S Horna

C Bennis

H Bourouchaki

C Delage

J F Rainaud

Isometric Unfolding of Stratigraphic Grid Units for Accurate Property Populating: Mathematical Concepts

In traditional methods used to populate stratigraphic units, the distortions can be very important and affect the setting up of the static and dynamic parameters necessary to the reservoir simulation, hence the simulation results. These distortions result from the mapping between the original curvilinear stratigraphic grid and the intermediate cartesian grid in which the property populating is processed.

To minimize the deformation and improve the populating process, we propose a new original isometric unfolding process based on the minimization of the elastic tensor deformation. This method could be applied for every type of deposit: horizontal, parallel to top, parallel to bottom, proportional.

Starting from a structural model defined into a coordinate line grid, the user chooses a reference iso-chronological level represented by a triangulated surface. This level can be the top, the bottom or any other characteristic surface of a litho stratigraphic unit. The contacts between this surface and fault surfaces are explicitly extracted as coincident edges. These coincident edges are used to constraint an unfolding process which minimizes the elastic deformation tensor on the whole surface and then, respecting the above constraints, join the fault lips opened by geological tectonic events.

To exploit this first 2D Unfolding for volumetric purposes, we use the coordinate line grids as a 3D support and define a complete mapping between the original curvilinear structural grid and its image in the deposition (unfolded) domain. This mapping which expresses the geometrical transformation between the today's world and the depositional period could now be used to transport today's well trajectory stations in the unfolded volume for geostatistical computation and, on the way back, define the geometrical relations needed for upscaling.

In this paper we will focus on mathematical concepts of the algorithms used in the whole unfolding process and present some results throw actual case studies.

Main Objectives:

Present the mathematical concept and methodology for a new unfolding method based on the minimization of the elastic tensor deformation. With this method, we will be able to associate to a stratigraphic grid unit in structural position to its cell to cell image in the depositional space. This mapping could be used to transport well trajectory stations in the unfolded volume for geostatistical computation.

New aspects covered :

We propose a new original isometric unfolding process based on the minimization of the elastic tensor deformation. We apply this algorithm to unfold iso-chronological surfaces and to unfold volumes in several depositional modes: Top and bottom conformable, proportional and parallel to any surface.

Introduction

The method presented in this article concerns the domain of the oil exploration, and more particularly an important phase of the characterization of the oil reservoirs: populate a lithostratigraphic unit (represented by a fine stratigraphic grid, figure 1) by the rock properties in the center of the cells of this grid (facies, porosity, permeability).

In many cases geostatistic methods are used to spread the information measured along the drilling trajectories on the totality of the fine stratigraphic grid. These geostatistic methods deliver more reliable and faster results when they are processed on a 3D regular cartesian grid representing the volume of sediment accumulated during the deposit period. Then, to realize geostatistic computing, our strategy consists in using the cartesian metrics of the deposit space to realize the simulations geostatistic. For this strategy, it is necessary to allocate to every point of the geographical space a position in the deposit space (see figure 2). This means restoring all lithostratigraphic units of the reservoir, that is crossing towards the past its tectonic history of fault sets.

Geographic space Chronostratigraphic space

Figure 2 Data set and result of unfolding method: (a) stratigraphic grid (b) deposit space.

Our method will provide a way to process independently one or more lithostratigraphic unit and facilitate partial update. In fact, with the wide usage of geo-modelling tools, users could have the need to enhance their previous geostatiscal population without rebuilding an entire stratigraphic model. This may be useful if a new well delivers updated data. In this case, if the user would like to apply new geostatiscal population methods or would like to constraint the property population after some non consistent fluid flow simulation tests. For this opportunity, they often need to extract with a best precision a single lithostratigraphic unit and "repopulate" it with other accurate methods.

In previous works, a very often used classic method consists in building a flat regular grid in the deposit domain. One layer limit is chosen as the reference level on which the sediments were deposed. This layer limit is horizontally flattened. The cells in X, Y, Z directions are then replaced relatively to this reference level in a regular cartesian grid. Dimensions I, J, and K were calculated from the original lithostratigraphic unit dimension. Properties measured in a [i, j, k] original cells transported in the same [i, j, k] cell of the regular stratigraphic grid defined (see figure 3 Unfortunately, using a regular grid produce important geometric deformation. To reduce this deformation, we propose a new unfolding process based on a isometric surface unfolding. In this process, we can start from the same layer limit than the classical method, and use it as a reference surface on which the sediments are deposed. But after having flattened this unfolded reference all layers included between top and base are straightened. The deformation applied on each reference surface point is computed along the corresponded coordinate-line in the stratigraphic grid. The process allow to minimize the grid deformation (see figure 3.c).

Method description

From the isometric unfolding of a selected Reference Surface (named RS there after), all interlayer limits between top and bottom layers selected by the user will be straightened. For that purpose, RS must be extracted first of all then unfolded. Secondly, all surfaces selected by the user are unfolded according to RS.

This work is composed of three steps (see figure 4):

1. extraction and triangulation of a reference surface ;

2. isometric unfolding of the reference surface ;

3. deformation of the wholes lithostratigraphic volume in function of the RS deformation realized during its isometric unfolding.

Stratigraphic unit construction

Inside a reservoir grid, stratigraphic unit are represented by a set of adjacent layers. Starting from this set of layer, we build a stratigraphic grid, which represent a discret subterranean formation, and its structure (layout organization of the sedimentary layers, faults, etc.). This stratigraphic grid is defined in an orthonormal coordinate system (x, y, z). So, every grid cells are located, at the current instant, by geographical address and coordinates x, y and z (depths). The stratigraphic unit is bounded by a upper surface and a lower surface and represents a homogeneous sedimentary layer (see figure 5).

Extraction and triangulation of the reference surface

To operate, the user isolates from a I,J,K coordinate-line grid a stratigraphic unit between two K-values (Ktop and K-bottom). In this unit, the user choose an inter layer limit as reference surface between K-top and K-bottom. This layer is being represented by all grid points having the same K-value.

All faces included in this layer are extracted from the grid to produce the RS. This surface is triangulated in order to be used by the unfolding algorithms and the horizon / fault contact sealing. The preprocessing of RS extraction from a stratigraphic pillar grid (I,J,K) is made in two steps:

1. a matrix of face is defined from the K-layer and a direction (top or bottom -i. e. topper or lower faces). It contains the surface points of the triangulated surface;

2. topology is checked and corrected where mistakes are detected.

