=Paper=
{{Paper
|id=Vol-65/paper-16
|storemode=property
|title=The biology Petri net markup language
|pdfUrl=https://ceur-ws.org/Vol-65/12chen.pdf
|volume=Vol-65
}}
==The biology Petri net markup language==
https://ceur-ws.org/Vol-65/12chen.pdf
The Biology Petri Net Markup Language
Ming Chen, Andreas Freier, Jacob Köhler and Alexander Rüegg
Bioinformatics / Medical Informatics
Technische Fakultaet, Universitaet Bielefeld
Postfach 10 01 31, D-33501 Bielefeld
E-mail: mchen@techfak.uni-bielefeld.de
Abstract: In this paper a proposal for the Biology Petri Net Markup Language
(BioPNML) is presented. The concepts and terminology of the interchange format as well
as its syntax that is based on XML (eXtensible Markup Language) are introduced.
BioPNML is designed to provide a starting point for the development of a standard inter-
change format for Bioinformatics and Petri nets. The language will make it possible to
present biology Petri net diagrams between all supported hardware platforms and ver-
sions. It is also designed to bridge Petri net models to other known metabolic simulators.
1 Introduction
Petri nets were first introduced and formally defined by Prof. Dr. Carl Adam Petri. Petri
nets and its concepts have been extended and developed since then and both the theory
and the applications of this model have been flourishing. Its intuitively understandable
graphical notation and the representation of multiple independent dynamic entities
within a system is supported make Petri nets the model of choice highly suitable for
many applications, such as manufacturing systems, communication networks, business
process management, traffic and logistic systems, client-server networks and control
systems. A large amount of literature on Petri net investigations has been compiled
[http://www.daimi.au.dk/PetriNets/bibl/].
With the rapid development of bioinformatics, more and more experimental data both on
genome and cell levels are systematically collected and stored in specific databases
[Bax02]. In the post-genomic era, new methods are proposed to store, retrieve and ana-
lyze these data. XML, as an emerging standard for data exchange, is widely adopted as a
structured data format in bioinformatics.
In this paper, prospects and problems concerning the use of Petri nets for biological data
exchange are discussed; a proposal for Biology Petri Net Markup Language (BioPNML)
is introduced. It is dedicated to serve as a starting point for the development of a stan-
dard interchange format for Petri nets and bioinformatics.
1.1 XML & Bioinformatics
There are already two good review papers on this topic by V.H.Guerrini [GJ00] and
F.Achard [AVB01]. We would like to highlight a few of their points and supplement
them with examples for metabolic pathway applications.
XML is derived from the Standard Generalized Markup Language (SGML), the interna-
tional standard for defining descriptions of the structure and content of different types of
electronic documents. XML is a web-dedicated data exchange language, which omits the
complex and less used parts of SGML. The World Wide Web Consortium (W3C) has
supervised the specifications of XML since its inception in 1996. More documentation
can be found at http://www.w3.org/XML/.
In bioinformatics, XML is widely used within the last few years, and several XML based
data formats have been developed. BSML (Bioinformatic Sequence Markup Language)
[http://www.bsml.org/] uses XML to provide genomic information and a graphical
BSML browser was developed. BioML (Biopolymer Markup Language)
[http://www.bioml.com/BIOML/] integrates nucleotide and protein sequence data. The
XML based RDF format [http://www.w3.org/RDF/] is also adopted by the Gene Ontol-
ogy Consortium [http://www.geneontology.org] to provide controlled vocabularies for
the description of molecular functions, biological processes and cellular locations of
gene products. Moreover, major biology databases such as NCBI, WIT and Expasy also
provide XML output after users’ database queries. Obviously, XML is widely adopted as
a standard for the exchange of biological data.
Both CellML (Cell Markup Language) [http://www.cellml.org/] and SBML (Systems
Biology Markup Language) [http://www.cds.caltech.edu/erato/] present description lan-
guages for cellular simulation. CellML is intended to be used to represent many different
types of models, for instance biochemical pathway models. Aside from specifying a
model purely in terms of mathematics, CellML can use some additional elements to fully
capture the information in biochemical pathway models. SBML is oriented towards rep-
resenting biochemical networks common in research on a number of topics, including
cell signaling pathways, metabolic pathways, biochemical reactions, genomic interac-
tions, and many others. The main difference is that CellML has a very general and flexi-
ble syntax, while SBML’s syntax is specific to metabolic pathway modeling. Currently,
SBML is closely collaborated among several teams that develop metabolic simulators.
