Limits...
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

Related in: MedlinePlus

Heat map of the similarity matrix among the ten attractors of the GRN.A strict consensus phenogram was obtained for the GRN attractors (vectors of zeros and ones) by using the Manhattan distance similarity index (see Methods). This phenogram is shown below the attractors that are ordered along the X and Y axes of the heat map. Attractors that group together had the highest similarity indexes between them (i.e. the lowest Manhattan distance). Color scale: darker colors indicate more similar, while lighter ones indicate more different attractors in the pairs compared.
© Copyright Policy
Related In: Results  -  Collection


getmorefigures.php?uid=PMC2572848&req=5

pone-0003626-g002: Heat map of the similarity matrix among the ten attractors of the GRN.A strict consensus phenogram was obtained for the GRN attractors (vectors of zeros and ones) by using the Manhattan distance similarity index (see Methods). This phenogram is shown below the attractors that are ordered along the X and Y axes of the heat map. Attractors that group together had the highest similarity indexes between them (i.e. the lowest Manhattan distance). Color scale: darker colors indicate more similar, while lighter ones indicate more different attractors in the pairs compared.

Mentions: In the simulations of the stochastic versions of the GRN presented in this work, we did not consider the inflorescence attractors (I1–I4) because they are substantially separated from the floral primordia attractors. The distance between the two sets of attractors (inflorescence and floral) is clearly depicted by the way they are grouped in a phenogram (Figure 2). This is a branching diagram that groups entities according to their similarity (see Methods). The inflorescence meristem and floral organ primordia attractors cluster into two clearly distinct groups (Figure 2). Indeed, in simulations that considered all of the attractors, we found that, for a wide range of noise levels, the system never leaped out of the inflorescence attractors. On the other hand, when large noise magnitudes were considered, the system went from the inflorescence attractors to the carpel or stamen attractors, without visiting the sepal and petal attractors. Dismissing the I1–I4 attractors in the simulations allows for a better exploration of the temporal pattern in which the attractors corresponding to each of the four floral organ primordial cells are attained.


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)

Heat map of the similarity matrix among the ten attractors of the GRN.A strict consensus phenogram was obtained for the GRN attractors (vectors of zeros and ones) by using the Manhattan distance similarity index (see Methods). This phenogram is shown below the attractors that are ordered along the X and Y axes of the heat map. Attractors that group together had the highest similarity indexes between them (i.e. the lowest Manhattan distance). Color scale: darker colors indicate more similar, while lighter ones indicate more different attractors in the pairs compared.
© Copyright Policy
Related In: Results  -  Collection

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

pone-0003626-g002: Heat map of the similarity matrix among the ten attractors of the GRN.A strict consensus phenogram was obtained for the GRN attractors (vectors of zeros and ones) by using the Manhattan distance similarity index (see Methods). This phenogram is shown below the attractors that are ordered along the X and Y axes of the heat map. Attractors that group together had the highest similarity indexes between them (i.e. the lowest Manhattan distance). Color scale: darker colors indicate more similar, while lighter ones indicate more different attractors in the pairs compared.
Mentions: In the simulations of the stochastic versions of the GRN presented in this work, we did not consider the inflorescence attractors (I1–I4) because they are substantially separated from the floral primordia attractors. The distance between the two sets of attractors (inflorescence and floral) is clearly depicted by the way they are grouped in a phenogram (Figure 2). This is a branching diagram that groups entities according to their similarity (see Methods). The inflorescence meristem and floral organ primordia attractors cluster into two clearly distinct groups (Figure 2). Indeed, in simulations that considered all of the attractors, we found that, for a wide range of noise levels, the system never leaped out of the inflorescence attractors. On the other hand, when large noise magnitudes were considered, the system went from the inflorescence attractors to the carpel or stamen attractors, without visiting the sepal and petal attractors. Dismissing the I1–I4 attractors in the simulations allows for a better exploration of the temporal pattern in which the attractors corresponding to each of the four floral organ primordial cells are attained.

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
Related in: MedlinePlus