Qualitative analysis of biochemical reaction systems

Reddy, Venkatramana N.; Liebman, Michael; Mavrovouniotis, Michael L.

doi:10.1016/0010-4825(95)00042-9

Cited by 127 publications

(81 citation statements)

References 13 publications

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“…A transition may transform some elements of a state, and more than one transition can be allowed to occur at the same time. Thanks to their intuitive graphical representations, some variants of Petri Nets have been successfully developed to model biological systems (see, e.g., [27,30,63,55,34,42]). More sophisticated models like selfmodified Petri Nets [34], Hybrid Petri Nets [46], Stochastic Activity Networks [49] and MetaNets [42] have been used, too.…”

Section: Introductionmentioning

confidence: 99%

Process Calculi Abstractions for Biology

Guerriero

Prandi

Priami

et al. 2009

Algorithmic Bioprocesses

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Several approaches have been proposed to model biological systems by means of the formal techniques and tools available in computer science. To mention just a few of them, some representations are inspired by Petri Nets theory, and some other by stochastic processes. A most recent approach consists in interpreting the living entities as terms of process calculi where the behavior of the represented systems can be inferred by applying syntaxdriven rules.A comprehensive picture of the state of the art of the process calculi approach to biological modeling is still missing. This paper goes in the direction of providing such a picture by presenting a comparative survey of the process calculi that have been used and proposed to describe the behavior of living entities.

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Section: Introductionmentioning

confidence: 99%

Process Calculi Abstractions for Biology

Guerriero

Prandi

Priami

et al. 2009

Algorithmic Bioprocesses

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“…Consequently, qualitative approaches have been developed for the modeling, analysis, and simulation of genetic regulatory networks and other networks of biological interactions: Boolean networks [20,30], Petri nets [22,27], process algebras [28], qualitative differential equations [17], hybrid automata [11],... In this chapter, we concentrate on one particular class of qualitative models of genetic regulatory networks, originally proposed by Glass and Kauffman [12]: piecewise-linear (PL) differential equations.…”

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confidence: 99%

Piecewise-Linear Models of Genetic Regulatory Networks: Theory and Example

Grognard

Jong

Gouzé

2007

Biology and Control Theory: Current Challenges

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Summary. The experimental study of genetic regulatory networks has made tremendous progress in recent years resulting in a huge amount of data on the molecular interactions in model organisms. It is therefore not possible anymore to intuitively understand how the genes and interactions together influence the behavior of the system. In order to answer such questions, a rigorous modeling and analysis approach is necessary. In this chapter, we present a family of such models and analysis methods enabling us to better understand the dynamics of genetic regulatory networks. We apply such methods to the network that underlies the nutritional stress response of the bacterium E. coli.The functioning and development of living organisms is controlled by large and complex networks of genes, proteins, small molecules, and their interactions, socalled genetic regulatory networks. The study of these networks has recently taken a qualitative leap through the use of modern genomic techniques that allow for the simultaneous measurement of the expression levels of all genes of an organism. This has resulted in an ever growing description of the interactions in the studied genetic regulatory networks. However, it is necessary to go beyond the simple description of the interactions in order to understand the behavior of these networks and their relation with the actual functioning of the organism. Since the networks under study are usually very large, an intuitive approach for their understanding is out of question. In order to support this work, mathematical and computer tools are necessary: the unambiguous description of the phenomena that mathematical models provide allows for a detailed analysis of the behaviors at play, though they might not exactly represent the exact behavior of the networks.In this chapter, we will be mostly interested in the modeling of the genetic regulatory networks by means of differential equations. This classical approach allows precise numerical predictions of deterministic dynamic properties of genetic regulatory networks to be made. However, for most networks of biological interest the application of differential equations is far from straightforward. First, the biochemical reaction mechanisms underlying the interactions are usually not or incompletely

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“…Reddy was the first to use Petri nets for modelling of biochemical reactions. He presented a basic translation of a biological narrative into a Petri net and an analysis with invariants [9]. Since that time, numerous papers applying Petri nets to biological modelling were published, for example [6,[19][20][21].…”

Section: Related Workmentioning

confidence: 99%

“…[20]. More advanced structural analysis involves determining invariants or checking for deadlocks [9,19] and model checking, e.g. [28].…”

Section: Related Workmentioning

confidence: 99%

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Design Issues for Qualitative Modelling of Biological Cells with Petri Nets

Krepska

Bonzanni

Feenstra

et al.

Formal Methods in Systems Biology

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Abstract. Petri nets are a widely used formalism to qualitatively model concurrent systems such as a biological cell. We present techniques for modelling biological processes as Petri nets for further analyses and insilico experiments. Instead of extending the formalism with ,,colours" or rates, as is most often done, we focus on preserving the simplicity of the formalism and developing an execution semantics which resembles biology -we apply a principle of maximal parallelism and introduce the novel concept of bounded execution with overshooting. A number of modelling solutions are demonstrated using the example of the wellstudied C. elegans vulval development process. To date our model is still under development, but first results, based on Monte Carlo simulations, are promising.

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Qualitative analysis of biochemical reaction systems

Cited by 127 publications

References 13 publications

Process Calculi Abstractions for Biology

Process Calculi Abstractions for Biology

Piecewise-Linear Models of Genetic Regulatory Networks: Theory and Example

Design Issues for Qualitative Modelling of Biological Cells with Petri Nets

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