Biology Reference
In-Depth Information
Recently, Petri nets have been applied also to conceptual modeling of biological pathways. Knowledge
representation has been reported in either Petri nets [3,4] or bipartite graphs [5] for qualitative behavior
of signaling pathways. Knowledge representation in Petri nets has the advantage of intuitive and concise
representation of complicated networks, as well as of readiness for quantitative systems analysis of the
networks based on mathematical background. However, all of the existing Petri net representations
include inconsistencies, which prevents us from reusing, sharing, and scaling up the accumulating
Petri net models. The inconsistency is revealed in the representation of catalytic reactions in molecular
complexes. In Fas-induced apoptosis pathway [3], catalytic reactions in molecular complexes are omitted
from the Petri net representation. Every molecular complex is regarded as a whole, so that individual
states of components of the complex are disregarded. In the IL-1-induced NF-
κ
B pathway [4], a catalytic
reaction in a molecular complex is represented in the Petri net. However, special
places
without any
labels are used to represent the catalytic reaction, even though all the other
places
are explicitly labeled.
The authors did not explain what the unlabeled places account for. The unlabeled places seem to account
not for biological entities but imaginary ones. In a model for the TGF-
β
pathway [5], the authors
invented a 'virtual decomposition' arc in order to represent a catalytic reaction in a molecular complex.
The 'virtual decomposition' arc connects a place representing a molecular complex as a whole to a
place
representing a component of the complex. However, we cannot find any existing event accounting for
the 'virtual decomposition' arc, nor can we find semantic consistency between this arc and the others.
While metabolic pathways consist of catalytic reactions uniformly, signaling pathways consist of
combinations of catalytic reactions, complex formations, and transportations. The chemical view draws
a distinction between the three types of reactions. However, in the context of signaling pathways, every
kind of reactions ought to play a common role of the
process of signaling
. While an entire Petri net is
obviously modeled with the intention of representing a certain signaling process, individual reactions
are modeled with the intention of the process of chemical reactions. One sees semantic discrepancy
between the entire net and the individual reactants. If both these semantics become consistent, then the
representation will be uniformed. The individual reactions should be represented on the basis of not only
chemical reactions but also the common essence unique to the
process of signaling
. The essence is in
need of ontological explication.
We have developed an ontology for signaling pathway, Cell Signaling Networks Ontology (CSNO),
which gives an intrinsic definition to the
process of signaling
[6,7]. CSNO defines the
process of signaling
as 'the transmission of
activity
through
molecular recognition
'. Based on this definition, I propose units
of Petri nets that standardize the representation of signaling pathways in Petri nets. The units make us
free of ambiguity in constructing Petri net models of signaling pathways.
Owing to the intuitive and concise graphical representation of biological concepts as well as the
quantitatively analytical notation of dynamical behaviors of biological entities, Petri nets will become
more popular with biologists for their modeling of biological pathways. More and more Petri net models
will be accumulated rapidly. Our final goal is about modeling the entire cellular networks, which will be
impossible without reusing and scaling up existing models. The more complicated and expanded Petri
nets become, the more consistent the nets should be. Therefore standardization of Petri net units will
make for foundations of modeling the entire cellular system.
METHODS
Ontological Definitions of the Process of Signaling
Signal
in general is defined as something that is coded into a certain variation of certain physical
