The VLDB journal : the international journal on very large data bases.

We give a description of a Petri net-based framework for modelling and analysing biochemical pathways, which unifies the qualitative, stochastic and continuous paradigms. Each perspective adds its contribution 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 qualitative descriptions are abstractions over stochastic or continuous descriptions, 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.

/pdf/petri-nets-for-systems-and-synthetic-biology-2phlqoy7lg.pdf

Petri nets for systems and synthetic biology

The tool Snoopy provides a unifying Petri net framework which has particularly many application scenarios in systems and synthetic biology. The framework consists of two levels: uncoloured and coloured. Each level comprises a family of related Petri net classes, sharing structure, but being specialized by their kinetic information. Petri nets of all net classes within one level can be converted into each other, while changing the level involves user-guided folding or automatic unfolding. Models can be hierarchically structured, allowing for the mastering of larger networks. Snoopy supports the simultaneous use of several Petri net classes; the graphical user interface adapts dynamically to the active one. Built-in animation and simulation (depending on the net class) are complemented by export to various analysis tools. Snoopy facilitates the extension by new Petri net classes thanks to its generic design.

Snoopy --- a unifying petri net tool

This paper addresses the problem of finding attractors in synchronous Boolean networks. The existing Boolean decision diagram-based algorithms have limited capacity due to the excessive memory requirements of decision diagrams. The simulation-based algorithms can be applied to larger networks, however, they are incomplete. We present an algorithm, which uses a SAT-based bounded model checking to find all attractors in a Boolean network. The efficiency of the presented algorithm is evaluated by analyzing seven networks models of real biological processes, as well as 150,000 randomly generated Boolean networks of sizes between 100 and 7,000. The results show that our approach has a potential to handle an order of magnitude larger models than currently possible.

A SAT-Based Algorithm for Finding Attractors in Synchronous Boolean Networks

Summary: To investigate biomolecular networks, Snoopy provides a unifying Petri net framework comprising a family of related Petri net classes. Models can be hierarchically structured, allowing for the mastering of larger networks. To move easily between the qualitative, stochastic and continuous modelling paradigms, models can be converted into each other. We get models sharing structure, but specialized by their kinetic information. The analysis and iterative reverse engineering of biomolecular networks is supported by the simultaneous use of several Petri net classes, while the graphical user interface adapts dynamically to the active one. Built-in animation and simulation are complemented by exports to various analysis tools. Snoopy facilitates the addition of new Petri net classes thanks to its generic design.

Availability: Our tool with Petri net samples is available free of charge for non-commercial use at http://www-dssz.informatik.tu-cottbus.de/snoopy.html; supported operating systems: Mac OS X, Windows and Linux (selected distributions).

Contact: snoopy@informatik.tu-cottbus.de

Snoopy - a unifying Petri net framework to investigate biomolecular networks

We give a description of a Petri net-based framework for modelling and analysing biochemical pathways, which unifies the qualitative, stochastic and continuous paradigms. Each perspective adds its contribution 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 qualitative descriptions are abstractions over stochastic or continuous descriptions, and show that the stochastic and continuous models approximate each other. A key contribution of the paper consists in a precise definition of biochemically interpreted stochastic Petri nets. 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.

/pdf/a-unifying-framework-for-modelling-and-analysing-biochemical-47ski52h08.pdf

A unifying framework for modelling and analysing biochemical pathways using Petri nets

This paper introduces extended stochastic Petri nets to model wetlab experiments. The extentions include read and inhibitor arcs, stochastic transitions with freestyle rate functions as well as several deterministically timed transition types: immediate firing, deterministic firing delay, and scheduled firing. The extensions result into non-Markovian behaviour, which precludes analytical analysis approaches. But there are adapted stochastic simulation analysis (SSA) methods, ready to deal with the extended behaviour. Having the simulation traces, we apply simulative model checking of PLTL, a linear-time temporal logic (LTL) in a probabilistic setting.

We present some typical model components, demonstrating the suitability of the introduced Petri net class for the envisaged application scenario. We conclude by looking briefly at a classical example of prokaryotic gene regulation, the lac operon case.

https://www-dssz.informatik.tu-cottbus.de/publications/papers/Heiner-2009-xspn.pdf

Extended Stochastic Petri Nets for Model-Based Design of Wetlab Experiments

Fuzzy logic is a well-established formalism in computer science being strongly influenced by the work of Zadeh [17, 16]. It provides us with a means to deal with vagueness and uncertainty. Fuzzy logic is based on t-norms and t-conorms for intersection and union, respectively, on membership values of fuzzy sets.

On the Relation between Fuzzy and Quantum Logic

Evaluating a traditional database query against a data tuple yields true on match and false on mismatch. Unfortunately, there are many application scenarios where such an evaluation is not possible or does not adequately meet user expectations about vague and uncertain conditions. Thus, there is a need for incorporating impreciseness and proximity into a logic-based query language. The calculus query language CQQL [24] has been developed for such scenarios by exploiting results from quantum logic. In this work we will show how to integrate underlying ideas and concepts of CQQL into SQL.

https://link.springer.com/content/pdf/10.1007%2F978-3-642-12026-8_33.pdf

QSQL: incorporating logic-based retrieval conditions into SQL

A Boolean logic-based evaluation of a database query returns true on match and false on mismatch. Unfortunately, there are many application scenarios where such an evaluation is not possible or does not adequately meet user expectations about vague and uncertain conditions. Consequently, there is a need for incorporating impreciseness and proximity into a logic-based query language. In this work we propose a probabilistic interpretation for our query language CQQL which is based on a geometric retrieval model. In detail, we show that the CQQL can evaluate arbitrary similarity conditions in a probabilistic fashion. Furthermore, we lay a theoretical foundation for the combination of CQQL with other probabilistic semantics.

Sebastian Lehrack

Papers

A unifying framework for modelling and analysing biochemical pathways using Petri nets

Extended Stochastic Petri Nets for Model-Based Design of Wetlab Experiments

On the Relation between Fuzzy and Quantum Logic

QSQL: incorporating logic-based retrieval conditions into SQL

A probabilistic interpretation for a geometric similarity measure