Reconstructing the regulatory network controlling commitment and sporulation in Physarum polycephalum based on hierarchical Petri Net modelling and simulation

Marwan, Wolfgang; Sujatha, Arumugam; Starostzik, Christine

doi:10.1016/j.jtbi.2005.03.018

Cited by 43 publications

(25 citation statements)

References 32 publications

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“…Alternatively, we might consider the dynamically stable states (i.e. orbits 5 ) of a discrete dynamical system and take a smaller m < |Q| and start with a tuple (q 1 , . .…”

Section: Boolean Variablementioning

confidence: 99%

“…In the model here, states 5 , NAD = a 6 } and the action δ 1 : 20 Thus, our first model of the Krebs cycle yields K 1 = (X 1 , A 1 , δ 1 ) with characteristic semigroup S(K 1 ) and transformation semigroup (X 1 , S(K 1 )). In [34], we described a hierarchical decomposition of this automaton having cyclic permutation groups as non-trivial computing levels.…”

Section: (B) Krebs Cyclementioning

confidence: 99%

“…Methods to address the kind of structures that appear in biological and biochemical systems, and artificial systems with similar characteristics, include those of Dittrich and co-workers [78][79][80][81][82][83], who introduced a general theory of chemical organization, while Paun and colleagues [84][85][86]; developed a theory of membrane computing; in addition, there are attempts to apply Milner's π -calculus [87] to systems biology [88][89][90]. Other useful methods in biological and adaptive complex systems include Petri net modelling [1,40,41] with hierarchical extensions [5], multi-valued logical modelling (generalizing Kauffman's Boolean network approach [4]) combined with constraint analysis [1,3,6,91,92].…”

Section: Interaction Machines (A) Dynamically Growing and Changing Aumentioning

confidence: 99%

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Symmetry structure in discrete models of biochemical systems: natural subsystems and the weak control hierarchy in a new model of computation driven by interactions

Nehaniv

Rhodes

Egri-Nagy

et al. 2015

Phil. Trans. R. Soc. A.

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Interaction computing is inspired by the observation that cell metabolic/regulatory systems construct order dynamically, through constrained interactions between their components and based on a wide range of possible inputs and environmental conditions. The goals of this work are to (i) identify and understand mathematically the natural subsystems and hierarchical relations in natural systems enabling this and (ii) use the resulting insights to define a new model of computation based on interactions that is useful for both biology and computation. The dynamical characteristics of the cellular pathways studied in systems biology relate, mathematically, to the computational characteristics of automata derived from them, and their internal symmetry structures to computational power. Finite discrete automata models of biological systems such as the lac operon, the Krebs cycle and p53-mdm2 genetic regulation constructed from systems biology models have canonically associated algebraic structures (their transformation semigroups). These contain permutation groups (local substructures exhibiting symmetry) that correspond to 'pools of reversibility'. These natural subsystems are related to one another in a hierarchical manner by the notion of 'weak control'. We present natural subsystems arising from several biological examples and their weak control hierarchies in detail. Finite simple non-Abelian groups are found in biological examples and can be harnessed to realize finitary universal computation. This allows ensembles of cells to achieve any desired finitary computational transformation, depending on external inputs, via suitably constrained interactions. Based on this, interaction machines that grow and change their structure recursively are introduced and applied, providing a natural model of computation driven by interactions.In the 21st century, algebra will be as important for biology as chemistry was in the 20th century.-Günter P. Wagner

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“…Alternatively, we might consider the dynamically stable states (i.e. orbits 5 ) of a discrete dynamical system and take a smaller m < |Q| and start with a tuple (q 1 , . .…”

Section: Boolean Variablementioning

confidence: 99%

Section: (B) Krebs Cyclementioning

confidence: 99%

Section: Interaction Machines (A) Dynamically Growing and Changing Aumentioning

confidence: 99%

See 1 more Smart Citation

Symmetry structure in discrete models of biochemical systems: natural subsystems and the weak control hierarchy in a new model of computation driven by interactions

Nehaniv

Rhodes

Egri-Nagy

et al. 2015

Phil. Trans. R. Soc. A.

View full text Add to dashboard Cite

show abstract

“…When a SPN models a metabolic pathway, the firing rate of a transition t may be a function of both the environment conditions (e.g., temperature, pressure, pH) and the concentrations of the reactants. SPNs are used for modelling biological systems, e.g., in [55,81,53,60].…”

Section: Petri Net Extensionsmentioning

confidence: 99%

“…The authors employ also the MCT-sets introduced in [103]. The papers [81,72,57] use different kinds of PNs for modelling purposes and different analysis techniques. However, they have a similar starting point and goal: by using literature and experimental data, they study biological pathways which are not yet fully understood.…”

Section: Quantitative Modelling and Analysismentioning

confidence: 99%

Petri nets for modelling metabolic pathways: a survey

et al. 2010

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Abstract. In the last fifteen years, several research efforts have been directed towards the representation and the analysis of metabolic pathways by using Petri nets. The goal of this paper is twofold. First, we discuss how the knowledge about metabolic pathways can be represented with Petri nets. We point out the main problems that arise in the construction of a Petri net model of a metabolic pathway and we outline some solutions proposed in the literature. Second, we present a comprehensive review of recent research on this topic, in order to assess the maturity of the field and the availability of a methodology for modelling a metabolic pathway by a corresponding Petri net.

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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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Reconstructing the regulatory network controlling commitment and sporulation in Physarum polycephalum based on hierarchical Petri Net modelling and simulation

Cited by 43 publications

References 32 publications

Symmetry structure in discrete models of biochemical systems: natural subsystems and the weak control hierarchy in a new model of computation driven by interactions

Symmetry structure in discrete models of biochemical systems: natural subsystems and the weak control hierarchy in a new model of computation driven by interactions

Petri nets for modelling metabolic pathways: a survey

Petri Nets – A Mathematical Formalism to Analyze Chemical Reaction Networks

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