Integrated energy and flux balance based multiobjective framework for large-scale metabolic networks

Resource allocation in mammalian systems

Cells execute biological functions to support phenotypes such as growth, migration, and secretion. Complementarily, each function of a cell has resource costs that constrain phenotype. Resource allocation by a cell allows it to manage these costs and optimize their phenotypes. In fact, the management of resource constraints (e.g., nutrient availability, bioenergetic capacity, and macromolecular machinery production) shape activity and ultimately impact phenotype. In mammalian systems, quantification of resource allocation provides important insights into higher-order multicellular functions; it shapes intercellular interactions and relays environmental cues for tissues to coordinate individual cells to overcome resource constraints and achieve population-level behavior. Furthermore, these constraints, objectives, and phenotypes are context-dependent, with cells adapting their behavior according to their microenvironment, resulting in distinct steady-states. This review will highlight the biological insights gained from probing resource allocation in mammalian cells and tissues.

Metabolic collateral lethal target identification reveals MTHFD2 paralogue dependency in ovarian cancer

Recurrent loss-of-function deletions cause frequent inactivation of tumour suppressor genes but often also involve the collateral deletion of essential genes in chromosomal proximity, engendering dependence on paralogues that maintain similar function. Although these paralogues are attractive anticancer targets, no methodology exists to uncover such collateral lethal genes. Here we report a framework for collateral lethal gene identification via metabolic fluxes, CLIM, and use it to reveal MTHFD2 as a collateral lethal gene in UQCR11-deleted ovarian tumours. We show that MTHFD2 has a non-canonical oxidative function to provide mitochondrial NAD+, and demonstrate the regulation of systemic metabolic activity by the paralogue metabolic pathway maintaining metabolic flux compensation. This UQCR11-MTHFD2 collateral lethality is confirmed in vivo, with MTHFD2 inhibition leading to complete remission of UQCR11-deleted ovarian tumours. Using CLIM's machine learning and genome-scale metabolic flux analysis, we elucidate the broad efficacy of targeting MTHFD2 despite distinct cancer genetic profiles co-occurring with UQCR11 deletion and irrespective of stromal compositions of tumours.

A Computational Framework for Studying Gut-Brain Axis in Autism Spectrum Disorder

Introduction

The integrity of the intestinal epithelium is crucial for human health and is harmed in autism spectrum disorder (ASD). An aberrant gut microbial composition resulting in gut-derived metabolic toxins was found to damage the intestinal epithelium, jeopardizing tissue integrity. These toxins further reach the brain via the gut-brain axis, disrupting the normal function of the brain. A mechanistic understanding of metabolic disturbances in the brain and gut is essential to design effective therapeutics and early intervention to block disease progression. Herein, we present a novel computational framework integrating constraint based tissue specific metabolic (CBM) model and whole-body physiological pharmacokinetics (PBPK) modeling for ASD. Furthermore, the role of gut microbiota, diet, and oxidative stress is analyzed in ASD.

Methods

A representative gut model capturing host-bacteria and bacteria-bacteria interaction was developed using CBM techniques and patient data. Simultaneously, a PBPK model of toxin metabolism was assembled, incorporating multi-scale metabolic information. Furthermore, dynamic flux balance analysis was performed to integrate CBM and PBPK. The effectiveness of a probiotic and dietary intervention to improve autism symptoms was tested on the integrated model.

Results

The model accurately highlighted critical metabolic pathways of the gut and brain that are associated with ASD. These include central carbon, nucleotide, and vitamin metabolism in the host gut, and mitochondrial energy and amino acid metabolisms in the brain. The proposed dietary intervention revealed that a high-fiber diet is more effective than a western diet in reducing toxins produced inside the gut. The addition of probiotic bacteria Lactobacillus acidophilus, Bifidobacterium longum longum, Akkermansia muciniphila, and Prevotella ruminicola to the diet restores gut microbiota balance, thereby lowering oxidative stress in the gut and brain.

Conclusion

The proposed computational framework is novel in its applicability, as demonstrated by the determination of the whole-body distribution of ROS toxins and metabolic association in ASD. In addition, it emphasized the potential for developing novel therapeutic strategies to alleviate autism symptoms. Notably, the presented integrated model validates the importance of combining PBPK modeling with COBRA -specific tissue details for understanding disease pathogenesis.

Tumour heterogeneity and the evolutionary trade-offs of cancer

Tumours vary in gene expression programmes and genetic alterations. Understanding this diversity and its biological meaning requires a theoretical framework, which could in turn guide the development of more accurate prognosis and therapy. Here, we review the theory of multi-task evolution of cancer, which is based upon the premise that tumours evolve in the host and face selection trade-offs between multiple biological functions. This theory can help identify the major biological tasks that cancer cells perform and the trade-offs between these tasks. It introduces the concept of specialist tumours, which focus on one task, and generalist tumours, which perform several tasks. Specialist tumours are suggested to be sensitive to therapy targeting their main task. Driver mutations tune gene expression towards specific tasks in a tissue-dependent manner and thus help to determine whether a tumour is specialist or generalist. We discuss potential applications of the theory of multi-task evolution to interpret the spatial organization of tumours and intratumour heterogeneity.

