Economics of membrane occupancy and respiro-fermentation

Bacterial economics: adaptation to stress conditions via stage-wise changes in the response mechanism

Common features of microbial adaptation are analysed with mathematical models and extended to stress conditions when the bacterial population declines before growing again. A parallel is drawn between bacterial and human communities in terms of non-mutation-based adaptation (acclimation) to stress. For a case study, the behaviour of Escherichia coli under osmotic stress, is detailed. It is suggested that stress modelling adaptation should be the focus of further developments in predictive food microbiology.

Understanding carbon catabolite repression in Escherichia coli using quantitative models

Carbon catabolite repression (CCR) controls the order in which different carbon sources are metabolized. Although this system is one of the paradigms of the regulation of gene expression in bacteria, the underlying mechanisms remain controversial. CCR involves the coordination of different subsystems of the cell that are responsible for the uptake of carbon sources, their breakdown for the production of energy and precursors, and the conversion of the latter to biomass. The complexity of this integrated system, with regulatory mechanisms cutting across metabolism, gene expression, and signaling, and that are subject to global physical and physiological constraints, has motivated important modeling efforts over the past four decades, especially in the enterobacterium Escherichia coli. Different hypotheses concerning the dynamic functioning of the system have been explored by a variety of modeling approaches. We review these studies and summarize their contributions to the quantitative understanding of CCR, focusing on diauxic growth in E. coli. Moreover, we propose a highly simplified representation of diauxic growth that makes it possible to bring out the salient features of the models proposed in the literature and confront and compare the explanations they provide.

Minimization of extracellular space as a driving force in prokaryote association and the origin of eukaryotes

BACKGROUND

Internalization-based hypotheses of eukaryotic origin require close physical association of host and symbiont. Prior hypotheses of how these associations arose include chance, specific metabolic couplings between partners, and prey-predator/parasite interactions. Since these hypotheses were proposed, it has become apparent that mixed-species, close-association assemblages (biofilms) are widespread and predominant components of prokaryotic ecology. Which forces drove prokaryotes to evolve the ability to form these assemblages are uncertain. Bacteria and archaea have also been found to form membrane-lined interconnections (nanotubes) through which proteins and RNA pass. These observations, combined with the structure of the nuclear envelope and an energetic benefit of close association (see below), lead us to propose a novel hypothesis of the driving force underlying prokaryotic close association and the origin of eukaryotes.

RESULTS

Respiratory proton transport does not alter external pH when external volume is effectively infinite. Close physical association decreases external volume. For small external volumes, proton transport decreases external pH, resulting in each transported proton increasing proton motor force to a greater extent. We calculate here that in biofilms this effect could substantially decrease how many protons need to be transported to achieve a given proton motor force. Based as it is solely on geometry, this energetic benefit would occur for all prokaryotes using proton-based respiration.

CONCLUSIONS

This benefit may be a driving force in biofilm formation. Under this hypothesis a very wide range of prokaryotic species combinations could serve as eukaryotic progenitors. We use this observation and the discovery of prokaryotic nanotubes to propose that eukaryotes arose from physically distinct, functionally specialized (energy factory, protein factory, DNA repository/RNA factory), obligatorily symbiotic prokaryotes in which the protein factory and DNA repository/RNA factory cells were coupled by nanotubes and the protein factory ultimately internalized the other two. This hypothesis naturally explains many aspects of eukaryotic physiology, including the nuclear envelope being a folded single membrane repeatedly pierced by membrane-bound tubules (the nuclear pores), suggests that species analogous or homologous to eukaryotic progenitors are likely unculturable as monocultures, and makes a large number of testable predictions.

REVIEWERS

This article was reviewed by Purificación López-García and Toni Gabaldón.

An evolutionary perspective on the Crabtree effect

The capability to ferment sugars into ethanol is a key metabolic trait of yeasts. Crabtree-positive yeasts use fermentation even in the presence of oxygen, where they could, in principle, rely on the respiration pathway. This is surprising because fermentation has a much lower ATP yield than respiration (2 ATP vs. approximately 18 ATP per glucose). While genetic events in the evolution of the Crabtree effect have been identified, the selective advantages provided by this trait remain controversial. In this review we analyse explanations for the emergence of the Crabtree effect from an evolutionary and game-theoretical perspective. We argue that an increased rate of ATP production is likely the most important factor behind the emergence of the Crabtree effect.

