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is described by individual MCTS (11 and 13), the former consisting of reactions, which are shared by
alomst three quarter (73%) of all T-invariants. All MCTS further validate the model network, capturing
crucial parts of the U1 and U2 snRNP maturation, U1 independent 5'ss recognition and the Prp16
involved discard pathway. For a more detailed model of U1 snRNP assembly see Kielbassa
et al.
, 2008.
Clustering of T-invariants and MCTS
Computed T-invariants (see Supplementary Table S2) were aligned to determine the individual distance
between the signaling pathways. Similar to sequence alignments the pairwise comparisons among all
T-invariants can be used to build a distance matrix, based on which a clustering can be performed.
Clusters reflect groups of signaling pathways, which share a given percentage of reactions. Here, a
threshold of 80% was chosen to merge T-invariants with less than 20% difference into the same subtree.
For example, the T-invariants i13 and i14 show a difference in four reactions in a total pathway length
of 92 transitions,
i.e.
, only one transition (
t13.17S U2 matur2
) is missing in i14 and three transitions
(
t12.ASFp U170K bdg
,
t22.17S U2 matur1
,
t109.SF3b125 in
) are absent in i13, which makes both
invariant to 96% similar. Comparing different subclusters helps to identify those reactions, which define
different functions in different stages of spliceosome assembly.
The cluster representation depicts all trivial T-invariants in one group in the lower part of the tree
(Fig. 10, C1-C13, C22, C23), which is reasonable since they share maximal two transitions with
the remaining T-invariants (cluster I). Also three short T-invariants, which describe the NTC-complex
formation, the subpathway of U4 snRNP maturation and the PTB inhibition pathway group separately,
indicating that these reactions model side-pathways, which are not shared by other signaling fluxes. In
contrast to the outgroup, cluster I combines all T-invariants of at least four reactions.
Subclusters can contain complete or partial MCTS. For example, cluster C17 and C18 together
constitute MCTS 10, which is composed of five reactions. This MCTS describes the subpathway of
bridging the U1/U2 snRNP by Prp5 and occurs in four T-invariants. In contrast, T-invariants i15-i20
and i62-i67 share five reactions involving ASF/SF2 within MCTS 5 but are part of the two different
major clusters, I and IV. These clusters partition the T-invariants in two reaction sets: one is reaching
the productive end of the spliceosomal assembly pathway (resulting in spliced mRNA) and the other
one is representing the discard pathway during C-Complex stage. This splitting can also be seen by
visualizing all invariant pathways and their shared reactions via a color map (see Fig. 11). The color
map representation was used to aid and accelerate the visual identification of groups of reactions that
participate in different T-invariants in conjunction with the dendrogram (Fig. 10). It is thought to
introduce a compact representation of network structure to facilitate the interpretation of differences
between signaling pathways. Here, darker colors in vertical direction accentuate the transitions of each
individual T-invariant, while in horizintal direction the participation of an individual transition in different
T-invariants can be read.
Bright colors mean that a reaction is not present in T-invariants and consequently also not in MCTSs.
This representation suggests to extend the analysis of MCTSs also for reactions, which do not occur in
specific MCTSs. For example, in Fig. 11 one can easily recognize two brighter colored horizontal areas
within the line of transition
t103.ASF SF2 out
, which stretches exactly over the columns that contain the
T-invariants of MCTS 5 (see dashed rectangle in Fig. 11). This means, transition
t103.ASF SF2 out
is
specifically not involved in 12 T-invariants, i15-i20 and i62-i67.
Further analysis of the line within the color map (Fig. 11), which represents the transition
t103.ASF SF2 out
reveals that this transition is present in most of the other T-invariants, but why is
it absent from a specific set of T-Invariants? We expect this reaction in the trivial T-Invariant i12, which