Construction of faces matrix

This matrix contains every face of each layer cell, for the given direction. The aim is that all matrix faces will contain an index on its four incident vertices. So, the top-face (resp. bottom) of a unit cell of grid contains 4 indications of vertices numbered in order logic (see figure 6.b). Note : with this process, if all node vertices have the same coordinates, those vertices correspond to the same unique vertex in the generated surface.

Topology checking and fault lips association

To use our unfolding process, we need manifold surfaces. To generate manifold surfaces, a specific process is applied on nodes. The correction must be made on faces matrix, before the generation of triangulated surface to guarantee a correct fault detection. For that purpose, the topology is corrected node by node "by cutting" the grid (i.e. nodes are duplicated to eliminate the presence of non manifold area).

To keep the explicit information contained in the stratigraphic grid, for every cut node, a reference to the corresponding node is stored (see figure 6.b). This data will allow to put in correspondence the fault lips during unfolding process (see figure 6.c).

Triangulation and topological links set up on RS

To be as generic as possible, the flattering process was developed on triangulated surfaces associated by topological links. In this paper, as we are starting from I,J,K coordinate 3D grids (see figure 7.a), we need to generate the triangulated surfaces from 2D grids extracted from 3D grids and to associate equivalent horizon / faults contacts.

A first step consists in extracting preexisting fault planes (see figure 7.b) along with we will be able to associate correspondent edges (edges of horizon / faults contacts), which edges were located at the same place during the deposit period and moved by tectonic events. Then, the triangulation of the different patchs (see figure 7.c) representing RS are cleaned (sometimes, the original coordinate line grid is not explicit enough). At least, using this triangulation as the base of the geometry, all horizon / faults contacts are explicitly tagged and all correspondent edges are topologically linked from one side to the other side of the horizon along all horizon / fault contacts. This preprocessing is mandatory before unfolding (see figure 7.d).

Isometric unfolding of reference surface

The first step of the unfolding process is applied on the RS. This process is computed by using a specific extension of Aplat, software developed by university of technology of Troyes [START_REF]Aplat software[END_REF].The original Aplat process is used to flatten triangulated surface without tears. A specific code was developed here to associate horizon fault contacts separated during tectonic periods.

Isometric unfolding works in the following way: from a 3D folded surface, we compute an unfolded plane surface, in which the deformations are minimal. The criterion chosen is a minimization of the deformation of tensor elastic deformation. During the deformation, all "Z" coordinate are computed to obtain a plane surface. At the level of the faults, both horizon / fault contacts are put in correspondences and smoothed "to block" holes at the level this one. Figure 8 illustrates the result of the isometric unfolding of a surface.

Unfolding of stratigraphic grid

Then, we need to unfold all layers included in stratigraphic unit. From the unfolded reference surface chosen by user, layers included between bottom and top selected by user are "straightened". For every RS points, a deformation is calculated and applied along all the corresponding coord-lines in the stratigraphic grid (see figure 9). This method implies the correspondence between the reference surface and each of the grid coord-line.

It is thus necessary to assure that every cood-line corresponds strictly to a point of the reference surface.

For it: i) the horizon / fault contacts must correctly coincide (i. e. no hole) ii) the removal of edge to simplify triangular mesh does not have to remove needed information.

The algorithm takes place according to various steps developed afterward:

• correspondence between the points of the triangulated reference surface and the grid nodes;

• for each reference surface point P:

computing of the transformation T on P (folded surface → unfolded surface);

on all coord-line point crossing P, the transformation T is applied.

Correspondance between grid and surface

To apply the same deformation realized on RS during isometric unfolding to every grid nodes, a correspondence between RS points and grid points must be defined. Every RS vertex is then associated to one coord-line.

Along faults, several vertices can belong to the same coord-line (see figure 10). Each of these vertices must be processed separately even it they belong to the same coord-line. This feature implies a dedicated processing along faults. This will be explain in the following section.

Figure 10 Surface discontinuity representation.

Transformation on each surface point

To handle all vertices built during the RS unfolding, the corresponding surface coord-lines is processed iteratively (and not on the all grid nodes). For every RS vertices, two cartesian coordinate bases are defined. The one with regard to the unfolded surface (see figure 11), the other one with regard to the folded surface (see figure 12

Figure 12 Cartesian coordinate on vertex S included in folded surface (a) Z is the normal on S (average of each normal incident faces) ; (b) X' is included to Z plan, along an incident edge, X (1, 0, 0) was perpendicular to Z ; (c) Y is cross product between Z and X.

From produced cartesian coordinate, a transformation by bases change allows to deduct its new position for each horizon. The figure 13 illustrates the unfolding of 3 horizons. In this example, RS is the lower surface 0, and horizons 0 to 2 are unfolded.

S 0 S 1 S 2 S' 0 S' 1 S' 2 (a) S 0 S 1 S 2 S' 0 S' 1 S' 2 (b)
S" 0 S" 1 S" 2 (c) S 0 S 1 S 2
S" 0 S" 1 S" 2 (d)

Figure 13 Unfolding horizons from one reference surface.

But this method, along faults, can produce surface discontinuity. Several RS vertices will correspond to the same (i, j) grid node which referred the same coord-line. During unfolding surface process, horizons / fault contacts will be adjusted to remain in correspondence (see figure 14).

(a) (b)

Figure 14 During unfolding, fault lips are put in correspondence to produce a surface without discontinuity.

In fact, when we are in a non faulted area (see figure 13), we can base the computation of a normal on a vertex on several faces orientations. The normal obtained is reliable. But, when the vertex is located on an horizons / fault contact, we can base this computation on less faces orientations by considering only the faces located in the same horizon patch (on the same side of the fault, figure 15).

It is the reason why a new normal is calculated for every couple of vertices on fault edge, such as Z is the average of Z 1 andZ 2 . Normal used in S 1 and S 2 being equal, the applied transformations are equivalent (see figure 16).

So, resulting points S 0 1 and S 0 2 have the same coordinate X, Y. We suggest afterward to the user to keep this result (see figure 16

Unfolding along a coord-line

Every coord-line can be identified by an address i, j corresponding to the address of the origin grid node. So, every RS vertex is associated with one coord-line, from which cartesian coordinate are calculated. The unfolding is so realized along the coord-line for each contained vertices.

Results and comparison

Figure 17 present the deposit space computed with our unfolding process. To compare grid deformations between classical methods (described in section ) and our unfolding process, we propose to use an approximative representation which objective is to illustrate why the isometric method restore better the distances. Distances separating reference points presented in figure 18 are measured and compared in table 1. Classic method: the number of cells is respected and the mean value of width of a cell is equal to the average of original cells size. Its illustrated in figure 18.b. We obtain distances

D 1 = d 0 1 + d 0 2 and D 2 = d 0 3 + d 0 4 .
Isometric method: the positions of cell corners are computed from the reference surface isometric unfolding. The sizes of cells are not identical to the original cells. In figure 18 The advantage of our method could ever be more evident if the area organization of the reservoir grid (which most be optimized for fluid flow simulation) looks like the given example presented in figure 19. This is due to the fact that the reservoir grid and the geostatistical grid support can be designed on a total independence.