Reconstruction and modeling protein translocation and compartmentalization in Escherichia coli at the genome-scale

Background

Membranes play a crucial role in cellular functions. Membranes provide a physical barrier, control the trafficking of substances entering and leaving the cell, and are a major determinant of cellular ultra-structure. In addition, components embedded within the membrane participate in cell signaling, energy transduction, and other critical cellular functions. All these processes must share the limited space in the membrane; thus it represents a notable constraint on cellular functions. Membrane- and location-based processes have not yet been reconstructed and explicitly integrated into genome-scale models.

Results

The recent genome-scale model of metabolism and protein expression in Escherichia coli (called a ME-model) computes the complete composition of the proteome required to perform whole cell functions. Here we expand the ME-model to include (1) a reconstruction of protein translocation pathways, (2) assignment of all cellular proteins to one of four compartments (cytoplasm, inner membrane, periplasm, and outer membrane) and a translocation pathway, (3) experimentally determined translocase catalytic and porin diffusion rates, and (4) a novel membrane constraint that reflects cell morphology. Comparison of computations performed with this expanded ME-model, named iJL1678-ME, against available experimental data reveals that the model accurately describes translocation pathway expression and the functional proteome by compartmentalized mass.

Conclusion

iJL1678-ME enables the computation of cellular phenotypes through an integrated computation of proteome composition, abundance, and activity in four cellular compartments (cytoplasm, periplasm, inner and outer membrane). Reconstruction and validation of the model has demonstrated that the iJL1678-ME is capable of capturing the functional content of membranes, cellular compartment-specific composition, and that it can be utilized to examine the effect of perturbing an expanded set of network components. iJL1678-ME takes a notable step towards the inclusion of cellular ultra-structure in genome-scale models.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-014-0110-6) contains supplementary material, which is available to authorized users.

A genome-scale metabolic flux model of Escherichia coli K-12 derived from the EcoCyc database

BACKGROUND

Constraint-based models of Escherichia coli metabolic flux have played a key role in computational studies of cellular metabolism at the genome scale. We sought to develop a next-generation constraint-based E. coli model that achieved improved phenotypic prediction accuracy while being frequently updated and easy to use. We also sought to compare model predictions with experimental data to highlight open questions in E. coli biology.

RESULTS

We present EcoCyc-18.0-GEM, a genome-scale model of the E. coli K-12 MG1655 metabolic network. The model is automatically generated from the current state of EcoCyc using the MetaFlux software, enabling the release of multiple model updates per year. EcoCyc-18.0-GEM encompasses 1445 genes, 2286 unique metabolic reactions, and 1453 unique metabolites. We demonstrate a three-part validation of the model that breaks new ground in breadth and accuracy: (i) Comparison of simulated growth in aerobic and anaerobic glucose culture with experimental results from chemostat culture and simulation results from the E. coli modeling literature. (ii) Essentiality prediction for the 1445 genes represented in the model, in which EcoCyc-18.0-GEM achieves an improved accuracy of 95.2% in predicting the growth phenotype of experimental gene knockouts. (iii) Nutrient utilization predictions under 431 different media conditions, for which the model achieves an overall accuracy of 80.7%. The model's derivation from EcoCyc enables query and visualization via the EcoCyc website, facilitating model reuse and validation by inspection. We present an extensive investigation of disagreements between EcoCyc-18.0-GEM predictions and experimental data to highlight areas of interest to E. coli modelers and experimentalists, including 70 incorrect predictions of gene essentiality on glucose, 80 incorrect predictions of gene essentiality on glycerol, and 83 incorrect predictions of nutrient utilization.

CONCLUSION

Significant advantages can be derived from the combination of model organism databases and flux balance modeling represented by MetaFlux. Interpretation of the EcoCyc database as a flux balance model results in a highly accurate metabolic model and provides a rigorous consistency check for information stored in the database.

