A Petri net approach to the study of persistence in chemical reaction networks

David Angeli; Patrick De Leenheer; Eduardo D. Sontag

doi:10.1016/j.mbs.2007.07.003

A Petri net approach to the study of persistence in chemical reaction networks

David Angeli, Patrick De Leenheer, Eduardo D. Sontag

Research output: Contribution to journal › Article › peer-review

129 Scopus citations

Abstract

Persistence is the property, for differential equations in Rⁿ, that solutions starting in the positive orthant do not approach the boundary of the orthant. For chemical reactions and population models, this translates into the non-extinction property: provided that every species is present at the start of the reaction, no species will tend to be eliminated in the course of the reaction. This paper provides checkable conditions for persistence of chemical species in reaction networks, using concepts and tools from Petri net theory, and verifies these conditions on various systems which arise in the modeling of cell signaling pathways.

Original language	English (US)
Pages (from-to)	598-618
Number of pages	21
Journal	Mathematical Biosciences
Volume	210
Issue number	2
DOIs	https://doi.org/10.1016/j.mbs.2007.07.003
State	Published - Dec 2007

All Science Journal Classification (ASJC) codes

Statistics and Probability
Modeling and Simulation
Biochemistry, Genetics and Molecular Biology(all)
Immunology and Microbiology(all)
Agricultural and Biological Sciences(all)
Applied Mathematics

Keywords

Biochemical networks
Enzymatic cycles
Nonlinear dynamics
Persistence

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10.1016/j.mbs.2007.07.003

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abstract = "Persistence is the property, for differential equations in Rn, that solutions starting in the positive orthant do not approach the boundary of the orthant. For chemical reactions and population models, this translates into the non-extinction property: provided that every species is present at the start of the reaction, no species will tend to be eliminated in the course of the reaction. This paper provides checkable conditions for persistence of chemical species in reaction networks, using concepts and tools from Petri net theory, and verifies these conditions on various systems which arise in the modeling of cell signaling pathways.",

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AU - De Leenheer, Patrick

AU - Sontag, Eduardo D.

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N2 - Persistence is the property, for differential equations in Rn, that solutions starting in the positive orthant do not approach the boundary of the orthant. For chemical reactions and population models, this translates into the non-extinction property: provided that every species is present at the start of the reaction, no species will tend to be eliminated in the course of the reaction. This paper provides checkable conditions for persistence of chemical species in reaction networks, using concepts and tools from Petri net theory, and verifies these conditions on various systems which arise in the modeling of cell signaling pathways.

AB - Persistence is the property, for differential equations in Rn, that solutions starting in the positive orthant do not approach the boundary of the orthant. For chemical reactions and population models, this translates into the non-extinction property: provided that every species is present at the start of the reaction, no species will tend to be eliminated in the course of the reaction. This paper provides checkable conditions for persistence of chemical species in reaction networks, using concepts and tools from Petri net theory, and verifies these conditions on various systems which arise in the modeling of cell signaling pathways.

KW - Biochemical networks

KW - Enzymatic cycles

KW - Nonlinear dynamics

KW - Persistence

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JF - Mathematical Biosciences

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ER -

A Petri net approach to the study of persistence in chemical reaction networks

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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