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

Angeli, David; Leenheer, Patrick De; Sontag, Eduardo D.

doi:10.1016/j.mbs.2007.07.003

Cited by 174 publications

(288 citation statements)

References 33 publications

Supporting

Mentioning

280

Contrasting

Unclassified

Order By: Relevance

“…It can be removed as follows. The reaction path through S 0 E is S 0 + E −→ S 0 E −→ S 1 + E. We first collapse the path into S 0 + E −→ S 1 + E, and then cancel out the emerging catalyst E. This yields the reaction S 0 −→ S 1 ; see (2).…”

Section: Removal Of Intermediatesmentioning

confidence: 99%

“…And in view of Theorem 3, if these hypotheses are satisfied, then (P1) and (P2) can also be checked in G * . The hypothesis of bounded-persistence in Proposition 3 can be checked using the graphical conditions in [2]. As shown in [12], these graphical conditions for bounded-persistence can also be checked in G * -one need only to decouple the reversible reactions in order to apply the formalism in [12] (see also [3, pp.…”

Section: Invariance Under the Successive Removal Of Intermediatesmentioning

confidence: 99%

See 1 more Smart Citation

Intermediates and Generic Convergence to Equilibria

2017

View full text Add to dashboard Cite

show abstract

Section: Removal Of Intermediatesmentioning

confidence: 99%

Section: Invariance Under the Successive Removal Of Intermediatesmentioning

confidence: 99%

Intermediates and Generic Convergence to Equilibria

2017

View full text Add to dashboard Cite

show abstract

“…A reaction network is said to be persistent if it starts in the positive orthant and does not approach the boundary of the orthant, in other words, if 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. Conditions for persistence are given by Angeli et al [21].…”

Section: Basic Propertiesmentioning

confidence: 99%

Engineering Model Reduction and Entropy-based Lyapunov Functions in Chemical Reaction Kinetics

Hangos

2010

Entropy

View full text Add to dashboard Cite

In this paper, the structural properties of chemical reaction systems obeying the mass action law are investigated and related to the physical and chemical properties of the system. An entropy-based Lyapunov function candidate serves as a tool for proving structural stability, the existence of which is guaranteed by the second law of thermodynamics. The commonly used engineering model reduction methods, the so-called quasi equilibrium and quasi steady state assumption based reductions, together with the variable lumping are formally defined as model transformations acting on the reaction graph. These model reduction transformations are analysed to find conditions when (a) the reduced model remains in the same reaction kinetic system class, (b) the reduced model retains the most important properties of the original one including structural stability. It is shown that both variable lumping and quasi equilibrium based reduction preserve both the reaction kinetic form and the structural stability of reaction kinetic models of closed systems with mass action law kinetics, but this is not always the case for the reduction based on quasi steady state assumption.

show abstract

“…Petri-net models -both deterministic and stochastic-are widely used for the analysis of qualitative dynamic properties, such as persistency [1], stability [2], etc. Qualitative dynamic models in the form of nonlinear ordinary differential equations (ODEs) are also widely used when good quality measured data are available for model parameter estimation, model verification, validation and detailed dynamic analysis.…”

Section: Introductionmentioning

confidence: 99%

On the Verification and Correction of Large-Scale Kinetic Models in Systems Biology

Gábor

Hangos

Szederkényi

et al. 2013

Computational Methods in Systems Biology

View full text Add to dashboard Cite

Abstract. In this paper we consider the problem of verification of large dynamic models of biological systems. We present syntactical criteria based on biochemical kinetics to ensure the plausibility of a model and the positivity of its solution. These criteria include the positivity of the rate functions, their kinetic type dependence on the reactant species concentrations, and the absence of the negative cross-effects that together guarantee the nonnegativity of the dynamics. Further, the stoichiometric matrix of the truncated reaction system is checked against conservation using its algebraic properties. Algorithmic procedures are then proposed for checking these criteria with emphasis on good scaling up properties. In addition to these verification procedures, we also provide, for certain typical errors, model correcting methods. The capabilities and usefulness of these procedures are illustrated on biochemical models taken from the Biomodels database. In particular, a set of 11 kinetic models related with E. coli are checked, finding two with deficiencies. Correcting actions for these models are proposed.

show abstract

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

Cited by 174 publications

References 33 publications

Intermediates and Generic Convergence to Equilibria

Intermediates and Generic Convergence to Equilibria

Engineering Model Reduction and Entropy-based Lyapunov Functions in Chemical Reaction Kinetics

On the Verification and Correction of Large-Scale Kinetic Models in Systems Biology

Contact Info

Product

Resources

About