Constraint-based Modeling Methods Research Articles

Resource allocation modeling for autonomous prediction of plant cell phenotypes

Predicting the plant cell response in complex environmental conditions is a challenge in plant biology. Here we developed a resource allocation model of cellular and molecular scale for the leaf photosynthetic cell of Arabidopsis thaliana, based on the Resource Balance Analysis (RBA) constraint-based modeling framework. The RBA model contains the metabolic network and the major macromolecular processes involved in the plant cell growth and survival and localized in cellular compartments. We simulated the model for varying environmental conditions of temperature, irradiance, partial pressure of CO2 and O2, and compared RBA predictions to known resource distributions and quantitative phenotypic traits such as the relative growth rate, the C:N ratio, and finally to the empirical characteristics of CO2 fixation given by the well-established Farquhar model. In comparison to other standard constraint-based modeling methods like Flux Balance Analysis, the RBA model makes accurate quantitative predictions without the need for empirical constraints. Altogether, we show that RBA significantly improves the autonomous prediction of plant cell phenotypes in complex environmental conditions, and provides mechanistic links between the genotype and the phenotype of the plant cell.

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].

FluxomicsExplorer: Differential visual analysis of Flux Sampling based on Metabolomics

Flux Sampling (FS) is an unbiased constraint-based modeling method in systems biology that characterizes the admissible metabolic flux space of cells and organisms at a molecular level. It returns information about reaction flux ranges and their probability from a genome-scale metabolic model (GEM), which can be used to predict metabolic phenotypes. FS is particularly beneficial if a cellular objective cannot be easily identified. We present FluxomicsExplorer, a web-based visual analysis application that facilitates a data- and task-driven exploratory analysis of FS results. It was designed together with experts in medicine and systems biology to satisfy their requirements and offers multiple linked views that visualize the standardized scoring of flux differences, flux distributions, and the network of biological pathways to guide the analysis process. Instead of focusing on a subset of known influential reactions for the analysis, it allows users to assess the results as a whole concerning the underlying GEM. The visualizations guide the user to affected reactions, metabolites, and network areas by highlighting relevant changes between two conditions. These flux changes can then be analyzed in detail by visualizing the reaction flux distributions. We show FluxomicsExplorer’s utility using a case study of the red blood cell metabolism in different blood plasma environments.

Bayesian Integrative Modeling of Genome-Scale Metabolic and Regulatory Networks

The integration of high-throughput data to build predictive computational models of cellular metabolism is a major challenge of systems biology. These models are needed to predict cellular responses to genetic and environmental perturbations. Typically, this response involves both metabolic regulations related to the kinetic properties of enzymes and a genetic regulation affecting their concentrations. Thus, the integration of the transcriptional regulatory information is required to improve the accuracy and predictive ability of metabolic models. Integrative modeling is of primary importance to guide the search for various applications such as discovering novel potential drug targets to develop efficient therapeutic strategies for various diseases. In this paper, we propose an integrative predictive model based on techniques combining semantic web, probabilistic modeling, and constraint-based modeling methods. We applied our approach to human cancer metabolism to predict in silico the growth response of specific cancer cells under approved drug effects. Our method has proven successful in predicting the biomass rates of human liver cancer cells under drug-induced transcriptional perturbations.

Improving the accuracy of flux balance analysis through the implementation of carbon availability constraints for intracellular reactions.

Constraint-based modeling methods, such as Flux Balance Analysis (FBA), have been extensively used to decipher complex, informationrich -omics datasets to elicit system-wide behavioral patterns of cellular metabolism. FBA has been successfully used to gain insight in a wide range of applications, such as range of substrate utilization, product yields and to design metabolic engineering strategies to improve bioprocess performance. A well-known challenge associated with large genome-scale metabolic networks is that they result in underdetermined problem formulations. Consequently, rather than unique solutions, FBA and related methods examine ranges of reaction flux values that are consistent with the studied physiological conditions. The wider the reported flux ranges, the higher the uncertainty in the determination of basic reaction properties, limiting interpretability of and confidence in the results. Herein, we propose a new, computationally efficient approach that refines flux range predictions by constraining reaction fluxes on the basis of the elemental balance of carbon. We compared carbon constraint FBA (ccFBA) against experimentally-measured intracellular fluxes using the latest CHO GEM (iCHO1766) and were able to substantially improve the accuracy of predicted flux values compared with FBA. ccFBA can be used as a stand-alone method but is also compatible with and complimentary to other constraint-based approaches.

