The structure of MESSI biological systems

We introduce a general framework for biological systems, called MESSI systems, that describe Modifications of type Enzyme-Substrate or Swap with Intermediates, and we prove general results based on the network structure. Many posttranslational modification networks are MESSI systems. Examples are th...

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Detalles Bibliográficos
Publicado: 2017
Materias:
Biological networks
MESSI system
Multistationarity
Steady states
Biological systems
Phosphorylation
Rate constants
Intermediate complex
Post-translational modifications
Rational parametrizations
Steady state
Two component systems
Linear networks
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15360040_v17_n2_p1650_Millan
http://hdl.handle.net/20.500.12110/paper_15360040_v17_n2_p1650_Millan
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_15360040_v17_n2_p1650_Millan
record_format dspace
spelling paper:paper_15360040_v17_n2_p1650_Millan2023-06-08T16:20:08Z The structure of MESSI biological systems Biological networks MESSI system Multistationarity Steady states Biological systems Phosphorylation Rate constants Biological networks Intermediate complex MESSI system Multistationarity Post-translational modifications Rational parametrizations Steady state Two component systems Linear networks We introduce a general framework for biological systems, called MESSI systems, that describe Modifications of type Enzyme-Substrate or Swap with Intermediates, and we prove general results based on the network structure. Many posttranslational modification networks are MESSI systems. Examples are the motifs in [E. Feliu and C. Wiuf, J. R. Soc. Interface, 9 (2012), pp. 1224-1232], sequential distributive and processive multisite phosphorylation networks, most of the examples in [D. Angeli, P. De Leenher, and E. Sontag, Math. Biosci., 210 (2007), pp. 598-618], phosphorylation cascades, two component systems as in [V. B. Kothamachu et al., J. R. Soc. Interface, 12 (2015), 20150234], the bacterial EnvZ/OmpR network in [G. Shinar and M. Feinberg, Science, 327 (2010), pp. 1389-1391], and all linear networks. We show that, under mass-action kinetics, MESSI systems are conservative. We simplify the study of steady states of these systems by explicit elimination of intermediate complexes, and we give conditions to ensure an explicit rational parametrization of the variety of steady states (inspired by [E. Feliu and C. Wiuf, J. R. Soc. Interface, 10 (2013), 20130484, J. Math. Biol., 66 (2013), pp. 281-310; M. Thomson and J. Gunawardena, J. Theoret. Biol., 261 (2009), pp. 626-636]). We define an important subclass of MESSI systems with toric steady states [M. Pérez Millán et al., Bull. Math. Biol., 74 (2012), pp. 1027-1065], and we give for MESSI systems with toric steady states an easy algorithm to determine the capacity for multistationarity. In this case, the algorithm provides rate constants for which multistationarity takes place, based on the theory of oriented matroids. © 2018 Society for Industrial and Applied Mathematics. 2017 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15360040_v17_n2_p1650_Millan http://hdl.handle.net/20.500.12110/paper_15360040_v17_n2_p1650_Millan
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Biological networks
MESSI system
Multistationarity
Steady states
Biological systems
Phosphorylation
Rate constants
Biological networks
Intermediate complex
MESSI system
Multistationarity
Post-translational modifications
Rational parametrizations
Steady state
Two component systems
Linear networks
spellingShingle Biological networks
MESSI system
Multistationarity
Steady states
Biological systems
Phosphorylation
Rate constants
Biological networks
Intermediate complex
MESSI system
Multistationarity
Post-translational modifications
Rational parametrizations
Steady state
Two component systems
Linear networks
The structure of MESSI biological systems
topic_facet Biological networks
MESSI system
Multistationarity
Steady states
Biological systems
Phosphorylation
Rate constants
Biological networks
Intermediate complex
MESSI system
Multistationarity
Post-translational modifications
Rational parametrizations
Steady state
Two component systems
Linear networks
description We introduce a general framework for biological systems, called MESSI systems, that describe Modifications of type Enzyme-Substrate or Swap with Intermediates, and we prove general results based on the network structure. Many posttranslational modification networks are MESSI systems. Examples are the motifs in [E. Feliu and C. Wiuf, J. R. Soc. Interface, 9 (2012), pp. 1224-1232], sequential distributive and processive multisite phosphorylation networks, most of the examples in [D. Angeli, P. De Leenher, and E. Sontag, Math. Biosci., 210 (2007), pp. 598-618], phosphorylation cascades, two component systems as in [V. B. Kothamachu et al., J. R. Soc. Interface, 12 (2015), 20150234], the bacterial EnvZ/OmpR network in [G. Shinar and M. Feinberg, Science, 327 (2010), pp. 1389-1391], and all linear networks. We show that, under mass-action kinetics, MESSI systems are conservative. We simplify the study of steady states of these systems by explicit elimination of intermediate complexes, and we give conditions to ensure an explicit rational parametrization of the variety of steady states (inspired by [E. Feliu and C. Wiuf, J. R. Soc. Interface, 10 (2013), 20130484, J. Math. Biol., 66 (2013), pp. 281-310; M. Thomson and J. Gunawardena, J. Theoret. Biol., 261 (2009), pp. 626-636]). We define an important subclass of MESSI systems with toric steady states [M. Pérez Millán et al., Bull. Math. Biol., 74 (2012), pp. 1027-1065], and we give for MESSI systems with toric steady states an easy algorithm to determine the capacity for multistationarity. In this case, the algorithm provides rate constants for which multistationarity takes place, based on the theory of oriented matroids. © 2018 Society for Industrial and Applied Mathematics.
title The structure of MESSI biological systems
title_short The structure of MESSI biological systems
title_full The structure of MESSI biological systems
title_fullStr The structure of MESSI biological systems
title_full_unstemmed The structure of MESSI biological systems
title_sort structure of messi biological systems
publishDate 2017
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15360040_v17_n2_p1650_Millan
http://hdl.handle.net/20.500.12110/paper_15360040_v17_n2_p1650_Millan
_version_ 1768544656616849408

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