A central role for carbon-overflow pathways in the modulation of bacterial cell death

Similar to developmental programs in eukaryotes, the death of a subpopulation of cells is thought to benefit bacterial biofilm development. However mechanisms that mediate a tight control over cell death are not clearly understood at the population level. Here we reveal that CidR dependent pyruvate oxidase (CidC) and α-acetolactate synthase/decarboxylase (AlsSD) overflow metabolic pathways, which are active during staphylococcal biofilm development, modulate cell death to achieve optimal biofilm biomass. Whereas acetate derived from CidC activity potentiates cell death in cells by a mechanism dependent on intracellular acidification and respiratory inhibition, AlsSD activity effectively counters CidC action by diverting carbon flux towards neutral rather than acidic byproducts and consuming intracellular protons in the process. Furthermore, the physiological features that accompany metabolic activation of cell death bears remarkable similarities to hallmarks of eukaryotic programmed cell death, including the generation of reactive oxygen species and DNA damage. Finally, we demonstrate that the metabolic modulation of cell death not only affects biofilm development but also biofilm-dependent disease outcomes. Given the ubiquity of such carbon overflow pathways in diverse bacterial species, we propose that the metabolic control of cell death may be a fundamental feature of prokaryotic development.

Many bacterial species including the pathogen Staphylococcus aureus are capable of adhering to surfaces and forming complex communities called biofilms. This mode of growth can be particularly challenging from an infection control standpoint, as they are often refractory to antibiotics and host immune system. Although developmental processes underlying biofilm formation are not entirely clear, recent evidence suggests that cell death of a subpopulation is crucial for its maturation. In this study we provide insight regarding the metabolic pathways that control cell death and demonstrate that acetate, a by-product of glucose catabolism, potentiates a form of cell death that exhibits physiological and biochemical hallmarks of apoptosis in eukaryotic organisms. Finally, we demonstrate that altering the ability of metabolic pathways that regulate acetate mediated cell death in S. aureus affects the outcome of biofilm-related diseases, such as infective endocarditis.

Interactions in the microbiome: communities of organisms and communities of genes

A central challenge in microbial community ecology is the delineation of appropriate units of biodiversity, which can be taxonomic, phylogenetic, or functional in nature. The term 'community' is applied ambiguously; in some cases, the term refers simply to a set of observed entities, while in other cases, it requires that these entities interact with one another. Microorganisms can rapidly gain and lose genes, potentially decoupling community roles from taxonomic and phylogenetic groupings. Trait-based approaches offer a useful alternative, but many traits can be defined based on gene functions, metabolic modules, and genomic properties, and the optimal set of traits to choose is often not obvious. An analysis that considers taxon assignment and traits in concert may be ideal, with the strengths of each approach offsetting the weaknesses of the other. Individual genes also merit consideration as entities in an ecological analysis, with characteristics such as diversity, turnover, and interactions modeled using genes rather than organisms as entities. We identify some promising avenues of research that are likely to yield a deeper understanding of microbial communities that shift from observation-based questions of 'Who is there?' and 'What are they doing?' to the mechanistically driven question of 'How will they respond?'

Structural control of metabolic flux

Organisms have to continuously adapt to changing environmental conditions or undergo developmental transitions. To meet the accompanying change in metabolic demands, the molecular mechanisms of adaptation involve concerted interactions which ultimately induce a modification of the metabolic state, which is characterized by reaction fluxes and metabolite concentrations. These state transitions are the effect of simultaneously manipulating fluxes through several reactions. While metabolic control analysis has provided a powerful framework for elucidating the principles governing this orchestrated action to understand metabolic control, its applications are restricted by the limited availability of kinetic information. Here, we introduce structural metabolic control as a framework to examine individual reactions' potential to control metabolic functions, such as biomass production, based on structural modeling. The capability to carry out a metabolic function is determined using flux balance analysis (FBA). We examine structural metabolic control on the example of the central carbon metabolism of Escherichia coli by the recently introduced framework of functional centrality (FC). This framework is based on the Shapley value from cooperative game theory and FBA, and we demonstrate its superior ability to assign “share of control” to individual reactions with respect to metabolic functions and environmental conditions. A comparative analysis of various scenarios illustrates the usefulness of FC and its relations to other structural approaches pertaining to metabolic control. We propose a Monte Carlo algorithm to estimate FCs for large networks, based on the enumeration of elementary flux modes. We further give detailed biological interpretation of FCs for production of lactate and ATP under various respiratory conditions.