Figure 19 Extraction of the top view of a reservoir grid in a complex faulting geometry.

Conclusion

The objective to apply our methods is to avoid lateral deformation due to the influence of the setting up of complex fault network as presented in [START_REF] Galera | Construction of coherent 3D geological blocks[END_REF] and [START_REF] Gibbs | Balanced cross section from seismic sections in area of extensional tectonics[END_REF]. Then, the original distance between geological bodies will be restored as it was historically and the computed geostatistical parameters will be more consistent.

Applying this method, as we have seen in the table 1 the user will obtain a more accurate measurement to define vertical and horizontal variograms which are one of the main tools used for geostistical simulations. The quality of the the realization will be a lot improved and no more anisotropy bias will be inherited from reservoir fluid flow gridding constraints. The grid which will be constituted for the geostatiscal population (or any other style) could be totally independently constrained by only geological behaviors.

This method allows to update only a part of the geological model (only one stratigraphic unit) without recomputing all the properties (geometric or petrophysic) of the stratigraphic grid even if we choose a new depositional mode. The ability to process independently the stratigraphic units open the way to update a complete model in parallel on several processors. This will facilitate efficient history matching procedures.

Figure 1

 1 Figure 1 Reservoir characterization workflow.

Figure 3

 3 Figure 3 Deposit space comparison (a) stratigraphic folded grid (b) deposit space represented by a regular grid (c) deposit space computed by our unfolding process.

2 1 3 Figure 4

 234 Figure 4 Unfolding workflow representation: (1) reference surface extraction (2) reference surface unfolding (3) deposit space computing.

Figure 5

 5 Figure 5 Stratigraphic unit construction (a) unit detection (b) unit construction from layer 0 to 7.

Figure 6

 6 Figure 6 Surface vertices construction from grid vertices. Each face is incident to 4 vertices.Surface vertices are generated by a iteration on of all incident nodes of the K-layer cells. All vertices of every node are covered in a circular way (A → B → C → D, figure 6.c). For each vertex, its curvilinear coordinate is compared with the previous vertex. If this one is different, a new vertex is added to the generated surface.

Figure 7

 7 Figure 7 Explicit information extraction (a) stratigraphic unit (b) fault detected in stratigraphic grid (c) surface extracted with fault lips correspondence stored (d) fault contacts and correspondent edges.

Figure 8

 8 Figure 8 Isometric unfolding: (a) folded 3D surface (b) horizon / fault contact correspondence (c) corresponding unfolded surface with fault resticking.

Figure 9

 9 Figure 9 Surface unfolding by normal straightened (a) folded surface (b) unfolded surface.

Figure 11

 11 Figure11Cartesian coordinate on vertex S included in flat surface (a) Z is vector (0, 0, 1), the normal on S ; (b) X is vector along an incident edge (c) Y is cross product between Z and X.

  .b), or to compute a new point calculated by interpolation of S 0 1 and S 0 2 (see figure 16.c).

Figure 15 Figure 16

 1516 Figure 15 Discontinuity on unfolded surfaces: (a) bad result produce by a fault unfolding (b) vertices S 1 and S 2 correspond to each fault lips, their normal are different; (c) produces vertices S 0 1 and S 0 2 are disconnected.

Figure 17 Figure 18

 1718 Figure 17 Results illustration (a) stratigraphic grid (b) resulting deposit space

Table 1

 1 In real case, the same effects are felt, what shows the importance of its use to be able to analyze correctly variogram horizons and propose estimations more reliable in geostatistic.

	.c. We obtain distances

-9 September 2010, Oxford, UK


S Horna

C Bennis

T Crabiet

S Peltier

J F Rainaud

Extracting and Unfolding a Stratigraphic Unit to update property population

With the wide usage of geo-modelling tools, users could have the need to enhance their previous geostatiscal population without rebuilding an entire stratigraphic model In this paper we explain how we can extract non explicit information from a stratigraphic model (reference iso-chronological surfaces, faults used to constraint the model), and then, use this information to realise 3D flattening on iso-chronological surfaces prior to geostatiscal population.

Three methods were presented here: traditional by topological correspondence, vertical shear and an original isometric unfolding process based on the minimization of the elastic tensor deformation. These methods could be applied for every type of deposit: Horizontal, Parallel to Top, parallel to Bottom, Proportional.

Then, we compare the application of these methods on several case studies and develop the advantages to reengineer a stratigraphic model and repopulate it after flattening. Even if the "traditional" and vertical shear methods could be applied on certain situations, following multiple test bed as the ones presented in this paper, we are thinking that the isometric unfolding presented here is much reliable. As a consequence, we will exploit more and more this isometric unfolding method in the next future and process each lithostratigraphic unit independently than the others.

Introduction

With the wide usage of geo-modelling tools, users could have the need to enhance their previous geostatiscal population without rebuilding an entire stratigraphic model. This may be useful if a new well delivers updated data, if the user would like to apply new geostatiscal population methods or would like to constraint the property population after some non consistent fluid flow simulation tests. For this opportunity, they often need to extract with a chirurgical precision a single lithostratigraphic unit and "repopulate" it with other accurate methods.

In this paper we explain how we can extract non explicit information from a stratigraphic model (reference iso-chronological surfaces, faults used to constraint the model), and then, use this information to realise 3D flattening on iso-chronological surfaces prior to geostatiscal population. With our methods this 3D Flattening can be optimised for every type of deposit: Horizontal, Parallel to Top, parallel to Bottom, Proportional (Figure 1). In every of these use cases, the objective to apply our methods is to avoid lateral deformation due to the influence of the setting up of complex fault network as presented in [START_REF] Galera | Construction of coherent 3D geological blocks[END_REF] and [START_REF] Gibbs | Balanced cross section from seismic sections in area of extensional tectonics[END_REF]. Then, the original distance between geological bodies will be restored as it was historically and the computed geostatistical parameters (experimental lateral and vertical variograms) will be more consistent.

Depending on the use case we can apply 1/ a traditional topological relationship between the litho stratigraphic grid and a flat regular grid designed to handle geostatistical computation, 2/ a simple vertical shear, 3/ a single isometric unfolding or 4/ a double isometric unfolding method. Then, using any of these restoration policies, we can replace the well bore trajectories and the measurements along this trajectory in the historical depositional situation.

