1
|
Robaina-Estévez S, Nikoloski Z. Flux-based hierarchical organization of Escherichia coli's metabolic network. PLoS Comput Biol 2020; 16:e1007832. [PMID: 32310959 PMCID: PMC7192501 DOI: 10.1371/journal.pcbi.1007832] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/04/2019] [Revised: 04/30/2020] [Accepted: 03/30/2020] [Indexed: 11/18/2022] Open
Abstract
Biological networks across scales exhibit hierarchical organization that may constrain network function. Yet, understanding how these hierarchies arise due to the operational constraint of the networks and whether they impose limits to molecular phenotypes remains elusive. Here we show that metabolic networks include a hierarchy of reactions based on a natural flux ordering that holds for every steady state. We find that the hierarchy of reactions is reflected in experimental measurements of transcript, protein and flux levels of Escherichia coli under various growth conditions as well as in the catalytic rate constants of the corresponding enzymes. Our findings point at resource partitioning and a fine-tuning of enzyme levels in E. coli to respect the constraints imposed by the network structure at steady state. Since reactions in upper layers of the hierarchy impose an upper bound on the flux of the reactions downstream, the hierarchical organization of metabolism due to the flux ordering has direct applications in metabolic engineering.
Collapse
Affiliation(s)
- Semidán Robaina-Estévez
- Systems Biology and Mathematical Modeling Group. Max Planck Institute of Molecular Plant Physiology, Potsdam, Germany
- Bioinformatics Group, University of Potsdam, Potsdam, Germany
- Ronin Institute for Independent Scholarship, Montclair, New Jersey, United States of America
- * E-mail:
| | - Zoran Nikoloski
- Systems Biology and Mathematical Modeling Group. Max Planck Institute of Molecular Plant Physiology, Potsdam, Germany
- Bioinformatics Group, University of Potsdam, Potsdam, Germany
| |
Collapse
|
2
|
Cesari G, Algaba E, Moretti S, Nepomuceno JA. An application of the Shapley value to the analysis of co-expression networks. APPLIED NETWORK SCIENCE 2018; 3:35. [PMID: 30839839 PMCID: PMC6214322 DOI: 10.1007/s41109-018-0095-y] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/20/2018] [Accepted: 08/14/2018] [Indexed: 06/09/2023]
Abstract
We study the problem of identifying relevant genes in a co-expression network using a (cooperative) game theoretic approach. The Shapley value of a cooperative game is used to asses the relevance of each gene in interaction with the others, and to stress the role of nodes in the periphery of a co-expression network for the regulation of complex biological pathways of interest. An application of the method to the analysis of gene expression data from microarrays is presented, as well as a comparison with classical centrality indices. Finally, making further assumptions about the a priori importance of genes, we combine the game theoretic model with other techniques from cluster analysis.
Collapse
Affiliation(s)
- Giulia Cesari
- Department of Mathematics, Politecnico di Milano, Milano, Italy
| | - Encarnación Algaba
- Department of Applied Mathematics and IMUS, University of Seville, Seville, Spain
| | - Stefano Moretti
- Université Paris-Dauphine, PSL Research University, CNRS, LAMSADE, Paris, 75016 France
| | - Juan A. Nepomuceno
- Department of Computer Languages and Systems, University of Seville, Seville, Spain
| |
Collapse
|
3
|
Sajitz-Hermstein M, Nikoloski Z. Functional centrality as a predictor of shifts in metabolic flux states. BMC Res Notes 2016; 9:317. [PMID: 27328671 PMCID: PMC4915090 DOI: 10.1186/s13104-016-2117-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2015] [Accepted: 06/02/2016] [Indexed: 11/30/2022] Open
Abstract
Background The flux phenotype describes the entirety of biochemical conversions in a cell, which renders it a key characteristic of metabolic function. To quantify the functional relevance of individual biochemical reactions, functional centrality has been introduced based on cooperative game theory and structural modeling. It was shown to be capable to determine metabolic control properties utilizing only structural information. Here, we demonstrate the capability of functional centrality to predict changes in the flux phenotype. Results We use functional centrality to successfully predict changes of metabolic flux triggered by switches in the environment. The predictions via functional centrality improve upon predictions using control-effective fluxes, another measure aiming at capturing metabolic control using structural information. Conclusions The predictions of flux changes via functional centrality corroborate the capability of the measure to gain a mechanistic understanding of metabolic control from the structure of metabolic networks.