Insight into the functioning of metabolic control to meet changing demands is a first step in rational engineering of biological systems towards a desired behavior. Metabolic control analysis provides the means to examine the impact of change of reaction fluxes on a specific target flux based on kinetic modeling, but suffers from limitations of the kinetic approach. Here, we introduce and analyze structural metabolic control as a framework to overcome these limitations. We utilize functional centrality, a framework based on the Shapley value from cooperative game theory and flux balance analysis, to determine the contribution of individual reactions to the functions accomplished by a metabolic network. These contributions, in turn, depend on the control exerted on the remaining network. Functional centrality provides the mathematical means to gain further understanding of metabolic control. The potential applications range from facilitating strategies of rational strain design to drug target identification.

Enzyme allocation problems in kinetic metabolic networks: optimal solutions are elementary flux modes

The survival and proliferation of cells and organisms require a highly coordinated allocation of cellular resources to ensure the efficient synthesis of cellular components. In particular, the total enzymatic capacity for cellular metabolism is limited by finite resources that are shared between all enzymes, such as cytosolic space, energy expenditure for amino-acid synthesis, or micro-nutrients. While extensive work has been done to study constrained optimization problems based only on stoichiometric information, mathematical results that characterize the optimal flux in kinetic metabolic networks are still scarce. Here, we study constrained enzyme allocation problems with general kinetics, using the theory of oriented matroids. We give a rigorous proof for the fact that optimal solutions of the non-linear optimization problem are elementary flux modes. This finding has significant consequences for our understanding of optimality in metabolic networks as well as for the identification of metabolic switches and the computation of optimal flux distributions in kinetic metabolic networks.

Genome-scale models of metabolism and gene expression extend and refine growth phenotype prediction

Growth is a fundamental process of life. Growth requirements are well-characterized experimentally for many microbes; however, we lack a unified model for cellular growth. Such a model must be predictive of events at the molecular scale and capable of explaining the high-level behavior of the cell as a whole. Here, we construct an ME-Model for Escherichia coli--a genome-scale model that seamlessly integrates metabolic and gene product expression pathways. The model computes ~80% of the functional proteome (by mass), which is used by the cell to support growth under a given condition. Metabolism and gene expression are interdependent processes that affect and constrain each other. We formalize these constraints and apply the principle of growth optimization to enable the accurate prediction of multi-scale phenotypes, ranging from coarse-grained (growth rate, nutrient uptake, by-product secretion) to fine-grained (metabolic fluxes, gene expression levels). Our results unify many existing principles developed to describe bacterial growth.

Glycolytic strategy as a tradeoff between energy yield and protein cost

Contrary to the textbook portrayal of glycolysis as a single pathway conserved across all domains of life, not all sugar-consuming organisms use the canonical Embden-Meyerhoff-Parnass (EMP) glycolytic pathway. Prokaryotic glucose metabolism is particularly diverse, including several alternative glycolytic pathways, the most common of which is the Entner-Doudoroff (ED) pathway. The prevalence of the ED pathway is puzzling as it produces only one ATP per glucose--half as much as the EMP pathway. We argue that the diversity of prokaryotic glucose metabolism may reflect a tradeoff between a pathway's energy (ATP) yield and the amount of enzymatic protein required to catalyze pathway flux. We introduce methods for analyzing pathways in terms of thermodynamics and kinetics and show that the ED pathway is expected to require several-fold less enzymatic protein to achieve the same glucose conversion rate as the EMP pathway. Through genomic analysis, we further show that prokaryotes use different glycolytic pathways depending on their energy supply. Specifically, energy-deprived anaerobes overwhelmingly rely upon the higher ATP yield of the EMP pathway, whereas the ED pathway is common among facultative anaerobes and even more common among aerobes. In addition to demonstrating how protein costs can explain the use of alternative metabolic strategies, this study illustrates a direct connection between an organism's environment and the thermodynamic and biochemical properties of the metabolic pathways it employs.

Multi-scale modeling for sustainable chemical production

With recent advances in metabolic engineering, it is now technically possible to produce a wide portfolio of existing petrochemical products from biomass feedstock. In recent years, a number of modeling approaches have been developed to support the engineering and decision-making processes associated with the development and implementation of a sustainable biochemical industry. The temporal and spatial scales of modeling approaches for sustainable chemical production vary greatly, ranging from metabolic models that aid the design of fermentative microbial strains to material and monetary flow models that explore the ecological impacts of all economic activities. Research efforts that attempt to connect the models at different scales have been limited. Here, we review a number of existing modeling approaches and their applications at the scales of metabolism, bioreactor, overall process, chemical industry, economy, and ecosystem. In addition, we propose a multi-scale approach for integrating the existing models into a cohesive framework. The major benefit of this proposed framework is that the design and decision-making at each scale can be informed, guided, and constrained by simulations and predictions at every other scale. In addition, the development of this multi-scale framework would promote cohesive collaborations across multiple traditionally disconnected modeling disciplines to achieve sustainable chemical production.

