Biology Reference
In-Depth Information
Table 1
Effects of the addition of five step gestation (GES), five step senescence (SEN) or both (GES
+
SEN) into the updated model of
Kar
et al.
(KAR) [20] on the variability of cell cycle events and regulatory molecule levels
Model
Cell cycle period Cell size at division
Number of Cdh1 molecules
mRNA protein
c
Average
CV
(%) Average
CV
(%) Average
CV
(%) Average
CV
(%)
KAR 115.31
±
0.32 23.31
±
0.62 28.30
±
0.41 15.72
±
0.40 8.00
a
35.35
b
2620
±
97 25.64
±
1.24
GES 114.91
±
0.20 20.02
±
0.96 28.41
±
0.26 13.74
±
0.74 7.98
±
0.04 27.73
±
0.65 2691
±
83 21.09
±
1.91
SEN 115.78
±
0.41 18.69
±
0.55 29.02
±
0.43 12.29
±
0.38 7.99
±
0.05 35.11
±
0.88 2687
±
67 20.54
±
1.83
GES
+
SEN 115.34
±
0.37 12.66
±
0.47 29.17
±
0.61 8.14
±
0.27 8.00
±
0.03 22.74
±
0.72 2665
±
77 11.95
±
0.67
a
In the KAR model, the number of mRNAs follows a Poisson distribution of parameter
k
smy
/
k
dmy
; we report here the exact
theoretical value, which is given by
k
smy
/
k
dmy
.
b
Theoretical
CV
for the number of mRNAs, which for a Poisson distribution is given by (
k
smy
/
k
dmy
)
−
1
/
2
.
c
Sum of the unphosphorylated forms.
only when the reaction they model is zero-order. This explains why we can model gestation with a single
zero-order Erlang distributed reaction, but we have to unpack the identical stages of mRNA senescence
in model SEN. The translation of Cdh1 protein molecules is modeled by transition Cdh1 syn, whose
firing rate is given by the product of the translation rate constant
k
sy
times the total number of molecules
of Cdh1 mRNA - that is by the total number of tokens in places mRNA Cdh1, mRNA Cdh1 old1,
mRNA Cdh1 old2,
...
, mRNA Cdh1 old4.
The models were studied by simulation, to determine the average values and the
CV
s of a set of metrics.
For each estimated measure, we computed statistics with 95% confidence level. The confidence intervals
for the
CV
statistic have been computed using the method described in [35]. Our measures are for a
synchronous population of cells (calculated from long time averages and variations of 2,000 cell cycles).
The M obius code of the models is available upon request from the authors.
RESULTS AND DISCUSSION
Our simulations show that even though the average amount of Cdh1 mRNA is stable during the cell
cycle, its fluctuations around the equilibrium value have profound consequences on the variability of
the Cdh1 protein levels, which in turn affect the variability of the cell cycle time and of the cell size at
division. These could be clearly noticed on the simulation plots of Figs 2B and 2C. The molecular noise
in Cdh1 mRNA and protein levels look quite much the same in the KAR model and in the GES-SEN
model, but the amplitude in mRNA noise and irregularity in protein peaks is greatly reduced in the
GES-SEN model.
In Table 1 we report the detailed statistics obtained by solving all the four model variants. The
outcomes of simulations show that the average number of Cdh1 mRNA molecules is the same (around
8) across all models (sixth column in Table 1). On the contrary, the
CV
of the number of Cdh1 mRNA
(seventh column in Table 1) is affected by the multi-stage transcription process (model GES) and by
the combined multi-stage transcription and degradation (model GES
+
SEN), validating the visually
noticeable differences on Fig. 2B. It is also interesting to notice that in model SEN the variance of
Cdh1 mRNA level stays practically unchanged with respect to those in model KAR. Though, when
combined with the multi-stage transcription process, the senescence contributes significantly to reduce
the variability of the mRNA levels (compare the mRNA
CV
results for GES and GES
+
SEN models).
To evaluate the effect that the noise of Cdh1 mRNA levels has on the variability of Cdh1 protein
levels we computed the average and
CV
of the number of unphosphorylated Cdh1 molecules as well
