Section: New Results

Meristem functioning and development

In axis 2 work focusses on the creation of a virtual meristem , at cell resolution, able to integrate the recent results in developmental biology and to simulate the feedback loops between physiology and growth. The approach is subdivided into several sub-areas of research.

Data acquisition and design of meristem models

Keywords : Meristem, laser microscopy, image reconstruction, cell segmentation, automatic lineaging.

Participants : Romain Fernandez, Jérôme Chopard, Frédéric Boudon, Christophe Godin, Vincent Mirabet, Jan Traas, Grégoire Malandain, Jean-Luc Verdeil.

This research theme is supported by the ATP CIRAD Meristem and the ANR GeneShape and FlowerModel projects.

Studies on plant development require the detailed observation of the tissue structure with cellular resolution. In this context it is important to develop methods that enable us to observe the inner parts of the organs, in order to analyse and simulate their behaviour. Here we focus on the apical meristems, that have been extensively studied using live imaging techniques and confocal microscopy. An important limitation of the confocal microscope lies in the data anisotropy. To overcome this limitation, we designed new protocols to achieve an accurate segmentation of the cells. Using these segmentations, a geometrical and topological representation of the meristem is built. Such representations may be used to analyze the meristem structure at cell level, to support the description of gene expression patterns and to initiate and assess virtual meristem simulations.

• Microscopy image reconstruction and automatic lineage tracking of the growing meristem cells

  Participants : Romain Fernandez [ Correspondant ] , Christophe Godin, Grégoire Malandain, Jean-Luc Verdeil, Jan Traas, Pradeep Das, Vincent Mirabet.

  We studied the tracking of meristem cells using time-lapse confocal microscopy acquisition on early stages flowers of Arabidopsis shoot apical meristems. We designed a reconstruction method (MARS, figure 5 ) and a tracking algorithm (ALT) in order to map the segmentations of the same meristem at different times, based on a network flow representation in order to solve the cell assignment problem. We validated the MARS-ALT pipeline on a four-steps timecourse of an early stage floral bud. The validation by biologists showed the efficiency of the segmentation algorithm on the reconstructed images (near to 96 % of well-identified cells) and of the lineaging algorithm (100 % of well-identified lineages in the easier case and 90 % in the harder) and leads to a better understanding of the floral bud dynamics. This work was submitted to the journal Nature Methods and is currently under review.

  Figure 5. Surface view of a flower meristem automatically segmented using MARS at cell resolution and a transversal cut showing the inner segmented tissues

• Design of a structural database for specifying gene expression patterns (Jérôme Chopard, Christophe Godin, Jan Traas, Françoise Monéger (ENS Lyon))

  This research theme is supported the ANR GeneShape and FlowerModel projects.

  To organise the various genetic, physiological, physical, temporal and positional informations, we build a spatialised and dynamic database. This database makes it possible to store all the collected information on a virtual 3D structure representing a typical organ. Each piece of information has to be located spatially and temporally in the database. Tools to retrieve and manipulate the information visually, quantitatively through space and time are being developed. For this, the 3D structure of a typical organ has been created at the different stages of development of the flower bud. This virtual structure contains spatial and temporal information on mean cell numbers, cell size, cell lineages, possible cell polarisation (transporters, microtubules), and gene expression patterns. Such a database is mainly descriptive. However, like for classical databases, specific tools make it possible to explore the database according to main index keys, in particular spatial and temporal keys. Both a dedicated language and a 3D user interface are being designed to investigate and query the database.

  A prototype version of such a database is currently being built and is integrated in V-Plants . Algorithms to explore such database at various levels of abstraction will have to be developed. Queries such as: get the number of cell of the L1 layer, get the volume ratio between two zones with different gene expression identities, perform the intersection of two expression zones, compute the curvature at the topmost cell, find the lineage of cells descending from this region, etc. would typically be carried out efficiently with such a database. The prototype of a 3D database presented on figure 6 shows a cell-based volumic tissue that can contain different types of information (cell lineage, cell size, cell identity, etc.)

