based metabolic models can provide a stable yet adaptable foundation for the integration of multimodal data with machine learning. Finally, we provide a step-by-step tutorial for the combination of machine learning and GSMMs, which includes: (i) tissue-specific constraint-based modeling; (ii) survival analysis using time-to-event prediction for cancer; and (iii) classification and regression approaches for multimodal machine learning. The code associated with the tutorial can be found at https://github.com/Angione-Lab/Tutorials_Combining_ML_and_GSMM .

Protocol for hybrid flux balance, statistical, and machine learning analysis of multi-omic data from the cyanobacterium Synechococcus sp. PCC 7002

Combining a computational framework for flux balance analysis with machine learning improves the accuracy of predicting metabolic activity across conditions, while enabling mechanistic interpretation. This protocol presents a guide to condition-specific metabolic modeling that integrates regularized flux balance analysis with machine learning approaches to extract key features from transcriptomic and fluxomic data. We demonstrate the protocol as applied to Synechococcus sp. PCC 7002; we also outline how it can be adapted to any species or community with available multi-omic data. For complete details on the use and execution of this protocol, please refer to Vijayakumar et al. (2020).

Advances in flux balance analysis by integrating machine learning and mechanism-based models

The availability of multi-omics data sets and genome-scale metabolic models for various organisms provide a platform for modeling and analyzing genotype-to-phenotype relationships. Flux balance analysis is the main tool for predicting flux distributions in genome-scale metabolic models and various data-integrative approaches enable modeling context-specific network behavior. Due to its linear nature, this optimization framework is readily scalable to multi-tissue or -organ and even multi-organism models. However, both data and model size can hamper a straightforward biological interpretation of the estimated fluxes. Moreover, flux balance analysis simulates metabolism at steady-state and thus, in its most basic form, does not consider kinetics or regulatory events. The integration of flux balance analysis with complementary data analysis and modeling techniques offers the potential to overcome these challenges. In particular machine learning approaches have emerged as the tool of choice for data reduction and selection of most important variables in big data sets. Kinetic models and formal languages can be used to simulate dynamic behavior. This review article provides an overview of integrative studies that combine flux balance analysis with machine learning approaches, kinetic models, such as physiology-based pharmacokinetic models, and formal graphical modeling languages, such as Petri nets. We discuss the mathematical aspects and biological applications of these integrated approaches and outline challenges and future perspectives.

What is quantitative plant biology?

Quantitative plant biology is an interdisciplinary field that builds on a long history of biomathematics and biophysics. Today, thanks to high spatiotemporal resolution tools and computational modelling, it sets a new standard in plant science. Acquired data, whether molecular, geometric or mechanical, are quantified, statistically assessed and integrated at multiple scales and across fields. They feed testable predictions that, in turn, guide further experimental tests. Quantitative features such as variability, noise, robustness, delays or feedback loops are included to account for the inner dynamics of plants and their interactions with the environment. Here, we present the main features of this ongoing revolution, through new questions around signalling networks, tissue topology, shape plasticity, biomechanics, bioenergetics, ecology and engineering. In the end, quantitative plant biology allows us to question and better understand our interactions with plants. In turn, this field opens the door to transdisciplinary projects with the society, notably through citizen science.

Dynamic Allocation of Carbon Storage and Nutrient-Dependent Exudation in a Revised Genome-Scale Model of Prochlorococcus