Although many biological databases and bioinformatic research groups use XML, XML
is so flexible that anyone can create his/her own versions in entirely different ways.
XML enables advancements in application integration, but they are hard to achieve
without a consistent framework for XML implementations.
1.2 Petri nets & Bioinformatics
Modeling and simulation of metabolic networks becomes a promising field of bioinfor-
matics in the post-genomic era. The development of computer science makes it possible
to represent the complex metabolic network of physical and functional interactions that
take place in the living cell, in ways which enable to manipulate, analyze and achieve
understanding of how cells function. Petri net theory exhibits a mathematical formalism
to model, analyze and simulate discrete event systems with inherent concurrency.
Following its first application of modeling metabolic pathways [RML93][Ho94], Petri
nets as a new tool for modeling and simulation of biological systems are investigated
more and more. Later Reddy [RLM96] exemplarily combined the glycolytic and pentose
phosphate pathways of the erythrocyte cell to illustrate the concepts of the methodology.
However, the reactions and other biological processes were modeled as discrete events
and it was not possible to simulate kinetic effects. Hofestaedt [HT98] investigated a
formalization showing that different classes of conditions can be interpreted as genes,
proteins, enzymes or cell communication; he also showed how self-modifying Petri nets
[Va78] could be applied to the quantitative modeling of regulatory biochemical net-
works. Chen [Ch00] introduced a hybrid Petri net (HPNs) approach, for expressing the
glycolysis pathway. Using this approach, quantitative modeling of metabolic networks is
also possible. Koch I. and M. Heiner et al. extended the model proposed by Reddy by
taking into account the reversibility of chemical reactions and time dependencies
[KSH99]. Later they analyzed steady states in metabolic pathways using Petri nets
[HKV01]. Kueffener [KZL00] exploited the knowledge available in current metabolic
databases for functional predictions and the interpretation of expression data on the level
of complete genomes. To achieve this, the enzyme databases BRENDA, ENZYME
[http://www.expasy.ch/enzyme/] and KEGG were compiled both into individual Petri
nets and unified Petri nets. They also discussed executable Petri net models for the
analysis of metabolic pathways [GKV01]. Goss [GP99] and Matsuno [Ma00] applied
Petri nets to model gene regulatory networks by using stochastic Petri nets (SPNs) and
HPNs respectively.
The above-mentioned papers are dedicated to the applications of Petri nets to bioinfor-
matics and show that Petri nets are suitable to model special molecular biological sys-
tems. However, they lack unity in their concepts, notations, and terminologies. This
makes it very difficult for new scientists to understand the potential applications of Petri
nets due to the various interpretations presented by different authors. Furthermore, no
Petri net tools exist which fulfill all requirements needed for the task of virtual cell mod-
eling. In principle it should be possible to build Petri nets semi-automatically from data
stored in molecular biological databases. However, the available Petri net tools do not
support this. Our motivation for the presentation of a standard interchange format is to
bridge this gap.
1.3 Petri nets & XML
At present most Petri net tools import and/or export Petri nets in proprietary file formats
and poorly support other data formats. In these proprietary file formats it is difficult to
add and remove features to the language and to make modularization of diagrams as easy
as it might be in an ASCII based text format such as XML.
In order to solve the problems caused by the use of different file formats, many Petri net
tools are currently being equipped with XML support. Matthias Jüngel et al. [JKW00]
presented the concepts and terminology of PNML (Petri Net Markup Language), and
thus provided a starting point for the development of a standard interchange format for
Petri nets.
Although the above mentioned Petri net XML standards are available, they are incom-
patible due to different design destinations. PNML is generic and can be extended ac-
cording to users’ specific needs. A special “Bio-PNTD” for PNML can be defined when
a simple biological system is modeled. However, a metabolic network model can contain
a large number of named components representing different parts of a model. In this
case, SBML model definitions are more suitable. Therefore, with regard to the applica-
tion of Petri net methodology to bioinformatics, particularly for modeling and simulation
of metabolic networks, a new interchange format is wanting.