A non-dominated sorting Differential Search Algorithm Flux Balance Analysis (ndsDSAFBA) for in silico multiobjective optimization in identifying reactions knockout

Metabolic engineering is defined as improving the cellular activities of an organism by manipulating the metabolic, signal or regulatory network. In silico reaction knockout simulation is one of the techniques applied to analyse the effects of genetic perturbations on metabolite production. Many methods consider growth coupling as the objective function, whereby it searches for mutants that maximise the growth and production rate. However, the final goal is to increase the production rate. Furthermore, they produce one single solution, though in reality, cells do not focus on one objective and they need to consider various different competing objectives. In this work, a method, termed ndsDSAFBA (non-dominated sorting Differential Search Algorithm and Flux Balance Analysis), has been developed to find the reaction knockouts involved in maximising the production rate and growth rate of the mutant, by incorporating Pareto dominance concepts. The proposed ndsDSAFBA method was validated using three genome-scale metabolic models. We obtained a set of non-dominated solutions, with each solution representing a different mutant strain. The results obtained were compared with the single objective optimisation (SOO) and multi-objective optimisation (MOO) methods. The results demonstrate that ndsDSAFBA is better than the other methods in terms of production rate and growth rate.

Spatial heterogeneity in the mammalian liver

Hepatocytes operate in highly structured repeating anatomical units termed liver lobules. Blood flow along the lobule radial axis creates gradients of oxygen, nutrients and hormones, which, together with morphogenetic fields, give rise to a highly variable microenvironment. In line with this spatial variability, key liver functions are expressed non-uniformly across the lobules, a phenomenon termed zonation. Technologies based on single-cell transcriptomics have constructed a global spatial map of hepatocyte gene expression in mice revealing that ~50% of hepatocyte genes are expressed in a zonated manner. This broad spatial heterogeneity suggests that hepatocytes in different lobule zones might have not only different gene expression profiles but also distinct epigenetic features, regenerative capacities, susceptibilities to damage and other functional aspects. Here, we present genomic approaches for studying liver zonation, describe the principles of liver zonation and discuss the intrinsic and extrinsic factors that dictate zonation patterns. We also explore the challenges and solutions for obtaining zonation maps of liver non-parenchymal cells. These approaches facilitate global characterization of liver function with high spatial resolution along physiological and pathological timescales.

System-level analysis of metabolic trade-offs during anaerobic photoheterotrophic growth in Rhodopseudomonas palustris

BACKGROUND

Living organisms need to allocate their limited resources in a manner that optimizes their overall fitness by simultaneously achieving several different biological objectives. Examination of these biological trade-offs can provide invaluable information regarding the biophysical and biochemical bases behind observed cellular phenotypes. A quantitative knowledge of a cell system's critical objectives is also needed for engineering of cellular metabolism, where there is interest in mitigating the fitness costs that may result from human manipulation.

RESULTS

To study metabolism in photoheterotrophs, we developed and validated a genome-scale model of metabolism in Rhodopseudomonas palustris, a metabolically versatile gram-negative purple non-sulfur bacterium capable of growing phototrophically on various carbon sources, including inorganic carbon and aromatic compounds. To quantitatively assess trade-offs among a set of important biological objectives during different metabolic growth modes, we used our new model to conduct an 8-dimensional multi-objective flux analysis of metabolism in R. palustris. Our results revealed that phototrophic metabolism in R. palustris is light-limited under anaerobic conditions, regardless of the available carbon source. Under photoheterotrophic conditions, R. palustris prioritizes the optimization of carbon efficiency, followed by ATP production and biomass production rate, in a Pareto-optimal manner. To achieve maximum carbon fixation, cells appear to divert limited energy resources away from growth and toward CO2 fixation, even in the presence of excess reduced carbon. We also found that to achieve the theoretical maximum rate of biomass production, anaerobic metabolism requires import of additional compounds (such as protons) to serve as electron acceptors. Finally, we found that production of hydrogen gas, of potential interest as a candidate biofuel, lowers the cellular growth rates under all circumstances.

CONCLUSIONS

Photoheterotrophic metabolism of R. palustris is primarily regulated by the amount of light it can absorb and not the availability of carbon. However, despite carbon's secondary role as a regulating factor, R. palustris' metabolism strives for maximum carbon efficiency, even when this increased efficiency leads to slightly lower growth rates.

Modeling the Metabolic State of Mycobacterium tuberculosis Upon Infection

Genome-scale metabolic models of Mycobacterium tuberculosis (Mtb), the causative agent of tuberculosis, have been envisioned as a platform for drug discovery. By systematically probing the networks that underpin such models, the reactions that are essential for Mtb are identified. A majority of these reactions are catalyzed by enzymes and thus represent candidate drug targets to fight an Mtb infection. Nevertheless, this is complicated by the limited knowledge on the environment that Mtb encounters during infection. Modeling the behavior of the bacteria during infection requires knowledge of the so-called biomass reaction that represents bacterial biomass composition. This composition varies in different environments or bacterial growth phases. Accurate modeling of the metabolic state requires a precise biomass reaction for the described condition. In recent years, additional insights in the in-host environment occupied by Mtb have been gained as transcript abundance data of interacting host and pathogen have become available. Therefore, we used transcript abundance data and developed a straightforward and systematic method to obtain a condition-specific biomass reaction for Mtb during in vitro growth and during infection of its host. The method described herein is virtually free of any pre-set assumptions on uptake rates of nutrients, making it suitable for exploring environments with limited accessibility. The condition-specific biomass reaction represents the “metabolic objective” of Mtb in a given environment (in-host growth and growth on defined medium) at a specific time point, and as such allows modeling the bacterial metabolic state in these environments. Five different biomass reactions were used to predict nutrient uptake rates and gene essentiality. Predictions were subsequently compared to available experimental data. Our results show that nutrient uptake can accurately be predicted. Gene essentiality can also be predicted but accurate predictions remain difficult to obtain. In conclusion, a viable strategy to model Mtb metabolism in hard-to-access environments that is virtually free of pre-set assumptions is provided.