Microbial life in the oceans impacts the entire marine ecosystem, global biogeochemistry and climate. The marine cyanobacterium Prochlorococcus, an abundant component of this ecosystem, releases a significant fraction of the carbon fixed through photosynthesis, but the amount, timing and molecular composition of released carbon are still poorly understood. These depend on several factors, including nutrient availability, light intensity and glycogen storage. Here we combine multiple computational approaches to provide insight into carbon storage and exudation in Prochlorococcus. First, with the aid of a new algorithm for recursive filling of metabolic gaps (ReFill), and through substantial manual curation, we extended an existing genome-scale metabolic model of Prochlorococcus MED4. In this revised model (iSO595), we decoupled glycogen biosynthesis/degradation from growth, thus enabling dynamic allocation of carbon storage. In contrast to standard implementations of flux balance modeling, we made use of forced influx of carbon and light into the cell, to recapitulate overflow metabolism due to the decoupling of photosynthesis and carbon fixation from growth during nutrient limitation. By using random sampling in the ensuing flux space, we found that storage of glycogen or exudation of organic acids are favored when the growth is nitrogen limited, while exudation of amino acids becomes more likely when phosphate is the limiting resource. We next used COMETS to simulate day-night cycles and found that the model displays dynamic glycogen allocation and exudation of organic acids. The switch from photosynthesis and glycogen storage to glycogen depletion is associated with a redistribution of fluxes from the Entner–Doudoroff to the Pentose Phosphate pathway. Finally, we show that specific gene knockouts in iSO595 exhibit dynamic anomalies compatible with experimental observations, further demonstrating the value of this model as a tool to probe the metabolic dynamic of Prochlorococcus.

Microbial inefficient substrate use through the perspective of resource allocation models

Microorganisms extract energy from substrates following strategies that may seem suboptimal at first glance. Beyond the so-called yield-rate trade-off, resource allocation models, which focus on assigning different functional roles to the limited number of enzymes that a cell can support, offer a framework to interpret the inefficient substrate use by microorganisms. We review here relevant examples of substrate conversions where a significant part of the available energy is not utilised and how resource allocation models offer a mechanistic interpretation thereof, notably for open mixed cultures. Future developments are identified, in particular, the challenge of considering metabolic flexibility towards uncertain environmental changes instead of strict fixed optimality objectives, with the final goal of increasing the prediction capabilities of resource allocation models. Finally, we highlight the relevance of resource allocation to understand and enable a promising biorefinery platform revolving around lactate, which would increase the flexibility of waste-to-chemical biorefinery schemes.

Opportunities at the Interface of Network Science and Metabolic Modeling

Metabolism plays a central role in cell physiology because it provides the molecular machinery for growth. At the genome-scale, metabolism is made up of thousands of reactions interacting with one another. Untangling this complexity is key to understand how cells respond to genetic, environmental, or therapeutic perturbations. Here we discuss the roles of two complementary strategies for the analysis of genome-scale metabolic models: Flux Balance Analysis (FBA) and network science. While FBA estimates metabolic flux on the basis of an optimization principle, network approaches reveal emergent properties of the global metabolic connectivity. We highlight how the integration of both approaches promises to deliver insights on the structure and function of metabolic systems with wide-ranging implications in discovery science, precision medicine and industrial biotechnology.

A Hybrid Flux Balance Analysis and Machine Learning Pipeline Elucidates Metabolic Adaptation in Cyanobacteria

Machine learning has recently emerged as a promising tool for inferring multi-omic relationships in biological systems. At the same time, genome-scale metabolic models (GSMMs) can be integrated with such multi-omic data to refine phenotypic predictions. In this work, we use a multi-omic machine learning pipeline to analyze a GSMM of Synechococcus sp. PCC 7002, a cyanobacterium with large potential to produce renewable biofuels. We use regularized flux balance analysis to observe flux response between conditions across photosynthesis and energy metabolism. We then incorporate principal-component analysis, k-means clustering, and LASSO regularization to reduce dimensionality and extract key cross-omic features. Our results suggest that combining metabolic modeling with machine learning elucidates mechanisms used by cyanobacteria to cope with fluctuations in light intensity and salinity that cannot be detected using transcriptomics alone. Furthermore, GSMMs introduce critical mechanistic details that improve the performance of omic-based machine learning methods.