2 Concepts and terminology
The intended BioPNML is a XML based description language that allows the representa-
tion of metabolic networks as Petri nets. Before introducing the syntax of the inter-
change format, we briefly discuss its basic concepts and terminology, which is inde-
pendent of the XML representation. Previous approaches proved that by using hybrid
Petri net methodology, it is feasible to model and simulate metabolic systems
[Ma00][Ma01][Ch00][Ch02]. Therefore the primer version of BioPNML supports the
hybrid Petri net type. BioPNML contains Petri net objects as well as data needed for the
exchange and graphical representation of metabolic networks; An XML schema defines
the labels for a Petri net and its objects and metabolic models.
2.1 Petri net objects and labels
It is possible to translate molecular biological terms into Petri net terms in a natural way
(Table 1).
Table 1. Mapping Metabolism to Petri nets
Metabolism terms Petri net terms
•S, P, E, metabolites, genes, promoters, signals... •Places
•Bioreaction, interaction, other bioprocesses, ... •Transitions
•Defines reagent of bioprocess •Input arcs
•Defines product of bioprocess •Output arcs
•Initial token or state of system •Initial marking
•State of reaction system •Marking
•Rate of reaction system •Weight function or differential function
•All reagents must be provided for the reaction •A transition enabled
•A single reaction •A firing transition
•... •...
Places can be used for the representation of biological subjects such as genes, metabo-
lites, proteins, enzymes, compounds and other molecules while transitions represent bio-
chemical reactions and interactions. The value of tokens in places can represent the ac-
tual concentrations of biological subjects. Transitions can be classified into two types:
discrete and continuous. A discrete transition fires if it has concession and a delay time
can be assigned to it. Continuous transitions are not comparable to the abrupt firing of
discrete transition. The firing speed assigned to a continuous transition is defined by a
constant or a function. Arcs between places and transitions fall into three categories:
normal arcs, inhibitor arcs and test arcs. In metabolic pathways, arc weights of continu-
ous transitions are assigned according to the stoichiometric coefficients of the biochemi-
cal reactions.
2.2 Petri net graphics
Every object is equipped with some graphical information. For a place and transition, the
information is its shape, size and position; for an arc, it is a list of positions that defines
start and end points of this arc. In biological Petri net models, the main properties are
that the arc weights are described by the stoichiometric coefficient of the biochemical
reaction and the transition condition is described by using functions or by assigning a
delay time. Fig. 1 shows the Petri net representation of a biochemical reaction. S, E, P
and ES denote substrate, enzyme and product. ES denotes the enzyme-substrate com-
plex. The biochemical reaction indicates that a substrate is enzymatically catalyzed into
a product with a transformation rate v. Three places represent substrate, enzyme and
product with S, E and P as the label of places. The tokens (real concentrations) of each
place in the Petri net can be used as variables, s1, s2 and s3, while the transition rate is
assigned with a known function, Michaelis-Menten equation.
Fig. 1 Petri net presentation in BioPNML
2.3 Molecular biological networks
In a living cell, hundreds and thousands of biochemical reactions occur simultaneously
per second. These reactions are catalyzed by enzymes. Most metabolites (substrates and
products) involved in a reaction, can also be found in other reactions where the metabo-
lite acts as a substrate or regulates the reaction speed (activators, repressors). Proteins
and enzymes are synthesized from genes which can also be switched on or off by mole-
cules. Thus, a densely connected, intricate and precisely regulated network is built. Tra-
ditionally, people divide those metabolic networks into three levels, namely metabolic
pathways, gene regulatory networks and signal transduction pathways.
2.3.1 Metabolic pathways
A metabolic pathway consists of enzymatically catalyzed metabolic reactions which are
interconnected in a way, that products of some reactions are the substrates of other reac-
tions. In BioPNML, the metabolic reaction class is defined as biochemical reactions and
related objects such as: enzyme, substrate(s), product(s), their stoichiometries, and pa-
rametric values for separately defined kinetic laws. In the fig. 2, the metabolic reaction
class structure that was derived by extending SBML’s biochemical reaction class [Hu01]
is shown.
