Complex-linear invariants of biochemical networks

The nonlinearities found in molecular networks usually prevent mathematical analysis of network behaviour, which has largely been studied by numerical simulation. This can lead to difficult problems of parameter determination. However, molecular networks give rise, through mass-action kinetics, to p...

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Autores principales:	Pérez Millán, Mercedes Soledad, Dickenstein, Alicia Marcela
Publicado:	2012
Materias:	Bifunctional enzyme Chemical Reaction Network Theory Invariant Robustness 6 phosphofructo 2 kinase fructose 2,6 bisphosphatase chemical reaction enzyme molecular analysis reaction kinetics theoretical study article complex formation complex linear invariant enzyme activity mammal mass action mathematical computing mathematical parameters molecular dynamics nonlinear system osmolarity priority journal process development theory Bacterial Outer Membrane Proteins Bacterial Proteins Escherichia coli Escherichia coli Proteins Glycolysis Models, Biological Multienzyme Complexes Phosphofructokinase-2 Trans-Activators Bacteria (microorganisms) Mammalia
Acceso en línea:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00225193_v311_n_p130_Karp http://hdl.handle.net/20.500.12110/paper_00225193_v311_n_p130_Karp
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	paper:paper_00225193_v311_n_p130_Karp
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spelling	paper:paper_00225193_v311_n_p130_Karp2023-06-08T14:51:23Z Complex-linear invariants of biochemical networks Pérez Millán, Mercedes Soledad Dickenstein, Alicia Marcela Bifunctional enzyme Chemical Reaction Network Theory Invariant Robustness 6 phosphofructo 2 kinase fructose 2,6 bisphosphatase chemical reaction enzyme molecular analysis reaction kinetics theoretical study article chemical reaction Chemical Reaction Network Theory complex formation complex linear invariant enzyme activity mammal mass action mathematical computing mathematical parameters molecular dynamics nonlinear system osmolarity priority journal process development theory Bacterial Outer Membrane Proteins Bacterial Proteins Escherichia coli Escherichia coli Proteins Glycolysis Models, Biological Multienzyme Complexes Phosphofructokinase-2 Trans-Activators Bacteria (microorganisms) Mammalia The nonlinearities found in molecular networks usually prevent mathematical analysis of network behaviour, which has largely been studied by numerical simulation. This can lead to difficult problems of parameter determination. However, molecular networks give rise, through mass-action kinetics, to polynomial dynamical systems, whose steady states are zeros of a set of polynomial equations. These equations may be analysed by algebraic methods, in which parameters are treated as symbolic expressions whose numerical values do not have to be known in advance. For instance, an "invariant" of a network is a polynomial expression on selected state variables that vanishes in any steady state. Invariants have been found that encode key network properties and that discriminate between different network structures. Although invariants may be calculated by computational algebraic methods, such as Gröbner bases, these become computationally infeasible for biologically realistic networks. Here, we exploit Chemical Reaction Network Theory (CRNT) to develop an efficient procedure for calculating invariants that are linear combinations of "complexes", or the monomials coming from mass action. We show how this procedure can be used in proving earlier results of Horn and Jackson and of Shinar and Feinberg for networks of deficiency at most one. We then apply our method to enzyme bifunctionality, including the bacterial EnvZ/OmpR osmolarity regulator and the mammalian 6-phosphofructo-2-kinase/fructose-2,6-bisphosphatase glycolytic regulator, whose networks have deficiencies up to four. We show that bifunctionality leads to different forms of concentration control that are robust to changes in initial conditions or total amounts. Finally, we outline a systematic procedure for using complex-linear invariants to analyse molecular networks of any deficiency. © 2012 Elsevier Ltd. Fil:Pérez Millán, M. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Dickenstein, A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2012 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00225193_v311_n_p130_Karp http://hdl.handle.net/20.500.12110/paper_00225193_v311_n_p130_Karp
