Flower Development as an Interplay between Dynamical Physical Fields and Genetic Networks (original) (raw)
Related papers
Floral Morphogenesis: Stochastic Explorations of a Gene Network Epigenetic Landscape
PLOS One, 2008
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.
Journal of Theoretical Biology, 2010
The Arabidopsis thaliana flower organ specification gene regulatory network (FOS-GRN) has been modeled previously as a discrete dynamical system, recovering as steady states configurations that match the genetic profiles described in primordial cells of inflorescence, sepals, petals, stamens and carpels during early flower development. In this study, we first update the FOS-GRN by adding interactions and modifying some rules according to new experimental data. A discrete model of this updated version of the network has a dynamical behavior identical to previous versions, under both wild type and mutant conditions, thus confirming its robustness. Then, we develop a continuous version of the FOS-GRN using a new methodology that builds upon previous proposals. The fixed point attractors of the discrete system are all observed in the continuous model, but the latter also contains new steady states that might correspond to genetic activation states present briefly during the early phases of flower development. We show that both the discrete and the continuous models recover the observed stable gene configurations observed in the inflorescence meristem, as well as the primordial cells of sepals, petals, stamens and carpels. Additionally, both models are subjected to perturbations in order to establish the nature of additional signals that may suffice to determine the experimentally observed order of appearance of floral organs. Our results thus describe a possible mechanism by which the network canalizes molecular signals and/or noise, thus conferring robustness to the differentiation process.
From Genes to Flower Patterns and Evolution: Dynamic Models of Gene Regulatory Networks
Journal of Plant Growth Regulation, 2006
Genes and proteins form complex dynamical systems or gene regulatory networks (GRN) that can reach several steady states (attractors). These may be associated with distinct cell types. In plants, the ABC combinatorial model establishes the necessary gene combinations for floral organ cell specification. We have developed dynamic gene regulatory network (GRN) models to understand how the combinatorial selection of gene activity is established during floral organ primordia specification as a result of the concerted action of ABC and non-ABC genes. Our analyses have shown that the floral organ specification GRN reaches six attractors with gene configurations observed in primordial cell types during early stages of flower development and four that correspond to regions of the inflorescence meristem. This suggests that it is the overall GRN dynamics rather than precise signals that underlie the ABC model. Furthermore, our analyses suggest that the steady states of the GRN are robust to random alterations of the logical functions that define the gene interactions. Here we have updated the GRN model and have systematically altered the outputs of all the logical functions and addressed in which cases the original attractors are recovered. We then reduced the original three-state GRN to a two-state (Boolean) GRN and performed the same systematic perturbation analysis. Interestingly, the Boolean GRN reaches the same number and type of attractors as reached by the three-state GRN, and it responds to perturbations in a qualitatively identical manner as the original GRN. These results suggest that a Boolean model is sufficient to capture the dynamical features of the floral network and provide additional support for the robustness of the floral GRN. These findings further support that the GRN model provides a dynamical explanation for the ABC model and that the floral GRN robustness could be behind the widespread conservation of the floral plan among eudicotyledoneous plants. Other aspects of evolution of flower organ arrangement and ABC gene expression patterns are discussed in the context of the approach proposed here.
Dynamics of the Genetic Regulatory Network for Arabidopsis thaliana Flower Morphogenesis
Journal of Theoretical Biology, 1998
We present a network model and its dynamic analysis for the regulatory relationships among 11 genes that participate inArabidopsis thalianaflower morphogenesis. The topology of the network and the relative strengths of interactions among these genes were based on published genetic and molecular data, mainly relying on mRNA expression patterns under wild type and mutant backgrounds. The network model is made of binary elements and we used a particular dynamic implementation for the network that we call semi-synchronic. Using this method the network reaches six attractors; four of them correspond to observed patterns of gene expression found in the floral organs ofArabidopsis(sepals, petals, stamens and carpels) as predicted by the ABC model of flower morphogenesis. The fifth state corresponds to cells that are not competent to flowering, and the sixth attractor predicted by the model is never found in wild-type plants, but it could be induced experimentally. We discuss the biological implications and the potential use of this network modeling approach to integrate functional data of regulatory genes of plant development.
Plant Cell, 2004
Flowers are icons in developmental studies of complex structures. The vast majority of 250,000 angiosperm plant species have flowers with a conserved organ plan bearing sepals, petals, stamens, and carpels in the center. The combinatorial model for the activity of the so-called ABC homeotic floral genes has guided extensive experimental studies in Arabidopsis thaliana and many other plant species. However, a mechanistic and dynamical explanation for the ABC model and prevalence among flowering plants is lacking. Here, we put forward a simple discrete model that postulates logical rules that formally summarize published ABC and non-ABC gene interaction data for Arabidopsis floral organ cell fate determination and integrates this data into a dynamic network model. This model shows that all possible initial conditions converge to few steady gene activity states that match gene expression profiles observed experimentally in primordial floral organ cells of wild-type and mutant plants. Therefore, the network proposed here provides a dynamical explanation for the ABC model and shows that precise signaling pathways are not required to restrain cell types to those found in Arabidopsis, but these are rather determined by the overall gene network dynamics. Furthermore, we performed robustness analyses that clearly show that the cell types recovered depend on the network architecture rather than on specific values of the model's gene interaction parameters. These results support the hypothesis that such a network constitutes a developmental module, and hence provide a possible explanation for the overall conservation of the ABC model and overall floral plan among angiosperms. In addition, we have been able to predict the effects of differences in network architecture between Arabidopsis and Petunia hybrida.
