An objective function exploiting suboptimal solutions in metabolic networks

Insights into yeast response to chemotherapeutic agent through time series genome-scale metabolic models

Organism-specific genome-scale metabolic models (GSMMs) can unveil molecular mechanisms within cells and are commonly used in diverse applications, from synthetic biology, biotechnology, and systems biology to metabolic engineering. There are limited studies incorporating time-series transcriptomics in GSMM simulations. Yeast is an easy-to-manipulate model organism for tumor research. Here, a novel approach (TS-GSMM) was proposed to integrate time-series transcriptomics with GSMMs to narrow down the feasible solution space of all possible flux distributions and attain time-series flux samples. The flux samples were clustered using machine learning techniques, and the clusters' functional analysis was performed using reaction set enrichment analysis. A time series transcriptomics response of Yeast cells to a chemotherapeutic reagent-doxorubicin-was mapped onto a Yeast GSMM. Eleven flux clusters were obtained with our approach, and pathway dynamics were displayed. Induction of fluxes related to bicarbonate formation and transport, ergosterol and spermidine transport, and ATP production were captured. Integrating time-series transcriptomics data with GSMMs is a promising approach to reveal pathway dynamics without any kinetic modeling and detects pathways that cannot be identified through transcriptomics-only analysis. The codes are available at https://github.com/karabekmez/TS-GSMM.

Predicting metabolic fluxes from omics data via machine learning: Moving from knowledge-driven towards data-driven approaches

The accurate prediction of phenotypes in microorganisms is a main challenge for systems biology. Genome-scale models (GEMs) are a widely used mathematical formalism for predicting metabolic fluxes using constraint-based modeling methods such as flux balance analysis (FBA). However, they require prior knowledge of the metabolic network of an organism and appropriate objective functions, often hampering the prediction of metabolic fluxes under different conditions. Moreover, the integration of omics data to improve the accuracy of phenotype predictions in different physiological states is still in its infancy. Here, we present a novel approach for predicting fluxes under various conditions. We explore the use of supervised machine learning (ML) models using transcriptomics and/or proteomics data and compare their performance against the standard parsimonious FBA (pFBA) approach using case studies of Escherichia coli organism as an example. Our results show that the proposed omics-based ML approach is promising to predict both internal and external metabolic fluxes with smaller prediction errors in comparison to the pFBA approach. The code, data, and detailed results are available at the project's repository[1].

Characterizing cancer metabolism from bulk and single-cell RNA-seq data using METAFlux

Cells often alter metabolic strategies under nutrient-deprived conditions to support their survival and growth. Characterizing metabolic reprogramming in the tumor microenvironment (TME) is of emerging importance in cancer research and patient care. However, recent technologies only measure a subset of metabolites and cannot provide in situ measurements. Computational methods such as flux balance analysis (FBA) have been developed to estimate metabolic flux from bulk RNA-seq data and can potentially be extended to single-cell RNA-seq (scRNA-seq) data. However, it is unclear how reliable current methods are, particularly in TME characterization. Here, we present a computational framework METAFlux (METAbolic Flux balance analysis) to infer metabolic fluxes from bulk or single-cell transcriptomic data. Large-scale experiments using cell-lines, the cancer genome atlas (TCGA), and scRNA-seq data obtained from diverse cancer and immunotherapeutic contexts, including CAR-NK cell therapy, have validated METAFlux's capability to characterize metabolic heterogeneity and metabolic interaction amongst cell types.

A Holistic Approach from Systems Biology Reveals the Direct Influence of the Quorum-Sensing Phenomenon on Pseudomonas aeruginosa Metabolism to Pyoverdine Biosynthesis

