Constraints-based models: Regulation of Gene Expression Reduces the Steady-state Solution Space

doi:10.1006/jtbi.2003.3071

Journal of Theoretical Biology

Volume 221, Issue 3, 7 April 2003, Pages 309-325

https://doi.org/10.1006/jtbi.2003.3071 Get rights and content

Abstract

Constraints-based models have been effectively used to analyse, interpret, and predict the function of reconstructed genome-scale metabolic models. The first generation of these models used “hard” non-adjustable constraints associated with network connectivity, irreversibility of metabolic reactions, and maximal flux capacities. These constraints restrict the allowable behaviors of a network to a convex mathematical solution space whose edges are extreme pathways that can be used to characterize the optimal performance of a network under a stated performance criterion. The development of a second generation of constraints-based models by incorporating constraints associated with regulation of gene expression was described in a companion paper published in this journal, using flux-balance analysis to generate time courses of growth and by-product secretion using a skeleton representation of core metabolism. The imposition of these additional restrictions prevents the use of a subset of the extreme pathways that are derived from the “hard” constraints, thus reducing the solution space and restricting allowable network functions. Here, we examine the reduction of the solution space due to regulatory constraints using extreme pathway analysis. The imposition of environmental conditions and regulatory mechanisms sharply reduces the number of active extreme pathways. This approach is demonstrated for the skeleton system mentioned above, which has 80 extreme pathways. As regulatory constraints are applied to the system, the number of feasible extreme pathways is reduced to between 26 and 2 extreme pathways, a reduction of between 67.5 and 97.5%. The method developed here provides a way to interpret how regulatory mechanisms are used to constrain network functions and produce a small range of physiologically meaningful behaviors from all allowable network functions.

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For more accurate and robust prediction of target metabolic behavior under different conditions or contexts, not only metabolic reactions but also the integration of genetic regulatory relationships involving transcription factors (TFs) that may regulate metabolic reactions, should be appropriately modeled. Due to the increasing computational complexity when considering multiple types of biomolecules in one computational system model, often transcription regulation has been integrated via “transcriptional regulatory constraints” with various heuristics for flux-balance analysis (FBA) of metabolic networks (Covert and Palsson, 2003; Shlomi et al., 2007; Covert et al., 2008; Shlomi et al., 2008; Fendt et al., 2010; Machado and Herrgård, 2014; Reiss et al., 2015; Reed, 2017; Motamedian et al., 2017; Yu and Blair, 2019). Many of these computational tools were often only validated for selected model organisms with curated data and network models.
There has been extensive research in predictive modeling of genome-scale metabolic reaction networks. Living systems involve complex stochastic processes arising from interactions among different biomolecules. For more accurate and robust prediction of target metabolic behavior under different conditions, not only metabolic reactions but also the genetic regulatory relationships involving transcription factors (TFs) affecting these metabolic reactions should be modeled. We have developed a modeling and simulation pipeline enabling the analysis of Transcription Regulation Integrated with Metabolic Regulation: TRIMER. TRIMER utilizes a Bayesian network (BN) inferred from transcriptomes to model the transcription factor regulatory network. TRIMER then infers the probabilities of the gene states relevant to the metabolism of interest, and predicts the metabolic fluxes and their changes that result from the deletion of one or more transcription factors at the genome scale. We demonstrate TRIMER’s applicability to both simulated and experimental data and provide performance comparison with other existing approaches.
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Living organisms have complex metabolic systems. Currently biologists are engaged in a comprehensive understanding of metabolic reactions to examine their role in rare genetic disorders, etc. Therefore bioinformatics has emerged as a promising field to analyze complex genomes. This study requires omics data and therefore metabolomics has emerged as an advanced field to examine such metabolic reactions. If we consider a simple unicellular organism, such as Escherichia coli, modeling of these systems would be computationally intensive because 1200 metabolic reactions occurred in these systems. Flux balance analysis (FBA) is a modeling technique that has emerged as a promising tool to work around these issues. In this chapter, we discussed metabolomics and FBA in detail and their applications. We also discussed different models, for example, E. coli, being developed to study the reaction rates and role of FBA in analyzing the flux rates in these models.
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SGL is then used to select a sparse set of genes that is the best predictor of a given phenotype. Phenotype prediction can be further enhanced by adding Boolean type constraints to GSM models to help incorporate regulation (Covert and Palsson, 2003) (e.g., under aerobic or anaerobic conditions), as indicated in Fig. 1(b). However, reconstructing a gene regulatory network (GRN) from high-throughput data remains challenging, as elucidated by the DREAM project for over 30 network inferences methods applied to E. coli, Saccharomyces cerevisiae, and Staphylococcus aureus (Marbach et al., 2012).
Understanding the governing principles behind organisms’ metabolism and growth underpins their effective deployment as bioproduction chassis. A central objective of metabolic modeling is predicting how metabolism and growth are affected by both external environmental factors and internal genotypic perturbations. The fundamental concepts of reaction stoichiometry, thermodynamics, and mass action kinetics have emerged as the foundational principles of many modeling frameworks designed to describe how and why organisms allocate resources towards both growth and bioproduction. This review focuses on the latest algorithmic advancements that have integrated these foundational principles into increasingly sophisticated quantitative frameworks.
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Such models can be transformed into stoichiometric representations, where the matrices represent the biological constraints associated with the studied system (e.g., genetic and physicochemical properties), while the solution space is defined by data resulting from gene expression and proteomic studies (Blazier and Papin, 2012). Constrained-based models are usually less computationally expensive compared to kinetic models and they are characterized by a decreased number of parameters (Covert and Palsson, 2003). In addition, there is a variety of software tools that facilitate the design of the metabolic network of interest (Lewis and Abdel-Haleem, 2013; Marinković and Orešič, 2016).
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FBA predicts the fluxes of reactions and the biomass production rate without accounting for the regulatory constraints that are crucial in determining the presence and activity of enzymes in an environmental condition (Orth et al., 2010). This omission of regulatory constraints is an important limitation of FBA (Covert and Palsson, 2002, 2003; Åkesson et al., 2004) and can partly explain incorrect predictions by this method on gene essentiality (Covert et al., 2004) and gene interactions (Szappanos et al., 2011). The metabolic state of a cell in a given condition is governed by the expression of metabolic genes encoding enzymes.
A major goal of systems biology is to build predictive computational models of cellular metabolism. Availability of complete genome sequences and wealth of legacy biochemical information has led to the reconstruction of genome-scale metabolic networks in the last 15 years for several organisms across the three domains of life. Due to paucity of information on kinetic parameters associated with metabolic reactions, the constraint-based modelling approach, flux balance analysis (FBA), has proved to be a vital alternative to investigate the capabilities of reconstructed metabolic networks. In parallel, advent of high-throughput technologies has led to the generation of massive amounts of omics data on transcriptional regulation comprising mRNA transcript levels and genome-wide binding profile of transcriptional regulators. A frontier area in metabolic systems biology has been the development of methods to integrate the available transcriptional regulatory information into constraint-based models of reconstructed metabolic networks in order to increase the predictive capabilities of computational models and understand the regulation of cellular metabolism. Here, we review the existing methods to integrate transcriptional regulatory information into constraint-based models of metabolic networks.