Spatial pattern formation in the flower of Arabidopsis thaliana: mathematical modeling
Doklady biological sciences : proceedings of the Academy of Sciences of the USSR, Biological sciences sections / translated from Russian
The research into the genetic control of flower formation is a rapidly evolving field of plant developmental biology. An ABC model of the genetic control of floral morphogenesis based on the studies of Arabidopsis thaliana mutants [1] envisaged the flower structure as a pattern comprising four organ whorls, with the particular organ development in each whorl specified by the combined activities of several genes. The expression of the A class genes APETALA1 ( AP1 ) and APETALA2 ( AP2 ) determines for the development of sepals (whorl 1). The development of carpels (whorl 4) is specified by the C class gene AGAMOUS ( AG ). The combined activities of the A and C genes together with the B genes APETALA3 ( AP 3 ) and PISTILLATA ( PI ) specify the development of petals and stamens (whorls 2 and 3, respectively). The ABC model postulates that the mutations in these genes would change the organ specificity in particular whorls. In several ABC mutants, the number of flower organs is changed; therefore a hypothesis was put forward that these genes specify both the identity of flower organs and flower organ initiation [2]. However, the mechanism of such specification is poorly understood. When working out the mathematical model of floral development based on the ABC-model postulates, we found that the existing evidence on the functions of the ABC genes did not sufficiently clarify the nature of changes in the arrangement of flower organs in the mutants. It follows that the processes that determine spatial pattern formation in the flower must be studied in more detail .
The Arabidopsis Book …, 2010
Some of the authors of this publication are also working on these related projects: evolution of gene networks regulating carpel development View project A computational model for angiogenesis and hemodynamics View project Adriana Corvera Universidad Nacional Autónoma de México 5 PUBLICATIONS 99 CITATIONS SEE PROFILE
BMC Systems Biology, 2015
Background: Gene regulatory network (GRN) dynamical models are standard systems biology tools for the mechanistic understanding of developmental processes and are enabling the formalization of the epigenetic landscape (EL) model. Methods: In this work we propose a modeling framework which integrates standard mathematical analyses to extend the simple GRN Boolean model in order to address questions regarding the impact of gene specific perturbations in cell-fate decisions during development. Results: We systematically tested the propensity of individual genes to produce qualitative changes to the EL induced by modification of gene characteristic decay rates reflecting the temporal dynamics of differentiation stimuli. By applying this approach to the flower specification GRN (FOS-GRN) we uncovered differences in the functional (dynamical) role of their genes. The observed dynamical behavior correlates with biological observables. We found a relationship between the propensity of undergoing attractor transitions between attraction basins in the EL and the direction of differentiation during early flower development-being less likely to induce upstream attractor transitions as the course of development progresses. Our model also uncovered a potential mechanism at play during the transition from EL basins defining inflorescence meristem to those associated to flower organs meristem. Additionally, our analysis provided a mechanistic interpretation of the homeotic property of the ABC genes, being more likely to produce both an induced inter-attractor transition and to specify a novel attractor. Finally, we found that there is a close relationship between a gene's topological features and its propensity to produce attractor transitions. Conclusions: The study of how the state-space associated with a dynamical model of a GRN can be restructured by modulation of genes' characteristic expression times is an important aid for understanding underlying mechanisms occurring during development. Our contribution offers a simple framework to approach such problem, as exemplified here by the case of flower development. Different GRN models and the effect of diverse inductive signals can be explored within the same framework. We speculate that the dynamical role of specific genes within a GRN, as uncovered here, might give information about which genes are more likely to link a module to other regulatory circuits and signaling transduction pathways.
Continuous-time modeling of cell fate determination in Arabidopsis flowers
BMC Systems Biology, 2010
Background: The genetic control of floral organ specification is currently being investigated by various approaches, both experimentally and through modeling. Models and simulations have mostly involved boolean or related methods, and so far a quantitative, continuous-time approach has not been explored.
22nd International Conference on Advanced Information Networking and Applications - Workshops (aina workshops 2008), 2008
Variations of fixed boundary conditions have been proven to have a significant influence in dynamical biological systems following a Hop-field-like rule such as genetic regulatory and neural networks. Classically, theoretical studies focusing on biological systems are based on toric networks, which does not seem to be coherent with the biological reality. We think that the dynamics of biological networks is also regulated by fixed boundaries, illustrated for instance by external magnetic fields, chemical potentials or environmental constraints. The aim of this paper is to go further in the study of the impact of fixed boundary conditions by showing that they significantly affect the relative size of certain basins of attraction. We argue that this is a critical point in real biological networks by giving an example of boundary influence in the genetic regulatory network of the flower's morphogenesis of the plant Arabidopsis thaliana.