The metabolic reaction class contains mandatory fields (enzyme, substrate, product, and
KineticLaw) as well as optional fields (enhancer and inhibitor). Enzyme is a reference to
the gene which encodes the enzyme. Both substrate and product are references to mole-
cules implemented using lists of SpecieReference structures. The SpecieReference struc-
ture contains fields for recording the names of molecules, the types of molecules which
are references to lists of TypeRef structure, the stoichiometry filed indicates the propor-
tions of substrate and product within a reaction. The KineticLaw structure is an optional
field of the type KineticLaw, used to provide a mathematical formula for the reaction
rate. The Boolean field, reversibility, indicates whether the reaction is reversible. The
field is optional, and should default to “true” when it is not specified. Information about
reversibility is useful in certain kinds of structural analyses such as elementary mode
analysis [SDF99].
In addition to these fields, the reaction structure also has a Thermodynamics field as a
reference to ThermodynamicsRef. The ThermodynamicsRef structure is an optional field
that is used to provide the Gibbs energy which indicates the favorability of the reaction.
2.3.2 Gene regulatory networks
A gene regulatory network is most often described and interpreted as the on-off switches
and/or rheostats of a cell, operating at the gene level. They dynamically orchestrate the
level of expression for each gene in the genome by controlling whether and how vigor-
ously that gene will be transcribed into RNA. Each RNA transcript then functions as the
template for synthesis of a specific protein by the translation process. These gene prod-
ucts may act as transcription factors which regulate the expression of other genes. Gene
regulatory networks are not restricted to the level of transcription, but may also be car-
ried out at the levels of translation, splicing, posttranslational protein degradation, active
membrane transport and other processes [AKK00]. In BioPNML, the gene regulation
class is defined as a set of objects such as gene, promoter, transcription factor, inducer,
repressor, the gene encoding protein, other metabolites and the effect of interaction and
kinetics (Fig. 2).
2.3.3 Signal transduction pathways
Cell communication or signal transduction is the means by which cells respond to sig-
nals coming from outside those cells. A “biological signal” could be defined as a mole-
cule which acts as a pre-arranged sign, indicating either the commencement and/or the
termination of (one or more) intracellular processes. In other words, the nature of the
signaling molecule decides it's effects, just as pre-arranged signals have pre-arranged
affects [Cl96]. The Signal transduction class in the BioPNML is defined as a set of sig-
nal instances through the message passing between source and target.
2.3.4 Other bioprocesses
Biological cells are highly complex systems. Some biological systems such as mem-
brane transportation do not fit in one of the above-mentioned three basic categories, but
should also be taken into account when required. Many models assume that the amount
of metabolites in a cell is uniform across the cell, i.e. it is assumed that the cell is a
“well-mixed pool”. In many situations, however, concentration gradients exist which
will affect the local rate of biochemical reactions. In particular for large systems with
different compartments, we must consider explicitly the effect of diffusion or transporta-
tion.
In BioPNML, other bioprocesses classes can be defined. This concerns not only all ef-
fects of metabolites, but also different compartments and properties of biological proc-
esses.
2.4 Pathway class diagram
BioPNML consists of two parts, one based on SMBL and another based on PNML. This
first draft of BioPNML was developed in a way, which should enable both SMBL and
PNML tools allow to read BioPNML.
Fig. 2 shows the classdiagram of BioPNML. The left side shows the Petri net part of
BioPNML which was derived by extending PNML slightly. The right part shows the
Biological part which is based on SBML. The Petri net part contains only very few ex-
tensions to PNML. More changes to SBML were made in the biological part, although
those changes are open for discussion. This is due to the fact that Petri nets have a com-
paratively long history and well defined generally accepted syntax and semantics,
whereas molecular biology is still evolving at a rapid pace. The purpose of the schema is
to give a rough idea of how Petri nets and biological systems are related. This diagram
can also serve as a conceptual guidance to researchers who are designing databases to
store networks and reaction data.
Fig. 2 Diagrammatic class relations of BioPNML
3 An example
In this section, we present some concrete XML syntax in order to exemplify the concepts
discussed in Section 2 by using a simple enzymatically catalyzed reaction (Fig. 3). The
model defines the single biochemical reaction from L-arginine to L-ornithine catalyzed
with the enzyme arginase. We assume the reaction kinetics complies with the Michaelis-
Menten equation, and the values of Km and Vmax are 0.5mM and 0.3mM respectively.