Computational modeling and simulation of biological systems have become valuable tools for understanding and predicting cellular performance and phenotype generation. This work aimed to construct, model, and dynamically simulate the virulence factor pyoverdine (PVD) biosynthesis in Pseudomonas aeruginosa through a systemic approach, considering that the metabolic pathway of PVD synthesis is regulated by the quorum-sensing (QS) phenomenon. The methodology comprised three main stages: (i) Construction, modeling, and validation of the QS gene regulatory network that controls PVD synthesis in P. aeruginosa strain PAO1; (ii) construction, curating, and modeling of the metabolic network of P. aeruginosa using the flux balance analysis (FBA) approach; (iii) integration and modeling of these two networks into an integrative model using the dynamic flux balance analysis (DFBA) approximation, followed, finally, by an in vitro validation of the integrated model for PVD synthesis in P. aeruginosa as a function of QS signaling. The QS gene network, constructed using the standard System Biology Markup Language, comprised 114 chemical species and 103 reactions and was modeled as a deterministic system following the kinetic based on mass action law. This model showed that the higher the bacterial growth, the higher the extracellular concentration of QS signal molecules, thus emulating the natural behavior of P. aeruginosa PAO1. The P. aeruginosa metabolic network model was constructed based on the iMO1056 model, the P. aeruginosa PAO1 strain genomic annotation, and the metabolic pathway of PVD synthesis. The metabolic network model included the PVD synthesis, transport, exchange reactions, and the QS signal molecules. This metabolic network model was curated and then modeled under the FBA approximation, using biomass maximization as the objective function (optimization problem, a term borrowed from the engineering field). Next, chemical reactions shared by both network models were chosen to combine them into an integrative model. To this end, the fluxes of these reactions, obtained from the QS network model, were fixed in the metabolic network model as constraints of the optimization problem using the DFBA approximation. Finally, simulations of the integrative model (CCBM1146, comprising 1123 reactions and 880 metabolites) were run using the DFBA approximation to get (i) the flux profile for each reaction, (ii) the bacterial growth profile, (iii) the biomass profile, and (iv) the concentration profiles of metabolites of interest such as glucose, PVD, and QS signal molecules. The CCBM1146 model showed that the QS phenomenon directly influences the P. aeruginosa metabolism to PVD biosynthesis as a function of the change in QS signal intensity. The CCBM1146 model made it possible to characterize and explain the complex and emergent behavior generated by the interactions between the two networks, which would have been impossible to do by studying each system's individual components or scales separately. This work is the first in silico report of an integrative model comprising the QS gene regulatory network and the metabolic network of P. aeruginosa.

Metabolic models of human gut microbiota: Advances and challenges

The human gut is a complex ecosystem consisting of hundreds of microbial species interacting with each other and with the human host. Mathematical models of the gut microbiome integrate our knowledge of this system and help to formulate hypotheses to explain observations. The generalized Lotka-Volterra model has been widely used for this purpose, but it does not describe interaction mechanisms and thus does not account for metabolic flexibility. Recently, models that explicitly describe gut microbial metabolite production and consumption have become popular. These models have been used to investigate the factors that shape gut microbial composition and to link specific gut microorganisms to changes in metabolite concentrations found in diseases. Here, we review how such models are built and what we have learned so far from their application to human gut microbiome data. In addition, we discuss current challenges of these models and how these can be addressed in the future.

Predicting stress response and improved protein overproduction in Bacillus subtilis

Bacillus subtilis is a well-characterized microorganism and a model for the study of Gram-positive bacteria. The bacterium can produce proteins at high densities and yields, which has made it valuable for industrial bioproduction. Like other cell factories, metabolic modeling of B. subtilis has discovered ways to optimize its metabolism toward various applications. The first genome-scale metabolic model (M-model) of B. subtilis was published more than a decade ago and has been applied extensively to understand metabolism, to predict growth phenotypes, and served as a template to reconstruct models for other Gram-positive bacteria. However, M-models are ill-suited to simulate the production and secretion of proteins as well as their proteomic response to stress. Thus, a new generation of metabolic models, known as metabolism and gene expression models (ME-models), has been initiated. Here, we describe the reconstruction and validation of a ME model of B. subtilis, iJT964-ME. This model achieved higher performance scores on the prediction of gene essentiality as compared to the M-model. We successfully validated the model by integrating physiological and omics data associated with gene expression responses to ethanol and salt stress. The model further identified the mechanism by which tryptophan synthesis is upregulated under ethanol stress. Further, we employed iJT964-ME to predict amylase production rates under two different growth conditions. We analyzed these flux distributions and identified key metabolic pathways that permitted the increase in amylase production. Models like iJT964-ME enable the study of proteomic response to stress and the illustrate the potential for optimizing protein production in bacteria.

