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Section: New Results
Multi-scale models and analysis: from cells to plant architecture (and back)
Modeling water transport in roots
Participants : Mikaël Lucas [IRD] , Christophe Pradal, Christophe Godin, Christophe Maurel [BPMP] .
This research theme is supported by the ANR project HydroRoot.
A model of Arabidopsis thaliana root hydraulics at the cellular level was developped in the OpenAlea modeling platform. The model relies on the integration throughout root architecture of elementary hydraulic components. Each component integrates local radial and axial water flows. Axial hydraulic conductivity is calculated according to Poiseuille’s law, based on local size of xylem vessels. Radial hydraulic conductivity is determined in part by aquaporin activity and was set constant throughout root architecture in the first model versions. In its current state, the model is parameterized using architectural, tissular and physiological data that were experimentally determined in the Aquaporin group at BPMP. The architectural reconstruction of the root system is based on a tridimensional multi-scale tree graph (MTG). The current model is capable of predicting the water flow that is transported by a root system in the standard experimental conditions used in the Aquaporin group. This model was used to perform sensitivity analyses and determine the respective contributions to root hydraulic dynamics of various biological parameters (axial and radial hydraulic conductivites, root architecture). One major finding is that the root hydraulic conductivity (Lpr) computed from the model is highly dependent on root architecture. This is due to the limiting role of axial (xylem) conductance, one feature that had been neglected in previous representations of root water transport. The radial hydraulic conductivity may primarily be limiting in conditions of Lpr inhibition, since its increase from values in control roots has marginal effects on Lpr. A new set of experimental data including root diameter repartitions in wild-type plants, and xylem vessel diameters in mutants with altered xylem morphology (irx3, esk1) will be used to implement the model. Root cell hydraulic conductivities will also be measured in these and aquaporin mutant phenotypes. Our aim is to check whether, based on anatomical and morphological data, the model can properly predict the radial hydraulic conductivity of these genotypes.
Mechanical modeling of fruit growth
Participants : Ibrahim Cheddadi [Inra, Avignon] , Mik Cieslak [U. Calgary] , Frédéric Boudon, Valentina Baldazzi [Inra, Avignon] , Nadia Bertin [Inra, Avignon] , Michel Genard [Inra, Avignon] , Christophe Godin.
This research theme is supported by the Agropolis project MecaFruit3D.
Understanding the controlling factors of fruit quality development is challenging, because fruit quality results from the interplay between physical and physiological processes that are under the control of genes and the environment. Although process-based models have been used to make significant progress in understanding these factors, they ignored to a large extent the shape and internal structure of the fruit, as well as mechanical interactions between tissue parts that are essential to properly model growth.
To help characterizing the effects of fruit shape and internal structure on quality, the creation of a 3D virtual fruit model that integrates fruit structure and function with growth governed by environmental inputs is being investigated, combining two tools previously developed in the team: on the one hand, a modeling pipeline that creates a 3D volumetric mesh of the internal fruit structure, including vasculature (see section 3 ), and couples it with water and carbon transport; on the other hand, a mechanical description of the growth of plant tissues (see section 6.3.3 ): growth is related to the extension of the cell walls, which is triggered when the so-called turgor pressure inside the cells exceeds a given threshold. The global shape of the tissue integrates mechanically all the local deformations of each cell.
In order to couple these two aspects of plant growth, we describe how volume variations are constrained by fluxes of matter, and how these fluxes depend on mechanical and physiological parameters. The corresponding set of equations are resolved thanks to the SOFA finite elements software.
This approach will be applied to study tomato fruit. Once the model is calibrated and evaluated, our approach will be suitable for studying the effects of internal fruit heterogeneity and overall shape on fruit quality development.
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Analyzing root growth and branching
Participants : Beatriz Moreno Ortega, Sixtine Passot, Yann Guédon, Laurent Laplaze [IRD, DIADE] , Mikaël Lucas [IRD, DIADE] , Bertrand Muller [INRA, LEPSE] .
This research theme is supported by two PhD programmes.
New 2D and 3D root phenotyping plateforms are emerging with associated image analysis toolbox (e.g. SmartRoot). The analysis of complex root phenotyping data is thus a new challenge in developmental biology.
We aim at developing a pipeline of methods for analyzing root systems at three scales:
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tissular scale to identify and characterize the meristem, elongation and mature zones along a root using piecewise heteroscedastic linear models,
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individual root scale to analyze the dynamics of root elongation,
This pipeline of analysis methods will be applied to different species (maize, millet and arabidopsis) and for different biological objectives (study of genetic diversity for millet and of metabolic and hormonal controls of morphogenesis for maize).
Analyzing shoot and leaf elongation
Participants : Maryline Lièvre, Yann Guédon, Leo Guignard, Christine Granier [INRA, LEPSE] .
This research theme is supported by one PhD programme.
