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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.

Show MeSH
Changes in the basins of attraction of the continuous model with respect to the Boolean model.Color map of the probability P(n/m) that a microscopic configuration whose associated Boolean configuration belongs to the basin of attraction of attractor m, ends up in attractor n using Glass dynamics. Note that the main transitions occur along the diagonal where attractors are reached by both dynamics (Boolean and Glass); however, the non-diagonal elements indicate that two microscopic configurations that correspond to the same Boolean configuration may end up in different attractors.
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pone-0003626-g004: Changes in the basins of attraction of the continuous model with respect to the Boolean model.Color map of the probability P(n/m) that a microscopic configuration whose associated Boolean configuration belongs to the basin of attraction of attractor m, ends up in attractor n using Glass dynamics. Note that the main transitions occur along the diagonal where attractors are reached by both dynamics (Boolean and Glass); however, the non-diagonal elements indicate that two microscopic configurations that correspond to the same Boolean configuration may end up in different attractors.

Mentions: Even when the Boolean dynamics and the Glass dynamics produce the same ten attractors, their basins of attraction do change from one model to the other. This is so because two different initial microscopic configurations that correspond to the same Boolean configuration may end up in two different attractors under the Glass dynamics. In order to show that this is indeed the case, for each of the Ω = 2N Boolean configurations of the network, we probed 10,000 compatible microscopic configurations. We evolved these 10,000 microscopic configurations in time until an attractor was reached, and determined the configuration in which the network fell. Figure 4 depicts in a color map the probability PG(n/m) that the network ends up in attractor n under the Glass dynamics, given that it started in a microscopic configuration whose corresponding Boolean configuration was in the basin of attraction of attractor m. As can be seen, the highest probabilities lie along the diagonal; however, the non-vanishing off-diagonal elements indicate that two different microscopic configurationss corresponding to the same Boolean configuration may end up in two different attractors.


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)

Changes in the basins of attraction of the continuous model with respect to the Boolean model.Color map of the probability P(n/m) that a microscopic configuration whose associated Boolean configuration belongs to the basin of attraction of attractor m, ends up in attractor n using Glass dynamics. Note that the main transitions occur along the diagonal where attractors are reached by both dynamics (Boolean and Glass); however, the non-diagonal elements indicate that two microscopic configurations that correspond to the same Boolean configuration may end up in different attractors.
© Copyright Policy
Related In: Results  -  Collection

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

pone-0003626-g004: Changes in the basins of attraction of the continuous model with respect to the Boolean model.Color map of the probability P(n/m) that a microscopic configuration whose associated Boolean configuration belongs to the basin of attraction of attractor m, ends up in attractor n using Glass dynamics. Note that the main transitions occur along the diagonal where attractors are reached by both dynamics (Boolean and Glass); however, the non-diagonal elements indicate that two microscopic configurations that correspond to the same Boolean configuration may end up in different attractors.
Mentions: Even when the Boolean dynamics and the Glass dynamics produce the same ten attractors, their basins of attraction do change from one model to the other. This is so because two different initial microscopic configurations that correspond to the same Boolean configuration may end up in two different attractors under the Glass dynamics. In order to show that this is indeed the case, for each of the Ω = 2N Boolean configurations of the network, we probed 10,000 compatible microscopic configurations. We evolved these 10,000 microscopic configurations in time until an attractor was reached, and determined the configuration in which the network fell. Figure 4 depicts in a color map the probability PG(n/m) that the network ends up in attractor n under the Glass dynamics, given that it started in a microscopic configuration whose corresponding Boolean configuration was in the basin of attraction of attractor m. As can be seen, the highest probabilities lie along the diagonal; however, the non-vanishing off-diagonal elements indicate that two different microscopic configurationss corresponding to the same Boolean configuration may end up in two different attractors.

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