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viewpoint. First, the oscillation death (OD) described above is stable far from any
Hopf bifurcation in a wide range of parameter space. This contrasts with other
situations [Herrero et al. (2000); Wang et al. (2000)], where OD occurred only in
a small range close to a Hopf bifurcation. Second, the phase-repulsive character of
the coupling leads to multistability between the regimes of OD, IHLC and the single
xed point. The simultaneous availability of these dierent dynamical regimes to
the cellular population improves its adaptability and robustness. Such an improved
eciency induced by coupling can probably exist in natural genetic networks, and
can be denitely exploited in synthetic devices. The theoretical predictions reported
here are amenable to experimental observation at the single-cell level via time-lapse
uorescence microscopy [Rosenfeld et al. (2005)]. This technique is very useful to
experimentally test theoretical predictions in genetic networks [Suel et al. (2007)].
The results discussed here lead to several open questions in the eld of syn-
thetic biology of genetic networks. One of them is the inuence of stochasticity
arising from the small number of reactant molecules involved in gene regulation
(sometimes around 1 mRNA molecule per cell in average), which can lead to signi-
cant uctuations in intracellular mRNA and protein concentrations [Ozbudak et al.
(2002); Elowitz et al. (2002)]. Hence it is important to understand how the vari-
ety of dynamical regimes discussed here will change in the presence of noise. Here
one should distinguish intrinsic and extrinsic noise acting upon the gene regulation
process [Swain et al. (2002)]. For the simulations with intrinsic noise usually the
Gillespie algorithm is used [Gillespie (1977)], whereas in some situations the chem-
ical Langevin equation approach can be employed [Gillespie (2000)]. In the system
presented here, the dynamics can be expected to be quite complicated and counter-
intuitive, if extrinsic noise leads to noise-induced ordering. It has been reported that
noise may induce a bistable behaviour qualitatively dierent from what is possible
deterministically [Samoilov et al. (2005)], induce stochastic focusing [Paulsson et al.
(2000)], or increase the robustness of oscillations. Especially interesting would be
to identify mechanisms through which noise-resistance appears due to the phase-
repulsive property of the coupling. Taking into account the fact that stochastic
eects in biomolecular systems have been recognized as a major factor, functionally
and evolutionarily important, and that only a small amount of the recently discov-
ered noise-induced phenomena in general dynamical systems have been identied
in gene expression systems, this opens very wide perspectives for further research.
Another interesting question regards the inuence of time delay on the phe-
nomena discussed above. This issue has been discussed in single genetic oscillators
[Chen and Aihara (2002)], where it has been seen that time delay generally increases
the stability region of the oscillations, thereby making them more robust. In cou-
pled oscillators, such as the ones discussed above, the eect of delay could be much
more complicated. In particular, it was reported that delay in coupling may sup-
press synchronization without suppression of the individual oscillations [Rosenblum
and Pikovsky (2004)]. Interestingly, delay in the coupling can seemingly change
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