Information Technology Reference
In-Depth Information
B
C
C
cI
lacI
lacI
LuxR
AI
AI
tetR
luxI
A
A
Fig. 3.1. Scheme of the repressilator network coupled to a quorum-sensing mechanism. The
original repressilator module is located at the left of the vertical dashed line, while the coupling
module appears at the right.
3.2.1. Phase-attractive coupling
Quorum sensing has been theoretically shown to lead to synchronization in en-
sembles of identical genetic oscillators [McMillen et al. (2002)]. The oscillators
considered in that work were relaxational, analogous to neural oscillators. The re-
pressilator, on the other hand, is sinusoidal rather than relaxational. Furthermore,
in the experimental implementation of the repressilator [Elowitz and Leibler (2000)],
individual cells were found to oscillate in a \noisy" fashion, exhibiting cell-cell vari-
ation in period length, as well as variation from period to period within a single
cell.
Accordingly, it seems natural to consider the eect of inter-cell signaling on a
population of non-identical and noisy repressilators coupled by reinforcing quorum
sensing. Using computational modeling, Garc a-Ojalvo et al. (2004) showed that a
diverse population of such oscillators is able to self-synchronize, even if the periods
of the individual cells are broadly distributed. The onset of synchronization is
sudden, not gradual, as a function of varying cell density. In other words, the
system exhibits a phase transition to mutual synchrony. This behavior has been
experimentally reported in the zebrash somitogenesis clock [Riedel-Kruse et al.
(2007)].
The coupling also has a second benecial eect: it reduces the system's noisiness,
eectively transforming an ensemble of \sloppy" clocks into a very reliable collective
oscillator [Enright (1980); Somers and Kopell (1995); Needleman et al. (2001)].
The results of Garc a-Ojalvo et al. (2004) suggest that the constraints that local
cell oscillators have to face in order to be noise resistant, could be relaxed in the
presence of intercell coupling, since coupling itself provides a powerful mechanism
of noise resistance.
3.2.1.1. Model
The repressilator consists of three genes, lacI, tetR, and cI, whose protein products
repress transcription of the genes cyclically [Elowitz and Leibler (2000)]. Garc a-
Ojalvo et al. (2004) proposed to incorporate the quorum-sensing system of the
