Abstract
In contrast to the classical view of development as a preprogrammed and deterministic process, recent studies have demonstrated that stochastic perturbations of highly non-linear systems may underlie the emergence and stability of biological patterns. Herein, we address the question of whether noise contributes to the generation of the stereotypical temporal pattern in gene expression during flower development. We modeled the regulatory network of organ identity genes in the Arabidopsis thaliana flower as a stochastic system. This network has previously been shown to converge to ten fixed-point attractors, each with gene expression arrays that characterize inflorescence cells and primordial cells of sepals, petals, stamens, and carpels. The network used is binary, and the logical rules that govern its dynamics are grounded in experimental evidence. We introduced different levels of uncertainty in the updating rules of the network. Interestingly, for a level of noise of around 0.5–10%, the system exhibited a sequence of transitions among attractors that mimics the sequence of gene activation configurations observed in real flowers. We also implemented the gene regulatory network as a continuous system using the Glass model of differential equations, that can be considered as a first approximation of kinetic-reaction equations, but which are not necessarily equivalent to the Boolean model. Interestingly, the Glass dynamics recover a temporal sequence of attractors, that is qualitatively similar, although not identical, to that obtained using the Boolean model. Thus, time ordering in the emergence of cell-fate patterns is not an artifact of synchronous updating in the Boolean model. Therefore, our model provides a novel explanation for the emergence and robustness of the ubiquitous temporal pattern of floral organ specification. It also constitutes a new approach to understanding morphogenesis, providing predictions on the population dynamics of cells with different genetic configurations during development.
Highlights
A stochastic Boolean model of the Gene regulatory network (GRN) enables the study of transitions among network attractors
We first present the results obtained from the Boolean model of the GRN, and we present the equivalent results obtained from a continuous model
The state of expression of the genes in the entire network, is represented by a vector with the set of Boolean variables {x1,x2,...,xN}, where xn is the state of expression of the nth gene and N is the total number of genes in the network
Summary
‘‘All [the] epistemological value of the theory of probability is based on this: That large scale random phenomena in their collective action create strict, non random regularity’’. A floral meristem is sequentially partitioned into four regions, from which the floral organ primordia are formed and eventually give rise to sepals in the outermost whorl, to petals in the second whorl, stamens in the third, and carpels in the fourth whorl in the central part of the flower (Figures 1B and C) This spatio-temporal sequence is widely conserved among the quarter of a million flowering plant species [11]; the dynamic mechanisms underlying this robust pattern are not yet understood. The obtained results demonstrate that noise alone is able to drive transitions among attractors with temporal patterns that mimic the sequence with which ABC-genes are activated (first A genes, B genes, and the C gene) during early flower development [13] These results are in line with the finding that the GRN in question is a robust developmental module that is widely conserved among flowering plant species [3]. The results presented support the idea that random fluctuations in a system may be important for physiological adaptation, plasticity, and cell differentiation (examples in: [14,15,16,17,18,19,20,21,22,23,24])
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