Dynamics of the Genetic Regulatory Network for Arabidopsis thaliana Flower Morphogenesis (original) (raw)
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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.
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.
2011 IEEE Workshops of International Conference on Advanced Information Networking and Applications, 2011
This paper aims at warning modellers in systems biology against several traps encountered in the modelling of Boolean thresholded automata networks, i.e. the Hopfield-like networks that are often used in the context of neural and genetic networks. It introduces a new manner based on inverse methods to conceive such models. Using these techniques, we re-visit the model of regulatory network of Arabidopsis thaliana morphogenetic network. In this context, we discuss about the non-uniqueness of models, on a possible taxonomy of the set of valid models and on the sense of the relative size of the basin of attractions within or between these models.
A quantitative and dynamic model of the Arabidopsis flowering time gene regulatory network
PloS one, 2015
Various environmental signals integrate into a network of floral regulatory genes leading to the final decision on when to flower. Although a wealth of qualitative knowledge is available on how flowering time genes regulate each other, only a few studies incorporated this knowledge into predictive models. Such models are invaluable as they enable to investigate how various types of inputs are combined to give a quantitative readout. To investigate the effect of gene expression disturbances on flowering time, we developed a dynamic model for the regulation of flowering time in Arabidopsis thaliana. Model parameters were estimated based on expression time-courses for relevant genes, and a consistent set of flowering times for plants of various genetic backgrounds. Validation was performed by predicting changes in expression level in mutant backgrounds and comparing these predictions with independent expression data, and by comparison of predicted and experimental flowering times for s...
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.
A model comparison study of the flowering time regulatory network in Arabidopsis
BMC Systems Biology, 2014
Background: Several dynamic models of a gene regulatory network of the light-induced floral transition process in Arabidopsis have been developed to capture the behavior of gene transcription and infer predictions based on experimental observations. It has been proven that the models can make accurate and novel predictions, which generate testable hypotheses. Two major issues were addressed in this study. First, construction of dynamic models for gene regulatory networks requires the use of mathematic modeling that comprises equations of a large number of parameters. Second, the binding mechanism of the transcription factor with DNA is another factor that requires detailed modeling. The first issue was tackled by adopting an optimization algorithm, and the second was addressed by comparing the performance of three alternative modeling approaches, namely the S-system, the Michaelis-Menten model and the Mass-action model. The efficiencies of parameter estimation and modeling performance were calculated based on least square error (O(p)), mean relative error (MRE) and Akaike Information Criterion (AIC). Results: We compared three models to describe gene regulation of the flowering transition process in Arabidopsis. The Mass-action model is the simplest and has the least parameters. It is therefore less computation-intensive with the smallest AIC value. The disadvantage, however, is that it assumes the system is simply a second order reaction which is not the case in our study. The Michaelis-Menten model also assumes the system is homogeneous and ignores the intracellular protein transport process. The S-system model has the best performance and it does describe the diffusion effects. A disadvantage of the S-system is that it involves the most parameters. The largest AIC value also implies an over-fitting may occur in parameter estimation. Conclusions: Three dynamic models were adopted to describe the dynamics of the gene regulatory network of the flowering transition process in Arabidopsis. Based on MRE, the least square error and global sensitivity analysis, the S-system has the best performance. However, the fact that it has the highest AIC suggests an over-fitting may occur in parameter estimation. The result of this study may need to be applied carefully when modeling complex gene regulatory networks.
Mathematical modelling of Arabidopsis flowering time gene regulatory network
2018
Experimental studies of the flowering of Arabidopsis Thaliana have shown that a large complex gene regulatory network (GRN) is responsible for its regulation. This process has recently been modelled with deterministic differential equations by considering the interactions between gene activators and inhibitors [Valentim et al., 2015, van Mourik et al., 2010]. However, due to the complexity of the models, the properties of the network and the roles of the individual genes cannot be deduced from the numerical solution the published work offers. In this study, deterministic and stochastic dynamic models of Arabidopsis flowering GRN are considered by following the deterministic delayed model introduced in [Valentim et al., 2015]. A stable solution of this model is sought by its linearisation, which contributes to further investigation of the role of the individual genes to the flowering. By decoupling some concentrations, the system has been reduced to emphasise the role played by the t...
Modelling gene networks controlling transition to flowering in Arabidopsis
2004
Flowering is a critical stage in plant development that initiates grain production and is vulnerable to stress. The genes controlling flowering time in the model plant Arabidopsis thaliana are reviewed. Previously, interactions between these genes were described by qualitative network diagrams. We present a generalized mathematical formalism that relates environmentally dependent transcription, RNA processing, translation, and protein-protein interaction rates to resultant phenotypes. We have developed models (reported elsewhere) based on this concept that simulate flowering times for novel A. thaliana genotype-environment combinations and critical short day lengths (CSDL) in rice (Oryza sativa ssp. japonica cv. Nipponbare). Here we show how CSDL phenotypes emerge from gene expression dynamics. Functionally different but homologous photoperiod measurement genes in rice and A. thaliana nevertheless yield similar results. Other technologies for interrelating genotypes, phenotypes, and the environment are crop simulation models and the theory of quantitative genetics (QG). Some potential synergies between genetic networking (GN) and these older approaches are discussed. Twelve contrasts are drawn between QG and GN revealing that both have equal contributions to make to an ideal theory. Such a theory is initiated by discussing epistasis, dominance, and additivity (all QG basics) in GN terms. Three or less genes can account for the first two but additivity is a complex property dependent on the structure and function of entire subnets. Finally, the utility of simple models is evidenced by 80 years of quantitative genetics and mathematical ecology. Media summary Mathematical studies of plants whose genomes have been deciphered are leading to new insights regarding theories that have underpinned crop breeding efforts for many decades.
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.