  Figure 6. Prototype of a 3D database represented as a cell-based volumic tissue that can contain different types of information (cell lineage, cell size, cell identity, ...)

Transport models

Participants : Mikaël Lucas, Jérôme Chopard, Christophe Godin, Yann Guédon, Laurent Laplaze, Jan Traas, Michael Walker.

This research theme is supported by the ANR GeneShape project and a Post-doc Grant from CPIB.

The transport of plant hormones, proteines, water and sugars is critical to plant development. In particular, the active transport of the plant hormone auxin has been shown to play a key role in the initiation of organs at the shoot apex. Polar localized membrane proteins of the PIN1 and AUX/LAX family facilitate this transport and recent observations and models suggest that the coherent organization of these proteins in the L1 layer is responsible for the creation of auxin maxima, which in turn triggers organ initiation close to the meristem centre [37] [1] .

In the previous years, we built models of auxin transport in the L1 layer and inner tissues to understand the observed distribution of PIN transporters and study possible hypotheses related to their regulation. Now, we try to get farther in the understanding of auxin transport on two different systems.

• Simulating auxin transport in 3D digital meristem cellular structures.

  Our first goal is to embed the auxin models developed previously in 3D meristem digital mock-ups obtained from confocal microscopy. This is a crucial step as main problems with auxin transport seem to be related with the 2D approximation which has been made until now. Realistic models of auxin transport in 3D cells will make it possible to compare different hypotheses based on solid ground and to look for realistic transport parameters throughout the meristem dome.

• Modeling axillary root initiation (Mikael Lucas, Christophe Godin, Laurent Laplaze, Malcolm Bennet (CPIB, University of Nottingham, UK))

  Root architecture is a crucial part of plant adaptation to soil heterogeneity and is mainly controlled by root branching. The process of root system development can be divided into two successive steps: lateral root initiation and lateral root development/emergence which are controlled by different fluxes of the plant hormone auxin. In previous studies we showed that a transport model based on competition for auxin between lateral organs was able to account for the branching patterns observed on lateral roots, including in mutant phenotypes [33] , [34] . We now intend to study the distribution of PIN transporters (and other influx transporters) during the emergence of lateral roots. For this we are currently digitizing in 3D lateral roots during initiation and emergence. The dynamics of different transporters and key proteins is being described during this process so that we can depict a clear scenario of auxin homeostasis during lateral meristem development. A Languedoc-Roussillon Region project has just been obtained by our collaborator L. Laplaze at the end of 2009 to support further this research.

Mechanical model

Participants : Jérôme Chopard, Christophe Godin, Jan Traas, Olivier Hamant [ ENS-Lyon ] .

This research theme is supported by the ANR project Virtual Flower and Geneshape projects.

The rigid cell walls that surround plant cells is responsible for their shape. These structures are under constraint due to turgor pressure inside the cell. To study the overall shape of a plant tissue and morphogenesis, its evolution throughout time, we therefore need a mechanical model of cells. We developed such a model, in which walls are characterized by their mechanical properties like the Young modulus which describes the elasticity of the material. Wall deformation results from forces due to turgor pressure. Growth results from an increase in cell wall synthesis when this deformation is too high. The final shape of the tissue integrate mechanically all the local deformation of each cell.

To model this process, we used a tensorial approach to describe both tissue deformation and stresses. Deformations were decomposed into elementary transformations that can be related to underlying biological processes. However, we showed that the observed deformations does not map directly local growth instructions given by genes and physiology in each cell. Instead, the growth is a two-stage process where genes are specifying by their activity a targeted shape for each cell (or small homogeneous region) and the final cell shape results from the confrontation between this specified shape and the physical constraints imposed by the cell neighbors. Hence the final shape of the tissue results from the integration of all these local rules and constraints at organ level. This work is being described in a paper which will be submitted for publication at the beginning of 2010.

Cell cycle model

Participants : Romain Fernandez, Christophe Godin, Pradeep Das, Jan Traas.

This research theme is supported by the ANR project Virtual Flower and Geneshape projects.

A very simple model of cell cycle is necessary to determine cell division events. Here cell division occurs when the cell volume gets above a certain threshold.