Alternative Crassulacean Acid Metabolism Modes Provide Environment-Specific Water-Saving Benefits in a Leaf Metabolic Model

Crassulacean acid metabolism (CAM) evolved in arid environments as a water-saving alternative to C₃ photosynthesis. There is great interest in engineering more drought-resistant crops by introducing CAM into C₃ plants. However, it is unknown whether full CAM or alternative water-saving modes would be more productive in the environments typically experienced by C₃ crops. To study the effect of temperature and relative humidity on plant metabolism in the context of water saving, we coupled a time-resolved diel (based on a 24-h day-night cycle) model of leaf metabolism to an environment-dependent gas-exchange model. This combined model allowed us to study the emergence of CAM as a trade-off between leaf productivity and water saving. We show that vacuolar storage capacity in the leaf is a major determinant of the extent of CAM. Moreover, our model identified an alternative CAM cycle involving mitochondrial isocitrate dehydrogenase as a potential contributor to initial carbon fixation at night. Simulations across a range of environmental conditions show that the water-saving potential of CAM strongly depends on the daytime weather conditions and that the additional water-saving effect of carbon fixation by isocitrate dehydrogenase can reach 11% total water saving for the conditions tested.

Regulatory dynamic enzyme-cost flux balance analysis: A unifying framework for constraint-based modeling

Integrated modeling of metabolism and gene regulation continues to be a major challenge in computational biology. While there exist approaches like regulatory flux balance analysis (rFBA), dynamic flux balance analysis (dFBA), resource balance analysis (RBA) or dynamic enzyme-cost flux balance analysis (deFBA) extending classical flux balance analysis (FBA) in various directions, there have been no constraint-based methods so far that allow predicting the dynamics of metabolism taking into account both macromolecule production costs and regulatory events. In this paper, we introduce a new constraint-based modeling framework named regulatory dynamic enzyme-cost flux balance analysis (r-deFBA), which unifies dynamic modeling of metabolism, cellular resource allocation and transcriptional regulation in a hybrid discrete-continuous setting. With r-deFBA, we can predict discrete regulatory states together with the continuous dynamics of reaction fluxes, external substrates, enzymes, and regulatory proteins needed to achieve a cellular objective such as maximizing biomass over a time interval. The dynamic optimization problem underlying r-deFBA can be reformulated as a mixed-integer linear optimization problem, for which there exist efficient solvers.

Dynamic metabolic resource allocation based on the maximum entropy principle

Organisms have evolved a variety of mechanisms to cope with the unpredictability of environmental conditions, and yet mainstream models of metabolic regulation are typically based on strict optimality principles that do not account for uncertainty. This paper introduces a dynamic metabolic modelling framework that is a synthesis of recent ideas on resource allocation and the powerful optimal control formulation of Ramkrishna and colleagues. In particular, their work is extended based on the hypothesis that cellular resources are allocated among elementary flux modes according to the principle of maximum entropy. These concepts both generalise and unify prior approaches to dynamic metabolic modelling by establishing a smooth interpolation between dynamic flux balance analysis and dynamic metabolic models without regulation. The resulting theory is successful in describing 'bet-hedging' strategies employed by cell populations dealing with uncertainty in a fluctuating environment, including heterogenous resource investment, accumulation of reserves in growth-limiting conditions, and the observed behaviour of yeast growing in batch and continuous cultures. The maximum entropy principle is also shown to yield an optimal control law consistent with partitioning resources between elementary flux mode families, which has important practical implications for model reduction, selection, and simulation.

Formalizing Metabolic-Regulatory Networks by Hybrid Automata

Computational approaches in systems biology have become a powerful tool for understanding the fundamental mechanisms of cellular metabolism and regulation. However, the interplay between the regulatory and the metabolic system is still poorly understood. In particular, there is a need for formal mathematical frameworks that allow analyzing metabolism together with dynamic enzyme resources and regulatory events. Here, we introduce a metabolic-regulatory network model (MRN) that allows integrating metabolism with transcriptional regulation, macromolecule production and enzyme resources. Using this model, we show that the dynamic interplay between these different cellular processes can be formalized by a hybrid automaton, combining continuous dynamics and discrete control.

