Dependencies and Simultaneity in Membrane Systems

Membrane system computations proceed in a synchronous fashion: at each step all the applicable rules are actually applied. Hence each step depends on the previous one. This coarse view can be refined by looking at the dependencies among rule occurrences, by recording, for an object, which was the a rule that produced it and subsequently (in a later step), which was the a rule that consumed it. In this paper we propose a way to look also at the other main ingredient in membrane system computations, namely the simultaneity in the rule applications. This is achieved using zero-safe nets that allows to synchronize transitions, i.e., rule occurrences. Zero-safe nets can be unfolded into occurrence nets in a classical way, and to this unfolding an event structure can be associated. The capability of capturing simultaneity of zero-safe nets is transferred on the level of event structure by adding a way to express which events occur simultaneously

Qualitative modelling and analysis of regulations in multi-cellular systems using Petri nets and topological collections

In this paper, we aim at modelling and analyzing the regulation processes in multi-cellular biological systems, in particular tissues. The modelling framework is based on interconnected logical regulatory networks a la Rene Thomas equipped with information about their spatial relationships. The semantics of such models is expressed through colored Petri nets to implement regulation rules, combined with topological collections to implement the spatial information. Some constraints are put on the the representation of spatial information in order to preserve the possibility of an enumerative and exhaustive state space exploration. This paper presents the modelling framework, its semantics, as well as a prototype implementation that allowed preliminary experimentation on some applications.Comment: In Proceedings MeCBIC 2010, arXiv:1011.005

Membrane Systems with Priority, Dissolution, Promoters and Inhibitors and Time Petri Nets

We continue the investigations on exploring the connection between membrane systems and time Petri nets already commenced in [4] by extending membrane systems with promoters/inhibitors, membrane dissolution and priority for rules compared to the simple symbol-object membrane system. By constructing the simulating Petri net, we retain one of the main characteristics of the Petri net model, namely, the firings of the transitions can take place in any order: we do not impose any additional stipulation on the transition sequences in order to obtain a Petri net model equivalent to the general Turing machine. Instead, we substantially exploit the gain in computational strength obtained by the introduction of the timing feature for Petri nets

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

An introduction to Biomodel engineering, illustrated for signal transduction pathways

BioModel Engineering is the science of designing, constructing and analyzing computational models of biological systems. It is inspired by concepts from software engineering and computing science. This paper illustrates a major theme in BioModel Engineering, namely that identifying a quantitative model of a dynamic system means building the structure, finding an initial state, and parameter fitting. In our approach, the structure is obtained by piecewise construction of models from modular parts, the initial state is obtained by analysis of the structure and parameter fitting comprises determining the rate parameters of the kinetic equations. We illustrate this with an example in the area of intracellular signalling pathways

Process Calculi Abstractions for Biology

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 syntax-driven 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. This is the preliminary version of a paper that was published in Algorithmic Bioprocesses. The original publication is available at http://www.springer.com/computer/foundations/book/978-3-540-88868-

Membrane Systems and Time Petri Nets

We investigate the relationship of time Petri nets and di erent variants of membrane systems. First we show that the added feature of \time" in time Petri nets makes it possible to simulate the maximal parallel rule application of membrane systems without introducing maximal parallelism to the Petri net semantics, then we de ne local time P systems and explore how time Petri nets and the computations of local time P systems can be related