Biomedical Engineering Reference
In-Depth Information
sheet 18
60
SG2M
G1
50
40
30
20
10
0
0
20
40
60
80
100
120
140
time ( / 15 min)
G1
cycle
Fig. 1
Graphic method used to determine the durations of the whole cell cycle and of
G
1
phase.
The duration of phase
S
/
G
2
/
M
was deduced by subtracting the duration of phase
G
1
from the
duration of the cell cycle
nor external control on their proliferation. It is noteworthy that, though we deal
with PDEs, our method is simpler than methods involving inverse problem solving
(which nevertheless have been used on comparable situations, for instance in [
51
]),
and this is due to the fact that using the FUCCI reporter technique we have access
to precisely defined data in individual cells, with the counterpart that quite few
individual proliferating cells have been recorded. A graph representing a time series
from an individual cell and the method used to record phase durations is presented
on Fig.
1
.
We used these experimental data to identify the parameters of our model by
fitting shifted Gamma distributions
f
)=
ρ
−
k
))
−
1
k
−
1
e
−
(
x
−
a
)
/
ρ
(
x
(
Γ
(
k
(
x
−
a
)
on
[
M
durations within the
population (recall that variable
x
stands for age in each one of the two phases). These
Gamma distributions were approximations of the probability density functions of
a
,
+
∞
[
to frequencies of appearance of
G
1
and
S
/
G
2
/
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