Modelling microbial communities using biochemical resource allocation analysis

To understand the functioning and dynamics of microbial communities is a fundamental challenge in current biology. To tackle this challenge, the construction of computational models of interacting microbes is an indispensable tool. There is, however, a large chasm between ecologically motivated descriptions of microbial growth used in many current ecosystems simulations, and detailed metabolic pathway and genome-based descriptions developed in the context of systems and synthetic biology. Here, we seek to demonstrate how resource allocation models of microbial growth offer the potential to advance ecosystem simulations and their parametrization. In particular, recent work on quantitative resource allocation allow us to formulate mechanistic models of microbial growth that are physiologically meaningful while remaining computationally tractable. These models go beyond Michaelis-Menten and Monod-type growth models, and are capable of accounting for emergent properties that underlie the remarkable plasticity of microbial growth. We outline the utility and advantages of using biochemical resource allocation models by considering a coarse-grained model of cyanobacterial growth and demonstrate how the model allows us to address specific questions of relevance for the simulation of marine microbial ecosystems, including the physiological acclimation of protein expression to different environments, the description of co-limitation by several nutrients and the differential use of alternative nutrient sources, as well as the description of metabolic diversity based on our increasing knowledge about quantitative cell physiology.

Seeing the wood for the trees: a forest of methods for optimization and omic-network integration in metabolic modelling

Metabolic modelling has entered a mature phase with dozens of methods and software implementations available to the practitioner and the theoretician. It is not easy for a modeller to be able to see the wood (or the forest) for the trees. Driven by this analogy, we here present a 'forest' of principal methods used for constraint-based modelling in systems biology. This provides a tree-based view of methods available to prospective modellers, also available in interactive version at http://modellingmetabolism.net, where it will be kept updated with new methods after the publication of the present manuscript. Our updated classification of existing methods and tools highlights the most promising in the different branches, with the aim to develop a vision of how existing methods could hybridize and become more complex. We then provide the first hands-on tutorial for multi-objective optimization of metabolic models in R. We finally discuss the implementation of multi-view machine learning approaches in poly-omic integration. Throughout this work, we demonstrate the optimization of trade-offs between multiple metabolic objectives, with a focus on omic data integration through machine learning. We anticipate that the combination of a survey, a perspective on multi-view machine learning and a step-by-step R tutorial should be of interest for both the beginner and the advanced user.

DynamicME: dynamic simulation and refinement of integrated models of metabolism and protein expression

BACKGROUND

Genome-scale models of metabolism and macromolecular expression (ME models) enable systems-level computation of proteome allocation coupled to metabolic phenotype.

RESULTS

We develop DynamicME, an algorithm enabling time-course simulation of cell metabolism and protein expression. DynamicME correctly predicted the substrate utilization hierarchy on a mixed carbon substrate medium. We also found good agreement between predicted and measured time-course expression profiles. ME models involve considerably more parameters than metabolic models (M models). We thus generate an ensemble of models (each model having its rate constants perturbed), and then analyze the models by identifying archetypal time-course metabolite concentration profiles. Furthermore, we use a metaheuristic optimization method to calibrate ME model parameters using time-course measurements such as from a (fed-) batch culture. Finally, we show that constraints on protein concentration dynamics ("inertia") alter the metabolic response to environmental fluctuations, including increased substrate-level phosphorylation and lowered oxidative phosphorylation.

CONCLUSIONS

Overall, DynamicME provides a novel method for understanding proteome allocation and metabolism under complex and transient environments, and to utilize time-course cell culture data for model-based interpretation or model refinement.