Tuning primary metabolism for heterologous pathway productivity

Tuning expression of competing endogenous pathways has been identified as an effective strategy in the optimization of heterologous production pathways. However, intervention at the first step of glycolysis, where no alternate routes of carbon utilization exist, remains unexplored. In this work we have engineered a viable E. coli host that decouples glucose transport and phosphorylation, enabling independent control of glucose flux to a heterologous pathway of interest through glucokinase (glk) expression. Using community sourced and curated promoters, glk expression was varied over a 3-fold range while maintaining cellular viability. The effects of glk expression on the productivity of a model glucose-consuming pathway were also studied. Through control of glycolytic flux we were able to explore a number of cellular phenotypes and vary the yield of our model pathway by up to 2-fold in a controllable manner.

Dynamic strain scanning optimization: an efficient strain design strategy for balanced yield, titer, and productivity. DySScO strategy for strain design

Background

In recent years, constraint-based metabolic models have emerged as an important tool for metabolic engineering; a number of computational algorithms have been developed for identifying metabolic engineering strategies where the production of the desired chemical is coupled with the growth of the organism. A caveat of the existing algorithms is that they do not take the bioprocess into consideration; as a result, while the product yield can be optimized using these algorithms, the product titer and productivity cannot be optimized. In order to address this issue, we developed the Dynamic Strain Scanning Optimization (DySScO) strategy, which integrates the Dynamic Flux Balance Analysis (dFBA) method with existing strain algorithms.

Results

In order to demonstrate the effective of the DySScO strategy, we applied this strategy to the design of Escherichia coli strains targeted for succinate and 1,4-butanediol production respectively. We evaluated consequences of the tradeoff between growth yield and product yield with respect to titer and productivity, and showed that the DySScO strategy is capable of producing strains that balance the product yield, titer, and productivity. In addition, we evaluated the economic viability of the designed strain, and showed that the economic performance of a strain can be strongly affected by the price difference between the product and the feedstock.

Conclusion

Our study demonstrated that the DySScO strategy is a useful computational tool for designing microbial strains with balanced yield, titer, and productivity, and has potential applications in evaluating the economic performance of the design strains.

Basic and applied uses of genome-scale metabolic network reconstructions of Escherichia coli

The genome-scale model (GEM) of metabolism in the bacterium Escherichia coli K-12 has been in development for over a decade and is now in wide use. GEM-enabled studies of E. coli have been primarily focused on six applications: (1) metabolic engineering, (2) model-driven discovery, (3) prediction of cellular phenotypes, (4) analysis of biological network properties, (5) studies of evolutionary processes, and (6) models of interspecies interactions. In this review, we provide an overview of these applications along with a critical assessment of their successes and limitations, and a perspective on likely future developments in the field. Taken together, the studies performed over the past decade have established a genome-scale mechanistic understanding of genotype-phenotype relationships in E. coli metabolism that forms the basis for similar efforts for other microbial species. Future challenges include the expansion of GEMs by integrating additional cellular processes beyond metabolism, the identification of key constraints based on emerging data types, and the development of computational methods able to handle such large-scale network models with sufficient accuracy.

From measurement to implementation of metabolic fluxes

The intracellular reaction rates (fluxes) are the ultimate outcome of the activities of the complete inventory (from DNA to metabolite) and in their sum determine the cellular phenotype. The genotype-phenotype relationship is fundamental in such different fields as cancer research and biotechnology. Here, we summarize the developments in determining metabolic fluxes, inferring major pathways from the DNA-sequence, estimating optimal flux distributions, and how these flux distributions can be achieved in vivo. The technical advances to intervene with the many levels of the cellular architecture allow the implementation of new strategies in for example Metabolic Engineering.

