Biology Reference
In-Depth Information
Biological Petri Nets
Petri Nets for Steady State Analysis of
Metabolic Systems
Klaus Voss
a
, Monika Heiner
b
and Ina Koch
c
,∗
a
Fraunhofer-Institute for Algorithms and Scientific Computing
(
SCAI
)
[GMD], Sankt Augustin, Germany
b
Computer Science Department, Brandenburg University of Technology at Cottbus, Cottbus, Germany
c
Molecular Bioinformatics, Institute for Computer Science, Johann Wolfgang Goethe-University Frankfurt a.
Main, Germany
ABSTRACT:
Computer assisted analysis and simulation of biochemical pathways can improve the understanding of the
structure and the dynamics of cell processes considerably. The construction and
quantitative
analysis of kinetic models is often
impeded by the lack of reliable data. However, as the topological structure of biochemical systems can be regarded to remain
constant in time, a
qualitative
analysis of a pathway model was shown to be quite promising as it can render a lot of useful
knowledge, e. g., about its structural invariants. The topic of this paper are pathways whose substances have reached a dynamic
concentration equilibrium (steady state). It is argued that appreciated tools from biochemistry and also low-level Petri nets can
yield only part of the desired results, whereas executable high-level net models lead to a number of valuable additional insights
by combining symbolic analysis and simulation.
KEYWORDS:
Metabolic pathway, steady state, elementary mode, high-level Petri net, S-invariant, T-invariant
INTRODUCTION
With the rapidly growing amount of new experimental data, the modeling of biological pathways
occuring in the cell regained great interest. For this challenge in biosciences, biologists need theoretical
methods and computational tools in order to prove, analyse, compare, and simulate these complex net-
works for different organisms and tissues. The results are of major importance also for the biotechnology
and the pharmaceutical industry.
“The main focus in the mathematical modeling in biochemistry has traditionally been on the con-
struction of
kinetic
models. The aim of these models is to predict the system dynamics” [Heinrich and
Schuster, 1998]. Their analysis is commonly based on the solution of systems of differential equations.
In this way, numerous kinetic models for different metabolic systems and membrane transport process-
es have been developed (for a review, see Heinrich and Schuster, 1996). A severe restriction, often
encountered in the construction of these models, is the imperfect knowledge of the kinetic parameters.
On the other hand, a
structural
analysis of metabolic pathways mainly deals with the topology of
how substances are linked by reactions.
A central role is played by stoichiometric matrices, which
∗
Corresponding author. E-mail:
ina.koch@bioinformatik.uni-frankfurt.de
.
