Identification of Conserved Moieties in Metabolic Networks by Graph Theoretical Analysis of Atom Transition Networks

Conserved moieties are groups of atoms that remain intact in all reactions of a metabolic network. Identification of conserved moieties gives insight into the structure and function of metabolic networks and facilitates metabolic modelling. All moiety conservation relations can be represented as nonnegative integer vectors in the left null space of the stoichiometric matrix corresponding to a biochemical network. Algorithms exist to compute such vectors based only on reaction stoichiometry but their computational complexity has limited their application to relatively small metabolic networks. Moreover, the vectors returned by existing algorithms do not, in general, represent conservation of a specific moiety with a defined atomic structure. Here, we show that identification of conserved moieties requires data on reaction atom mappings in addition to stoichiometry. We present a novel method to identify conserved moieties in metabolic networks by graph theoretical analysis of their underlying atom transition networks. Our method returns the exact group of atoms belonging to each conserved moiety as well as the corresponding vector in the left null space of the stoichiometric matrix. It can be implemented as a pipeline of polynomial time algorithms. Our implementation completes in under five minutes on a metabolic network with more than 4,000 mass balanced reactions. The scalability of the method enables extension of existing applications for moiety conservation relations to genome-scale metabolic networks. We also give examples of new applications made possible by elucidating the atomic structure of conserved moieties.

[1]  S. Schuster,et al.  Determining all extreme semi-positive conservation relations in chemical reaction systems: a test criterion for conservativity , 1991 .

[2]  H. Sauro,et al.  Conservation analysis in biochemical networks: computational issues for software writers. , 2004, Biophysical chemistry.

[3]  Steffen Klamt,et al.  Minimal cut sets in biochemical reaction networks , 2004, Bioinform..

[4]  David Avis,et al.  A pivoting algorithm for convex hulls and vertex enumeration of arrangements and polyhedra , 1991, SCG '91.

[5]  Robert E. Tarjan,et al.  Depth-First Search and Linear Graph Algorithms , 1972, SIAM J. Comput..

[6]  Bernhard O Palsson,et al.  The convex basis of the left null space of the stoichiometric matrix leads to the definition of metabolically meaningful pools. , 2003, Biophysical journal.

[7]  B. Palsson.  Systems Biology: Constraint-based Reconstruction and Analysis , 2015 .

[8]  Ronan M. T. Fleming,et al.  Quantitative prediction of cellular metabolism with constraint-based models: the COBRA Toolbox v2.0 , 2007, Nature Protocols.

[9]  H. Kacser,et al.  Metabolic control analysis of moiety-conserved cycles. , 1986, European journal of biochemistry.

[10]  J. Reich,et al.  Energy metabolism of the cell : a theoretical treatise , 1981 .

[11]  Hans-Jürgen Zimmermann,et al.  Fuzzy Set Theory - and Its Applications , 1985 .

[12]  Sylvain Soliman,et al.  Invariants and Other Structural Properties of Biochemical Models as a Constraint Satisfaction Problem , 2012, Algorithms for Molecular Biology.

[13]  Costas D. Maranas,et al.  CLCA: Maximum Common Molecular Substructure Queries within the MetRxn Database , 2014, J. Chem. Inf. Model..

[14]  Ronan M. T. Fleming,et al.  Reconstruction and Use of Microbial Metabolic Networks: the Core Escherichia coli Metabolic Model as an Educational Guide. , 2010, EcoSal Plus.

[15]  G. Stephanopoulos,et al.  Elementary metabolite units (EMU): a novel framework for modeling isotopic distributions. , 2007, Metabolic engineering.

[16]  Ronan M. T. Fleming,et al.  A community-driven global reconstruction of human metabolism , 2013, Nature Biotechnology.

[17]  O. de Weck,et al.  Overview of metrics and their correlation patterns for multiple-metric topology analysis on heterogeneous graph ensembles. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  P. Corio,et al.  Theory of reaction mechanisms , 1989 .

[19]  R. Heinrich,et al.  Minimization of intermediate concentrations as a suggested optimality principle for biochemical networks , 1991 .

