Structural conserved moiety splitting of a stoichiometric matrix

Ghaderi, Susan; Haraldsdóttir, Hulda S.; Ahookhosh, Masoud; Arreckx, Sylvain; Fleming, Ronan M.T.

doi:10.1016/j.jtbi.2020.110276

Structural conserved moiety splitting of a stoichiometric matrix

Journal Article · Thu Apr 23 00:00:00 EDT 2020 · Journal of Theoretical Biology

DOI:https://doi.org/10.1016/j.jtbi.2020.110276· OSTI ID:1802109

Ghaderi, Susan ^[1]; Haraldsdóttir, Hulda S. ^[2]; Ahookhosh, Masoud ^[3]; ^[2]; ^[4]

Univ. of Luxembourg, Belvaux, (Luxembourg); OSTI
Univ. of Luxembourg, Belvaux, (Luxembourg)
Univ. of Luxembourg, Belvaux, (Luxembourg); Katholieke Univ. Leuven, Heverlee (Belgium)
Univ. of Luxembourg, Belvaux, (Luxembourg); Leiden Univ. (Netherlands)

Characterising biochemical reaction network structure in mathematical terms enables the inference of functional biochemical consequences from network structure with existing mathematical techniques and spurs the development of new mathematics that exploits the peculiarities of biochemical network structure. The structure of a biochemical network may be specified by reaction stoichiometry, that is, the relative quantities of each molecule produced and consumed in each reaction of the network. A biochemical network may also be specified at a higher level of resolution in terms of the internal structure of each molecule and how molecular structures are transformed by each reaction in a network. The stoichiometry for a set of reactions can be compiled into a stoichiometric matrix N ϵ Z ^mxn where each row corresponds to a molecule and each column corresponds to a reaction. We demonstrate that a stoichiometric matrix may be split into the sum of m - rank(N) moiety transition matrices, each of which corresponds to a subnetwork accessible to a structurally identifiable conserved moiety. The existence of this moiety matrix splitting is a property that distinguishes a stoichiometric matrix from an arbitrary rectangular matrix.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of Luxembourg, Esch-sur-Alzette, (Luxembourg)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); Marie Sklodowska-Curie Innovative Training Network

Grant/Contract Number:: SC0010429

OSTI ID:: 1802109

Journal Information:: Journal of Theoretical Biology, Journal Name: Journal of Theoretical Biology Journal Issue: C Vol. 499; ISSN 0022-5193

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (19)

Stoichiometric network analysis Clarke, Bruce L. Cell Biophysics, Vol. 12, Issue 1 https://doi.org/10.1007/BF02918360	journal	January 1988
Local convergence of the Levenberg–Marquardt method under Hölder metric subregularity Ahookhosh, Masoud; Aragón Artacho, Francisco J.; Fleming, Ronan M. T. Advances in Computational Mathematics https://doi.org/10.1007/s10444-019-09708-7	journal	June 2019
Maintaining LU factors of a general sparse matrix Gill, Philip E.; Murray, Walter; Saunders, Michael A. Linear Algebra and its Applications, Vol. 88-89 https://doi.org/10.1016/0024-3795(87)90112-1	journal	April 1987
The Convex Basis of the Left Null Space of the Stoichiometric Matrix Leads to the Definition of Metabolically Meaningful Pools Famili, Iman; Palsson, Bernhard O. Biophysical Journal, Vol. 85, Issue 1 https://doi.org/10.1016/S0006-3495(03)74450-6	journal	July 2003
A variational principle for computing nonequilibrium fluxes and potentials in genome-scale biochemical networks Fleming, R. M. T.; Maes, C. M.; Saunders, M. A. Journal of Theoretical Biology, Vol. 292 https://doi.org/10.1016/j.jtbi.2011.09.029	journal	January 2012
Mass conserved elementary kinetics is sufficient for the existence of a non-equilibrium steady state concentration Fleming, R. M. T.; Thiele, I. Journal of Theoretical Biology, Vol. 314 https://doi.org/10.1016/j.jtbi.2012.08.021	journal	December 2012
Conditions for duality between fluxes and concentrations in biochemical networks Fleming, Ronan M. T.; Vlassis, Nikos; Thiele, Ines Journal of Theoretical Biology, Vol. 409 https://doi.org/10.1016/j.jtbi.2016.06.033	journal	November 2016
Comparison of network-based pathway analysis methods Papin, Jason A.; Stelling, Joerg; Price, Nathan D. Trends in Biotechnology, Vol. 22, Issue 8 https://doi.org/10.1016/j.tibtech.2004.06.010	journal	August 2004
Recon3D enables a three-dimensional view of gene variation in human metabolism Brunk, Elizabeth; Sahoo, Swagatika; Zielinski, Daniel C. Nature Biotechnology, Vol. 36, Issue 3 https://doi.org/10.1038/nbt.4072	journal	February 2018
Network biology: understanding the cell's functional organization Barabási, Albert-László; Oltvai, Zoltán N. Nature Reviews Genetics, Vol. 5, Issue 2 https://doi.org/10.1038/nrg1272	journal	February 2004
A New Principle of Equilibrium Lewis, G. N. Proceedings of the National Academy of Sciences, Vol. 11, Issue 3 https://doi.org/10.1073/pnas.11.3.179	journal	March 1925
Analysis of optimality in natural and perturbed metabolic networks Segre, D.; Vitkup, D.; Church, G. M. Proceedings of the National Academy of Sciences, Vol. 99, Issue 23 https://doi.org/10.1073/pnas.232349399	journal	November 2002
Finding zeros of Hölder metrically subregular mappings via globally convergent Levenberg–Marquardt methods Ahookhosh, Masoud; Fleming, Ronan M. T.; Vuong, Phan T. Optimization Methods and Software https://doi.org/10.1080/10556788.2020.1712602	journal	January 2020
Conservation analysis of large biochemical networks Vallabhajosyula, R. R.; Chickarmane, V.; Sauro, H. M. Bioinformatics, Vol. 22, Issue 3 https://doi.org/10.1093/bioinformatics/bti800	journal	November 2005
Reaction Decoder Tool (RDT): extracting features from chemical reactions Rahman, Syed Asad; Torrance, Gilliean; Baldacci, Lorenzo Bioinformatics, Vol. 32, Issue 13 https://doi.org/10.1093/bioinformatics/btw096	journal	February 2016
CellDesigner 3.5: A Versatile Modeling Tool for Biochemical Networks Funahashi, A.; Matsuoka, Y.; Jouraku, A. Proceedings of the IEEE, Vol. 96, Issue 8 https://doi.org/10.1109/JPROC.2008.925458	journal	August 2008
Multiple Equilibria in Complex Chemical Reaction Networks: II. The Species-Reaction Graph Craciun, Gheorghe; Feinberg, Martin SIAM Journal on Applied Mathematics, Vol. 66, Issue 4 https://doi.org/10.1137/050634177	journal	January 2006
Hypergraphs and Cellular Networks Klamt, Steffen; Haus, Utz-Uwe; Theis, Fabian PLoS Computational Biology, Vol. 5, Issue 5 https://doi.org/10.1371/journal.pcbi.1000385	journal	May 2009
Identification of Conserved Moieties in Metabolic Networks by Graph Theoretical Analysis of Atom Transition Networks Haraldsdóttir, Hulda S.; Fleming, Ronan M. T. PLOS Computational Biology, Vol. 12, Issue 11 https://doi.org/10.1371/journal.pcbi.1004999	journal	November 2016

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Structural conserved moiety splitting of a stoichiometric matrix

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