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Über dieses Buch

The emerging, multi-disciplinary field of systems biology is devoted to the study of the relationships between various parts of a biological system, and computer modeling plays a vital role in the drive to understand the processes of life from an holistic viewpoint. Advancements in experimental technologies in biology and medicine have generated an enormous amount of biological data on the dependencies and interactions of many different molecular cell processes, fueling the development of numerous computational methods for exploring this data. The mathematical formalism of Petri net theory is able to encompass many of these techniques. This essential text/reference presents a comprehensive overview of cutting-edge research in applications of Petri nets in systems biology, with contributions from an international selection of experts. Those unfamiliar with the field are also provided with a general introduction to systems biology, the foundations of biochemistry, and the basics of Petri net theory. Further chapters address Petri net modeling techniques for building and analyzing biological models, as well as network prediction approaches, before reviewing the applications to networks of different biological classification. Topics and features: investigates the modular, qualitative modeling of regulatory networks using Petri nets, and examines an Hybrid Functional Petri net simulation case study; contains a glossary of the concepts and notation used in the book, in addition to exercises at the end of each chapter; covers the topological analysis of metabolic and regulatory networks, the analysis of models of signaling networks, and the prediction of network structure; provides a biological case study on the conversion of logical networks into Petri nets; discusses discrete modeling, stochastic modeling, fuzzy modeling, dynamic pathway modeling, genetic regulatory network modeling, and quantitative analysis techniques; includes a Foreword by Professor Jens Reich, Professor of Bioinformatics at Humboldt University and Max Delbrück Center for Molecular Medicine in Berlin. This unique guide to the modeling of biochemical systems using Petri net concepts will be of real utility to researchers and students of computational biology, systems biology, bioinformatics, computer science, and biochemistry.





Chapter 1. Introduction

This chapter gives a general introduction into the field of systems biology and the motivation for using Petri nets in this field. We consider modeling processes in the context of biological modeling approaches providing different examples. Starting from a general description of the purpose of a model and the modeling process, we cover the range from qualitative to quantitative modeling. We compile different modeling techniques at different abstraction levels, for example, at discrete, stochastic, and continuous levels. In this context, we introduce Petri nets and give the motivation for using Petri nets in particular for modeling biochemical systems. We describe the first applications of Petri nets in biology and give a brief overview of the progress made so far. Furthermore, we discuss the main public data resources for systems biology, giving an overview of microarray data repositories, protein–protein interaction databases, and pathway databases. Finally, we describe methods and tools for the visualization of biochemical systems and Petri net models.
Ina Koch, Falk Schreiber

Chapter 2. Biochemical Fundamentals

Living organisms are among the most complex phenomena in our world. To describe, model, and simulate living organisms or at least parts thereof, formal descriptions such as Petri nets are needed. As the focus of this book is the use of Petri net theory in biology, the readership will be very diverse. Thus, this chapter is meant to provide a general introduction to biology, especially those areas that will be modeled with the use of Petri net approaches throughout this book. The experienced biochemist might want to skip this chapter, but for computer scientists and readers from similar fields this chapter contains important fundamentals.
Tiina Liiving, Syed M. Baker, Björn H. Junker

Chapter 3. Petri Nets

This chapter introduces the basic notions and notations, as employed in the rest of this book. This includes the distinct modeling of substances and reactions, together with their logical connection. We explain the graphical representation of Petri nets, as well as the “token flow mechanics”, representing dynamic behavior. We show how sequential, alternative and concurrent occurrences of reactions are modeled, including quantitative aspects of stoichiometric reactions. We present a number of specific analysis techniques for Petri nets, including place invariants and transition invariants, based on systems of linear equations. Further analysis techniques such as traps and siphons exploit the graph-based structure of nets. The use of Petri nets as a modeling- and analysis technique for biological process is illustrated by a fraction of the combined glucose and pentose phosphate pathway.
Wolfgang Reisig

Modeling Techniques


Chapter 4. Discrete Modeling

A discrete Petri net (PN) considers only discrete objects, that is, its marking is specified by an integer number of tokens distributed over its places. This chapter deals with model development and qualitative analysis of discrete PNs. Latter lays emphasis on the net’s invariants. Caused by the special usage of P-invariants representing an anticoincidence, read arcs appear in the net, here given as loops. In order to nevertheless base a sound consideration on the set of T-invariants, they are processed to built feasible T-invariants. Their examination aims at a validation of the net’s structure. For this purpose, initially MCT-sets are built on the set of feasible T-invariants. Subsequently, they may be clustered in T-clusters aiming at gaining knowledge about the involved components and their relationships. In-/dependency of involved processes can be verified. The sets of T-invariants may additionally serve as basis of theoretical knockout analyses as given for instance through the Mauritius maps.
Andrea Sackmann