The following step is common to all use cases, a regular orthogonal 3D grid embedding these measurements in the deposit space is defined. This grid represents a regular media on which complex fault network effects are erased, and is used to apply geostatistical population.

In this paper we compare the application of these diverse methods on several case studies and develop the advantages to reengineer a stratigraphic model and repopulate it after flattening. We do not cover the total reconstruction of an assemblage of several lithostratigraphic grids in a [U,V,T] parametric grid as it is proposed by the SKUA product from Paradigm (http://www.pdgm.com/products/skua.aspx), because we are just extracting and filling one existing lithostratigraphic unit without rebuilding the whole model.

Preliminary extraction of non explicit information (iso-chronostratigraphic surface, Horizon/Faults contacts):

As a first step, we will show how we can re-engineer a "coordinate line" designed stratigraphic grid to extract significant stratigraphic surfaces and embedded fault networks.

Our starting point is a coordinate line (or pillar organised) 3D grid with a regular I, J, K organisation. A first exploration of this 3D grid allows to define which K = Cte limit could be chosen as an isochrono-stratigraphic surface. Barcelona, Spain, 14 -17 June 2010 A deeper exploration allows determining "horizon/faults contacts", computing the link between upper and lower margin of a fault on its horizon/fault contact for each discontinuity and informing the topological framework on the entire 3D stratigraphic grid. This step is not the simplest part of the process and a lot of heuristics have to be considered to obtain a 100 % consistent framework. Figure 2 present horizons and faults and their links extracted from a faulted 3D stratigraphic model. Unfolding process methods

1/Traditional method:

This method is commonly used by most of geo-modelling tools. It consists in building a flat regular grid in the deposit domain. In this case the stratigraphic grid deposit domain will be an orthogonal grid with dimensions along I, J, and K calculated from the original Lithostratigraphic unit dimension ( an average of the height, length and depth value of the cells is often used). The value of the properties measured in a [i, j, k] cell of the original lithostratigraphic grid is transported in the same [i, j, k] cell of the regular stratigraphic grid defined in the deposit domain.

2/ 3D Flattening using a simple vertical shear

This method, which is very fast, is very well fitted if the deposition mode is horizontal but it could be used also for the other deposition mode if the structure is not too complex. We must chose one K= Cte limit as the reference iso-chronological surface. Far from the faulted area, we compute the vertical distance of each node (each I, J, K corner) of the original stratigraphic grid, to the iso-chronological surface.

By this way we can build a partial flattened stratigraphic grid which is an image of 80 % to 95 % of the original stratigraphic grid as it was historically located during the deposition period in the depositional domain. Then, along the faults, considering that very often the thickness of the layer doesn't vary too much, we can extend smoothly the partial flattened stratigraphic grid to the faulted area and complete it at 100%. Two options are provided to the user: impose or not the adjacency along the faults in the deposit space.

3/ 3D Flattening using an isometric unfolding

This method is very well sweated if the deposition mode is parallel to an iso-chronological surface.

We must choose also one K= Cte limit as the reference iso-chronological surface. It is here mandatory to start from a very consistent structural model on which horizon/fault contacts are explicitly known. The preliminary extraction presented before guarantees the respect of this constraint.

The mathematical concepts of the flattening algorithm are detailed in a paper proposed to the next ECMOR conference. This algorithm is based on an isometric unfolding process. The unfold surface is computed by deforming a 3D fold surface. The criterion chosen is the minimization of the elastic tensor deformation. Barcelona, Spain, 14 -17 June 2010

From an unfolded reference surface (RS) chosen by user, all horizons included between base and roof are "redressed" [START_REF] Bennis | Piecewise surface flattening for non-distorted texture mapping[END_REF]. For this, the deformation apply on each reference surface point is firstly compute and secondly is apply along the corresponded coordinate-line in the stratigraphic grid.

Computing the well bore trajectory in the depositional domain

Both presented process (Vertical shear and Isometric) gave a complete correspondence exists between all the cells of the two grids.

Starting from the (x i , y i , z i ) trajectory of the well bore, we can calculate from each well measurement (mw x , mw y , mw z ) the local mu, mv, mw coordinates of the well measurements in each (crossed) cell of the original stratigraphical grid, then replace this well measurement in each corresponding cell of the flattened stratigraphic grid and obtain the dw x , dw y , dw z coordinates of this well measurement in the depositional domain. This property value is now "located" as it was in the 3D space during the deposition period (Figure 3). This property and its location can now be used to calculate geostatistical population in this depositional domain.

Examples discussions and comparisons

In this section we are going to compare what is the effect on the spatial features of the first three methods presented on two examples: a "bended" and a "faulted" litho stratigraphic grid. For these two use cases a number of connected cells was embedded into these grids to represent a 3D sedimentary body embedded into a Lithostratigraphic unit. The objective of this exercise is to determine which method will deliver the best information to compute experimental variograms for geostatistics, so which method can keep the original lateral and vertical extension of this sedimentary body.

1/ For the "bended" stratigraphic unit (Figure 4) on which have a measured length of 3800 m in the maximal lateral extension of the sedimentary body, we obtain 3335 m for the "traditional method", 3327 m for the Vertical Shear method, 3776 m for the isometric method. For maximal vertical extension we obtain the following values: 66.8 m; 66.8 m; 68.2 and 67.0 m. It is not very "flashy" in 2D but the 3D effect is difficult to represent in so small figures. 2/ For the "faulted" stratigraphic unit (Figure 5), we will consider the shape of the flattened sedimentary body and verify that the "fault effect" could be erased if we do not use the Vertical shear method as well as the distance are conserved. In this example, coming from a realistic data set, the cells defined in the original stratigraphic grid are transported in the historical depositional refined grid as pseudo well bore measurements, ready to be used by geostatistical methods.

Conclusions and Future works

After explaining how we extract geometry and topology features from "already defined" stratigraphic grids embedded into a wide reservoir grid, we presented here several unfolding methods used to transfer all measurements along well trajectories in a flat depositional domain. By using these methods on an updating loop, we will be able to start from an existing model already populated, introduce new information (measurements along well bores or new seismic attribute constraints) and decide to change our mind on the deposition mode before computing an up to date geostatistical estimation. It will be also possible to introduce this new step in the reservoir characterisation process and build up optimisation loop with.