This study is based on the observation of a lack of methods enabling the integrated analysis of the processes controlling the vegetative development in Arabidopsis thaliana. We developed a pipeline of analysis methods combining image analysis techniques and statistical models to integrate the measurements made at the leaf and shoot scales. Semi-Markov switching models were built for different genotypes, allowing a more thorough characterization of the studied mutants. These models validated the hypothesis that the rosette can be structured into successive developmental phases that could change depending on the genotype. They also highlighted the structuring role of the abaxial trichome trait, although the developmental phases cannot be explained entirely by this trait. We developed a second pipeline of analysis methods combining a semi-automatic method for segmenting leaf epidermis images based on the ilastik software, and the analysis of the obtained cell areas using a gamma mixture model whose parameters of gamma components are tied by a scaling rule. This model allowed us to estimate the distribution of the number of endocycles. We highlighted in this way that the mean number of endocycles changes drastically with leaf rank. Finally, we built a multi-scale model that integrates tissular, morphological, dynamical and dimension traits for each successive leaf along the shoot. This model gave us for the first time an integrative view of the development of the Arabidopsis rosette.
Analyzing perturbations in Arabidopsis thaliana phyllotaxis
Participants : Yassin Refahi, Fabrice Besnard, Yann Guédon, Christophe Godin, Etienne Farcot, Teva Vernoux [RDP, ENS] .
This research theme has been supported by iSam, IBC and the Inria Project Lab Morphogenetics.
The geometric arrangement of lateral organs along plant stems, named phyllotaxis, shows a variety of striking patterns with remarkable regularities and symmetries. This has interested biologists, physicists, mathematicians and computer scientists for decades. These studies have lead to a commonly accepted standard interpretation of phyllotaxis that postulates that organs inhibit the formation of new organs in their vicinity. At a molecular scale, these inhibitory fields have been shown to result from the spatio-temporal distribution of the plant hormone auxin. This model theoretically explains a large part of the diversity of phyllotactic patterns observed in plants.
The cytokinin hormones are known to play a significant role in the regulation of phyllotaxis. Fabrice Besnard and Teva Vernoux realized that Arabidopsis thaliana ahp6 mutants, which are perturbed in the cytokinin signaling pathway, showed unusual chaotic perturbations of the phyllotaxis at macroscopic level.
In order to characterize these perturbations, we designed a pipeline of models and methods [60] , [53] which relies of combinatorial and statistical techniques. Using this pipeline of methods, we have shown that the perturbation patterns in both wild-type and mutant plants can be explained by permutations in the order of insertion along the stem of 2 or 3 consecutive organs.The number of successive synchronized organs between two permutations reveals unexpected patterns that depend on the nature of the preceding permutation (2- or 3-permutation). We identified significant individual deviations of the level of baseline segments with reference to 137.5°, which confirms theoretical model predictions. Finally, we highlighted a marked relationship between permutation of organs and defects in the elongation of the internodes in between these organs.
We then looked at the origin of these permutations using confocal microscopy and realized that organs were in fact frequently co-initiated in the mutant, leading after development randomly in half of the cases to permutations. We concluded that the mutant is actually perturbed in the time between consecutive organ initiation (i.e. the plastochrone), while relative angular positions are not affected. After closer inspection, we realized that the mutated gene encodes a protein diffusing from the organs and creating a field around the organs that regulates the plastochrone. We could demonstrate that in the mutant, the absence of this field leads to co-initiations and subsequently to the observed permutations.
Altogether, this study sheds a new light on our interpretation of phyllotaxis, revisiting the standard model and suggesting that several fields based on auxin and cytokinin with different properties are required to provide robustness to phyllotaxis. An overview of this work has been published in the journal Nature [15] .
A stochastic model of phyllotaxis
Participants : Yassin Refahi, Christophe Godin, Etienne Farcot, Teva Vernoux [RDP, ENS] .
This research theme has been supported by IBC and the Inria Project Lab Morphogenetics.
To proceed further and find a mechanistic interpretation of these results, we are currently developing a stochastic extension of the standard model of phyllotaxis. We first analyzed the properties of the inhibitory fields created by the existing primordia on the initiation of new promordia, and concluded that the angular positions of organs are very robust to perturbations while plastochrons may be dramatically affected. This suggested that there exists a strong decoupling between space and time in the patterning process. To account for this observation, we modeled the perception of the initiation signal by cells using stochastic processes coupled with the intensity of inhibitory fields and showed that the observed permutation patterns emerge spontaneously from this purely local processes. A paper describing this model will be submitted for publication in 2015.
The role of auxin and sugar in rose bud outgrowth control
Participants : Jessica Bertheloot [INRA, Angers] , Frédéric Boudon, Christophe Godin.
Auxin in the stem is known to be a key regulator of apical dominance. Over the last decades, many studies have been undertaken to understand its action mode, which is indirect because auxin in the main stem does not enter into the bud. Recently, apical dominance over basal buds in pea has been related to low sugar availability caused by high sugar demand of growing apical organs. Auxin and sugar are two signals regulating the entrance of bud into sustained growth in opposite ways. Recently it has been demonstrated that sugar effect on bud outgrowth was preceded by a modification of the hormonal network involved in auxin effect, which suggests that auxin and sugar pathways do interact in a non-trivial way. But auxin and sugar effects have been studied separately until now. In this work, we investigate what is the combined effect of sugar and auxin on bud outgrowth, and how they integrate to control bud entrance into sustained growth. For this, a series of experiments has been carried on a single-node cuttings of Rosa hybrida grown in vitro in which different combinations of sugar and auxin levels have been tested. A model the regulatory networks controling stem-bud molecular interaction is currently being investigated.