Glycosylation Flux Analysis of Immunoglobulin G in Chinese Hamster Ovary Perfusion Cell Culture

The terminal sugar molecules of the N-linked glycan attached to the fragment crystalizable (Fc) region is a critical quality attribute of therapeutic monoclonal antibodies (mAbs) such as immunoglobulin G (IgG). There exists naturally-occurring heterogeneity in the N-linked glycan structure of mAbs, and such heterogeneity has a significant influence on the clinical safety and efficacy of mAb drugs. We previously proposed a constraint-based modeling method called glycosylation flux analysis (GFA) to characterize the rates (fluxes) of intracellular glycosylation reactions. One contribution of this work is a significant improvement in the computational efficiency of the GFA, which is beneficial for analyzing large datasets. Another contribution of our study is the analysis of IgG glycosylation in continuous perfusion Chinese Hamster Ovary (CHO) cell cultures. The GFA of the perfusion cell culture data indicated that the dynamical changes of IgG glycan heterogeneity are mostly attributed to alterations in the galactosylation flux activity. By using a random forest regression analysis of the IgG galactosylation flux activity, we were further able to link the dynamics of galactosylation with two process parameters: cell-specific productivity of IgG and extracellular ammonia concentration. The characteristics of IgG galactosylation dynamics agree well with what we previously reported for fed-batch cultivations of the same CHO cell strain.

Improved Metabolic Models for E. coli and Mycoplasma genitalium from GlobalFit, an Algorithm That Simultaneously Matches Growth and Non-Growth Data Sets.

Constraint-based metabolic modeling methods such as Flux Balance Analysis (FBA) are routinely used to predict the effects of genetic changes and to design strains with desired metabolic properties. The major bottleneck in modeling genome-scale metabolic systems is the establishment and manual curation of reliable stoichiometric models. Initial reconstructions are typically refined through comparisons to experimental growth data from gene knockouts or nutrient environments. Existing methods iteratively correct one erroneous model prediction at a time, resulting in accumulating network changes that are often not globally optimal. We present GlobalFit, a bi-level optimization method that finds a globally optimal network, by identifying the minimal set of network changes needed to correctly predict all experimentally observed growth and non-growth cases simultaneously. When applied to the genome-scale metabolic model of Mycoplasma genitalium, GlobalFit decreases unexplained gene knockout phenotypes by 79%, increasing accuracy from 87.3% (according to the current state-of-the-art) to 97.3%. While currently available computers do not allow a global optimization of the much larger metabolic network of E. coli, the main strengths of GlobalFit are already played out when considering only one growth and one non-growth case simultaneously. Application of a corresponding strategy halves the number of unexplained cases for the already highly curated E. coli model, increasing accuracy from 90.8% to 95.4%.

Quantitative prediction of genome-wide resource allocation in bacteria

Predicting resource allocation between cell processes is the primary step towards decoding the evolutionary constraints governing bacterial growth under various conditions. Quantitative prediction at genome-scale remains a computational challenge as current methods are limited by the tractability of the problem or by simplifying hypotheses. Here, we show that the constraint-based modeling method Resource Balance Analysis (RBA), calibrated using genome-wide absolute protein quantification data, accurately predicts resource allocation in the model bacterium Bacillus subtilis for a wide range of growth conditions. The regulation of most cellular processes is consistent with the objective of growth rate maximization except for a few suboptimal processes which likely integrate more complex objectives such as coping with stressful conditions and survival. As a proof of principle by using simulations, we illustrated how calibrated RBA could aid rational design of strains for maximizing protein production, offering new opportunities to investigate design principles in prokaryotes and to exploit them for biotechnological applications.

CycleFreeFlux: efficient removal of thermodynamically infeasible loops from flux distributions.

Constraint-based metabolic modeling methods such as Flux Balance Analysis (FBA) are routinely used to predict metabolic phenotypes, e.g. growth rates, ATP yield or the fitness of gene knockouts. One frequent difficulty of constraint-based solutions is the inclusion of thermodynamically infeasible loops (or internal cycles), which add nonbiological fluxes to the predictions. We propose a simple postprocessing of constraint-based solutions, which removes internal cycles from any given flux distribution [Formula: see text] without disturbing other fluxes not involved in the loops. This new algorithm, termed CycleFreeFlux, works by minimizing the sum of absolute fluxes [Formula: see text] while (i) conserving the exchange fluxes and (ii) using the fluxes of the original solution to bound the new flux distribution. This strategy reduces internal fluxes until at least one reaction of every possible internal cycle is inactive, a necessary and sufficient condition for the thermodynamic feasibility of a flux distribution. If alternative representations of the input flux distribution in terms of elementary flux modes exist that differ in their inclusion of internal cycles, then CycleFreeFlux is biased towards solutions that maintain the direction given by [Formula: see text] and towards solutions with lower total flux [Formula: see text]. Our method requires only one additional linear optimization, making it computationally very efficient compared to alternative strategies. We provide freely available R implementations for the enumeration of thermodynamically infeasible cycles as well as for cycle-free FBA solutions, flux variability calculations and random sampling of solution spaces. lercher@cs.uni-duesseldorf.de.