Collapse
Affiliation(s)
- Max Sajitz-Hermstein
- Systems Biology and Mathematical Modeling Group, Max Planck Institute of Molecular Plant Physiology, Am Mühlenweg 1, 14476, Potsdam, Germany.
| | - Zoran Nikoloski
- Systems Biology and Mathematical Modeling Group, Max Planck Institute of Molecular Plant Physiology, Am Mühlenweg 1, 14476, Potsdam, Germany
| |
Collapse
|
4
|
Pires MM, Cantor M, Guimarães PR, de Aguiar MAM, Dos Reis SF, Coltri PP. The network organization of protein interactions in the spliceosome is reproduced by the simple rules of food-web models. Sci Rep 2015; 5:14865. [PMID: 26443080 PMCID: PMC4595644 DOI: 10.1038/srep14865] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/25/2015] [Accepted: 09/09/2015] [Indexed: 12/02/2022] Open
Abstract
The network structure of biological systems provides information on the underlying processes shaping their organization and dynamics. Here we examined the structure of the network depicting protein interactions within the spliceosome, the macromolecular complex responsible for splicing in eukaryotic cells. We show the interactions of less connected spliceosome proteins are nested subsets of the connections of the highly connected proteins. At the same time, the network has a modular structure with groups of proteins sharing similar interaction patterns. We then investigated the role of affinity and specificity in shaping the spliceosome network by adapting a probabilistic model originally designed to reproduce food webs. This food-web model was as successful in reproducing the structure of protein interactions as it is in reproducing interactions among species. The good performance of the model suggests affinity and specificity, partially determined by protein size and the timing of association to the complex, may be determining network structure. Moreover, because network models allow building ensembles of realistic networks while encompassing uncertainty they can be useful to examine the dynamics and vulnerability of intracelullar processes. Unraveling the mechanisms organizing the spliceosome interactions is important to characterize the role of individual proteins on splicing catalysis and regulation.
Collapse
Affiliation(s)
- Mathias M Pires
- Departamento de Ecologia, Instituto de Biociências, 05508-090, Universidade de São Paulo, São Paulo, Brazil
| | - Maurício Cantor
- Department of Biology, Dalhousie University, Halifax, Nova Scotia B3H 4J1, Canada
| | - Paulo R Guimarães
- Departamento de Ecologia, Instituto de Biociências, 05508-090, Universidade de São Paulo, São Paulo, Brazil
| | - Marcus A M de Aguiar
- Departamento de Física da Matéria Condensada, Instituto de Física 'Gleb Wataghin', 13083-859, Universidade Estadual de Campinas, Campinas, Brazil
| | - Sérgio F Dos Reis
- Departamento de Biologia Animal, Instituto de Biologia, 13083-970, Universidade Estadual de Campinas, Campinas, Brazil
| | - Patricia P Coltri
- Departamento de Biologia Celular e do Desenvolvimento, Instituto de Ciências Biomédicas, 05508-000, Universidade de São Paulo, São Paulo, Brazil
| |
Collapse
|
5
|
Cazzaniga P, Damiani C, Besozzi D, Colombo R, Nobile MS, Gaglio D, Pescini D, Molinari S, Mauri G, Alberghina L, Vanoni M. Computational strategies for a system-level understanding of metabolism. Metabolites 2014; 4:1034-87. [PMID: 25427076 PMCID: PMC4279158 DOI: 10.3390/metabo4041034] [Citation(s) in RCA: 41] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/01/2014] [Revised: 11/05/2014] [Accepted: 11/12/2014] [Indexed: 12/20/2022] Open
Abstract
Cell metabolism is the biochemical machinery that provides energy and building blocks to sustain life. Understanding its fine regulation is of pivotal relevance in several fields, from metabolic engineering applications to the treatment of metabolic disorders and cancer. Sophisticated computational approaches are needed to unravel the complexity of metabolism. To this aim, a plethora of methods have been developed, yet it is generally hard to identify which computational strategy is most suited for the investigation of a specific aspect of metabolism. This review provides an up-to-date description of the computational methods available for the analysis of metabolic pathways, discussing their main advantages and drawbacks. In particular, attention is devoted to the identification of the appropriate scale and level of accuracy in the reconstruction of metabolic networks, and to the inference of model structure and parameters, especially when dealing with a shortage of experimental measurements. The choice of the proper computational methods to derive in silico data is then addressed, including topological analyses, constraint-based modeling and simulation of the system dynamics. A description of some computational approaches to gain new biological knowledge or to formulate hypotheses is finally provided.