Reverse engineering the cancer metabolic network using flux analysis to understand drivers of human disease

Metabolic dysfunction has reemerged as an essential hallmark of tumorigenesis, and metabolic phenotypes are increasingly being integrated into pre-clinical models of disease. The complexity of these metabolic networks requires systems-level interrogation, and metabolic flux analysis (MFA) with stable isotope tracing present a suitable conceptual framework for such systems. Here we review efforts to elucidate mechanisms through which metabolism influences tumor growth and survival, with an emphasis on applications using stable isotope tracing and MFA. Through these approaches researchers can now quantify pathway fluxes in various in vitro and in vivo contexts to provide mechanistic insights at molecular and physiological scales respectively. Knowledge and discoveries in cancer models are paving the way toward applications in other biological contexts and disease models. In turn, MFA approaches will increasingly help to uncover new therapeutic opportunities that enhance human health.

Integrated Host-Pathogen Metabolic Reconstructions

The science and art of Genome scale metabolic network reconstructions have been explicitly documented in the literature for organisms across all the three kingdoms of life. Constraints-based models derived from such reconstructions have been used to assess metabolic phenotypes of their complex connections to genotype accurately. The problem of infectious disease is complex due to the multifactorial response of the host to the pathogen. Systems biology approaches and modeling allow one to study, understand, and predict emergent properties of such complex responses. The integration of the host and pathogen metabolic networks and the subsequent merger of their stoichiometric matrices is nontrivial and requires understanding of both pathogen and host metabolism and physiologies. The protocol here describes the detailed process of network and stoichiometric matrix merger using a salmonella-mouse macrophage model. The protocol also discusses the interfacial and objective functions required to actually embark on the analysis of host-pathogen interaction models.

Spatial transcriptomics: paving the way for tissue-level systems biology

The tissues in our bodies are complex systems composed of diverse cell types that often interact in highly structured repeating anatomical units. External gradients of morphogens, directional blood flow, as well as the secretion and absorption of materials by cells generate distinct microenvironments at different tissue coordinates. Such spatial heterogeneity enables optimized function through division of labor among cells. Unraveling the design principles that govern this spatial division of labor requires techniques to quantify the entire transcriptomes of cells while accounting for their spatial coordinates. In this review we describe how recent advances in spatial transcriptomics open the way for tissue-level systems biology.

Exo-MFA - A 13C metabolic flux analysis framework to dissect tumor microenvironment-secreted exosome contributions towards cancer cell metabolism

Dissecting the pleiotropic roles of tumor micro-environment (TME) on cancer progression has been brought to the foreground of research on cancer pathology. Extracellular vesicles such as exosomes, transport proteins, lipids, and nucleic acids, to mediate intercellular communication between TME components and have emerged as candidates for anti-cancer therapy. We previously reported that cancer-associated fibroblast (CAF) derived exosomes (CDEs) contain metabolites in their cargo that are utilized by cancer cells for central carbon metabolism and promote cancer growth. However, the metabolic fluxes involved in donor cells towards packaging of metabolites in extracellular vesicles and exosome-mediated metabolite flux upregulation in recipient cells are still not known. Here, we have developed a novel empirical and computational technique, exosome-mediated metabolic flux analysis (Exo-MFA) to quantify flow of cargo from source cells to recipient cells via vesicular transport. Our algorithm, which is based on ¹³C metabolic flux analysis, successfully predicts packaging fluxes to metabolite cargo in CAFs, dynamic changes in rate of exosome internalization by cancer cells, and flux of cargo release over time. We find that cancer cells internalize exosomes rapidly leading to depletion of extracellular exosomes within 24h. However, metabolite cargo significantly alters intracellular metabolism over the course of 24h by regulating glycolysis pathway fluxes via lactate supply. Furthermore, it can supply up to 35% of the TCA cycle fluxes by providing TCA intermediates and glutamine. Our algorithm will help gain insight into (i) metabolic interactions in multicellular systems (ii) biogenesis of extracellular vesicles and their differential packaging of cargo under changing environments, and (iii) regulation of cancer cell metabolism by its microenvironment.

Perception and regulatory principles of microbial growth control

Fast growth represents an effective strategy for microbial organisms to survive in competitive environments. To accomplish this task, cells must adapt their metabolism to changing nutrient conditions in a way that maximizes their growth rate. However, the regulation of the growth related metabolic pathways can be fundamentally different among microbes. We therefore asked whether growth control by perception of the cell’s intracellular metabolic state can give rise to higher growth than by direct perception of extracellular nutrient availability. To answer this question, we created a simplified dynamical computer model of a cellular metabolic network whose regulation was inferred by an optimization approach. We used this model for a competing species experiment, where a species with extracellular nutrient perception competes against one with intracellular nutrient perception by evaluating their respective average growth rate. We found that the intracellular perception is advantageous under situations where the up and down regulation of pathways cannot follow the fast changing nutrient availability in the environment. In this case, optimal regulation ignores any other nutrients except the most preferential ones, in agreement with the phenomenon of catabolite repression in prokaryotes. The corresponding metabolic pathways remain activated, despite environmental fluctuations. Therefore, the cell can take up preferential nutrients as soon as they are available without any prior regulation. As a result species that rely on intracellular perception gain a relevant fitness advantage in fluctuating nutrient environments, which enables survival by outgrowing competitors.