Towards metagenome-scale models for industrial applications--the case of Lactic Acid Bacteria

We review the uses and limitations of modelling approaches that are in use in the field of Lactic Acid Bacteria (LAB). We describe recent developments in model construction and computational methods, starting from application of such models to monocultures. However, since most applications in food biotechnology involve complex nutrient environments and mixed cultures, we extend the scope to discuss developments in modelling such complex systems. With metagenomics and meta-functional genomics data becoming available, the developments in genome-scale community models are discussed. We conclude that exploratory tools are available and useful, but truly predictive mechanistic models will remain a major challenge in the field.

Oxygen response of the wine yeast Saccharomyces cerevisiae EC1118 grown under carbon-sufficient, nitrogen-limited enological conditions

Discrete additions of oxygen play a critical role in alcoholic fermentation. However, few studies have quantitated the fate of dissolved oxygen and its impact on wine yeast cell physiology under enological conditions. We simulated the range of dissolved oxygen concentrations that occur after a pump-over during the winemaking process by sparging nitrogen-limited continuous cultures with oxygen-nitrogen gaseous mixtures. When the dissolved oxygen concentration increased from 1.2 to 2.7 μM, yeast cells changed from a fully fermentative to a mixed respirofermentative metabolism. This transition is characterized by a switch in the operation of the tricarboxylic acid cycle (TCA) and an activation of NADH shuttling from the cytosol to mitochondria. Nevertheless, fermentative ethanol production remained the major cytosolic NADH sink under all oxygen conditions, suggesting that the limitation of mitochondrial NADH reoxidation is the major cause of the Crabtree effect. This is reinforced by the induction of several key respiratory genes by oxygen, despite the high sugar concentration, indicating that oxygen overrides glucose repression. Genes associated with other processes, such as proline uptake, cell wall remodeling, and oxidative stress, were also significantly affected by oxygen. The results of this study indicate that respiration is responsible for a substantial part of the oxygen response in yeast cells during alcoholic fermentation. This information will facilitate the development of temporal oxygen addition strategies to optimize yeast performance in industrial fermentations.

Metabolic shifts: a fitness perspective for microbial cell factories

Performance of industrial microorganisms as cell factories is limited by the capacity to channel nutrients to desired products, of which optimal production usually requires careful manipulation of process conditions, or strain improvement. The focus in process improvement is often on understanding and manipulating the regulation of metabolism. Nonetheless, one encounters situations where organisms are remarkably resilient to further optimization or their properties become unstable. Therefore it is important to understand the origin of these apparent limitations to find whether and how they can be improved. We argue that by considering fitness effects of regulation, a more generic explanation for certain behaviour can be obtained. In this view, apparent process limitations arise from trade-offs that cells faced as they evolved to improve fitness. A deeper understanding of such trade-offs using a systems biology approach can ultimately enhance performance of cell factories.

Shrinking the metabolic solution space using experimental datasets

Constraint-based models of metabolism have been used in a variety of studies on drug discovery, metabolic engineering, evolution, and multi-species interactions. These genome-scale models can be generated for any sequenced organism since their main parameters (i.e., reaction stoichiometry) are highly conserved. Their relatively low parameter requirement makes these models easy to develop; however, these models often result in a solution space with multiple possible flux distributions, making it difficult to determine the precise flux state in the cell. Recent research efforts in this modeling field have investigated how additional experimental data, including gene expression, protein expression, metabolite concentrations, and kinetic parameters, can be used to reduce the solution space. This mini-review provides a summary of the data-driven computational approaches that are available for reducing the solution space and thereby improve predictions of intracellular fluxes by constraint-based models.

Optimality principles in the regulation of metabolic networks

One of the challenging tasks in systems biology is to understand how molecular networks give rise to emergent functionality and whether universal design principles apply to molecular networks. To achieve this, the biophysical, evolutionary and physiological constraints that act on those networks need to be identified in addition to the characterisation of the molecular components and interactions. Then, the cellular "task" of the network-its function-should be identified. A network contributes to organismal fitness through its function. The premise is that the same functions are often implemented in different organisms by the same type of network; hence, the concept of design principles. In biology, due to the strong forces of selective pressure and natural selection, network functions can often be understood as the outcome of fitness optimisation. The hypothesis of fitness optimisation to understand the design of a network has proven to be a powerful strategy. Here, we outline the use of several optimisation principles applied to biological networks, with an emphasis on metabolic regulatory networks. We discuss the different objective functions and constraints that are considered and the kind of understanding that they provide.

