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operating according either to rule 232 or according to a randomly selected rule.
The inclusion of such randomness leads to a progressive decrease in the richness
of the phase space of the system. We found that with as many as 1/4th of all
units operating according to random Boolean functions the model still displays a
rich phase space, including white, 1=f, and Brownian noise. But, if more than
1/4th of all the units operate according to randomly selected Boolean functions,
then the phase-space displays mostly white-noise dynamics, due to an increase in
the randomness of the system. Additionally, we explored the existing dynamical
behaviors for systems composed of units operating according to either rule 232 or
rule 50. When both rules are present in the system (and at least 50% of the units
operate according to rule 232) we still found several distinct classes of dynamical
behaviors, including a wide range of parameter values that generate 1=f noise.
5.5. Dynamics in Real Genetic Regulatory Networks
Given the rich dynamical behavior in response to noise that depends on the topology
and logical rules assumed, it becomes then very interesting to address the behavior
of real GRN. Thus, in this section we present the same type of analysis done above
for simple model networks, for the GRN underlying cell-fate determination during
early stages of ower development (herein: oral GRN) in Arabidopsis thaliana
(Fig. 5.6). This plant is the experimental system for molecular genetic studies.
Plants share many more aspects of their basic molecular components and regulatory
circuits with animals than thought before (Jones et al., 2008). But their cellular
structure is simpler than that of animals and are thus useful systems to scale from
the structure and function of GRN, to cell-fate determination and the emergence of
multicellular and morphogenetic patterns and dynamics in vivo. We focus here on
a GRN that underlies cell fate determination at early stages of ower development.
Flowers are the reproductive and most complex structures of plants. They are
characteristic of the most recently evolved lineage of plant species: the owering
plants or angiosperms. In contrast to animals, plant structures are formed along
their complete life cycles from groups of undierentiated cells, called meristems.
These are useful structures for in vivo studies of the dynamics of cell-fate deter-
mination. Upon induction to owering, the shoot apical meristem, from which the
aerial parts of plants are formed, turns into an inorescence meristem, from which
anks, ower meristems are produced. Adult oral morphology originates from
these oral meristems or buds originally constituted of undierentiated cells. Dur-
ing the three rst days after emergence from the inorescence anks, oral buds
are partitioned into four regions. Each one comprises the primordial cells of sepals,
petals, stamens and carpels, that are the four types of organs which characterize
the great majority of owers (Fig. 5.6). In fact, these organs are formed also in
a spatio-temporal stereotypical fashion from the outermost to the ower center:
rst sepals, then petals, stamens and nally carpels in the center [Bowman (1994)].
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