Evolutionary tradeoffs, Pareto optimality and the morphology of ammonite shells

Background

Organisms that need to perform multiple tasks face a fundamental tradeoff: no design can be optimal at all tasks at once. Recent theory based on Pareto optimality showed that such tradeoffs lead to a highly defined range of phenotypes, which lie in low-dimensional polyhedra in the space of traits. The vertices of these polyhedra are called archetypes- the phenotypes that are optimal at a single task. To rigorously test this theory requires measurements of thousands of species over hundreds of millions of years of evolution. Ammonoid fossil shells provide an excellent model system for this purpose. Ammonoids have a well-defined geometry that can be parameterized using three dimensionless features of their logarithmic-spiral-shaped shells. Their evolutionary history includes repeated mass extinctions.

Results

We find that ammonoids fill out a pyramid in morphospace, suggesting five specific tasks - one for each vertex of the pyramid. After mass extinctions, surviving species evolve to refill essentially the same pyramid, suggesting that the tasks are unchanging. We infer putative tasks for each archetype, related to economy of shell material, rapid shell growth, hydrodynamics and compactness.

Conclusions

These results support Pareto optimality theory as an approach to study evolutionary tradeoffs, and demonstrate how this approach can be used to infer the putative tasks that may shape the natural selection of phenotypes.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-015-0149-z) contains supplementary material, which is available to authorized users.

MetDFBA: incorporating time-resolved metabolomics measurements into dynamic flux balance analysis

This paper presents MetDFBA, a new approach incorporating experimental metabolomics time-series into constraint-based modeling. The method can be used for hypothesis testing and predicting dynamic flux profiles.

Predictive sulfur metabolism - a field in flux

The key role of sulfur metabolites in response to biotic and abiotic stress in plants, as well as their importance in diet and health has led to a significant interest and effort in trying to understand and manipulate the production of relevant compounds. Metabolic engineering utilizes a set of theoretical tools to help rationally design modifications that enhance the production of a desired metabolite. Such approaches have proven their value in bacterial systems, however, the paucity of success stories to date in plants, suggests that challenges remain. Here, we review the most commonly used methods for understanding metabolic flux, focusing on the sulfur assimilatory pathway. We highlight known issues with both experimental and theoretical approaches, as well as presenting recent methods for integrating different modeling strategies, and progress toward an understanding of flux at the whole plant level.

Evolutionary tradeoffs between economy and effectiveness in biological homeostasis systems

Biological regulatory systems face a fundamental tradeoff: they must be effective but at the same time also economical. For example, regulatory systems that are designed to repair damage must be effective in reducing damage, but economical in not making too many repair proteins because making excessive proteins carries a fitness cost to the cell, called protein burden. In order to see how biological systems compromise between the two tasks of effectiveness and economy, we applied an approach from economics and engineering called Pareto optimality. This approach allows calculating the best-compromise systems that optimally combine the two tasks. We used a simple and general model for regulation, known as integral feedback, and showed that best-compromise systems have particular combinations of biochemical parameters that control the response rate and basal level. We find that the optimal systems fall on a curve in parameter space. Due to this feature, even if one is able to measure only a small fraction of the system's parameters, one can infer the rest. We applied this approach to estimate parameters in three biological systems: response to heat shock and response to DNA damage in bacteria, and calcium homeostasis in mammals.

Many systems in the cell work to keep homeostasis, or balance. For example, damage repair systems make special repair proteins to resolve damage. These systems typically have many biochemical parameters such as biochemical rate constants, and it is not clear how much of the huge parameter space is filled by actual biological systems. We examined how natural selection acts on these systems when there are two important tasks: effectiveness – rapidly repairing damage, and economy – avoiding excessive production of repair proteins. We find that this multi-task optimization situation leads to natural selection of circuits that lie on a curve in parameter space. Thus, most of parameter space is empty. Estimating only a few parameters of the circuit is enough to predict the rest. This approach allowed us to estimate parameters for bacterial heat shock and DNA repair systems, and for a mammalian hormone system responsible for calcium homeostasis.

The ability of flux balance analysis to predict evolution of central metabolism scales with the initial distance to the optimum

The most powerful genome-scale framework to model metabolism, flux balance analysis (FBA), is an evolutionary optimality model. It hypothesizes selection upon a proposed optimality criterion in order to predict the set of internal fluxes that would maximize fitness. Here we present a direct test of the optimality assumption underlying FBA by comparing the central metabolic fluxes predicted by multiple criteria to changes measurable by a ¹³C-labeling method for experimentally-evolved strains. We considered datasets for three Escherichia coli evolution experiments that varied in their length, consistency of environment, and initial optimality. For ten populations that were evolved for 50,000 generations in glucose minimal medium, we observed modest changes in relative fluxes that led to small, but significant decreases in optimality and increased the distance to the predicted optimal flux distribution. In contrast, seven populations evolved on the poor substrate lactate for 900 generations collectively became more optimal and had flux distributions that moved toward predictions. For three pairs of central metabolic knockouts evolved on glucose for 600–800 generations, there was a balance between cases where optimality and flux patterns moved toward or away from FBA predictions. Despite this variation in predictability of changes in central metabolism, two generalities emerged. First, improved growth largely derived from evolved increases in the rate of substrate use. Second, FBA predictions bore out well for the two experiments initiated with ancestors with relatively sub-optimal yield, whereas those begun already quite optimal tended to move somewhat away from predictions. These findings suggest that the tradeoff between rate and yield is surprisingly modest. The observed positive correlation between rate and yield when adaptation initiated further from the optimum resulted in the ability of FBA to use stoichiometric constraints to predict the evolution of metabolism despite selection for rate.

