Information Technology Reference
In-Depth Information
2000
4000
12000
(a)
(c)
(e)
10000
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0
0
0
0.022
0.024
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0.022
0.024
0.026
0.022
0.024
0.026
frequency (min
-1
)
frequency (min
-1
)
frequency (min
-1
)
70
70
70
(b)
(d)
(f)
60
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10
0
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time (min)
time (min)
time (min)
Fig. 3.2. Frequency histogram (a, c, e) and time evolution of b
i
(t) for 10 cells (b, d, f) and
increasing cell density: (a, b) Q = 0:4, (c, d) Q = 0:63, (e, f) Q = 0:8. Other parameters are
N = 10
4
, = 216, = 20, n = 2:0, k
s0
= 1, = 2:0 and k
s1
= 0:01. The lifetime ratio in
the dierent cells is chosen from a random Gaussian distribution of mean = 1:0 and standard
deviation = 0:05.
standard deviation . The corresponding frequency distribution of a group of 10
4
uncoupled cells for = = 0:05 is shown in Fig. 3.2(a). The temporal evolution of
the cI mRNA concentration in 10 of those cells is plotted in Fig. 3.2(b), showing how
the global operation of the system is completely disorganized, so that no collective
rhythm can exist under these conditions.
As the cell density increases, diusion of extracellular AI molecules into the
cells provides a mechanism of intercell coupling, which leads to partial frequency
locking of the cells [Figs. 3.2(c,d)]. Finally, when the cell density is large enough
[Figs. 3.2(e,f)] perfect locking and synchronized oscillations are observed. In that
case the system behaves as a macroscopic clock with a well-dened period, even
though it is composed of a widely varied collection of oscillators. This results
indicate that a transition from an unsynchronized to a synchronized regime exists
as the strength of coupling increases (due to an increase in cell density). This
behavior is robust in the presence of noise. In fact, noise can be seen to enhance the
collective coherence of the system, leading to a better clock [Ullner et al. (2009)].
3.2.2. Phase-repulsive coupling
We now show how signicantly can cell-cell coupling inuence the dynamics of
synthetic gene network.
Only one rewiring in the connectivity between the ba-