[20]  Christodoulos A. Floudas,et al.  Stereochemically Consistent Reaction Mapping and Identification of Multiple Reaction Mechanisms through Integer Linear Optimization , 2012, J. Chem. Inf. Model..

[21]  Melanie I. Stefan,et al.  BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models , 2010, BMC Systems Biology.

[22]  M. Kanehisa,et al.  Computational assignment of the EC numbers for genomic-scale analysis of enzymatic reactions. , 2004, Journal of the American Chemical Society.

[23]  M. Kanehisa,et al.  Development of a chemical structure comparison method for integrated analysis of chemical and genomic information in the metabolic pathways. , 2003, Journal of the American Chemical Society.

[24]  Nikos Vlassis,et al.  Fast Reconstruction of Compact Context-Specific Metabolic Network Models , 2013, PLoS Comput. Biol..

[25]  Costas D Maranas,et al.  Elucidation and structural analysis of conserved pools for genome-scale metabolic reconstructions. , 2005, Biophysical journal.

[26]  Herbert M. Sauro,et al.  Conservation analysis of large biochemical networks , 2006, Bioinform..

[27]  S. Schuster,et al.  What Information about the Conserved-Moiety Structure of Chemical Reaction Systems Can be Derived from Their Stoichiometry? , 1995 .

[28]  Hugues Bersini,et al.  Decomposition of Complex Reaction Networks into Reactons , 2008 .

[29]  Peter D. Karp,et al.  Accurate Atom-Mapping Computation for Biochemical Reactions , 2012, J. Chem. Inf. Model..

[30]  Stephen A. Vavasis,et al.  On the Complexity of Nonnegative Matrix Factorization , 2007, SIAM J. Optim..

[31]  P. Gill,et al.  Maintaining LU factors of a general sparse matrix , 1987 .

[32]  Barbara M. Bakker,et al.  How yeast cells synchronize their glycolytic oscillations: a perturbation analytic treatment. , 2000, Biophysical journal.

[33]  D. E. Atkinson.  Cellular Energy Metabolism and its Regulation , 1977 .

[34]  R. Jackson,et al.  General mass action kinetics , 1972 .

[35]  Bernard Harris,et al.  Graph theory and its applications , 1970 .

[36]  W. Wiechert,et al.  Bidirectional reaction steps in metabolic networks: I. Modeling and simulation of carbon isotope labeling experiments. , 1997, Biotechnology and bioengineering.

[37]  Hiroaki Kitano,et al.  The systems biology markup language (SBML): a medium for representation and exchange of biochemical network models , 2003, Bioinform..

[38]  D J Park.  The Complete Stoichiometer. , 1986, Computer methods and programs in biomedicine.

[39]  Athel Cornish-Bowden,et al.  The Role of Stoichiometric Analysis in Studies of Metabolism: an Example , 2002 .

[40]  B. Palsson,et al.  Theory for the systemic definition of metabolic pathways and their use in interpreting metabolic function from a pathway-oriented perspective. , 2000, Journal of theoretical biology.

[41]  J. Field.  Energy metabolism of the cell. , 1947, Stanford medical bulletin.

[42]  S. Schuster,et al.  Minimization of intermediate concentrations as a suggested optimality principle for biochemical networks , 1991, Journal of mathematical biology.

[43]  Andrea Pagnani,et al.  Identifying All Moiety Conservation Laws in Genome-Scale Metabolic Networks , 2014, PloS one.

[44]  Barbara M. Bakker,et al.  Compartmentation protects trypanosomes from the dangerous design of glycolysis. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[45]  W. Wiechert.  13C metabolic flux analysis. , 2001, Metabolic engineering.

[46]  W. Wiechert,et al.  Bidirectional reaction steps in metabolic networks: III. Explicit solution and analysis of isotopomer labeling systems. , 1999, Biotechnology and bioengineering.

[47]  Steffen Klamt,et al.  Hypergraphs and Cellular Networks , 2009, PLoS Comput. Biol..