Petri nets for systems and synthetic biology

We give a description of a Petri net-based framework for modelling and analysing biochemical pathways, which uni¯es the qualita- tive, stochastic and continuous paradigms. Each perspective adds its con- tribution to the understanding of the system, thus the three approaches do not compete, but complement each other. We illustrate our approach by applying it to an extended model of the three stage cascade, which forms the core of the ERK signal transduction pathway. Consequently our focus is on transient behaviour analysis. We demonstrate how quali- tative descriptions are abstractions over stochastic or continuous descrip- tions, and show that the stochastic and continuous models approximate each other. Although our framework is based on Petri nets, it can be applied more widely to other formalisms which are used to model and analyse biochemical networks

Formal Verification of Real-time Systems with Preemptive Scheduling

International audienceIn this paper, we propose a method for the verification of timed properties for real-time systems featuring a preemptive scheduling policy: the system, modeled as a scheduling time Petri net, is first translated into a linear hybrid automaton to which it is time-bisimilar. Timed properties can then be verified using HyTech. The efficiency of this approach leans on two major points: first, the translation features a minimization of the number of variables (clocks) of the resulting automaton, which is a critical parameter for the efficiency of the ensuing verification. Second, the translation is performed by an over-approximating algorithm, which is based on Difference Bound Matrix and therefore efficient, that nonetheless produces a time-bisimilar automaton despite the over-approximation. The proposed modeling and verification method are generic enough to account for many scheduling policies. In this paper, we specifically show how to deal with Fixed Priority and Earliest Deadline First policies, with the possibility of using Round-Robin for tasks with the same priority. We have implemented the method and give some experimental results illustrating its efficiency

A case study in model-driven synthetic biology

We report on a case study in synthetic biology, demonstrating the modeldriven design of a self-powering electrochemical biosensor. An essential result of the design process is a general template of a biosensor, which can be instantiated to be adapted to specific pollutants. This template represents a gene expression network extended by metabolic activity. We illustrate the model-based analysis of this template using qualitative, stochastic and continuous Petri nets and related analysis techniques, contributing to a reliable and robust design

Enzymatic competition: Modeling and verification with timed hybrid petri nets

International audienceThe formalism of hybrid functional petri nets (HFPN) has proved its convenience for simulating biological systems. The drawback of the noticeable expressiveness of HFPN is the difficulty to perform formal verifications of dynamical properties. In this article, we propose a model-checking procedure for timed hybrid petri nets (THPN), a sub-class of HFPN. This procedure is based on the translation of the THPN model and of the studied property into real-time automata. It is applied to model enzymatic competitions existing in amphibian metamorphosis

Modeling and analysis using hybrid Petri nets

This paper is devoted to the use of hybrid Petri nets (PNs) for modeling and control of hybrid dynamic systems (HDS). Modeling, analysis and control of HDS attract ever more of researchers' attention and several works have been devoted to these topics. We consider in this paper the extensions of the PN formalism (initially conceived for modeling and analysis of discrete event systems) in the direction of hybrid modeling. We present, first, the continuous PN models. These models are obtained from discrete PNs by the fluidification of the markings. They constitute the first steps in the extension of PNs toward hybrid modeling. Then, we present two hybrid PN models, which differ in the class of HDS they can deal with. The first one is used for deterministic HDS modeling, whereas the second one can deal with HDS with nondeterministic behavior. Keywords: Hybrid dynamic systems; D-elementary hybrid Petri nets; Hybrid automata; Controller synthesi

Modelling epistasis in genetic disease using Petri nets, evolutionary computation and frequent itemset mining

Petri nets are useful for mathematically modelling disease-causing genetic epistasis. A Petri net model of an interaction has the potential to lead to biological insight into the cause of a genetic disease. However, defining a Petri net by hand for a particular interaction is extremely difficult because of the sheer complexity of the problem and degrees of freedom inherent in a Petri net’s architecture. We propose therefore a novel method, based on evolutionary computation and data mining, for automatically constructing Petri net models of non-linear gene interactions. The method comprises two main steps. Firstly, an initial partial Petri net is set up with several repeated sub-nets that model individual genes and a set of constraints, comprising relevant common sense and biological knowledge, is also defined. These constraints characterise the class of Petri nets that are desired. Secondly, this initial Petri net structure and the constraints are used as the input to a genetic algorithm. The genetic algorithm searches for a Petri net architecture that is both a superset of the initial net, and also conforms to all of the given constraints. The genetic algorithm evaluation function that we employ gives equal weighting to both the accuracy of the net and also its parsimony. We demonstrate our method using an epistatic model related to the presence of digital ulcers in systemic sclerosis patients that was recently reported in the literature. Our results show that although individual “perfect” Petri nets can frequently be discovered for this interaction, the true value of this approach lies in generating many different perfect nets, and applying data mining techniques to them in order to elucidate common and statistically significant patterns of interaction

Modeling and Analysis of Hybrid Dynamic Systems Using Hybrid Petri Nets

International audienceWe consider in this paper the extensions of the PN formalism in the direction of hybrid modeling. We briefly presents hybrid dynamic systems. Then the hybrid automata model. Is introduced and we discuss continuous Petri nets. These models are obtained from discrete PNs by the fluidification of the markings. They constitute the first steps in the extension of PNs toward hybrid modeling. Two hybrid PN models, which differ in the class of HDS they can deal with, are studied. The first one is used for deterministic HDS modeling, whereas the second one can deal with HDS with nondeterministic behavior. The general control structure based on hybrid PNs is briefly described