A model of cell division consistent with the observations coming from the confocal data is being investigated. The availability of 3-D geometric structures at cell resolution of real meristem and the possibility to follow their cell lineages will make it a unique opportunity to test in silico the validity of these cell division models.

Gene regulatory networks

Modelling gene activities within cells is of primary importance since cell identities correspond to stable combination of gene level activity.

• Gene networks. (Yassin Refahi, Etienne Farcot, Christophe Godin, Jan Traas, Teva Vernoux)

  Both methodological and applied works have been carried on during the last year on the topic of gene networks (in a broad sense, including other metabolites than the sole gene products, whenever they play a significant role in the regulation of gene activity).

  On the methodological side, in the context of Y. Refahi's thesis, some first necessary numerical experiments have been performed, as a benchmark for future implementations. These experiments have consisted in implementing already published spatial models of gene networks [32] , using 3D reconstructed shoot apical meristems obtained from R. Fernandez. The main conclusion is that simulations based on nonlinear differential equations (smooth or piecewise-linear) may be performed in a manageable time on a standard computer using Python/Scipy code, only for very simple systems. Hence it seems reasonable to use these formalisms, although some innovative approaches will have to be developed next year in terms of simulation algorithms and/or model simplification.

  Another methodological work was to continue the analysis of piecewise-linear formalism. Some new results have been obtained, namely existence and uniqueness of limit cycles for systems having a discrete abstraction displaying periodic trajectories. These results, published as a research report [20] have been accepted for publication in International Journal of Systems Science. Previously obtained results have also appeared during the year [13] . Finally, some new results have also been obtained concerning the control of periodic behaviour in piecewise-linear networks [21] . The main novelty is the use of dynamic control technique, i.e. the control of a gene network obtained by linking it to another network, designed to ensure (or preclude) stable periodic solutions in the first network. These technique may be used in the future to investigate specific properties of spatially interacting gene networks.

  Finally, on a more applied side, an ordinary differential model of the auxin signaling pathway have been developed in collaboration with T. Vernoux. The parameters of this model can be put in correspondence with different locations in the shoot apical meristem (SAM), hence representing spatial effects without the need to implement projections of this model on a full 3D meristem. Various experimental data have been obtained by T. Vernoux and his collaborators about the main proteins involved in this pathway, in particular their spatial expression patterns and all their possible interactions. Together with the model, this data provides a very consistent improvement of our understanding of the SAM functioning. A paper on this work is in preparation.

Model integration

Participants : Mikaël Lucas, Michael Walker, Jérôme Chopard, Frédéric Boudon, Christophe Godin, Laurent Laplaze, Jan Traas.

This research theme is supported by the ATP CIRAD Meristem, the ANR project Carpel and the Sy-Stem European RTN Project.

Our approach consists of building a programmable tissue able to accept different modelling components. This includes a central data structure representing the tissue in either 2- or 3-D and able to grow in time, models of gene activity and regulation, models of signal exchange (physical and chemical) between cells and models of cell cycle (which includes cell division). For each modelling component, one or several approaches is investigated in depth, possibly at different temporal and spatial scales, using the data available from the partners (imaging, gene networks, and expression patterns). Approaches are compared and assessed on the same data. As an outcome of each modelling subtask, the objective of each submodel component will be to provide plugin components, corresponding to simplified versions of their models if necessary, that can be injected in the programmable tissue platform.

• development of a computer platform for the 'programmable tissue'. (Jérôme Chopard, Michael Walker, Frédéric Boudon, Etienne Farcot, Christophe Godin)

  One key aspect of our approach is the development of a computer platform dedicated to programming virtual tissue development. This platform will be used to carry out integration of the different models developed in this research axis. The platform is based on OpenAlea . Partner models can be integrated in the platform in a non-intrusive way (the code of their model need not be rewritten). In this context, model integration will i) consist of designing adequate data-structures at different levels that will be exchanged and reused among the different plug-in models and ii) defining control flows at adequate levels to avoid the burden of excessive interaction between components.