A diurnal flux balance model of Synechocystis sp. PCC 6803 metabolism

Phototrophic organisms such as cyanobacteria utilize the sun's energy to convert atmospheric carbon dioxide into organic carbon, resulting in diurnal variations in the cell's metabolism. Flux balance analysis is a widely accepted constraint-based optimization tool for analyzing growth and metabolism, but it is generally used in a time-invariant manner with no provisions for sequestering different biomass components at different time periods. Here we present CycleSyn, a periodic model of Synechocystis sp. PCC 6803 metabolism that spans a 12-hr light/12-hr dark cycle by segmenting it into 12 Time Point Models (TPMs) with a uniform duration of two hours. The developed framework allows for the flow of metabolites across TPMs while inventorying metabolite levels and only allowing for the utilization of currently or previously produced compounds. The 12 TPMs allow for the incorporation of time-dependent constraints that capture the cyclic nature of cellular processes. Imposing bounds on reactions informed by temporally-segmented transcriptomic data enables simulation of phototrophic growth as a single linear programming (LP) problem. The solution provides the time varying reaction fluxes over a 24-hour cycle and the accumulation/consumption of metabolites. The diurnal rhythm of metabolic gene expression driven by the circadian clock and its metabolic consequences is explored. Predicted flux and metabolite pools are in line with published studies regarding the temporal organization of phototrophic growth in Synechocystis PCC 6803 paving the way for constructing time-resolved genome-scale models (GSMs) for organisms with a circadian clock. In addition, the metabolic reorganization that would be required to enable Synechocystis PCC 6803 to temporally separate photosynthesis from oxygen-sensitive nitrogen fixation is also explored using the developed model formalism.

Quantitative insights into the cyanobacterial cell economy

Phototrophic microorganisms are promising resources for green biotechnology. Compared to heterotrophic microorganisms, however, the cellular economy of phototrophic growth is still insufficiently understood. We provide a quantitative analysis of light-limited, light-saturated, and light-inhibited growth of the cyanobacterium Synechocystis sp. PCC 6803 using a reproducible cultivation setup. We report key physiological parameters, including growth rate, cell size, and photosynthetic activity over a wide range of light intensities. Intracellular proteins were quantified to monitor proteome allocation as a function of growth rate. Among other physiological acclimations, we identify an upregulation of the translational machinery and downregulation of light harvesting components with increasing light intensity and growth rate. The resulting growth laws are discussed in the context of a coarse-grained model of phototrophic growth and available data obtained by a comprehensive literature search. Our insights into quantitative aspects of cyanobacterial acclimations to different growth rates have implications to understand and optimize photosynthetic productivity.

Flux-dependent graphs for metabolic networks

Cells adapt their metabolic fluxes in response to changes in the environment. We present a framework for the systematic construction of flux-based graphs derived from organism-wide metabolic networks. Our graphs encode the directionality of metabolic flows via edges that represent the flow of metabolites from source to target reactions. The methodology can be applied in the absence of a specific biological context by modelling fluxes probabilistically, or can be tailored to different environmental conditions by incorporating flux distributions computed through constraint-based approaches such as Flux Balance Analysis. We illustrate our approach on the central carbon metabolism of Escherichia coli and on a metabolic model of human hepatocytes. The flux-dependent graphs under various environmental conditions and genetic perturbations exhibit systemic changes in their topological and community structure, which capture the re-routing of metabolic flows and the varying importance of specific reactions and pathways. By integrating constraint-based models and tools from network science, our framework allows the study of context-specific metabolic responses at a system level beyond standard pathway descriptions.

Cellular metabolism is the result of a highly enmeshed set of biochemical reactions that is naturally amenable to graph-based analyses. Yet there are multiple ways to construct a graph representation from any given metabolic model. Here an international research team of UK and Spain scientists presents a principled approach to study metabolic models through the lens of network science. They propose a framework to construct graphs for genome-scale metabolic models that resolve various challenges, such as the incorporation of pool metabolites, the preservation of the directionality of metabolic flows, and the capability to incorporate specific flux information. The method can be integrated into pipelines based on flux balance analysis and provides a systematic framework to explore changes in network connectivity as a result of environmental shifts or genetic perturbations. The framework thus allows to interrogate context-specific metabolic responses beyond standard pathway descriptions. The authors illustrate the approach through the analysis of Escherichia coli's core metabolism in different growth conditions, as well as a rare metabolic disease affecting human hepatocytes.

