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of kinetic properties, the development of a discrete structural model was considered as a good initial
choice for the computational analysis of the spliceosome. We chose Petri net (PN) theory, because it
offers the advantage to combine knowledge at different abstraction levels, an intuitive vizualization and
mathematical formalism, using graph-theoretical elements.
PNs have been applied to model, analyse, and simulate biochemical networks [Reddy
et al.
, 1996;
1997; Simao
et al.
, 2005; Koch and Heiner, 2008] of different types. Meanwhile, metabolic networks
[Hofestadt, 1994; Hofestadt and Thelen, 1998; Koch
et al.
, 2005; Zevedei-Oancea and Schuster, 2003]
as well as signal transduction [Heiner
et al.
, 2004; Sackmann
et al.
, 2006] and gene regulatory networks
[Matsuno
et al.
, 2000; 2006; Grunwald
et al.
, 2008] were successfully modeled using PNs. There are
parallel approaches to structural modeling such as those based on elementary flux modes of [Schuster
and Hilgetag, 1994; Schuster
et al.
, 1999] and on extreme pathways [Schilling
et al.
1999]. They have
primarily been applied to metabolic pathways (for reviews see [Papin
et al.
, 2004; Schuster
et al.
, 2007])
but also to signaling networks [Xiong
et al.
2004]. An interesting question is, whether the model of
stoichiometrically quantifiable mass flow inherent to metabolic networks, can be transferred to models
of information flow as occurring in signaling networks. This has been addressed by methods modeling
the mating pheromone response pathway [Sackmann
et al.
, 2006], the human iron homeostasis pathway
[Sackmann
et al.
, 2007] and apoptosis pathway [Heiner
et al.
, 2004]. Recently, a model of the U1 snRNP
subcomplex assembly demonstrated the applicability of PN theory [Kielbassa
et al.
, 2008].
The present work provides the first theoretical model on the entire spliceosomal assembly pathway.
Experimental evidence from literature had to be translated into single reactions steps according to
PN language. By connecting these reactions a model network was formed, consisting of protein and
RNA species, which relay signals rather than mass. The structural network exhibits dependencies and
concurrencies of reactions, but no kinetics, which is still unknown for most stages of spliceosome
assembly.
Spliceosome assembly has been shown to form a complex interacting network of subcomplex formation
[Makarov
et al.
, 2002] best described as an allosteric cascade [Brow, 2002] that frequently involves
cooperativity
[Berglund
et al.
, 1998]. Already a decade ago, it was proposed that the composition of
spliceosomal snRNPs could be different on different splicing substrates in a context-dependent manner
(tissue type, developmental stage). This has the consequence that many different combinations of factors
could potentially give rise to different types of active spliceosomes, thus, increasing the potential for
splicing regulation [Fortes
et al.
, 1999]. In light of the many proteins that up to now have been identified
around the spliceosome, it is necessary to go beyond cataloging the factors. Putting protein and mRNA
factors together into the context of a larger network poses a difficult task and requires the integration of
a standardized vocabulary to unambiguously describe all possible reactions. While this task will remain
a challenge for ontology and text mining specialists, we started to summarize reactions in a PN model.
We present a set of analysis strategies accustomed to Petri net representation of signaling networks.
The paper is organized as follows. In the next chapter biological foundations of spliceosomal assembly
are presented. The following chapter gives methods and definitions used, including MCTS and T-cluster.
We continue with a description of PN modules, which are suitable to describe biochemical reactions of
signaling processes. Next, the biological reactions referring to different stages of spliceosome assembly
are described and formalized. In the results chapter, T-invariants and MCTS are described and interpreted.
Finally, a dendrogram and color map representation are introduced to further explore the model network.
Biological background
Spliceosome assembly is a hierarchical process that progresses through several main stages designated
(P
→
)E
→
A
→
B
→
C(
→
P). Each stage E, A, B, C describes a complex that is built from a pool (P)