Even if the "traditional" and vertical shear methods could be applied on certain situation, following multiple test bed as the ones presented in this paper, we are thinking that the isometric unfolding presented here is much reliable. As a consequence, we will exploit this method in the next future. This method will be helpful to complete our geo-modelling process with more functions using geometrical correspondence like direct upscaling from deposit location to reservoir grid and/or grid refinement assisted by property contrast and structural constraints. Our policy will be to process each lithostratigraphic unit independently than the others.

Figure 1 :

 1 Figure 1: deposit domain (a) horizontal (b) parallel to top (c) parallel to bottom (d) proportional

Figure 2 :

 2 Figure 2: extraction of non explicit information (a) faulted stratigraphic 3D grid (b) one extracted horizon and corresponding horizon/faults contacts (c) set of extracted fault surfaces.

Figure 3 :

 3 Figure 3: Properties management (a) stratigraphic 3D model with wells properties (b) properties location in depositional domain.

Figure 4 :

 4 Figure 4: Distance measured in resulting grid between two points A and B: (a) lithostratigraphic grid; (b) flattened by the traditional method; (c) by the vertical shear, (d) by the isometric.

Figure 5 :

 5 Figure 5: Processing on a grid including fault:(a) original lithostratigraphic grid; (b) flattened by the traditional method; (c) by the vertical shear, (d) by the isometric.


Susana Saez-Aguayo

Corinne Rondeau-Mouro

Audrey Macquet

Ilkka Kronholm

Marie-Christine Ralet

Adeline Berger

Christine Salle

Damien Poulain

Fabienne Granier

Lucy Botran

Olivier Loudet

Juliette De Meaux

Annie Marion-Poll

Helen M North
email: helen.north@versailles.inra.fr

Local Evolution of Seed Flotation in Arabidopsis

Arabidopsis seeds rapidly release hydrophilic polysaccharides from the seed coat on imbibition. These form a heavy mucilage layer around the seed that makes it sink in water. Fourteen natural Arabidopsis variants from central Asia and Scandinavia were identified with seeds that have modified mucilage release and float. Four of these have a novel mucilage phenotype with almost none of the released mucilage adhering to the seed and the absence of cellulose microfibrils. Mucilage release was modified in the variants by ten independent causal mutations in four different loci. Seven distinct mutations affected one locus, coding the MUM2 b-D-galactosidase, and represent a striking example of allelic heterogeneity. The modification of mucilage release has thus evolved a number of times independently in two restricted geographical zones. All the natural mutants identified still accumulated mucilage polysaccharides in seed coat epidermal cells. Using nuclear magnetic resonance (NMR) relaxometry their production and retention was shown to reduce water mobility into internal seed tissues during imbibition, which would help to maintain seed buoyancy. Surprisingly, despite released mucilage being an excellent hydrogel it did not increase the rate of water uptake by internal seed tissues and is more likely to play a role in retaining water around the seed.

Introduction

Polysaccharides released from the seed coat on imbibition form a sticky, gelatinous halo called mucilage around the seed. This property, termed myxospermy, was observed in cress (Lepidium sativum) by Darwin [START_REF] Weitbrecht | First off the mark: early seed germination[END_REF] and is found in the model plant Arabidopsis. In addition to the Brassicaceae, this trait has been noted in a hundred plant families including Solanaceae, Linaceae and Plantaginaceae [START_REF] Western | The sticky tale of seed coat mucilages: production, genetics, and role in seed germination and dispersal[END_REF]. During seed development in Arabidopsis, the epidermal cells of the seed coat undergo a complex differentiation process during which mucilage polysaccharides are accumulated [START_REF] Beeckman | Histological study of seed coat development in Arabidopsis thaliana[END_REF][START_REF] Western | Differentiation of mucilage secretory cells of the Arabidopsis seed coat[END_REF][START_REF] Windsor | Arabidopsis seed coat development: morphological differentiation of the outer integument[END_REF]. The resulting epidermal cells of mature Arabidopsis seeds have a distinctive morphology with reinforced radial cell walls connected to a column of secondary cell wall material at their centre, called the columella, which is surrounded by dehydrated mucilage polysaccharides under a primary cell wall. Genes involved in the differentiation of these cells and the production of mucilage have mainly been identified through mutant phenotypes [START_REF] Western | The sticky tale of seed coat mucilages: production, genetics, and role in seed germination and dispersal[END_REF].

In Arabidopsis, seed mucilage forms two structurally distinct layers with the pectin domain rhamnogalacturonan I (RG I) the major component of each [START_REF] Western | Differentiation of mucilage secretory cells of the Arabidopsis seed coat[END_REF][START_REF] Penfield | MYB61 is required for mucilage deposition and extrusion in the Arabidopsis seed coat[END_REF][START_REF] Macquet | In situ, chemical and macromolecular study of the composition of Arabidopsis thaliana seed coat mucilage[END_REF]. The outer mucilage layer is diffuse and water-soluble. In contrast, the inner layer adheres strongly to the seed surface and requires harsh chemical treatment, or enzyme digestion, to remove it from the seed coat [START_REF] Western | Differentiation of mucilage secretory cells of the Arabidopsis seed coat[END_REF][START_REF] Macquet | In situ, chemical and macromolecular study of the composition of Arabidopsis thaliana seed coat mucilage[END_REF][START_REF] Huang | The Arabidopsis transcription factor LUH/MUM1 is required for extrusion of seed coat mucilage[END_REF][START_REF] Walker | The transcriptional regulator LEUNIG_HOMOLOG regulates mucilage release from the Arabidopsis testa[END_REF]. RG I attachment to the seed coat requires cellulose, as cesa5, fei2 and sos5 mutants implicated in cellulose synthesis have reduced adherent mucilage [START_REF] Harpaz-Saad | Cellulose synthesis via the FEI2 RLK/SOS5 pathway and CELLULOSE SYNTHASE 5 is required for the structure of seed coat mucilage in Arabidopsis[END_REF][START_REF] Mendu | Subfunctionalization of cellulose synthases in seed coat epidermal cells mediates secondary radial wall synthesis and mucilage attachment[END_REF][START_REF] Sullivan | CESA5 is required for the synthesis of cellulose with a role in structuring the adherent mucilage of Arabidopsis seeds[END_REF]; cesa5 is affected in a cellulose synthase catalytic subunit, fei2 is defective in a leucine-rich receptor kinase and sos5 carries a mutation in a fasciclin-like arabinogalactan protein with a glycophosphatidylinositol anchor. In cesa5 null mutants some cellulose was still observed within the reduced layer of adherent mucilage, implicating other CESA genes in its production. Precisely how pectin and cellulose interact to form the adherent mucilage layer has still to be determined.