Fig. 3 An example for a biology Petri net model, where S1, S2 and S3 are variables for the concen-
trations of the substances involved
The first part of the XML example contains the biological information, whereas the sec-
ond part is mainly PNML. idref tags are used to link the PNML 'place' and 'transition' tag
to the respective SBML based 'spiecie' tag. Since it was tried to develop BioPNML in a
way that it should be readable both by existing PNML and SBML tools, some redundan-
cies could not be avoided, i.e. the names of the compounds and the initial concentrations
appear in both parts of the file. Properties which are not part of the present PNML stan-
dard, such as the formula used to calculate the changes in the concentrations of the sub-
strates and the product are only stored in the SBML part of the file. The example shows
the basics of idea of BioPNML. In real applications, the PNML part may contain many
reactions.
L-arginine
0.1
10
red
1
10
yellow
1
blue
1
…
4 Disscussions
BioPNML is a XML framework for the exchange and unification of molecular biologi-
cal Petri net models. By formalizing the process of expressing bioprocess interchanges in
a consistent and extendible way, BioPNML makes it easier for users and developers of
biological software to map data in different formats. Easier mapping enables developers
of biological software who are using open standards, such as XML, to adopt changes in
biological data formats faster.
BioPNML defines a core set of XML elements, attributes, and tags that enable research-
ers to develop technologies that are optimized for data exchange. This XML based core
data model is important because it eliminates the need to find a common application
programming interface or implementation platform. Currently its XML schema is based
on the SBML and PNML standard. However, BioPNML is not static; we continue to
develop it. BioPNML will be updated in line with future changes of SBML and PNML.
Extensions to Petri nets have been developed which transform Petri nets into a powerful
tool for modeling biological systems. These enhancements include timing, token typing,
non-homogeneous places, priorities and resources. It is possible to extend our BioPNML
classes to these requirements by using additional tag sets.
BioPNML files can be generated computationally from existing data sources. By using
the W3C recommended Extensible Stylesheet Language Transformations (XSLT), new
structured data formats can be created from existing XML documents. That is, XSLT is
a language for transforming XML documents into other XML documents. Users can
extract XML data from molecular biological databases via the Internet and transform
them into BioPNML files via XSLT (Fig. 4).
There are many approaches that address the challenging problem of interoperability
among biological databases. They are based on different data integration techniques, e.g.
federated database systems, multi database systems and data warehouses. In order to
model and simulate gene controlled metabolic networks, we focus on a flexible and thin,
but universally applicable solution with powerful query and retrieval capabilities. The
architecture of our system MARGBench is a mediator-based approach for database inte-
gration. The aim of MARGBench is to support the seamless integration of multiple het-
erogeneous molecular biology databases and to allow the development and the execution
of global applications that extend beyond the boundaries of individual databases [Fr02].
The general principle of BioPNML data integration is shown in Fig. 4. Integration of
heterogeneous and physically distributed databases is implemented by the BioData-
Server (BDS) system, which provides a homogeneous database view. IIUDB (Individu-
ally Integrated User Database) accesses JDBC (Java Database Connectivity) interfaces
followed up by an object network. Provided with the JDBC driver, the IIUDB is devel-
oped for users to define their own specific integrated schemes, i.e., the system is adap-
tive by connecting to heterogeneous databases and integrates the information retrieved
into user-defined persistent databases and analyses the networks that can be found in
theses databases. The structure of metabolic networks and the molecular information
contained is changing and depending on the user view. Then based on the Object Man-
agement (OMG) architecture, we can do SQL queries and build up a metabolic network.
IIUDB also includes several interfaces to export the resulting networks into common
formats, e.g., CORBA, GML and XML as well as BioPNML.
So far, the IIUDB offers integrated access to biological databases, currently mainly to
KEGG, BRENDA and RegulonDB, which cover considerable features including details
on the enzymatic reactions, substrates and products, binding parameters, catalytic con-
stants and gene regulations. Based on these techniques, bio-Petri net tools could be pro-
vided with models of metabolic pathways, gene regulation and signaling pathways.
Fig. 4 BioPNML data integration schema
5 Conclusions
This paper presents, in its draft version, the concepts and the terminology of the Biology
Petri Net Markup Language. BioPNML can represent both graphical information and
metabolic network information. It serves as a starting point for the development of a
standard interchange format for Petri nets and other molecular biological modeling and
simulation tools.
Acknowledgments
Part of this work is supported by GK-Bioinformatics. Authors give particular thanks to
Dr. S. Philippi for useful suggestions. We would like to thank the anonymous referee for
his/her valuable comments and suggestions.
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