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5.5.1. A GRN underlying cell-fate determination during
early stages of ower development
We postulate Boolean models in which genes or proteins (GRN nodes) may attain
two values: 0 (OFF) or 1 (ON). The activity of each gene or protein depends on
updating logical Boolean functions grounded on experimental data. Such models
have been successful at recovering observed gene expression arrays in animal and
plant cells [von Dassow et al. (2000); Albert and Othmer (2003); Espinosa-Soto et al.
(2004)]. Discrete models are further justied because recent experimental evidence
is suggesting that gene expression is digital and stochastic at the individual cell
level, rather than continuous [Hume (2000); Ozbudak et al. (2002); Elowitz et al.
(2002); Blake et al. (2003); Paulsson (2004); Walters et al. (1995); Fiering et al.
(2000); Ho et al. (1996)]. As discussed in Sect. 5.1, random Boolean networks
(RBN) have successfully described in a qualitative way several important aspects
of gene regulation and cell dierentiation. But, in any case, it is important to work
with experimentally grounded GRNs.
In this particular case, the rules are derived from experimental data, see
Espinosa-Soto et al. (2004); Chaos et al. (2006). A particular Boolean GRN has
a 2
N
possible gene expression congurations or states, where N is the number of
nodes. Each state leads to another state or to itself in which case such state is a
point attractor (steady state). A system may have more than one attractor and,
eventually, all initial states will reach an attractor. The set of all states that lead
to a specic attractor correspond to the basin of that attractor. The basins of at-
traction and attractors of a GRN depend on the number of elements, the number
of possible states of each element, the topology of the network, and on the logical
rules of each gene. Consequently, the dynamics of the system is deterministic, in
which the fates of all states are known.
We have proposed a 15-node GRN that includes the ABC and non-ABC genes.
This model attains only ten xed-point attractors: four correspond to congura-
tions characteristic of the inorescence meristem, and the rest correspond to con-
gurations of primordial sepal (one attractor), petal (two attractors), stamen (two
attractors) and carpel (one attractor). These results suggested that the proposed
GRN model incorporates the key components of a developmental module or subnet-
work that underlies the combinatorial gene activities predicted in the ABC model
(Fig. 5.6).
In conclusion the proposed GRN provides a dynamical explanation for the ABC
model. It also shows that precise signaling pathways are not required to restrain
organ primordia cell types during A. thaliana ower development, but rather that
cell-fate are determined by overall gene network topology and dynamics. This was
conrmed by robustness analyses of random perturbations of gene interaction pa-
rameters and by the fact that a three-state and the Boolean GRN yielded the same
attractors [Espinosa-Soto et al. (2004); Chaos et al. (2006)]. It is likely that new
components are part of the uncovered module. But new components of mechanistic