A model of optimal protein allocation during phototrophic growth

Photoautotrophic growth depends upon an optimal allocation of finite cellular resources to diverse intracellular processes. Commitment of a certain mass fraction of the proteome to a specific cellular function typically reduces the proteome available for other cellular functions. Here, we develop a semi-quantitative kinetic model of cyanobacterial phototrophic growth to describe such trade-offs of cellular protein allocation. The model is based on coarse-grained descriptions of key cellular processes, in particular carbon uptake, metabolism, photosynthesis, and protein translation. The model is parameterized using literature data and experimentally obtained growth curves. Of particular interest are the resulting cyanobacterial growth laws as fundamental characteristics of cellular growth. We show that the model gives rise to similar growth laws as observed for heterotrophic organisms, with several important differences due to the distinction between light energy and carbon uptake. We discuss recent experimental data supporting the model results and show that coarse-grained growth models have implications for our understanding of the limits of phototrophic growth and bridge a gap between molecular physiology and ecology.

Optimization of Multi-Omic Genome-Scale Models: Methodologies, Hands-on Tutorial, and Perspectives

Genome-scale metabolic models are valuable tools for assessing the metabolic potential of living organisms. Being downstream of gene expression, metabolism is increasingly being used as an indicator of the phenotypic outcome for drugs and therapies. We here present a review of the principal methods used for constraint-based modelling in systems biology, and explore how the integration of multi-omic data can be used to improve phenotypic predictions of genome-scale metabolic models. We believe that the large-scale comparison of the metabolic response of an organism to different environmental conditions will be an important challenge for genome-scale models. Therefore, within the context of multi-omic methods, we describe a tutorial for multi-objective optimization using the metabolic and transcriptomics adaptation estimator (METRADE), implemented in MATLAB. METRADE uses microarray and codon usage data to model bacterial metabolic response to environmental conditions (e.g., antibiotics, temperatures, heat shock). Finally, we discuss key considerations for the integration of multi-omic networks into metabolic models, towards automatically extracting knowledge from such models.

Engineering photosynthetic production of L-lysine

L-lysine and other amino acids are commonly produced through fermentation using strains of heterotrophic bacteria such as Corynebacterium glutamicum. Given the large amount of sugar this process consumes, direct photosynthetic production is intriguing alternative. In this study, we report the development of a cyanobacterium, Synechococcus sp. strain PCC 7002, capable of producing L-lysine with CO2 as the sole carbon-source. We found that heterologous expression of a lysine transporter was required to excrete lysine and avoid intracellular accumulation that correlated with poor fitness. Simultaneous expression of a feedback inhibition resistant aspartate kinase and lysine transporter were sufficient for high productivities, but this was also met with a decreased chlorophyll content and reduced growth rates. Increasing the reductant supply by using NH4+, a more reduced nitrogen source relative to NO3-, resulted in a two-fold increase in productivity directing 18% of fixed carbon to lysine. Given this advantage, we demonstrated lysine production from media formulated with a municipal wastewater treatment sidestream as a nutrient source for increased economic and environmental sustainability. Based on our results, we project that Synechococcus sp. strain PCC 7002 could produce lysine at areal productivities approaching that of sugar cane to lysine via fermentation using non-agricultural lands and low-cost feedstocks.

A Protocol for Generating and Exchanging (Genome-Scale) Metabolic Resource Allocation Models

In this article, we present a protocol for generating a complete (genome-scale) metabolic resource allocation model, as well as a proposal for how to represent such models in the systems biology markup language (SBML). Such models are used to investigate enzyme levels and achievable growth rates in large-scale metabolic networks. Although the idea of metabolic resource allocation studies has been present in the field of systems biology for some years, no guidelines for generating such a model have been published up to now. This paper presents step-by-step instructions for building a (dynamic) resource allocation model, starting with prerequisites such as a genome-scale metabolic reconstruction, through building protein and noncatalytic biomass synthesis reactions and assigning turnover rates for each reaction. In addition, we explain how one can use SBML level 3 in combination with the flux balance constraints and our resource allocation modeling annotation to represent such models.

Cellular trade-offs and optimal resource allocation during cyanobacterial diurnal growth

Cyanobacteria are an integral part of 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 framework to investigate the optimal allocation of cellular resources during diurnal phototrophic growth using a genome-scale metabolic reconstruction of the cyanobacterium Synechococcus elongatus PCC 7942. We formulate phototrophic growth as an autocatalytic process and solve 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. The computational model 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 in qualitative agreement with experimental findings. 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 assess the optimality of metabolic strategies that evolved in phototrophic organisms under diurnal conditions.

