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(Table 1, last two columns). Active, unphosphorylated Cdh1 molecules exist in free and in two various
CycB-Cdk1 bound forms (species Y, XY and YX in [20]). The average number of Cdh1 molecules stays
quite constant across models, while model variants GES, SEN and GES
+
SEN reduce its
CV
compared
to model KAR. The most effective noise containment occurs in GES
+
SEN model, which reduces the
CV
by more than 50% compared to model KAR, whereas GES and SEN models both show a reduction
of around 20%. It is worthwhile noticing that even though in model SEN the
CV
of the mRNA level is
practically the same as the one in model KAR, there is a significant difference on the noise in protein
levels between the two models. The reason is to be found in the different holding times of the mRNA
levels, with model SEN having a slower pattern of variation than that of model KAR.
The effect of the variability of active Cdh1 protein level on the cell cycle time and cell size at division
statistics are also shown in Table 1. The average values of these two measures are practically constant
across all models, and match the values reported in [20]. Instead, the
CV
values obtained for GES and
SEN model show a reduced variability with respect to the one returned by model KAR, although they
are still far from realistic values. Not surprisingly, model GES
+
SEN, providing the smallest variability
of Cdh1 protein levels, is the one that also results in the smallest
CV
s of cell cycle time and cell mass
at division time. Model GES
+
SEN simulation outcomes indicate values of the
CV
for cell cycle time
and cell size at division (12.66% and 8.14%) that are very close to those reported in [20] (13.0% and
8.2%), but in our case we got these results with realistic mRNA half-lives. This further supports the idea,
that multi-step gestation and senescence could represent a more accurate way of modeling the complex
processes of mRNA transcription and degradation.
In this paper we focused only on the multi-step production and removal of Cdh1 mRNA, but as cyclins
are even more important regulators of the cell cycle, their production and degradation should be also
approximated by such multistep processes. As we showed above, this modeling can be effectively
supported by the usage of reaction times that follow properly selected Erlang distributions.
ACKNOWLEDGEMENTS
The authors thank Sandip Kar and John J. Tyson for helpful discussions and acknowledge support
from the Italian research fund FIRB (RBPR0523C3).
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