A metabolic modeling platform for the computation of microbial ecosystems in time and space (COMETS)

Genome-scale stoichiometric modeling of metabolism has become a standard systems biology tool for modeling cellular physiology and growth. Extensions of this approach are emerging as a valuable avenue for predicting, understanding and designing microbial communities. Computation of microbial ecosystems in time and space (COMETS) extends dynamic flux balance analysis to generate simulations of multiple microbial species in molecularly complex and spatially structured environments. Here we describe how to best use and apply the most recent version of COMETS, which incorporates a more accurate biophysical model of microbial biomass expansion upon growth, evolutionary dynamics and extracellular enzyme activity modules. In addition to a command-line option, COMETS includes user-friendly Python and MATLAB interfaces compatible with the well-established COBRA models and methods, as well as comprehensive documentation and tutorials. This protocol provides a detailed guideline for installing, testing and applying COMETS to different scenarios, generating simulations that take from a few minutes to several days to run, with broad applicability to microbial communities across biomes and scales.

Addressing uncertainty in genome-scale metabolic model reconstruction and analysis

The reconstruction and analysis of genome-scale metabolic models constitutes a powerful systems biology approach, with applications ranging from basic understanding of genotype-phenotype mapping to solving biomedical and environmental problems. However, the biological insight obtained from these models is limited by multiple heterogeneous sources of uncertainty, which are often difficult to quantify. Here we review the major sources of uncertainty and survey existing approaches developed for representing and addressing them. A unified formal characterization of these uncertainties through probabilistic approaches and ensemble modeling will facilitate convergence towards consistent reconstruction pipelines, improved data integration algorithms, and more accurate assessment of predictive capacity.

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

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

Microbial energy management-A product of three broad tradeoffs

Wherever thermodynamics allows, microbial life has evolved to transform and harness energy. Microbial life thus abounds in the most unexpected places, enabled by profound metabolic diversity. Within this diversity, energy is transformed primarily through variations on a few core mechanisms. Energy is further managed by the physiological processes of cell growth and maintenance that use energy. Some aspects of microbial physiology are streamlined for energetic efficiency while other aspects seem suboptimal or even wasteful. We propose that the energy that a microbe harnesses and devotes to growth and maintenance is a product of three broad tradeoffs: (i) economic, trading enzyme synthesis or operational cost for functional benefit, (ii) environmental, trading optimization for a single environment for adaptability to multiple environments, and (iii) thermodynamic, trading energetic yield for forward metabolic flux. Consideration of these tradeoffs allows one to reconcile features of microbial physiology that seem to opposingly promote either energetic efficiency or waste.

Human Systems Biology and Metabolic Modelling: A Review-From Disease Metabolism to Precision Medicine

In cell and molecular biology, metabolism is the only system that can be fully simulated at genome scale. Metabolic systems biology offers powerful abstraction tools to simulate all known metabolic reactions in a cell, therefore providing a snapshot that is close to its observable phenotype. In this review, we cover the 15 years of human metabolic modelling. We show that, although the past five years have not experienced large improvements in the size of the gene and metabolite sets in human metabolic models, their accuracy is rapidly increasing. We also describe how condition-, tissue-, and patient-specific metabolic models shed light on cell-specific changes occurring in the metabolic network, therefore predicting biomarkers of disease metabolism. We finally discuss current challenges and future promising directions for this research field, including machine/deep learning and precision medicine. In the omics era, profiling patients and biological processes from a multiomic point of view is becoming more common and less expensive. Starting from multiomic data collected from patients and N-of-1 trials where individual patients constitute different case studies, methods for model-building and data integration are being used to generate patient-specific models. Coupled with state-of-the-art machine learning methods, this will allow characterizing each patient's disease phenotype and delivering precision medicine solutions, therefore leading to preventative medicine, reduced treatment, and in silico clinical trials.