Restricted cooperative games on metabolic networks reveal functionally important reactions

Understanding the emerging properties of complex biological systems is in the crux of systems biology studies. Computational methods for elucidating the role of each component in the synergetic interplay can be used to identify targets for genetic and metabolic engineering. In particular, we aim at determining the importance of reactions in a metabolic network with respect to a specific biological function. Therefore, we propose a novel game-theoretic framework which integrates restricted cooperative games with the outcome of flux balance analysis. We define productivity games on metabolic networks and present an analysis of their unrestricted and restricted variants based on the game-theoretic solution concept of the Shapley value. Correspondingly, this concept provides a characterization of the robustness and functional centrality for each enzyme involved in a given metabolic network. Furthermore, the comparison of two different environments - feast and famine - demonstrates the dependence of the results on the imposed flux capacities.

Prediction of microbial growth rate versus biomass yield by a metabolic network with kinetic parameters

Identifying the factors that determine microbial growth rate under various environmental and genetic conditions is a major challenge of systems biology. While current genome-scale metabolic modeling approaches enable us to successfully predict a variety of metabolic phenotypes, including maximal biomass yield, the prediction of actual growth rate is a long standing goal. This gap stems from strictly relying on data regarding reaction stoichiometry and directionality, without accounting for enzyme kinetic considerations. Here we present a novel metabolic network-based approach, MetabOlic Modeling with ENzyme kineTics (MOMENT), which predicts metabolic flux rate and growth rate by utilizing prior data on enzyme turnover rates and enzyme molecular weights, without requiring measurements of nutrient uptake rates. The method is based on an identified design principle of metabolism in which enzymes catalyzing high flux reactions across different media tend to be more efficient in terms of having higher turnover numbers. Extending upon previous attempts to utilize kinetic data in genome-scale metabolic modeling, our approach takes into account the requirement for specific enzyme concentrations for catalyzing predicted metabolic flux rates, considering isozymes, protein complexes, and multi-functional enzymes. MOMENT is shown to significantly improve the prediction accuracy of various metabolic phenotypes in E. coli, including intracellular flux rates and changes in gene expression levels under different growth rates. Most importantly, MOMENT is shown to predict growth rates of E. coli under a diverse set of media that are correlated with experimental measurements, markedly improving upon existing state-of-the art stoichiometric modeling approaches. These results support the view that a physiological bound on cellular enzyme concentrations is a key factor that determines microbial growth rate.

While current genome-scale metabolic modeling approaches enable us to successfully predict a variety of metabolic phenotypes, identifying the factors that determine microbial growth rate and the prediction of growth rates under various conditions is still an open challenge. Here we present a metabolic network-based approach, MetabOlic Modeling with ENzyme kineTics (MOMENT), which predicts growth rates by integrating standard stoichiometric modeling with prior data on enzyme turnover rates and enzyme molecular weights, considering a physiological bound on total enzymes' concentration. The method is based on a finding that enzymes catalyzing high flux reactions tend to be more efficient in terms of having higher turnover numbers. MOMENT predicts growth rates of E. coli across a set of 24 different media that are significantly correlated with experimental measurements, while existing state-of-the art stoichiometric modeling approaches fail to do so. These results suggest that a bound on cellular enzyme concentrations is a key factor that determines microbial growth rate.

Redox balance is key to explaining full vs. partial switching to low-yield metabolism

BACKGROUND

Low-yield metabolism is a puzzling phenomenon in many unicellular and multicellular organisms. In abundance of glucose, many cells use a highly wasteful fermentation pathway despite the availability of a high-yield pathway, producing many ATP molecules per glucose, e.g., oxidative phosphorylation. Some of these organisms, including the lactic acid bacterium Lactococcus lactis, downregulate their high-yield pathway in favor of the low-yield pathway. Other organisms, including Escherichia coli do not reduce the flux through the high-yield pathway, employing the low-yield pathway in parallel with a fully active high-yield pathway. For what reasons do some species use the high-yield and low-yield pathways concurrently and what makes others downregulate the high-yield pathway? A classic rationale for metabolic fermentation is overflow metabolism. Because the throughput of metabolic pathways is limited, influx of glucose exceeding the pathway's throughput capacity is thought to be redirected into an alternative, low-yield pathway. This overflow metabolism rationale suggests that cells would only use fermentation once the high-yield pathway runs at maximum rate, but it cannot explain why cells would decrease the flux through the high-yield pathway.