Chapter 5. Modeling Genetic Regulatory Networks

Cellular systems are regulated by complex genetic control structures known as genetic regulatory networks (GRNs). In this chapter, we present a range of practical techniques for qualitatively modeling and analyzing GRNs using Petri nets. Our starting point is the well-known Boolean network approach, where regulatory entities (i.e., genes, proteins and environmental signals) are viewed abstractly as binary switches. We present an approach for translating synchronous Boolean networks into Petri net models and introduce the support tool GNaPN which automates model construction. We illustrate our techniques by modeling the GRN for carbon stress response in Escherichia coli and, in particular, consider how existing Petri net techniques and tools can be used to understand and analyze such a GRN model. While asynchronous GRN models are considered more realistic than their synchronous counterparts, they often suffer from the problem of capturing too much behavior. We investigate how techniques from asynchronous electronic circuit design based on Signal Transition Graphs (STGs) and Speed-Independent circuits can be used to address this, by identifying and refining conflicting behavioral choices within a model. We illustrate these techniques by developing an asynchronous model for the lysis–lysogeny switch in phage λ.
Richard Banks, Victor Khomenko, L. Jason Steggles

Chapter 6. Hybrid Functional Petri Net with Extension for Dynamic Pathway Modeling

Using elementary Petri nets, it is difficult to mixturely model the discrete, continuous and other complicated events, for example, DNA, RNA and amino acid sequence events. Therefore, Hybrid Functional Petri Net with extension (HFPNe) was introduced to overcome this difficulty and also to allow representation of pathway models without loss of biological details. First, this book chapter explains how modeling with Petri net is done. After which, a full definition of HFPNe is given, along with its relation to hybrid Petri net and other related Petri net extension. Finally, to demonstrate the elegance of HFPNe architecture in handling complex pathway modeling, we chose a biological pathway that involves discrete, continuous and sequence events (gene regulatory network of the cell fate determination in C. elegans). We provide the biological mechanisms of this network and show how intuitively it could be modeled on HFPNe architecture using a software tool, Cell Illustrator.
Ayumu Saito, Masao Nagasaki, Hiroshi Matsuno, Satoru Miyano

Chapter 7. Stochastic Modeling

This chapter provides an introduction to the concepts underlying the stochastic modeling of biological systems with Petri Nets. It introduces a timed interpretation of the occurrence of transitions in a net that suites the randomness observed in biochemical reactions occurring in living matter. Thanks to the foundational work of Gillespie in the 70s, this randomness can be easily accounted for by the representative power of Stochastic Petri Nets. The chapter illustrates the Stochastic Petri Net model specification process, the possibilities of analytical and numerical evaluation of model dynamics as well as the basic concepts underlying the simulative approaches, through the application to simple instances of biological systems to help the reader familiarizing with this discrete stochastic modeling formalism. Additional examples of larger scale models are presented, and exercises suggested to consolidate the understanding of the main concepts.
Ivan Mura

Chapter 8. Quantitative Analysis

The final aim of modeling biochemical processes is to gain a theoretical model which explains and predicts the dynamic behavior of the system in terms of quantities. The limitation of this type of modeling lies rather in the lacking of necessary kinetic data than in the mathematical concepts which are mostly based on coupled ordinary differential equations (ODEs). Whereas kinetic data can be found for some reactions, for the vast majority of pathways kinetic data have not been identified. For many biochemical processes, it still is a task to produce significant experimental data. Continuing efforts in well-designed experiments and data analysis have made kinetic data available for some pathways and some organisms, and with these data at hand quantitative methods become more and more useful. All quantitative methods, applied in modeling of biochemical processes, can easily be adapted to the Petri net formalism. The Petri net formalism offers the advantage of a combination of methods of classical systems biology with discrete Petri net modeling techniques, including an intuitive description of biochemical networks.
The aim of this chapter is to provide an introduction to basic methods for quantitative modeling of biochemical networks and a description in terms of the Petri net formalism. This includes for example, the classical principles of chemical reaction kinetics, the mass action, steady-states, stability and bifurcation analysis, Michaelis–Menten kinetics, and Hill kinetics. Moreover, we provide extensive references for further reading and give references to standard tools in this field.
Jörg Ackermann, Ina Koch

Chapter 9. Fuzzy Modeling

Petri nets are very well suited for the representation of biological systems. Biological entities like proteins, metabolites, genes etc. can be defined as places; biochemical reactions, regulatory effects, modifications etc. can be defined as transitions. This 1 to 1 correspondence of molecules/reactions and places/transitions allows a very intuitive setup of a computational model framework. In this chapter, we will show how, additionally, the current states of biological entities and the reaction effects can be defined in a very intuitive and natural way using elements taken from fuzzy logic theory. Often exact data or detailed knowledge about concentrations, reaction kinetics or regulatory effects is missing. Thus, computational modeling of a biological system requires dealing with uncertainty and rough information provided by qualitative knowledge and linguistic descriptions. The Petri net and fuzzy logic (PNFL) approach allows natural language based descriptions of entities as well as (if-then) rule based definitions of reaction effects, both of which can easily and directly be derived from qualitative (linguistic) knowledge. PNFL bridges the gap between qualitative knowledge and quantitative modeling.
Lukas Windhager, Florian Erhard, Ralf Zimmer