Analyzing and Designing Cell Factories with OptFlux

OptFlux was launched in 2010 as the first open-source and user-friendly platform containing all the major methods for performing metabolic engineering tasks in silico. Main features included the possibility of performing microbial strain simulations with widely used methods such as Flux Balance Analysis and strain design using Evolutionary Algorithms. Since then, OptFlux suffered a major re-factoring to improve its efficiency and reliability, while many features were added in the form of novel plug-ins, such as the BioVisualizer and the over/under expression plug-ins. The current chapter described the main mathematical formulations of the major methods implemented within OptFlux, also providing a detailed guide on the usage of those functionalities.

Mathematical modelling of clostridial acetone-butanol-ethanol fermentation

Clostridial acetone-butanol-ethanol (ABE) fermentation features a remarkable shift in the cellular metabolic activity from acid formation, acidogenesis, to the production of industrial-relevant solvents, solventogensis. In recent decades, mathematical models have been employed to elucidate the complex interlinked regulation and conditions that determine these two distinct metabolic states and govern the transition between them. In this review, we discuss these models with a focus on the mechanisms controlling intra- and extracellular changes between acidogenesis and solventogenesis. In particular, we critically evaluate underlying model assumptions and predictions in the light of current experimental knowledge. Towards this end, we briefly introduce key ideas and assumptions applied in the discussed modelling approaches, but waive a comprehensive mathematical presentation. We distinguish between structural and dynamical models, which will be discussed in their chronological order to illustrate how new biological information facilitates the ‘evolution’ of mathematical models. Mathematical models and their analysis have significantly contributed to our knowledge of ABE fermentation and the underlying regulatory network which spans all levels of biological organization. However, the ties between the different levels of cellular regulation are not well understood. Furthermore, contradictory experimental and theoretical results challenge our current notion of ABE metabolic network structure. Thus, clostridial ABE fermentation still poses theoretical as well as experimental challenges which are best approached in close collaboration between modellers and experimentalists.

Cancer cell metabolism as new targets for novel designed therapies

Metabolic processes are altered in cancer cells, which obtain advantages from this metabolic reprogramming in terms of energy production and synthesis of biomolecules that sustain their uncontrolled proliferation. Due to the conceptual progresses in the last decade, metabolic reprogramming was recently included as one of the new hallmarks of cancer. The advent of high-throughput technologies to amass an abundance of omic data, together with the development of new computational methods that allow the integration and analysis of omic data by using genome-scale reconstructions of human metabolism, have increased and accelerated the discovery and development of anticancer drugs and tumor-specific metabolic biomarkers. Here we review and discuss the latest advances in the context of metabolic reprogramming and the future in cancer research.

Predicting internal cell fluxes at sub-optimal growth

Background

Flux Balance Analysis (FBA) is a widely used tool to model metabolic behavior and cellular function. Applications of FBA span a breadth of research from synthetic engineering of biofuels to understanding evolutionary adaptations. FBA predicts metabolic reaction fluxes that optimize a given objective. This objective is generally defined for unicellular organisms by a theoretical reaction which simulates biomass production. FBA has been extremely successful at predicting in E. coli growth rates under different media and gene essentiality, amongst other things. In order to improve predictions, additional constraints are coupled with optimization of the biomass function. Studies have suggested, however, that unicellular organisms - like multicellular organisms - do not grow at optimal rates. To further improve FBA predictions, particularly of internal cell fluxes, new techniques to explore the sub-optimal solution space need to be developed.

Results

We present an innovative FBA method called corsoFBA based on the optimization of protein cost at sub-optimal objective levels. Our method shows good agreement with experimental data of E. coli grown at different dilution rates. Maintaining the objective function close to its maximum value predicts metabolic states that closely resemble low dilution rates; while higher dilution rates can be mirrored by lowering the biomass production value. By using a modified version of Extreme Pathways, we are also able to quantify the energy production and overall protein cost for all possible pathways in the central carbon metabolism.

