What is the background of this tutorial? During the last decade, the integrative research area of systems biology has constantly been gaining more importance. Experimental and computational approaches are combined to investigate biological systems systematically. To understand biology on its system level, the structural and dynamic properties of regulatory networks in biological systems have to be represented by a model describing the involved species and their interactions. Petri net theory offers the possibility to construct and analyse such models and to represent their structural and dynamic properties by various techniques.
Who should read this tutorial? This tutorial addresses scientists who are looking for an easy and intuitive way to translate a biological system into a Petri net model at an arbitrarily chosen level of abstraction with the option of representing time and space-dependent processes. The tutorial is equally suitable for experimental and theory oriented bio-scientists. The examples given in the tutorial can be used by the interested reader to model her/his biological system.
What can I learn? The tutorial offers an introduction to the Petri net formalism, how to construct a model of a biological system, analyse its structure and dynamic behaviour regarding time-dependent behaviour, which is shown by several intuitive examples. At the end of the tutorial, you will be able to model a biological system on your own using Petri nets. You will also know how to analyse the structure of your model, how to interpret the results and how to perform simulation studies to investigate the time-dependent dynamic behaviour. Also, we also provide a chapter about model checking, which might be helpful to evaluate your model by verifying specified properties that you are interested in. We also show how to use the two Petri net tools Snoopy [19] and Charlie [8]. Based on these instruments you will be able to enhance your knowledge about the modelled biological system and to draw new conclusions from that.
Why should I use Petri nets? The graphical notation and construction of Petri nets allow you to easily and intuitively construct models of biological systems and to characterise the structure, behavioural properties related to the structure and time-dependent dynamic behaviour of a model by several related techniques. Petri nets can describe concurrent and parallel processes, as well as communication and synchronisation in bipartite systems regardless of the abstraction level in a comprehensive and mathematically correct model [12]. Time, as well as space aspects, can be modelled by a Petri net. Several specialised Petri net classes are available to describe dierent scenarios and to consider dierent simulative approaches. Therefore, the kinetics of the qualitative Petri net model can be considered as stochastic, continuous or as a mixture of both (hybrid) [12]. In silico experiments with Petri net models, permit to analyse a biological system systematically by applying structural as well as dynamic analysing techniques to investigate perturbations. From the obtained results new insights can be achieved by the biological system. Thereby, you can increase your understanding, reveal gaps in knowledge, and detect missing and essential components. Based on a valid model it is possible to predict the system behaviour. This might be helpful to investigate pathological states and their molecular basis aimed at identifying potential targets to develop therapeutical intervention strategies. The Petri net formalism offers quite a few advantages over other and more broadly used modelling frameworks. The different Petri net classes are interconvertible with each other without changing the qualitative structure. Due to the graphical visualisation of molecular networks by Petri nets, a bioscientist can intuitively understand the modelled mechanisms. The user does not have to deal with many dierent representations of a molecular network which do not obviously correspond to each other like a biological cartoon, the structure of the biological network, the mathematical equations (stochastic, continuous, etc.) and the implementation of the equations. Besides, the transformation of a molecular network represented by a Petri net into e.g. ODE equations is unique, but not vice versa [24]. Several reliable analysis tools have been developing to investigate qualitative and quantitative properties of Petri nets by structural analysis, simulation of the time-dependent dynamic behaviour and model checking.
What is the scheme of this tutorial? First of all, you will learn all the basics about the Petri net formalism motivated by small biological examples that are easy to understand. Next, you will see how to analyse the structure of a model and how to interpret the obtained results and their biological meaning. Afterwards, you will learn how to perform simulations with your model. We also offer a chapter about model checking, where you can learn how to verify specific properties of your model. Then, we introduce the two Petri net tools Snoopy [19] and Charlie [8]. All sections, where theoretical concepts are explained, are divided into an informal and a formal part. We start with an informal introduction, where we explain the basics and the biological relations. Subsequently and to be complete, we give the formal definitions and a small help on \how to read" the definitions at the end of the section.
What tools do I need? Several tools are available to model biological systems, simulate their time-dependent dynamic behaviour and analyse their structure. Here, we use the Petri net editor Snoopy [19] to model biological systems and simulate/animate their time-dependent dynamic behaviour. Charlie [8] is used to analyse the Petri net structure. Both software tools were developed at the chair of Data Structures and Software Dependability at the Brandenburg University of Technology Cottbus and are freely available for non-commercial use. You can download them at
http://www-dssz.informatik. tu-cottbus.de/DSSZ/Software/Software [1].