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Bifunctional enzyme Chemical Reaction Network Theory Invariant Robustness 6 phosphofructo 2 kinase fructose 2,6 bisphosphatase chemical reaction enzyme molecular analysis reaction kinetics theoretical study article chemical reaction Chemical Reaction Network Theory complex formation complex linear invariant enzyme activity mammal mass action mathematical computing mathematical parameters molecular dynamics nonlinear system osmolarity priority journal process development theory Bacterial Outer Membrane Proteins Bacterial Proteins Escherichia coli Escherichia coli Proteins Glycolysis Models, Biological Multienzyme Complexes Phosphofructokinase-2 Trans-Activators Bacteria (microorganisms) Mammalia
spellingShingle	Bifunctional enzyme Chemical Reaction Network Theory Invariant Robustness 6 phosphofructo 2 kinase fructose 2,6 bisphosphatase chemical reaction enzyme molecular analysis reaction kinetics theoretical study article chemical reaction Chemical Reaction Network Theory complex formation complex linear invariant enzyme activity mammal mass action mathematical computing mathematical parameters molecular dynamics nonlinear system osmolarity priority journal process development theory Bacterial Outer Membrane Proteins Bacterial Proteins Escherichia coli Escherichia coli Proteins Glycolysis Models, Biological Multienzyme Complexes Phosphofructokinase-2 Trans-Activators Bacteria (microorganisms) Mammalia Pérez Millán, Mercedes Soledad Dickenstein, Alicia Marcela Complex-linear invariants of biochemical networks
topic_facet	Bifunctional enzyme Chemical Reaction Network Theory Invariant Robustness 6 phosphofructo 2 kinase fructose 2,6 bisphosphatase chemical reaction enzyme molecular analysis reaction kinetics theoretical study article chemical reaction Chemical Reaction Network Theory complex formation complex linear invariant enzyme activity mammal mass action mathematical computing mathematical parameters molecular dynamics nonlinear system osmolarity priority journal process development theory Bacterial Outer Membrane Proteins Bacterial Proteins Escherichia coli Escherichia coli Proteins Glycolysis Models, Biological Multienzyme Complexes Phosphofructokinase-2 Trans-Activators Bacteria (microorganisms) Mammalia
description	The nonlinearities found in molecular networks usually prevent mathematical analysis of network behaviour, which has largely been studied by numerical simulation. This can lead to difficult problems of parameter determination. However, molecular networks give rise, through mass-action kinetics, to polynomial dynamical systems, whose steady states are zeros of a set of polynomial equations. These equations may be analysed by algebraic methods, in which parameters are treated as symbolic expressions whose numerical values do not have to be known in advance. For instance, an "invariant" of a network is a polynomial expression on selected state variables that vanishes in any steady state. Invariants have been found that encode key network properties and that discriminate between different network structures. Although invariants may be calculated by computational algebraic methods, such as Gröbner bases, these become computationally infeasible for biologically realistic networks. Here, we exploit Chemical Reaction Network Theory (CRNT) to develop an efficient procedure for calculating invariants that are linear combinations of "complexes", or the monomials coming from mass action. We show how this procedure can be used in proving earlier results of Horn and Jackson and of Shinar and Feinberg for networks of deficiency at most one. We then apply our method to enzyme bifunctionality, including the bacterial EnvZ/OmpR osmolarity regulator and the mammalian 6-phosphofructo-2-kinase/fructose-2,6-bisphosphatase glycolytic regulator, whose networks have deficiencies up to four. We show that bifunctionality leads to different forms of concentration control that are robust to changes in initial conditions or total amounts. Finally, we outline a systematic procedure for using complex-linear invariants to analyse molecular networks of any deficiency. © 2012 Elsevier Ltd.
author	Pérez Millán, Mercedes Soledad Dickenstein, Alicia Marcela
author_facet	Pérez Millán, Mercedes Soledad Dickenstein, Alicia Marcela
author_sort	Pérez Millán, Mercedes Soledad
title	Complex-linear invariants of biochemical networks
title_short	Complex-linear invariants of biochemical networks
title_full	Complex-linear invariants of biochemical networks
title_fullStr	Complex-linear invariants of biochemical networks
title_full_unstemmed	Complex-linear invariants of biochemical networks
title_sort	complex-linear invariants of biochemical networks
publishDate	2012
url	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00225193_v311_n_p130_Karp http://hdl.handle.net/20.500.12110/paper_00225193_v311_n_p130_Karp
work_keys_str_mv	AT perezmillanmercedessoledad complexlinearinvariantsofbiochemicalnetworks AT dickensteinaliciamarcela complexlinearinvariantsofbiochemicalnetworks
_version_	1768544538844987392

Complex-linear invariants of biochemical networks

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