RESULTS

Using flux balance analysis with molecular crowding (FBAwMC), a recent extension to flux balance analysis (FBA) that assumes that the total flux through the metabolic network is limited, we investigate the differences between Saccharomyces cerevisiae and L. lactis that downregulate the high-yield pathway at increasing glucose concentrations, and E. coli, which keeps the high-yield pathway functioning at maximal rate. FBAwMC correctly predicts the metabolic switching mode in these three organisms, suggesting that metabolic network architecture is responsible for differences in metabolic switching mode. Based on our analysis, we expect gradual, "overflow-like" switching behavior in organisms that have an additional energy-yielding pathway that does not consume NADH (e.g., acetate production in E. coli). Flux decrease through the high-yield pathway is expected in organisms in which the high-yield and low-yield pathways compete for NADH. In support of this analysis, a simplified model of metabolic switching suggests that the extra energy generated during acetate production produces an additional optimal growth mode that smoothens the metabolic switch in E. coli.

CONCLUSIONS

Maintaining redox balance is key to explaining why some microbes decrease the flux through the high-yield pathway, while other microbes use "overflow-like" low-yield metabolism.

Modelling cyanobacteria: from metabolism to integrative models of phototrophic growth

Cyanobacteria are phototrophic microorganisms of global importance and have recently attracted increasing attention due to their capability to convert sunlight and atmospheric CO(2) directly into organic compounds, including carbon-based biofuels. The utilization of cyanobacteria as a biological chassis to generate third-generation biofuels would greatly benefit from an increased understanding of cyanobacterial metabolism and its interplay with other cellular processes. In this respect, metabolic modelling has been proposed as a way to overcome the traditional trial and error methodology that is often employed to introduce novel pathways. In particular, flux balance analysis and related methods have proved to be powerful tools to investigate the organization of large-scale metabolic networks-with the prospect of predicting modifications that are likely to increase the yield of a desired product and thereby to streamline the experimental progress and avoid futile avenues. This contribution seeks to describe the utilization of metabolic modelling as a research tool to understand the metabolism and phototrophic growth of cyanobacteria. The focus of the contribution is on a mathematical description of the metabolic network of Synechocystis sp. PCC 6803 and its analysis using constraint-based methods. A particular challenge is to integrate the description of the metabolic network with other cellular processes, such as the circadian clock, the photosynthetic light reactions, carbon concentration mechanism, and transcriptional regulation-aiming at a predictive model of a cyanobacterium in silico.

Constraining the metabolic genotype-phenotype relationship using a phylogeny of in silico methods

Reconstructed microbial metabolic networks facilitate a mechanistic description of the genotype-phenotype relationship through the deployment of constraint-based reconstruction and analysis (COBRA) methods. As reconstructed networks leverage genomic data for insight and phenotype prediction, the development of COBRA methods has accelerated following the advent of whole-genome sequencing. Here, we describe a phylogeny of COBRA methods that has rapidly evolved from the few early methods, such as flux balance analysis and elementary flux mode analysis, into a repertoire of more than 100 methods. These methods have enabled genome-scale analysis of microbial metabolism for numerous basic and applied uses, including antibiotic discovery, metabolic engineering and modelling of microbial community behaviour.

Supramolecular organization in prokaryotic respiratory systems

Prokaryotes are characterized by an extreme flexibility of their respiratory systems allowing them to cope with various extreme environments. To date, supramolecular organization of respiratory systems appears as a conserved evolutionary feature as supercomplexes have been isolated in bacteria, archaea, and eukaryotes. Most of the yet identified supercomplexes in prokaryotes are involved in aerobic respiration and share similarities with those reported in mitochondria. Supercomplexes likely reflect a snapshot of the cellular respiration in a given cell population. While the exact nature of the determinants for supramolecular organization in prokaryotes is not understood, lipids, proteins, and subcellular localization can be seen as key players. Owing to the well-reported supramolecular organization of the mitochondrial respiratory chain in eukaryotes, several hypotheses have been formulated to explain the consequences of such arrangement and can be tested in the context of prokaryotes. Considering the inherent metabolic flexibility of a number of prokaryotes, cellular distribution and composition of the supramolecular assemblies should be studied in regards to environmental signals. This would pave the way to new concepts in cellular respiration.