The most common method of modeling genome-scale metabolism, flux balance analysis, involves using known stoichiometry to define feasible metabolic states and then choosing between these states by proposing that evolution has selected a metabolic flux that optimizes fitness. But does evolution optimize metabolism, and if so, what component of metabolism equates to fitness? We directly tested the underlying assumption of stoichiometric optimality by comparing predicted flux distributions with changes in fluxes that occurred following experimental evolution. Across three experiments ranging in length from a few hundred to fifty thousand generations, we found that substrate uptake – an input to the model – always increased, but supposed optimality criteria such as yield only increased sometimes. Despite this, there was a clear trend. Highly optimal ancestors evolved slightly lower yield in the course of increasing the overall rate, whereas more sub-optimal strains were able to increase both. These results suggest that flux balance analysis is capable of predicting either the initial metabolic behavior of strains or how they will evolve, but not both.

Systems-level characterization of a host-microbe metabolic symbiosis in the mammalian gut

The human gut microbiota consists of ten times more microorganisms than there are cells in our body, processes otherwise indigestible nutrients, and produces important energy precursors, essential amino acids, and vitamins. In this study, we assembled and validated a genome-scale metabolic reconstruction of Bacteroides thetaiotaomicron (iAH991), a prominent representative of the human gut microbiota, consisting of 1488 reactions, 1152 metabolites, and 991 genes. To create a comprehensive metabolic model of host-microbe interactions, we integrated iAH991 with a previously published mouse metabolic reconstruction, which was extended for intestinal transport and absorption reactions. The two metabolic models were linked through a joint compartment, the lumen, allowing metabolite exchange and providing a route for simulating different dietary regimes. The resulting model consists of 7239 reactions, 5164 metabolites, and 2769 genes. We simultaneously modeled growth of mouse and B. thetaiotaomicron on five different diets varying in fat, carbohydrate, and protein content. The integrated model captured mutually beneficial cross-feeding as well as competitive interactions. Furthermore, we identified metabolites that were exchanged between the two organisms, which were compared with published metabolomics data. This analysis resulted for the first time in a comprehensive description of the co-metabolism between a host and its commensal microbe. We also demonstrate in silico that the presence of B. thetaiotaomicron could rescue the growth phenotype of the host with an otherwise lethal enzymopathy and vice versa. This systems approach represents a powerful tool for modeling metabolic interactions between a gut microbe and its host in health and disease.

Metabolic flux ratio analysis and multi-objective optimization revealed a globally conserved and coordinated metabolic response of E. coli to paraquat-induced oxidative stress

The ability of a microorganism to adapt to changes in the environment, such as in nutrient or oxygen availability, is essential for its competitive fitness and survival. The cellular objective and the strategy of the metabolic response to an extreme environment are therefore of tremendous interest and, thus, have been increasingly explored. However, the cellular objective of the complex regulatory structure of the metabolic changes has not yet been fully elucidated and more details regarding the quantitative behaviour of the metabolic flux redistribution are required to understand the systems-wide biological significance of this response. In this study, the intracellular metabolic flux ratios involved in the central carbon metabolism were determined by fractional (13)C-labeling and metabolic flux ratio analysis (MetaFoR) of the wild-type E. coli strain JM101 at an oxidative environment in a chemostat. We observed a significant increase in the flux through phosphoenolpyruvate carboxykinase (PEPCK), phosphoenolpyruvate carboxylase (PEPC), malic enzyme (MEZ) and serine hydroxymethyltransferase (SHMT). We applied an ε-constraint based multi-objective optimization to investigate the trade-off relationships between the biomass yield and the generation of reductive power using the in silico iJR904 genome-scale model of E. coli K-12. The theoretical metabolic redistribution supports that the trans-hydrogenase pathway should not play a direct role in the defence mounted by E. coli against oxidative stress. The agreement between the measured ratio and the theoretical redistribution established the significance of NADPH synthesis as the goal of the metabolic reprogramming that occurs in response to oxidative stress. Our work presents a framework that combines metabolic flux ratio analysis and multi-objective optimization to investigate the metabolic trade-offs that occur under varied environmental conditions. Our results led to the proposal that the metabolic response of E. coli to paraquat-induced oxidative stress is globally conserved and coordinated.

A systems biology approach to studying the role of microbes in human health

Host-microbe interactions play a crucial role in human health and disease. Of the various systems biology approaches, reconstruction of genome-scale metabolic networks combined with constraint-based modeling has been particularly successful at in silico predicting the phenotypic characteristics of single organisms. Here, we summarize recent studies, which have applied this approach to investigate microbe-microbe and host-microbe metabolic interactions. This approach can be also expanded to investigate the properties of an entire microbial community, as well as single organisms within the community. We illustrate that the constraint-based modeling approach is suitable to model host-microbe interactions at molecular resolution and will enable systematic investigation of metabolic links between the human host and its microbes. Such host-microbe models, combined with experimental data, will ultimately further our understanding of how microbes influence human health.