Biochemical Applications


Chapter 10. Topological Analysis of Metabolic and Regulatory Networks

The theoretical apparatus of Petri nets has been widely used for visualizing metabolic and regulatory networks and for describing their properties and behavior in a quantitative way. In this chapter, the theoretical basis, algorithmic issues and biological applications of using Petri nets in that field are reviewed, in particular, in view of topological (structural) analyses. Several useful notions such as T-invariants, P-invariants, and Maximal common transition sets are explained. The correspondence between several of these concepts and similar concepts in traditional biochemical modeling, such as between minimal T-invariants and elementary flux modes, is discussed. The presentation is illustrated by several hypothetical and biochemical examples. A larger running example is taken from sucrose metabolism in plants. For this, an important difference in functioning between monocotyledon and dicotyledon plants is explained. Algorithms and software tools for determining structural properties of Petri nets are briefly reviewed.
Stefan Schuster, Björn H. Junker

Chapter 11. Analysis of Dynamical Models of Signaling Networks with Petri Nets and Dynamic Graphs

The static representation of biological interaction networks can be misleading. All interactions do not occur simultaneously. On the other hand, differential equations can represent a dynamical system, but the topology of the interactions is not explicitly accessible from the calculations of system dynamics. To have a graph representation of a dynamical system, we have developed the dynamic graph. We used the Petri net representation of an ODE system and invariant analysis to identify the main components of a signaling network and thus bridge the two formalisms. The result is a method that can be used to analyze the dynamics of the network topology. Its main feature is the highlighting of the function and interactions of regulatory motifs in the emergence of a complex biological behavior. The example used here is the Bhalla–Iyengar model of the MAPK/PKC signaling pathway in fibroblasts. A property of this pathway is the ability to operate both in a monostable or bistable regime. We show with dynamic graphs that both the topology and the kinetics of this model are responsible for this behavior.
Simon Hardy, Ravi Iyengar

Chapter 12. A Modular, Qualitative Modeling of Regulatory Networks Using Petri Nets

Advances in high-throughput technologies have enabled the delineation of large networks of interactions that control cellular processes. To understand behavioral properties of these complex networks, mathematical and computational tools are required. The multi-valued logical formalism, initially defined by Thomas and coworkers, proved well adapted to account for the qualitative knowledge available on regulatory interactions, and also to perform analyses of their dynamical properties. In this context, we present two representations of logical models in terms of Petri nets. In a first step, we briefly show how logical models of regulatory networks can be transposed into standard (place/transition) Petri nets, and discuss the capabilities of such a representation. In the second part, we focus on logical regulatory modules and their composition, demonstrating that a high-level Petri net representation greatly facilitates the modeling of interconnected modules. Doing so, we introduce an explicit means to integrate signals from various interconnected modules, taking into account their spatial distribution. This provides a flexible modeling framework to handle regulatory networks that operate at both intra- and intercellular levels. As an illustration, we describe a simplified model of the segment-polarity module involved in the segmentation of the Drosophila embryo.
Claudine Chaouiya, Hanna Klaudel, Franck Pommereau

Chapter 13. A Case Study of HFPN Simulation: Finding Essential Roles of Ror Gene in the Interaction of Feedback Loops in Mammalian Circadian Clock

Mammalian circadian clock is composed of two feedback loops, a Per-Cry and Clock-Bmal loops. The role of Rev-Erb gene, which interconnects these two feedback loops by the inhibition of Bmal from PER/CRY complex, has been investigated through biological experiments as well as computational simulations. However, for the role of Ror gene, which exerts contrary effect on the same target gene Bmal as the Rev-Erb, enough consideration has not been paid so far. This paper first improves the previous hybrid functional Petri net (HFPN) model of the circadian clock so that both of the Per-Cry and Clock-Bmal loops can participate in the maintenance of the circadian oscillations. This improvement is incomplete, however, because a fixed level of PER/CRY eliminates all the circadian oscillations. Although this problem can be resolved by the introduction of Ror into the HFPN model, another inconsistency remains, Bmal oscillation is not abolished by the knock-out of the Cry. Then we further incorporate a hypothetical path into the HFPN model, succeeding in eliminating this inconsistency while keeping complementary actions of two feedback loop.
Natsumi Mitou, Hiroshi Matsuno, Satoru Miyano, Shin-Ichi T. Inouye

Chapter 14. Prediction of Network Structure

For many aspects of health and disease, it is important to understand different phenomena in biology and medicine. To gain the required insight, experiments are performed and the resulting experimental data have to be interpreted. This leads to the Network Reconstruction Problem, the challenging task to generate all models that explain the observed phenomena. As in systems biology, the framework of Petri nets is often used to describe models for the regulatory mechanisms of biological systems, our aim is to predict all the possible network structures being conformal with the given experimental data. We discuss a combinatorial approach proposed by Marwan et al. (Math. Methods Oper. Res. 67:117–132, 2008) and refined by Durzinsky et al. (Proc. of CMSB 2008, LNBI, vol. 5307, pp. 328–346, Springer, Berlin, 2008) to solve this problem. In addition, we also present an algorithm by Durzinsky et al. (J. Theor. Comput. Sci., 2009) that, based on these results, generates a complete list of all potential networks reflecting the experimentally observed behavior.
Annegret Wagler


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