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Corresponding author. Tel.: +1-858-534-5668; fax: +1-858-822-3120.

E-mail address: [email protected] (B.O. Palsson).

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Regular ArticleConstraints-based models: Regulation of Gene Expression Reduces the Steady-state Solution Space

Abstract

Complex biology with no parameters

Nature Biotechnol.

Flux analysis of underdetermined metabolic networks: the quest for the missing constraints

Trends Biotechnol.

Metabolic Modeling of Microbial Strains in silico

Trends Biochem. Sci.

Properties of the Haemophilus influenzae Rd metabolic genotype

J. Biol. Chem.

The E. coli MG1655 in silico metabolic genotype: its definition, characteristics, and capabilities

Proc. Natl Acad. Sci.

Metabolic flux balance analysis

In silico predictions of Escherichia coli metabolic capabilities are consistent with experimental data

Nature Biotechnol.

Characterizing the metabolic phenotype: a pheno-type phase plane analysis

Biotechnol. Bioeng.

Understanding the Control of Metabolism

Mathematical model-ling of metabolism

Curr. Opin. Biotechnol.

The Regulation of Cellular Systems

The Origins of Order

Towards a logical analysis of the immune response

J. Theor. Biol.

Investigation of Bacterial Growth on Mixed Substrates. Experimental Evaluation of Cybernetic Models

Biotechnol. Bioeng.

Incorporating qualitative knowledge in enzyme kinetic models using fuzzy logic

Biotechnol. Bioeng.

Stochastic mechanisms in gene expression

Proc. Natl Acad. Sci. U.S.A.

Simulation of prokaryotic genetic circuits

Ann. Rev. Biophys. Biomol. Struct.

It's a noisy business! Genetic regulation at the nanomolar scale

Trends Genet.

Regular Article
Constraints-based models: Regulation of Gene Expression Reduces the Steady-state Solution Space