Model-driven design of a Saccharomyces cerevisiae platform strain with improved tyrosine production capabilities

Saccharomyces cerevisiae, a eukaryotic model organism, is considered the ideal host for microbial production of plant secondary metabolites such as polyketides and alkaloids. However, industrial scale production of these valuable products using S. cerevisiae is limited by the availability of their precursor, aromatic amino acid tyrosine. Here, we describe a framework which uses a combination of computational modeling techniques to design an in silico metabolic engineering strategy that improves the flux through the aromatic amino acid pathway (shikimate pathway) in S. cerevisiae. The predicted yeast strain can be used as a platform strain for production of any heterologous products which require tyrosine, or any other aromatic amino acid pathway metabolites as precursors. The initial genome-scale strain design was performed using steady-state constraint-based modeling methods, Optknock and GDLS. The resulting design required deletion of multiple genes and was difficult to validate experimentally. In order to obtain an experimentally feasible design, a small-scale kinetic model was developed using Ensemble Modeling, and was used to prioritize the knockouts predicted by steady-state models for experimental validation.

A constraint-based model analysis of the metabolic consequences of increased NADPH oxidation in Saccharomyces cerevisiae

Controlling the amounts of redox cofactors to manipulate metabolic fluxes is emerging as a useful approach to optimizing byproduct yields in yeast biotechnological processes. Redox cofactors are extensively interconnected metabolites, so predicting metabolite patterns is challenging and requires in-depth knowledge of how the metabolic network responds to a redox perturbation. Our aim was to analyze comprehensively the metabolic consequences of increased cytosolic NADPH oxidation during yeast fermentation. Using a genetic device based on the overexpression of a modified 2,3-butanediol dehydrogenase catalyzing the NADPH-dependent reduction of acetoin into 2,3-butanediol, we increased the NADPH demand to between 8 and 40-fold the anabolic demand. We developed (i) a dedicated constraint-based model of yeast fermentation and (ii) a constraint-based modeling method based on the dynamical analysis of mass distribution to quantify the in vivo contribution of pathways producing NADPH to the maintenance of redox homeostasis. We report that yeast responds to NADPH oxidation through a gradual increase in the flux through the PP and acetate pathways, providing 80% and 20% of the NADPH demand, respectively. However, for the highest NADPH demand, the model reveals a saturation of the PP pathway and predicts an exchange between NADH and NADPH in the cytosol that may be mediated by the glycerol–DHA futile cycle. We also reveal the contribution of mitochondrial shuttles, resulting in a net production of NADH in the cytosol, to fine-tune the NADH/NAD+ balance. This systems level study helps elucidate the physiological adaptation of yeast to NADPH perturbation. Our findings emphasize the robustness of yeast to alterations in NADPH metabolism and highlight the role of the glycerol–DHA cycle as a redox valve, providing additional NADPH from NADH under conditions of very high demand.

Bacterial growth rate reflects a bottleneck in resource allocation

BackgroundGrowth rate management in fast-growing bacteria is currently an active research area. In spite of the huge progress made in our understanding of the molecular mechanisms controlling the growth rate, fundamental questions concerning its intrinsic limitations are still relevant today. In parallel, systems biology claims that mathematical models could shed light on these questions. MethodsThis review explores some possible reasons for the limitation of the growth rate in fast-growing bacteria, using a systems biology approach based on constraint-based modeling methods. ResultsRecent experimental results and a new constraint-based modelling method named Resource Balance Analysis (RBA) reveal the existence of constraints on resource allocation between biological processes in bacterial cells. In this context, the distribution of a finite amount of resources between the metabolic network and the ribosomes limits the growth rate, which implies the existence of a bottleneck between these two processes. Any mechanism for saving resources increases the growth rate. General SignificanceConsequently, the emergence of genetic regulation of metabolic pathways, e.g. catabolite repression, could then arise as a means to minimise the protein cost, i.e. maximising growth performance while minimising the resource allocation. This article is part of a Special Issue entitled Systems Biology of Microorganisms.