The ecophysiological role of mucilage production by seeds is ambiguous, diverse functions have been put forward, but none appears to be comprehensively applicable. The adhesive properties of mucilage led to proposals that it mediates long-distance seed dispersal by attachment to animals or that it prevents seed removal during soil erosion or by ants through fixation to soil particles [START_REF] Weitbrecht | First off the mark: early seed germination[END_REF][START_REF] Young | Mucilaginous seed coats[END_REF][START_REF] Garcı ´a-Fayos | Seed removal susceptibility through soil erosion shapes vegetation composition[END_REF][START_REF] Engelbrecht | Mucilage secretion by seeds doubles the chance to escape removal by ants[END_REF]. Comparison of the formation of mucilage in Artemisia taxa associated the trait with dry habitats, as had previously been observed in Lamiaceae [START_REF] Ryding | The distribution and evolution of myxocarpy in Lamiaceae[END_REF][START_REF] Kreitschitz | Mucilage formation in selected taxa of the genus Artemisia L. (Asteraceae, Anthemideae)[END_REF]. Nevertheless, a potential role of mucilage in modifying germination capacity [START_REF] Penfield | MYB61 is required for mucilage deposition and extrusion in the Arabidopsis seed coat[END_REF][START_REF] Witztum | Integumentary mucilage as an oxygen barrier during of Blepharis persica (Burm) Kuntze[END_REF][START_REF] Keijzer | A seed shape mutant of Arabidopsis that is affected in integument development[END_REF][START_REF] Arsovski | MUM ENHANCERS are important for seed coat mucilage production and mucilage secretory cell differentiation in Arabidopsis thaliana[END_REF] has not been consistently observed in tests with mutants defective for mucilage release [START_REF] Debeaujon | Influence of the testa on seed dormancy, germination, and longevity in Arabidopsis[END_REF][START_REF] Western | Isolation and characterization of mutants defective in seed coat mucilage secretory cell development in Arabidopsis[END_REF][START_REF] Johnson | TRANSPARENT TESTA GLABRA2, a trichome and seed coat development gene of Arabidopsis, encodes a WRKY transcription factor[END_REF][START_REF] Usadel | RHM2 is involved in mucilage pectin synthesis and is required for the development of the seed coat in Arabidopsis[END_REF]. Furthermore, differences in the composition and structure of mucilage layers could reflect specific physiological roles for each [START_REF] Macquet | A naturally occurring mutation in an Arabidopsis accession affects a b-Dgalactosidase that increases the hydrophilic potential of rhamnogalacturonan I in seed mucilage[END_REF].

Naturally occurring genetic variation provides an alternative source of mutations for functional analysis and gene cloning to that of induced mutations. In Arabidopsis thaliana a large number of accessions are available that have been derived from seeds harvested in the wild in a variety of geographical locations. These have generally been exploited for quantitative trait locus (QTL) mapping of important agronomic traits [START_REF] Alonso-Blanco | What has natural variation taught us about plant development, physiology, and adaptation?[END_REF]. In a previous study we identified a naturally occurring mutation in the Shahdara accession that affects the liberation of mucilage from the seed coat [START_REF] Macquet | A naturally occurring mutation in an Arabidopsis accession affects a b-Dgalactosidase that increases the hydrophilic potential of rhamnogalacturonan I in seed mucilage[END_REF]. The Shahdara accession is defective in the MUM2 b-Dgalactosidase. This enzyme trims galactan ramifications from RG I in seed mucilage, rendering it more hydrophilic, and increasing mucilage expansion on imbibition so that the outer cell wall breaks and mucilage is released [START_REF] Macquet | A naturally occurring mutation in an Arabidopsis accession affects a b-Dgalactosidase that increases the hydrophilic potential of rhamnogalacturonan I in seed mucilage[END_REF][START_REF] Dean | The Arabidopsis MUM2 gene encodes a b-galactosidase required for the production of seed coat mucilage with correct hydration properties[END_REF]. Except for the mucilage extrusion defect, no other visible phenotype was reported for the Shahdara accession or other mum2 mutants. Although the genetic basis of this phenotype was elucidated, its ecological relevance was not resolved. Seeds from the Shahdara accession had been collected in Tajikistan, near to the Shokhdara River. The collection of accessions previously screened for mucilage release defects contained mainly European accessions with few from central Asia [START_REF] Macquet | A naturally occurring mutation in an Arabidopsis accession affects a b-Dgalactosidase that increases the hydrophilic potential of rhamnogalacturonan I in seed mucilage[END_REF].

In this study, we analysed a larger panel of Arabidopsis accessions and identified a further nine genotypes that were defective in mucilage release; these were observed to float on the surface of water, unlike seeds with a thick layer of adherent mucilage that sink. A screen for seed flotation identified four other accessions whose seeds floated despite releasing mucilage, as they had little adherent mucilage. Analysis of the causal mutations responsible for the modified mucilage release observed in the variants indicated ten independent mutations that affected a minimum of four different loci and these had evolved in populations from two geographical zones, central Asia and Scandinavia. The investigation of water uptake by seeds using nuclear magnetic resonance (NMR) relaxometry showed that nonreleased mucilage polysaccharides contribute to the maintenance of buoyancy, and released mucilage does not improve imbibition, contrary to previous hypotheses.

Results

Seed mucilage retention is observed in Arabidopsis accessions from two discrete geographic locations and arises from mutations in three loci

During an expedition to central Asia, seeds were harvested from 25 plants at a site in Tajikistan believed to correspond to that where the original Shahdara population was collected, these were termed NeoShahdara (Neo) and have been shown to be closely related to the original Shahdara individual [START_REF] Simon | DNA fingerprinting and new tools for fine-scale discrimination of Arabidopsis thaliana accessions[END_REF]. Interestingly, descendants from just eight of the twenty-five Neo plants tested had the mum2 Sha deletion, identified as the causal mutation for mucilage retention in the original Shahdara [START_REF] Macquet | A naturally occurring mutation in an Arabidopsis accession affects a b-Dgalactosidase that increases the hydrophilic potential of rhamnogalacturonan I in seed mucilage[END_REF]. Individuals from two Kyrgyzstan and six Scandinavian populations were also found to be defective in mucilage release [START_REF] Saez-Aguayo | PECTIN METHYLESTERASE INHIBITOR6 promotes Arabidopsis mucilage release by limiting methylesterification of homogalacturonan in seed coat epidermal cells[END_REF] (Table 1); the trait was fixed in 7 of the 9 populations. In 488 accessions examined representing the species-wide distribution of Arabidopsis, 71 exhibit the mucilage release defect [START_REF] Macquet | A naturally occurring mutation in an Arabidopsis accession affects a b-Dgalactosidase that increases the hydrophilic potential of rhamnogalacturonan I in seed mucilage[END_REF] (Table 1). The sites of origin for these accessions were confined to central Asia and Scandinavia.

