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the dierent cells. After its conception, the repressilator immediately has become a
milestone example of how natural dynamical processes can be mimicked within cells
through the design of articial circuits built from standard genetic parts. Other ex-
amples of such genetic gene circuits included a toggle switch [Gardner et al. (2000)],
a metabolic relaxator [Fung et al. (2005)], or a relaxation oscillator [Atkinson et al.
(2003)].
Natural genetic networks, however, do not usually operate in isolation. Not
only in multicellular higher organisms, but even in bacterial populations, cells con-
spicuously communicate among each other by dierent means, e.g. electrically or
chemically. A particularly useful (and common) means of communication between
bacteria is quorum sensing, which relies on the relatively free diusion of small
molecules, known as autoinducers, through the bacterial membrane. When such
an autoinducer is part of a feedback loop that regulates the expression of certain
genes, bacteria are able to determine the local density of similar cells around them
by monitoring the level of expression of these autoinducer-controlled genes [Miller
and Bassler (2001)]. An example of this mechanism is provided by the Lux system,
used by the bacterium Vibrio scheri to provide bioluminiscence only when the
bacterial density is high (which happens within specialized light organs of certain
marine organisms with whom the bacteria live in symbiosis).
Cell-cell coupling often leads to exceptional examples of cooperative behavior.
In order to understand how such collective phenomena emerge from passive inter-
cellular communication, it seems natural to make use of the synthetic approaches
described above. The Lux system described above has been used, for instance, as a
communication module to build a synthetic mechanism for programmed population
control in a bacterial population [You et al. (2004)]. In this Chapter, we review
recent developments that are helping us to understand the rich dynamical behavior
that can be produced in coupled synthetic gene networks. We concentrate on two
dierent types of genetic oscillators, the repressilator and a relaxator oscillator, and
consider two dierent types of coupling, namely a phase-attractive and a phase-
repulsive coupling, both resulting from the autoinducer diusion. As we will see,
many dierent dynamical scenarios arise from these types of coupling, including
multistability, oscillation death, and quantized cycling, among others.
3.2. Coupled Repressilators
As mentioned above, the repressilator is a synthetic network of three genes whose
products inhibit the transcription of each other cyclically [Elowitz and Leibler
(2000)] (see left module of Fig. 3.1). A readout module using uorescent proteins
provides access to the time-resolved dynamics of the repressilator proteins. Exper-
iments reveal oscillations with a period of the order of an hour, i.e. slower than the
cell-division cycle. The limited number of interacting genes and proteins and the
well-understood interactions between them enable a precise theoretical description
of this oscillator by means of coupled dierential equations.
