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Floral morphogenesis: stochastic explorations of a gene network epigenetic landscape.

Alvarez-Buylla ER, Chaos A, Aldana M, Benítez M, Cortes-Poza Y, Espinosa-Soto C, Hartasánchez DA, Lotto RB, Malkin D, Escalera Santos GJ, Padilla-Longoria P - PLoS ONE (2008)

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: Instituto de Ecología, Universidad Nacional Autónoma de México, Cd. Universitaria, México, D. F., México. elena.alvarezbuylla@gmail.com

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.

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Effects of the choice of the relaxation time on Glass dynamics with noise.Two typical realizations of Glass dynamics for a given gene xn showing that the choices of the relaxation time τ and the perturbation time Δtp do not affect the qualitative dynamics, so long as Δtp>τ. Both trajectories started from the same initial conditions, and were followed through the same set of perturbations. The black trajectory corresponds to Δtp = 2.5 and τ = 1, whereas the red trajectory corresponds to Δtp = 2.5 and τ = 1/20.
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pone-0003626-g005: Effects of the choice of the relaxation time on Glass dynamics with noise.Two typical realizations of Glass dynamics for a given gene xn showing that the choices of the relaxation time τ and the perturbation time Δtp do not affect the qualitative dynamics, so long as Δtp>τ. Both trajectories started from the same initial conditions, and were followed through the same set of perturbations. The black trajectory corresponds to Δtp = 2.5 and τ = 1, whereas the red trajectory corresponds to Δtp = 2.5 and τ = 1/20.

Mentions: We have to choose the value of Δtp in such a way that the gene has enough time to relax to its new state after the perturbation has been produced. In other words, Δtp has to be larger (or at least of the same order of magnitude) than the relaxation time τ = α−1 appearing in Eq. (5). Figure 5 shows two typical noisy realizations of the temporal evolution of a particular xn(t) as a function of time, for two different choices of τ and Δtp: One for Δtp = 2.5 and τ = 1 (black curve), and the other for Δtp = 2.5 and τ = 1/20 (red curve). The two realizations started out from the same initial conditions, and underwent the same set of perturbations. The only difference was the value of τ. As can be seen from this figure, the trajectories are qualitatively the same as long as Δtp>τ. In what follows, we selected Δtp = 2.5 or 1 (Figures 6A and B, respectively), and τ = 1 to simulate Glass dynamics with noise (see methods for further details).


Floral morphogenesis: stochastic explorations of a gene network epigenetic landscape.

Alvarez-Buylla ER, Chaos A, Aldana M, Benítez M, Cortes-Poza Y, Espinosa-Soto C, Hartasánchez DA, Lotto RB, Malkin D, Escalera Santos GJ, Padilla-Longoria P - PLoS ONE (2008)

Effects of the choice of the relaxation time on Glass dynamics with noise.Two typical realizations of Glass dynamics for a given gene xn showing that the choices of the relaxation time τ and the perturbation time Δtp do not affect the qualitative dynamics, so long as Δtp>τ. Both trajectories started from the same initial conditions, and were followed through the same set of perturbations. The black trajectory corresponds to Δtp = 2.5 and τ = 1, whereas the red trajectory corresponds to Δtp = 2.5 and τ = 1/20.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC2572848&req=5

pone-0003626-g005: Effects of the choice of the relaxation time on Glass dynamics with noise.Two typical realizations of Glass dynamics for a given gene xn showing that the choices of the relaxation time τ and the perturbation time Δtp do not affect the qualitative dynamics, so long as Δtp>τ. Both trajectories started from the same initial conditions, and were followed through the same set of perturbations. The black trajectory corresponds to Δtp = 2.5 and τ = 1, whereas the red trajectory corresponds to Δtp = 2.5 and τ = 1/20.
Mentions: We have to choose the value of Δtp in such a way that the gene has enough time to relax to its new state after the perturbation has been produced. In other words, Δtp has to be larger (or at least of the same order of magnitude) than the relaxation time τ = α−1 appearing in Eq. (5). Figure 5 shows two typical noisy realizations of the temporal evolution of a particular xn(t) as a function of time, for two different choices of τ and Δtp: One for Δtp = 2.5 and τ = 1 (black curve), and the other for Δtp = 2.5 and τ = 1/20 (red curve). The two realizations started out from the same initial conditions, and underwent the same set of perturbations. The only difference was the value of τ. As can be seen from this figure, the trajectories are qualitatively the same as long as Δtp>τ. In what follows, we selected Δtp = 2.5 or 1 (Figures 6A and B, respectively), and τ = 1 to simulate Glass dynamics with noise (see methods for further details).

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: Instituto de Ecología, Universidad Nacional Autónoma de México, Cd. Universitaria, México, D. F., México. elena.alvarezbuylla@gmail.com

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.

Show MeSH