Crosses were carried out between Shahdara and ten representative individuals from among the 70 new mutant accessions (Table S1). For Neo, a representative carrying the mum2 Sha deletion, Neo-3, and one that did not, Neo-6, were used. Dja-1 and Sk-1-1 complemented the Shahdara mum2 mutant phenotype. Furthermore, reciprocal crosses between Dja-1 and Sk-1-1 showed that their mutations were not allelic. The gene affecting mucilage release in Dja-1 has been identified and codes the pectin methylesterase inhibitor PMEI6 [START_REF] Saez-Aguayo | PECTIN METHYLESTERASE INHIBITOR6 promotes Arabidopsis mucilage release by limiting methylesterification of homogalacturonan in seed coat epidermal cells[END_REF]. A combination of mapping and whole-genome sequencing identified a point mutation in At3g50990 in the Sk-1-1 accession; this gene codes PEROXI-DASE36 (PER36) and the mutation causes the conversion of Tyr-262 to a stop codon. PER36 has recently been shown to be required for mucilage release [START_REF] Kunieda | Spatiotemporal secretion of PEROXIDASE36 is required for seed coat mucilage extrusion in Arabidopsis[END_REF]. All the remaining accessions failed to complement the Shahdara mum2 mutant allele. MUM2 gene polymorphisms were determined for the accessions affected in mucilage release and five causal mutations, distinct from the original Shahdara mutation, were identified in six of the accessions, four of these introduced premature stop codons (Figure 1A, Table S2). Segregation for mucilage release or nonrelease in the Ale and Sku populations always correlated with the absence or presence of the causal mutation, respectively.

For the Lom3-1 accession no causal mutation was identified in MUM2, despite genetic non-complementation demonstrating it to be a mutant allele (Table S2) and no mutation was identified in 208 base pairs (bp) upstream of the ATG or 192 bp downstream of TGA. Analysis of MUM2 expression, by quantitative RT-PCR (qRT-PCR), confirmed that Lom3-1 was affected in MUM2,a s RNA steady-state levels were extremely low, similar to those of the mum2-11 knockout mutant (Figure 1B). Interestingly, MUM2 transcript abundance was markedly reduced in all the accessions where mutation introduced a premature stop codon (Figure 1B). As these stop codons should only directly affect translation, the observed reduction in transcript levels indicates the possible intervention of nonsense mediated mRNA mechanisms to degrade aberrant transcripts [START_REF] Reznik | Regulated and quality-control mRNA turnover pathways in eukaryotes[END_REF]. As expected, MUM2 expression levels were similar to those observed for wild-type Col-0 for the accessions Nfro1-1, Dja-1 and Sk-1-1 (Figure 1B). The latter two are not mum2 mutants and Nfro1-1 contains an amino-acid

Author Summary

Seeds of the model plant Arabidopsis release sticky mucilage on imbibition that is constituted of complex polysaccharides. In this study, we have identified and characterised natural Arabidopsis variants that do not release mucilage and found that their seeds float. The accumulation of unreleased polysaccharides in the seed coat reduced water uptake rates on imbibition and would maintain buoyancy. We subsequently identified additional floating natural variants where mucilage is released, but is not attached to the seed, apparently due to defective cellulose production. The different variants arise from at least ten independent unique mutations and were collected from two discrete geographical areas. Arabidopsis seed flotation has thus evolved several times due to modifications in mucilage release. Released mucilage was found to retain water, but did not improve imbibition of internal seed tissues, indicating a role in maintaining seeds hydrated. These findings highlight the physical and potential physiological effects of mucilage production by the seed coat. substitution in MUM2. The natural mucilage release mutants are therefore the result of 9 independent mutation events, with 7 in the same gene MUM2.

The identification of MUM2 loss-of-function alleles in two specific geographic regions could result from local selection pressures. We examined patterns of differentiation between local populations within geographical regions, using previously described patterns of neutral variation [START_REF] Kronholm | Influence of mutation rate on estimators of genetic differentiation -lessons from Arabidopsis thaliana[END_REF] (Protocol S1). Patterns of population differentiation at either the MUM2 locus or for mucilage release did not deviate from neutral expectations (Table S3). Although the repeated evolution of independent loss-offunction mutations in central Asia and Norway remains intriguing, there is no evidence for local adaptation for mucilage retention.

Impairment of adherent mucilage maturation by natural mutations

Forced mucilage release by breaking the outer cell wall of seed coat epidermal cells with acid and alkali has previously shown that mum2-11 seeds form a thinner layer of adherent mucilage; branched RG I does not expand to the same degree as unbranched RG I when hydrated (Figure S1A and S1B) [START_REF] Mendu | Subfunctionalization of cellulose synthases in seed coat epidermal cells mediates secondary radial wall synthesis and mucilage attachment[END_REF]. In accessions containing a premature stop codon, adherent mucilage was observed as a thin layer, like that of mum2-11 seeds, coherent with reduced MUM2 transcript abundance (Figure 1C and Figure S1C to S1H). The adherent mucilage was reduced less for Nfro1-1 and Lom-3-1 consistent with the production of normal amounts of a hypofunctional enzyme or a reduced amount of functional enzyme, respectively (Figure 1C). The adherent mucilage of Dja-1 and Sk-1-1 accessions had a different appearance to that of mum2 mutants, in agreement with their causal mutations being in PMEI6 and PER36, respectively (Figure S1I andS1J).

Imbibition is modified in mutants that do not release mucilage

In order to examine in more detail the ecological significance of the absence of mucilage release in Arabidopsis accessions, physiological characteristics were examined in more detail. For these studies, insertion mutants in genes affecting mucilage production were used as the natural variants contain other polymorphisms that could influence the phenotypes examined. Three mucilage-release mutants were used, all in the reference accession Col-0; mum2-11 accumulates normal amounts of polysaccharides, whereas myb61 and myb5-1 have reduced polysaccharide accumulation [START_REF] Penfield | MYB61 is required for mucilage deposition and extrusion in the Arabidopsis seed coat[END_REF][START_REF] Macquet | A naturally occurring mutation in an Arabidopsis accession affects a b-Dgalactosidase that increases the hydrophilic potential of rhamnogalacturonan I in seed mucilage[END_REF][START_REF] Li | The Arabidopsis MYB5 transcription factor regulates mucilage synthesis, seed coat development, and trichome morphogenesis[END_REF][START_REF] Gonzalez | TTG1 complex MYBs, MYB5 and TT2, control outer seed coat differentiation[END_REF]. No consistent differences in germination were observed for different seed lots of wildtype, mum2-11 or myb61 seeds grown on high PEG concentrations (Figure S2; Protocol S2). As seeds for the same genotype from three independent cultures showed different germination capacities at high osmotic potential, this phenotype would appear to vary depending on the environmental conditions of mother plant culture.