Switching of metabolic programs in response to light availability is an essential function of the cyanobacterial circadian output pathway

The transcription factor RpaA is the master regulator of circadian transcription in cyanobacteria, driving genome-wide oscillations in mRNA abundance. Deletion of rpaA has no effect on viability in constant light conditions, but renders cells inviable in cycling conditions when light and dark periods alternate. We investigated the mechanisms underlying this viability defect, and demonstrate that the rpaA^- strain cannot maintain appropriate energy status at night, does not accumulate carbon reserves during the day, and is defective in transcription of genes crucial for utilization of carbohydrate stores at night. Reconstruction of carbon utilization pathways combined with provision of an external carbon source restores energy charge and viability of the rpaA^- strain in light/dark cycling conditions. Our observations highlight how a circadian output pathway controls and temporally coordinates essential pathways in carbon metabolism to maximize fitness of cells facing periodic energy limitations.

DOI:http://dx.doi.org/10.7554/eLife.23210.001

The cycle of day and night is one of the most recurrent and predictable environmental changes on our planet. Consequently, organisms have evolved mechanisms that allow them to measure time over 24 hours and prepare for the periodic changes between light and dark. These mechanisms, known as circadian clocks, alter the activity of some of the organism’s genes in a rhythmic way across the course of a day. This in turn causes certain behaviors and biological activities of the organism to follow a daily cycle.

The bacterium Synechococcus elongatus needs to be able to track the daily cycle of light and dark because it performs photosynthesis and depends on sunlight to form sugars, which can later be broken down to release energy. The time information encoded in the circadian clock of S. elongatus is transmitted to the protein RpaA, which drives the regular circadian changes in gene activity in the cell. If RpaA is removed from the cell or prevented from working, S. elongatus can no longer control rhythmic gene activity and is unable to survive the night.

To better understand how the circadian system schedules biological tasks to help an organism to survive, Puszynska and O'Shea studied S. elongatus cells. This revealed that the bacteria normally prepare for darkness by storing sugars during the day and activating several genes at dusk to make enzymes that are required to break down stored sugars. This provides the cells with energy that they need to survive the night. But mutant cells that lack the gene that produces RpaA do not prepare for darkness; they do not accumulate a store of sugars during the day or activate the vital genes at dusk. They have low internal energy levels in the dark and they cannot survive long periods of darkness.

Providing the mutant cells with sugar and restoring the activity of the genes responsible for breaking down sugar enabled the cells to maintain energy in darkness and survive the night. It therefore appears that one role of the circadian system of S. elongatus is to coordinate building up sugar reserves during the day with breaking down sugar stores to generate energy during the night.

Puszynska and O'Shea also found many other genes that are not activated at dusk in the mutant cells. It will therefore be important to study whether other pathways that help cells to survive and grow are defective in these mutant cells.

DOI:http://dx.doi.org/10.7554/eLife.23210.002

Toward Multiscale Models of Cyanobacterial Growth: A Modular Approach

Oxygenic photosynthesis dominates global primary productivity ever since its evolution more than three billion years ago. While many aspects of phototrophic growth are well understood, it remains a considerable challenge to elucidate the manifold dependencies and interconnections between the diverse cellular processes that together facilitate the synthesis of new cells. Phototrophic growth involves the coordinated action of several layers of cellular functioning, ranging from the photosynthetic light reactions and the electron transport chain, to carbon-concentrating mechanisms and the assimilation of inorganic carbon. It requires the synthesis of new building blocks by cellular metabolism, protection against excessive light, as well as diurnal regulation by a circadian clock and the orchestration of gene expression and cell division. Computational modeling allows us to quantitatively describe these cellular functions and processes relevant for phototrophic growth. As yet, however, computational models are mostly confined to the inner workings of individual cellular processes, rather than describing the manifold interactions between them in the context of a living cell. Using cyanobacteria as model organisms, this contribution seeks to summarize existing computational models that are relevant to describe phototrophic growth and seeks to outline their interactions and dependencies. Our ultimate aim is to understand cellular functioning and growth as the outcome of a coordinated operation of diverse yet interconnected cellular processes.

