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ABSTRACT: We argue for the need of mathematical models as integrative tools for understanding processes of cell differentiation and
morphogenesis, involving the concerted action of multiple components at different spatiotemporal scales during plant development.
We propose dynamical models of gene regulatory networks (GRNs) as the basis for such means. Such models enable the identification
of specific steady-state gene expression patterns (attractors), which correspond to different cell types. A comparison between
discrete and continuous models is then presented, and we propose that the dynamical structure of a GRN subject to noise conceptually
corresponds to Waddington's “epigenetic landscape”. In the third section, we review methods to infer GRN topology from microarray
experiments. These include reverse engineering techniques such as Bayesian networks, mutual information, and continuous analysis
models. We discuss the application of these approaches to plant cases. However, detailed molecular biology experiments have
been very successful in deciphering the structure of underlying small networks. Therefore, we then focus our attention on
GRN models of such small modules for various processes of plant development. The first example corresponds to a single-cell
GRN for primordial cell specification during early stages of Arabidopsis thaliana flower development. Then, some examples of coupled GRN dynamics in spatiotemporal domains are recalled: cell differentiation
in A. thaliana leaf and root epidermis, and the spatiotemporal pattern of genes responsible for the apical shoot meristem behavior. Furthermore,
we consider models on auxin transport mechanisms that are sufficient to generate observed morphogenetic shoot and root patterns.
We also present several approaches to model signal transduction pathways that consider crosstalk among several biochemical
pathways, as well as the influence of environmental factors. In Section 1.5 we consider the constructive role of noise in
pattern formation in complex systems. We finally conclude that studies on GRN structure and dynamics aid at understanding
evolutionary morphological patterns.
12/2009: pages 3-20;
