Petri Net Applications in Molecular Biology

Abstract

At the time when “classical” bioinformatics developed further towards modern systems biology, the idea of a holistic view of a biological system was not completely new: the aim to provide a comprehensive picture, e.g. about the genes and their regulatory features encoded in a genome, was inherent in bioinformatics research from the very beginning. Also the attempt to come up with an integrative view across the different levels of organisation was at least conceptually implicit in the numerous approaches to integrate the rapidly growing information about biological objects into comprehensive knowledge bases. However, to transcend the research focus on static objects and to step forward to the computer-aided investigation of biological processes was significantly pushed ahead by the emerging field of systems biology. The new paradigm to formally represent the processes that make up a biological system is now the “network”. The term “process” implies dynamic events, changes, that we may wish to simulate with the aid of a computer in order to predict the behavior of a biological system under certain circumstances. Biochemistry provides the formal instruments to do so for defined (bio)chemical reactions, usually resulting in a set of ordinary differential equations (ODEs). Solving the large number of ODEs that are required to exactly describe the behavior of a complex biological system may be cumbersome, but computationally feasible as soon as we have at hand all necessary parameters such as the corresponding kinetic constants for all reactions involved. Even in those cases where these kinetics have been studied in vitro, it is still questionable whether the insights we gained from these experiments are applicable on specific in vivo conditions. Nevertheless, this approach has been proven to work for (parts of) the metabolic network of living cells, but regulatory events that depend on just a very low number of individual molecules per cell may require different approaches. Moreover, applying ODEs onto a large complex system may be mere overkill, and a (presumably) less exact approach might be of even more appropriate granularity, at least for the larger part of the network under consideration. Several years ago, Petri nets have been suggested to be well suited for modeling metabolic networks by overcoming some of the limitations outlined above [Reddy et al., 1993]. Since then, a lot of further conceptual work, technical tool implementations and applications onto biological problems have been reported and demonstrated the usefulness of this concept for what we know today as systems biology. Being intuitively understandable to scientists trained in life sciences, they also have a robust mathematical foundation and provide the required flexibility with regard to the models’ granularity. As a result, Petri net technology appears to be a very promising approach to modeling biological systems.