Collapse
Affiliation(s)
- Paolo Cazzaniga
- SYSBIO Centre of Systems Biology, Piazza della Scienza 2, 20126 Milano, Italy.
| | - Chiara Damiani
- SYSBIO Centre of Systems Biology, Piazza della Scienza 2, 20126 Milano, Italy.
| | - Daniela Besozzi
- SYSBIO Centre of Systems Biology, Piazza della Scienza 2, 20126 Milano, Italy.
| | - Riccardo Colombo
- SYSBIO Centre of Systems Biology, Piazza della Scienza 2, 20126 Milano, Italy.
| | - Marco S Nobile
- SYSBIO Centre of Systems Biology, Piazza della Scienza 2, 20126 Milano, Italy.
| | - Daniela Gaglio
- SYSBIO Centre of Systems Biology, Piazza della Scienza 2, 20126 Milano, Italy.
| | - Dario Pescini
- SYSBIO Centre of Systems Biology, Piazza della Scienza 2, 20126 Milano, Italy.
| | - Sara Molinari
- Dipartimento di Biotecnologie e Bioscienze, Università degli Studi di Milano-Bicocca, Piazza della Scienza 2, 20126 Milano, Italy.
| | - Giancarlo Mauri
- SYSBIO Centre of Systems Biology, Piazza della Scienza 2, 20126 Milano, Italy.
| | - Lilia Alberghina
- SYSBIO Centre of Systems Biology, Piazza della Scienza 2, 20126 Milano, Italy.
| | - Marco Vanoni
- SYSBIO Centre of Systems Biology, Piazza della Scienza 2, 20126 Milano, Italy.
| |
Collapse
|
6
|
Abstract
Organisms have to continuously adapt to changing environmental conditions or undergo developmental transitions. To meet the accompanying change in metabolic demands, the molecular mechanisms of adaptation involve concerted interactions which ultimately induce a modification of the metabolic state, which is characterized by reaction fluxes and metabolite concentrations. These state transitions are the effect of simultaneously manipulating fluxes through several reactions. While metabolic control analysis has provided a powerful framework for elucidating the principles governing this orchestrated action to understand metabolic control, its applications are restricted by the limited availability of kinetic information. Here, we introduce structural metabolic control as a framework to examine individual reactions' potential to control metabolic functions, such as biomass production, based on structural modeling. The capability to carry out a metabolic function is determined using flux balance analysis (FBA). We examine structural metabolic control on the example of the central carbon metabolism of Escherichia coli by the recently introduced framework of functional centrality (FC). This framework is based on the Shapley value from cooperative game theory and FBA, and we demonstrate its superior ability to assign “share of control” to individual reactions with respect to metabolic functions and environmental conditions. A comparative analysis of various scenarios illustrates the usefulness of FC and its relations to other structural approaches pertaining to metabolic control. We propose a Monte Carlo algorithm to estimate FCs for large networks, based on the enumeration of elementary flux modes. We further give detailed biological interpretation of FCs for production of lactate and ATP under various respiratory conditions. Insight into the functioning of metabolic control to meet changing demands is a first step in rational engineering of biological systems towards a desired behavior. Metabolic control analysis provides the means to examine the impact of change of reaction fluxes on a specific target flux based on kinetic modeling, but suffers from limitations of the kinetic approach. Here, we introduce and analyze structural metabolic control as a framework to overcome these limitations. We utilize functional centrality, a framework based on the Shapley value from cooperative game theory and flux balance analysis, to determine the contribution of individual reactions to the functions accomplished by a metabolic network. These contributions, in turn, depend on the control exerted on the remaining network. Functional centrality provides the mathematical means to gain further understanding of metabolic control. The potential applications range from facilitating strategies of rational strain design to drug target identification.
Collapse
|