Multidimensional optimality of microbial metabolism

Although the network topology of metabolism is well known, understanding the principles that govern the distribution of fluxes through metabolism lags behind. Experimentally, these fluxes can be measured by (13)C-flux analysis, and there has been a long-standing interest in understanding this functional network operation from an evolutionary perspective. On the basis of (13)C-determined fluxes from nine bacteria and multi-objective optimization theory, we show that metabolism operates close to the Pareto-optimal surface of a three-dimensional space defined by competing objectives. Consistent with flux data from evolved Escherichia coli, we propose that flux states evolve under the trade-off between two principles: optimality under one given condition and minimal adjustment between conditions. These principles form the forces by which evolution shapes metabolic fluxes in microorganisms' environmental context.

Advanced stoichiometric analysis of metabolic networks of mammalian systems

Metabolic engineering tools have been widely applied to living organisms to gain a comprehensive understanding about cellular networks and to improve cellular properties. Metabolic flux analysis (MFA), flux balance analysis (FBA), and metabolic pathway analysis (MPA) are among the most popular tools in stoichiometric network analysis. Although application of these tools into well-known microbial systems is extensive in the literature, various barriers prevent them from being utilized in mammalian cells. Limited experimental data, complex regulatory mechanisms, and the requirement of more complex nutrient media are some major obstacles in mammalian cell systems. However, mammalian cells have been used to produce therapeutic proteins, to characterize disease states or related abnormal metabolic conditions, and to analyze the toxicological effects of some medicinally important drugs. Therefore, there is a growing need for extending metabolic engineering principles to mammalian cells in order to understand their underlying metabolic functions. In this review article, advanced metabolic engineering tools developed for stoichiometric analysis including MFA, FBA, and MPA are described. Applications of these tools in mammalian cells are discussed in detail, and the challenges and opportunities are highlighted.

Stoichiometry based steady-state hepatic flux analysis: computational and experimental aspects

: The liver has many complex physiological functions, including lipid, protein and carbohydrate metabolism, as well as bile and urea production. It detoxifies toxic substances and medicinal products. It also plays a key role in the onset and maintenance of abnormal metabolic patterns associated with various disease states, such as burns, infections and major traumas. Liver cells have been commonly used in in vitro experiments to elucidate the toxic effects of drugs and metabolic changes caused by aberrant metabolic conditions, and to improve the functions of existing systems, such as bioartificial liver. More recently, isolated liver perfusion systems have been increasingly used to characterize intrinsic metabolic changes in the liver caused by various perturbations, including systemic injury, hepatotoxin exposure and warm ischemia. Metabolic engineering tools have been widely applied to these systems to identify metabolic flux distributions using metabolic flux analysis or flux balance analysis and to characterize the topology of the networks using metabolic pathway analysis. In this context, hepatic metabolic models, together with experimental methodologies where hepatocytes or perfused livers are mainly investigated, are described in detail in this review. The challenges and opportunities are also discussed extensively.

Optimality and thermodynamics determine the evolution of transcriptional regulatory networks

Transcriptional motifs are small regulatory interaction patterns that regulate biological functions in highly-interacting cellular networks. Recently, attempts have been made to explain the significance of transcriptional motifs through dynamic function. However, fundamental questions remain unanswered. Why are certain transcriptional motifs with similar dynamic function abundant while others occur rarely? What are the criteria for topological generalization of these motifs into complex networks? Here, we present a novel paradigm that combines non-equilibrium thermodynamics with multiobjective-optimality for network analysis. We found that energetic cost, defined herein as specific dissipation energy, is minimal at the optimal environmental conditions and it correlates inversely with the abundance of the network motifs obtained experimentally for E. coli and S. cerevisiae. This yields evidence that dissipative energetics is the underlying criteria used during evolution for motif selection and that biological systems during transcription tend towards evolutionary selection of subgraphs which produces minimum specific heat dissipation under optimal conditions, thereby explaining the abundance/rare occurrence of some motifs. We show that although certain motifs had similar dynamical functionality, they had significantly different energetic cost, thus explaining the abundance/rare occurrence of these motifs. The presented insights may establish global thermodynamic analysis as a backbone in designing and understanding complex networks systems, such as metabolic and protein interaction networks.

A variational principle for computing nonequilibrium fluxes and potentials in genome-scale biochemical networks

We derive a convex optimization problem on a steady-state nonequilibrium network of biochemical reactions, with the property that energy conservation and the second law of thermodynamics both hold at the problem solution. This suggests a new variational principle for biochemical networks that can be implemented in a computationally tractable manner. We derive the Lagrange dual of the optimization problem and use strong duality to demonstrate that a biochemical analogue of Tellegen's theorem holds at optimality. Each optimal flux is dependent on a free parameter that we relate to an elementary kinetic parameter when mass action kinetics is assumed.

