A Petri Net Approach to Persistence Analysis in Chemical Reaction Networks

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

doi:10.1007/978-3-540-71988-5_9

Cited by 37 publications

(83 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Our goal in this paper is to show why, as it is apparent from the example Sections in [1], many relevant examples of reaction networks arising in biochemistry have the remarkable property that all of its chemical species do not asymptotically disappear (precise definitions will be found later).…”

Section: Background On Chemical Reaction Networkmentioning

confidence: 99%

See 1 more Smart Citation

On modularity and persistence of chemical reaction networks

Angeli

2008

2008 47th IEEE Conference on Decision and Control

Self Cite

View full text Add to dashboard Cite

show abstract

Section: Background On Chemical Reaction Networkmentioning

confidence: 99%

“…Let us consider, as an illustrative example, the doublephosphorilation and de-phosphorilation network which was also analyzed in [1]. We recall one plausible hypothesis of its constitutive reactions below:…”

Section: Background On Chemical Reaction Networkmentioning

confidence: 99%

On modularity and persistence of chemical reaction networks

Angeli

2008

2008 47th IEEE Conference on Decision and Control

Self Cite

View full text Add to dashboard Cite

show abstract

“…This approach has rapidly developed in Systems Biology for reasoning on large interaction networks, with for instance, the analysis of qualitative attractors in a logical dynamics of gene networks à la Thomas [3,4,5], reachability and temporal logic properties in reaction networks [6,7,8,9,10], structural invariants in the Petri net representation of the reactions [11,12,13,14,15,16], or model reductions using graph theory concepts [17,18]. These qualitative analysis tools do not rely on kinetic information, but on the structure of the reaction network which has thus to be correctly written as a set of formal reactions, with well-identified reactants, products and modifiers (and in certain cases their stoichiometry) for each reaction.…”

Section: Introductionmentioning

confidence: 99%

“…For instance, [25] applies network decomposition for a modular parameter estimation approach, [13] introduces a structural persistence criterion, Petri net place invariants reveal conservation laws in [26], while transition invariants can be used to identify fragile nodes and the core of a network [27], or to determine steady state solutions [28].…”

Section: Introductionmentioning

confidence: 99%

Inferring reaction systems from ordinary differential equations

Fages

Gay

Soliman

2015

Theoretical Computer Science

View full text Add to dashboard Cite

In Mathematical Biology, many dynamical models of biochemical reaction systems are presented with Ordinary Differential Equations (ODE). Once kinetic parameter values are fixed, this simple mathematical formalism completely defines the dynamical behavior of a system of biochemical reactions and provides powerful tools for deterministic simulations, parameter sensitivity analysis, bifurcation analysis, etc. However, without requiring any information on the reaction kinetics and parameter values, various qualitative analyses can be performed using the structure of the reactions, provided the reactants, products and modifiers of each reaction are precisely defined. In order to apply these structural methods to parametric ODE models, we study a mathematical condition for expressing the consistency between the structure and the kinetics of a reaction, without restricting to Mass Action law kinetics. This condition, satisfied in particular by standard kinetic laws, entails a remarkable property of independence of the influence graph from the kinetics of the reactions. We derive from this study a heuristic algorithm which, given a system of ODEs as input, computes a system of reactions with the same ODE semantics, by inferring well-formed reactions whenever possible. We show how this strategy is capable of automatically curating the writing of ODE models in SBML, and present some statistics obtained on the model repository biomodels.net. 1 .

show abstract

“…P-invariants provide structural conservation laws that can be directly used to eliminate variables in mathematical models based on ordinary differential equation models [47]. The notion of siphons and traps provide sufficient conditions for persistence and accumulation of molecular species in a network of reactions [1,36]. Petri nets have also been generalized to handle continuous dynamics [34,35,44] and to model gene regulatory networks [10].…”

Section: Introductionmentioning

confidence: 99%

Cells as Machines: Towards Deciphering Biochemical Programs in the Cell

Fages

2014

Distributed Computing and Internet Technology

View full text Add to dashboard Cite

Abstract. Systems biology aims at understanding complex biological processes in terms of their basic mechanisms at the molecular level in cells. The bet of applying theoretical computer science concepts and software engineering methods to the analysis of distributed biochemical reaction systems in the cell, designed by natural evolution, has led to interesting challenges in computer science, and new model-based insights in biology. In this paper, we review the development over the last decade of the biochemical abstract machine (Biocham) software environment for modeling cell biology molecular reaction systems, reasoning about them at different levels of abstraction, formalizing biological behaviors in temporal logic with numerical constraints, and using them to infer non-measurable kinetic parameter values, evaluate robustness, decipher natural biochemical processes and implement new programs in synthetic biology.

show abstract

A Petri Net Approach to Persistence Analysis in Chemical Reaction Networks

Cited by 37 publications

References 31 publications

On modularity and persistence of chemical reaction networks

On modularity and persistence of chemical reaction networks

Inferring reaction systems from ordinary differential equations

Cells as Machines: Towards Deciphering Biochemical Programs in the Cell

Contact Info

Product

Resources

About