Flux balance analysis of photoautotrophic metabolism: Uncovering new biological details of subsystems involved in cyanobacterial photosynthesis

We have constructed and experimentally tested a comprehensive genome-scale model of photoautotrophic growth, denoted iSyp821, for the cyanobacterium Synechococcus sp. PCC 7002. iSyp821 incorporates a variable biomass objective function (vBOF), in which stoichiometries of the major biomass components vary according to light intensity. The vBOF was constrained to fit the measured cellular carbohydrate/protein content under different light intensities. iSyp821 provides rigorous agreement with experimentally measured cell growth rates and inorganic carbon uptake rates as a function of light intensity. iSyp821 predicts two observed metabolic transitions that occur as light intensity increases: 1) from PSI-cyclic to linear electron flow (greater redox energy), and 2) from carbon allocation as proteins (growth) to carbohydrates (energy storage) mode. iSyp821 predicts photoautotrophic carbon flux into 1) a hybrid gluconeogenesis-pentose phosphate (PP) pathway that produces glycogen by an alternative pathway than conventional gluconeogenesis, and 2) the photorespiration pathway to synthesize the essential amino acid, glycine. Quantitative fluxes through both pathways were verified experimentally by following the kinetics of formation of ¹³C metabolites from ¹³CO₂ fixation. iSyp821 was modified to include changes in gene products (enzymes) from experimentally measured transcriptomic data and applied to estimate changes in concentrations of metabolites arising from nutrient stress. Using this strategy, we found that iSyp821 correctly predicts the observed redistribution pattern of carbon products under nitrogen depletion, including decreased rates of CO₂ uptake, amino acid synthesis, and increased rates of glycogen and lipid synthesis.

Computational metabolic engineering strategies for growth-coupled biofuel production by Synechocystis

Chemical and fuel production by photosynthetic cyanobacteria is a promising technology but to date has not reached competitive rates and titers. Genome-scale metabolic modeling can reveal limitations in cyanobacteria metabolism and guide genetic engineering strategies to increase chemical production. Here, we used constraint-based modeling and optimization algorithms on a genome-scale model of Synechocystis PCC6803 to find ways to improve productivity of fermentative, fatty-acid, and terpene-derived fuels. OptGene and MOMA were used to find heuristics for knockout strategies that could increase biofuel productivity. OptKnock was used to find a set of knockouts that led to coupling between biofuel and growth. Our results show that high productivity of fermentation or reversed beta-oxidation derived alcohols such as 1-butanol requires elimination of NADH sinks, while terpenes and fatty-acid based fuels require creating imbalances in intracellular ATP and NADPH production and consumption. The FBA-predicted productivities of these fuels are at least 10-fold higher than those reported so far in the literature. We also discuss the physiological and practical feasibility of implementing these knockouts. This work gives insight into how cyanobacteria could be engineered to reach competitive biofuel productivities.

Synthetic biology and regulatory networks: where metabolic systems biology meets control engineering

Metabolic pathways can be engineered to maximize the synthesis of various products of interest. With the advent of computational systems biology, this endeavour is usually carried out through in silico theoretical studies with the aim to guide and complement further in vitro and in vivo experimental efforts. Clearly, what counts is the result in vivo, not only in terms of maximal productivity but also robustness against environmental perturbations. Engineering an organism towards an increased production flux, however, often compromises that robustness. In this contribution, we review and investigate how various analytical approaches used in metabolic engineering and synthetic biology are related to concepts developed by systems and control engineering. While trade-offs between production optimality and cellular robustness have already been studied diagnostically and statically, the dynamics also matter. Integration of the dynamic design aspects of control engineering with the more diagnostic aspects of metabolic, hierarchical control and regulation analysis is leading to the new, conceptual and operational framework required for the design of robust and productive dynamic pathways.