Metabolic profiling based quantitative evaluation of hepatocellular metabolism in presence of adipocyte derived extracellular matrix

The elucidation of the effect of extracellular matrices on hepatocellular metabolism is critical to understand the mechanism of functional upregulation. We have developed a system using natural extracellular matrices [Adipogel] for enhanced albumin synthesis of rat hepatocyte cultures for a period of 10 days as compared to collagen sandwich cultures. Primary rat hepatocytes isolated from livers of female Lewis rats recover within 4 days of culture from isolation induced injury while function is stabilized at 7 days post-isolation. Thus, the culture period can be classified into three distinct stages viz. recovery stage [day 0–4], pre-stable stage [day 5–7] and the stable stage [day 8–10]. A Metabolic Flux Analysis of primary rat hepatocytes cultured in Adipogel was performed to identify the key metabolic pathways modulated as compared to collagen sandwich cultures. In the recovery stage [day 4], the collagen-soluble Adipogel cultures shows an increase in TriCarboxylic Acid [TCA] cycle fluxes; in the pre-stable stage [day 7], there is an increase in PPP and TCA cycle fluxes while in the stable stage [day 10], there is a significant increase in TCA cycle, urea cycle fluxes and amino acid uptake rates concomitant with increased albumin synthesis rate as compared to collagen sandwich cultures throughout the culture period. Metabolic analysis of the collagen-soluble Adipogel condition reveals significantly higher transamination reaction fluxes, amino acid uptake and albumin synthesis rates for the stable vs. recovery stages of culture. The identification of metabolic pathways modulated for hepatocyte cultures in presence of Adipogel will be a useful step to develop an optimization algorithm to further improve hepatocyte function for Bioartificial Liver Devices. The development of this framework for upregulating hepatocyte function in Bioartificial Liver Devices will facilitate the utilization of an integrated experimental and computational approach for broader applications of Adipogel in tissue e engineering and regenerative medicine.

HepatoNet1: a comprehensive metabolic reconstruction of the human hepatocyte for the analysis of liver physiology

We present HepatoNet1, the first reconstruction of a comprehensive metabolic network of the human hepatocyte that is shown to accomplish a large canon of known metabolic liver functions. The network comprises 777 metabolites in six intracellular and two extracellular compartments and 2539 reactions, including 1466 transport reactions. It is based on the manual evaluation of >1500 original scientific research publications to warrant a high-quality evidence-based model. The final network is the result of an iterative process of data compilation and rigorous computational testing of network functionality by means of constraint-based modeling techniques. Taking the hepatic detoxification of ammonia as an example, we show how the availability of nutrients and oxygen may modulate the interplay of various metabolic pathways to allow an efficient response of the liver to perturbations of the homeostasis of blood compounds.

In situ metabolic flux analysis to quantify the liver metabolic response to experimental burn injury

Trauma such as burns induces a hypermetabolic response associated with altered central carbon and nitrogen metabolism. The liver plays a key role in these metabolic changes; however, studies to date have evaluated the metabolic state of liver using ex vivo perfusions or isotope labeling techniques targeted to specific pathways. Herein, we developed a unique mass balance approach to characterize the metabolic state of the liver in situ, and used it to quantify the metabolic changes to experimental burn injury in rats. Rats received a sham (control uninjured), 20% or 40% total body surface area (TBSA) scald burn, and were allowed to develop a hypermetabolic response. One day prior to evaluation, all animals were fasted to deplete glycogen stores. Four days post-burn, blood flow rates in major vessels of the liver were measured, and blood samples harvested. We combined measurements of metabolite concentrations and flow rates in the major vessels entering and leaving the liver with a steady-state mass balance model to generate a quantitative picture of the metabolic state of liver. The main findings were: (1) Sham-burned animals exhibited a gluconeogenic pattern, consistent with the fasted state; (2) the 20% TBSA burn inhibited gluconeogenesis and exhibited glycolytic-like features with very few other significant changes; (3) the 40% TBSA burn, by contrast, further enhanced gluconeogenesis and also increased amino acid extraction, urea cycle reactions, and several reactions involved in oxidative phosphorylation. These results suggest that increasing the severity of injury does not lead to a simple dose-dependent metabolic response, but rather leads to qualitatively different responses.

Transcriptional and metabolic flux profiling of triadimefon effects on cultured hepatocytes

Conazoles are a class of azole fungicides used to prevent fungal growth in agriculture, for treatment of fungal infections, and are found to be tumorigenic in rats and/or mice. In this study, cultured primary rat hepatocytes were treated to two different concentrations (0.3 and 0.15 mM) of triadimefon, which is a tumorigenic conazole in rat and mouse liver, on a temporal basis with daily media change. Following treatment, cells were harvested for microarray data ranging from 6 to 72 h. Supernatant was collected daily for three days, and the concentrations of various metabolites in the media and supernatant were quantified. Gene expression changes were most significant following exposure to 0.3 mM triadimefon and were characterized mainly by metabolic pathways related to carbohydrate, lipid and amino acid metabolism. Correspondingly, metabolic network flexibility analysis demonstrated a switch from fatty acid synthesis to fatty acid oxidation in cells exposed to triadimefon. It is likely that fatty acid oxidation is active in order to supply energy required for triadimefon detoxification. In 0.15 mM triadimefon treatment, the hepatocytes are able to detoxify the relatively low concentration of triadimefon with less pronounced changes in hepatic metabolism.