Conclusion

Metabolic flux distributions at the optimal objective can be substantially different from the near-optimal distributions. Importantly, the behavior of E. coli central carbon metabolism can be better predicted by exploring the sub-optimal FBA solution space. The corsoFBA method presented here is able to predict the behavior of PEP Carboxylase, the glyoxylate shunt and the Entner-Doudoroff pathway at different glucose levels, a behavior not predicted by the minimization of metabolic steps and FBA alone. This technique can be used to better predict internal cell fluxes under different conditions, and corsoFBA will be of great help for the study of cells from multicellular organisms using Flux Balance Analysis.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-015-0153-3) contains supplementary material, which is available to authorized users.

Validation of an FBA model for Pichia pastoris in chemostat cultures

Background

Constraint-based metabolic models and flux balance analysis (FBA) have been extensively used in the last years to investigate the behavior of cells and also as basis for different industrial applications. In this context, this work provides a validation of a small-sized FBA model of the yeast Pichia pastoris. Our main objective is testing how accurate is the hypothesis of maximum growth to predict the behavior of P. pastoris in a range of experimental environments.

Results

A constraint-based model of P. pastoris was previously validated using metabolic flux analysis (MFA). In this paper we have verified the model ability to predict the cells behavior in different conditions without introducing measurements, experimental parameters, or any additional constraint, just by assuming that cells will make the best use of the available resources to maximize its growth. In particular, we have tested FBA model ability to: (a) predict growth yields over single substrates (glucose, glycerol, and methanol); (b) predict growth rate, substrate uptakes, respiration rates, and by-product formation in scenarios where different substrates are available (glucose, glycerol, methanol, or mixes of methanol and glycerol); (c) predict the different behaviors of P. pastoris cultures in aerobic and hypoxic conditions for each single substrate. In every case, experimental data from literature are used as validation.

Conclusions

We conclude that our predictions based on growth maximisation are reasonably accurate, but still far from perfect. The deviations are significant in scenarios where P. pastoris grows on methanol, suggesting that the hypothesis of maximum growth could be not dominating in these situations. However, predictions are much better when glycerol or glucose are used as substrates. In these scenarios, even if our FBA model is small and imposes a strong assumption regarding how cells will regulate their metabolic fluxes, it provides reasonably good predictions in terms of growth, substrate preference, product formation, and respiration rates.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-014-0142-y) contains supplementary material, which is available to authorized users.

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.

Comparison and analysis of objective functions in flux balance analysis

Flux balance analysis (FBA) is currently one of the most important and used techniques for estimation of metabolic reaction rates (fluxes). This mathematical approach utilizes an optimization criterion in order to select a distribution of fluxes from the feasible space delimited by the metabolic reactions and some restrictions imposed over them, assuming that cellular metabolism is in steady state. Therefore, the obtained flux distribution depends on the specific objective function used. Multiple studies have been aimed to compare distinct objective functions at given conditions, in order to determine which of those functions produces values of fluxes closer to real data when used as objective in the FBA; in other words, what is the best objective function for modeling cell metabolism at a determined environmental condition. However, these comparative studies have been designed in very dissimilar ways, and in general, several factors that can change the ideal objective function in a cellular condition have not been adequately considered. Additionally, most of them have used only one dataset for representing one condition of cell growth, and different measuring techniques have been used. For these reasons, a rigorous study on the effect of factors such as the quantity of used data, the number and type of fluxes utilized as input data, and the selected classification of growth conditions, are required in order to obtain useful conclusions for these comparative studies, allowing limiting clearly the application range on any of those results.

Promise and reality in the expanding field of network interaction analysis: metabolic networks

In the last few decades, metabolic networks revealed their capabilities as powerful tools to analyze the cellular metabolism. Many research fields (eg, metabolic engineering, diagnostic medicine, pharmacology, biochemistry, biology and physiology) improved the understanding of the cell combining experimental assays and metabolic network-based computations. This process led to the rise of the “systems biology” approach, where the theory meets experiments and where two complementary perspectives cooperate in the study of biological phenomena. Here, the reconstruction of metabolic networks is presented, along with established and new algorithms to improve the description of cellular metabolism. Then, advantages and limitations of modeling algorithms and network reconstruction are discussed.