Identification of Potential Pathway Mediation Targets in Toll-like Receptor Signaling

Recent advances in reconstruction and analytical methods for signaling networks have spurred the development of large-scale models that incorporate fully functional and biologically relevant features. An extended reconstruction of the human Toll-like receptor signaling network is presented herein. This reconstruction contains an extensive complement of kinases, phosphatases, and other associated proteins that mediate the signaling cascade along with a delineation of their associated chemical reactions. A computational framework based on the methods of large-scale convex analysis was developed and applied to this network to characterize input–output relationships. The input–output relationships enabled significant modularization of the network into ten pathways. The analysis identified potential candidates for inhibitory mediation of TLR signaling with respect to their specificity and potency. Subsequently, we were able to identify eight novel inhibition targets through constraint-based modeling methods. The results of this study are expected to yield meaningful avenues for further research in the task of mediating the Toll-like receptor signaling network and its effects.

Constraint-Based Modeling and Kinetic Analysis of the Smad Dependent TGF-β Signaling Pathway

BackgroundInvestigation of dynamics and regulation of the TGF-β signaling pathway is central to the understanding of complex cellular processes such as growth, apoptosis, and differentiation. In this study, we aim at using systems biology approach to provide dynamic analysis on this pathway.Methodology/Principal FindingsWe proposed a constraint-based modeling method to build a comprehensive mathematical model for the Smad dependent TGF-β signaling pathway by fitting the experimental data and incorporating the qualitative constraints from the experimental analysis. The performance of the model generated by constraint-based modeling method is significantly improved compared to the model obtained by only fitting the quantitative data. The model agrees well with the experimental analysis of TGF-β pathway, such as the time course of nuclear phosphorylated Smad, the subcellular location of Smad and signal response of Smad phosphorylation to different doses of TGF-β.Conclusions/SignificanceThe simulation results indicate that the signal response to TGF-β is regulated by the balance between clathrin dependent endocytosis and non-clathrin mediated endocytosis. This model is useful to be built upon as new precise experimental data are emerging. The constraint-based modeling method can also be applied to quantitative modeling of other signaling pathways.

Analysis of Growth of Lactobacillus plantarum WCFS1 on a Complex Medium Using a Genome-scale Metabolic Model

A genome-scale metabolic model of the lactic acid bacterium Lactobacillus plantarum WCFS1 was constructed based on genomic content and experimental data. The complete model includes 721 genes, 643 reactions, and 531 metabolites. Different stoichiometric modeling techniques were used for interpretation of complex fermentation data, as L. plantarum is adapted to nutrient-rich environments and only grows in media supplemented with vitamins and amino acids. (i) Based on experimental input and output fluxes, maximal ATP production was estimated and related to growth rate. (ii) Optimization of ATP production further identified amino acid catabolic pathways that were not previously associated with free-energy metabolism. (iii) Genome-scale elementary flux mode analysis identified 28 potential futile cycles. (iv) Flux variability analysis supplemented the elementary mode analysis in identifying parallel pathways, e.g. pathways with identical end products but different co-factor usage. Strongly increased flexibility in the metabolic network was observed when strict coupling between catabolic ATP production and anabolic consumption was relaxed. These results illustrate how a genome-scale metabolic model and associated constraint-based modeling techniques can be used to analyze the physiology of growth on a complex medium rather than a minimal salts medium. However, optimization of biomass formation using the Flux Balance Analysis approach, reported to successfully predict growth rate and by product formation in Escherichia coli and Saccharomyces cerevisiae, predicted too high biomass yields that were incompatible with the observed lactate production. The reason is that this approach assumes optimal efficiency of substrate to biomass conversion, and can therefore not predict the metabolically inefficient lactate formation.

Thermodynamic-based computational profiling of cellular regulatory control in hepatocyte metabolism

Thermodynamic-based constraints on biochemical fluxes and concentrations are applied in concert with mass balance of fluxes in glycogenesis and glycogenolysis in a model of hepatic cell metabolism. Constraint-based modeling methods that facilitate predictions of reactant concentrations, reaction potentials, and enzyme activities are introduced to identify putative regulatory and control sites in biological networks by computing the minimal control scheme necessary to switch between metabolic modes. Computational predictions of control sites in glycogenic and glycogenolytic operational modes in the hepatocyte network compare favorably with known regulatory mechanisms. The developed hepatic metabolic model is used to computationally analyze the impairment of glucose production in von Gierke's and Hers' diseases, two metabolic diseases impacting glycogen metabolism. The computational methodology introduced here can be generalized to identify downstream targets of agonists, to systematically probe possible drug targets, and to predict the effects of specific inhibitors (or activators) on integrated network function.