Modeling with a view to target identification in metabolic engineering: a critical evaluation of the available tools

The state of the art tools for modeling metabolism, typically used in the domain of metabolic engineering, were reviewed. The tools considered are stoichiometric network analysis (elementary modes and extreme pathways), stoichiometric modeling (metabolic flux analysis, flux balance analysis, and carbon modeling), mechanistic and approximative modeling, cybernetic modeling, and multivariate statistics. In the context of metabolic engineering, one should be aware that the usefulness of these tools to optimize microbial metabolism for overproducing a target compound depends predominantly on the characteristic properties of that compound. Because of their shortcomings not all tools are suitable for every kind of optimization; issues like the dependence of the target compound's synthesis on severe (redox) constraints, the characteristics of its formation pathway, and the achievable/desired flux towards the target compound should play a role when choosing the optimization strategy.

Soft constraints-based multiobjective framework for flux balance analysis

The current state of the art for linear optimization in Flux Balance Analysis has been limited to single objective functions. Since mammalian systems perform various functions, a multiobjective approach is needed when seeking optimal flux distributions in these systems. In most of the available multiobjective optimization methods, there is a lack of understanding of when to use a particular objective, and how to combine and/or prioritize mutually competing objectives to achieve a truly optimal solution. To address these limitations we developed a soft constraints based linear physical programming-based flux balance analysis (LPPFBA) framework to obtain a multiobjective optimal solutions. The developed framework was first applied to compute a set of multiobjective optimal solutions for various pairs of objectives relevant to hepatocyte function (urea secretion, albumin, NADPH, and glutathione syntheses) in bioartificial liver systems. Next, simultaneous analysis of the optimal solutions for three objectives was carried out. Further, this framework was utilized to obtain true optimal conditions to improve the hepatic functions in a simulated bioartificial liver system. The combined quantitative and visualization framework of LPPFBA is applicable to any large-scale metabolic network system, including those derived by genomic analyses.

Adipocyte-derived basement membrane extract with biological activity: applications in hepatocyte functional augmentation in vitro

Natural and synthetic biomaterials utilized in tissue engineering applications require a dynamic interplay of complex macromolecular compositions of hydrated extracellular matrices (ECMs) and soluble growth factors. The challenges in utilizing synthetic ECMs is the effective control of temporal and spatial complexity of multiple signal presentation, as compared to natural ECMs that possess the inherent properties of biological recognition, including presentation of receptor-binding ligands, susceptibility to cell-triggered proteolytic degradation, and remodeling. We have developed a murine preadipocyte differentiation system for generating a natural basement membrane extract (Adipogel) comprising ECM proteins (collagen IV, laminin, hyaluronan, and fibronectin) and including relevant growth factors (hepatocyte growth factor, vascular endothelial growth factor, and leukemia inhibitory factor). We have shown the effective utilization of the growth factor-enriched extracellular matrix for enhanced albumin synthesis rate of primary hepatocyte cultures for a period of 10 d as compared to collagen sandwich cultures and comparable or higher function as compared to Matrigel cultures. We have also demonstrated comparable cytochrome P450 1A1 activity for the collagen-Adipogel condition to the collagen double-gel and Matrigel culture conditions. A metabolic analysis revealed that utilization of Adipogel in primary hepatocyte cultures increased serine, glycine, threonine, alanine, tyrosine, valine, methionine, lysine, isoleucine, leucine, phenylalanine, taurine, cysteine, and glucose uptake rates to enhance hepatocyte protein synthesis as compared to collagen double-gel cultures. The demonstrated synthesis, isolation, characterization, and application of Adipogel provide immense potential for tissue engineering and regenerative medicine applications.

Large-scale identification of genetic design strategies using local search

In the past decade, computational methods have been shown to be well suited to unraveling the complex web of metabolic reactions in biological systems. Methods based on flux–balance analysis (FBA) and bi-level optimization have been used to great effect in aiding metabolic engineering. These methods predict the result of genetic manipulations and allow for the best set of manipulations to be found computationally. Bi-level FBA is, however, limited in applicability because the required computational time and resources scale poorly as the size of the metabolic system and the number of genetic manipulations increase. To overcome these limitations, we have developed Genetic Design through Local Search (GDLS), a scalable, heuristic, algorithmic method that employs an approach based on local search with multiple search paths, which results in effective, low-complexity search of the space of genetic manipulations. Thus, GDLS is able to find genetic designs with greater in silico production of desired metabolites than can feasibly be found using a globally optimal search and performs favorably in comparison with heuristic searches based on evolutionary algorithms and simulated annealing.

A rational design approach for amino acid supplementation in hepatocyte culture

Improvement of culture media for mammalian cells is conducted via empirical adjustments, sometimes aided by statistical design methodologies. Here, we demonstrate a proof of principle for the use of constraints-based modeling to achieve enhanced performance of liver-specific functions of cultured hepatocytes during plasma exposure by adjusting amino acid supplementation and hormone levels in the medium. Flux balance analysis (FBA) is used to determine an amino acid flux profile consistent with a desired output; this is used to design an amino acid supplementation. Under conditions of no supplementation, empirical supplementation, and designed supplementation, hepatocytes were exposed to plasma and their morphology, specific cell functions (urea, albumin production) and lipid metabolism were measured. Urea production under the designed amino acid supplementation was found to be increased compared with previously reported (empirical) amino acid supplementation. Not surprisingly, the urea production attained was less than the theoretical value, indicating the existence of pathways or constraints not present in the current model. Although not an explicit design objective, albumin production was also increased by designed amino acid supplementation, suggesting a functional linkage between these outputs. In conjunction with traditional approaches to improving culture conditions, the rational design approach described herein provides a novel means to tune the metabolic outputs of cultured hepatocytes.