An analysis of the Petri net based model of the human body iron homeostasis process

Sackmann, Andrea; Formanowicz, Dorota; Formanowicz, Piotr; Koch, Ina; Błażewicz, Jacek

doi:10.1016/j.compbiolchem.2006.09.005

Cited by 56 publications

(45 citation statements)

References 20 publications

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“…Since any invariant can be obtained as a linear combination of some minimal invariants, it is sufficient to consider only the minimal ones. From the biological point of view, feasible t-invariants are especially interesting (Sackmann et al, 2006;Sackmann et al, 2007;Sackmann, 2011). An invariant of this type is a minimal t-invariant so that all its transitions can be fired without firing any transition which does not belong to this invariant.…”

Section: Petri Netsmentioning

confidence: 99%

“…The arcs whose weights are equal to one usually are not explicitly labeled by this weight in the graphical representation of the net (cf. Reisig, 1985;Murata, 1989;Sackmann et al, 2007;Reisig, 2011).…”

Section: Petri Netsmentioning

confidence: 99%

“…In particular, they can be grouped into so-called Maximal Common Transition sets (MCT-sets) which contain transitions being elements of exactly the same feasible t-invariants. These sets are disjoint and correspond to a partition of the modeled biological system into some functional units whose biological meaning should be determined (Sackmann et al, 2006;Sackmann et al, 2007;Sackmann, 2011;Formanowicz et al, 2011).…”

Section: Petri Netsmentioning

confidence: 99%

“…A p-invariant is vector y 0 N n satisfying the equation (Murata, 1989;Sackmann et al, 2007;Sackmann, 2011):…”

Section: Petri Netsmentioning

confidence: 99%

“…Here, in general, various similarity measures can be used. For the construction of t-clusters, standard clustering algorithms such as UPGMA can be applied (Sackmann et al, 2007;Grafahren-Belau et al, 2008;Sackmann, 2011;Formanowicz et al, 2011).…”

Section: Petri Netsmentioning

confidence: 99%

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RESEARCH PAPER Selected aspects of endothelial dysfunction and their influence on the atherosclerosis process modeled and analyzed by Petri net based approach

Formanowicz¹,

Kozak²,

Formanowicz³

2011

bta

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In this paper a Petri net based model of the process of endothelial dysfunction is presented. The model describes some selected aspects of this process and their relation with atherosclerosis. Models expressed in the language of Petri net theory have, on the one hand, an intuitive graphical interpretation, and on the other hand, they can be analyzed using rigorous mathematical methods. Such analysis and simulation of the net behavior can be supported by many freely available software tools. Here, results of an analysis based on t-invariants of the proposed model are presented. In particular, feasible t-invariants, MCT-sets and t-clusters have been calculated and their biological meaning has been determined.

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Section: Petri Netsmentioning

confidence: 99%

Section: Petri Netsmentioning

confidence: 99%

Section: Petri Netsmentioning

confidence: 99%

“…A p-invariant is vector y 0 N n satisfying the equation (Murata, 1989;Sackmann et al, 2007;Sackmann, 2011):…”

Section: Petri Netsmentioning

confidence: 99%

Section: Petri Netsmentioning

confidence: 99%

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RESEARCH PAPER Selected aspects of endothelial dysfunction and their influence on the atherosclerosis process modeled and analyzed by Petri net based approach

Formanowicz¹,

Kozak²,

Formanowicz³

2011

bta

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Petri Nets – A Mathematical Formalism to Analyze Chemical Reaction Networks

Koch¹

2010

Molecular Informatics

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In this review we introduce and discuss Petri nets - a mathematical formalism to describe and analyze chemical reaction networks. Petri nets were developed to describe concurrency in general systems. We find most applications to technical and financial systems, but since about twenty years also in systems biology to model biochemical systems. This review aims to give a short informal introduction to the basic formalism illustrated by a chemical example, and to discuss possible applications to the analysis of chemical reaction networks, including cheminformatics. We give a short overview about qualitative as well as quantitative modeling Petri net techniques useful in systems biology, summarizing the state-of-the-art in that field and providing the main literature references. Finally, we discuss advantages and limitations of Petri nets and give an outlook to further development.

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Discrete Modelling: Petri Net and Logical Approaches

Koch

Chaouiya

2010

Systems Biology for Signaling Networks

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An analysis of the Petri net based model of the human body iron homeostasis process

Cited by 56 publications

References 20 publications

RESEARCH PAPER Selected aspects of endothelial dysfunction and their influence on the atherosclerosis process modeled and analyzed by Petri net based approach

RESEARCH PAPER Selected aspects of endothelial dysfunction and their influence on the atherosclerosis process modeled and analyzed by Petri net based approach

Petri Nets – A Mathematical Formalism to Analyze Chemical Reaction Networks

Discrete Modelling: Petri Net and Logical Approaches

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