The effect of mucilage retention on seed imbibition was examined in more detail for mum2-11 and myb5-1. Water mobility during seed imbibition was analysed by low-field NMR spectroscopy. The proton spin-spin relaxation times (T 2 ) depend on their molecular environment. NMR relaxation time measurements carried out on plant tissues are sensitive to the water content and localization of water in cells [START_REF] Hills | The influence of chemical and diffusive exchange on water proton transverse relaxation in plant tissues[END_REF][START_REF] Snaar | Probing water compartments and membrane permeability in plant cells by proton NMR relaxation measurements[END_REF] and relaxation signals are generally described by a multi-exponential behaviour reflecting different water compartments [START_REF] Sibgatullin | Analysis of diffusion and relaxation behavior of water in apple parenchymal cells[END_REF][START_REF] Musse | NMR study of water distribution inside tomato cells: effects of water stress[END_REF]. T 2 relaxation times were firstly attributed to water associated with different seed compartments using wild-type seeds (Table 2).

Water transfer rates between compartments were determined from the evolution of signal amplitudes. Although, wild-type seeds showed the expected rapid water uptake by mucilage polysaccharides over the first 90 minutes (Figure 2A), water transfer to internal seed tissues was slower for wild-type seeds than in mucilage release mutants (Figure 2B and Figure S3). This indicates that during early imbibition while water is transferred into the mum2-11 and myb5-1 seeds to interact with macromolecules, in the wild type it remains trapped outside the seed in mucilage. Furthermore, transfer of water to internal seed tissues was higher in myb5-1 than mum2-11, with amplitude already at high levels after the 5 minutes that had elapsed before the first measurement (Figure 2B). The presence of more non-released mucilage polysaccharides in mum2-11, therefore, reduced water transfer inside the seed compared to myb5-1.

A previous study has shown that myb5-1 seeds have higher oil contents than wild type [START_REF] Shi | Arabidopsis glabra2 mutant seeds deficient in mucilage biosynthesis produce more oil[END_REF]. Determination of seed oil content for dry seeds (

Seeds of mucilage release mutants float

Mutations of MUM2, PMEI6 and PER36 may result in modifications in other tissues where these genes are transcribed. Although MUM2 is almost exclusively expressed in vascular tissue in vegetative tissues [START_REF] Macquet | A naturally occurring mutation in an Arabidopsis accession affects a b-Dgalactosidase that increases the hydrophilic potential of rhamnogalacturonan I in seed mucilage[END_REF], the naturally occurring mutations are unlikely to increase fitness through improved water management as no difference was observed for mum2 mutants compared to wild type on water deficit (Figure S4; Protocol S3). Dry seeds of Plantago coronopus, a myxospermous species that grows in desert highlands, can be dispersed by run-on rainwater before sinking and adhering to soil by released mucilage [START_REF] Gutterman | Structure and function of the mucilaginous seed coats of Plantago coronopus inhabiting the Negev desert of Israel[END_REF]. In a similar manner, it was noted that when water was added to seeds of the mum2-11 mutant or accessions that do not release mucilage, the majority of seeds floated at the surface, whereas most wild-type Col-0 or mucilage releasing seeds sank (Figure 3A). Wild-type Col-0 seeds floated for a few seconds before mucilage was released and increased seed specific weight, whereas mutant seeds continued to float for many hours and even germinated at the water surface (Figure 3B) confirming that floating seeds were imbibed. The floating phenotype was also observed for seeds of myb5, ttg1, gl2 and mum4 mucilage release mutants where mucilage accumulation is reduced [START_REF] Western | Isolation and characterization of mutants defective in seed coat mucilage secretory cell development in Arabidopsis[END_REF][START_REF] Usadel | RHM2 is involved in mucilage pectin synthesis and is required for the development of the seed coat in Arabidopsis[END_REF][START_REF] Li | The Arabidopsis MYB5 transcription factor regulates mucilage synthesis, seed coat development, and trichome morphogenesis[END_REF][START_REF] Gonzalez | TTG1 complex MYBs, MYB5 and TT2, control outer seed coat differentiation[END_REF][START_REF] Western | MUCILAGE-MODIFIED4 encodes a putative pectin biosynthetic enzyme developmentally regulated by APETALA2, TRANSPARENT TESTA GLABRA1, and GLABRA2 in the Arabidopsis seed coat[END_REF]. Buoyancy maintenance was not due to differences in mutant dry seed surface area or weight (Figure S5; Protocol S4).

Identification of a new class of natural mucilage variants that float

Since flotation was observed in central Asian and Scandinavian accessions, we screened for seed flotation in an extra set of 53 Arabidopsis accessions from central Asia (including Russia) and Scandinavia (Table S4). Seeds were examined for flotation by imbibition in water followed by ruthenium red staining; seeds of four accessions floated and these originated from the Altaı Republic of Russia, close to the border with Kazakhstan. Interestingly, staining indicated that mucilage had been released from these accessions, and that the adherent layer of mucilage was greatly reduced (Figure 4C compared to 4A); these accessions were termed Floating Mucilage Releasing (FMR) accessions.

Cellulose in adherent mucilage is necessary for fixing mucilage pectin domains to the seed; seeds of cesa5, fei2 and sos5 mutants are affected in cellulose production and have a reduced amount of adherent mucilage (Figure 4B) [START_REF] Harpaz-Saad | Cellulose synthesis via the FEI2 RLK/SOS5 pathway and CELLULOSE SYNTHASE 5 is required for the structure of seed coat mucilage in Arabidopsis[END_REF][START_REF] Mendu | Subfunctionalization of cellulose synthases in seed coat epidermal cells mediates secondary radial wall synthesis and mucilage attachment[END_REF][START_REF] Sullivan | CESA5 is required for the synthesis of cellulose with a role in structuring the adherent mucilage of Arabidopsis seeds[END_REF]. Imbibed seeds of FMR accessions showed little or no cellulose labelling within the thin layer of adherent mucilage, in contrast to the wild-type Col-0 accession where cellulose was visible as rays originating from the tops of columella as well as diffuse labelling between rays (Figure 4D and4G). Labelling of FMR seeds was even more reduced than that observed with cesa5 (Figure 4E and4H). Nevertheless, in the FMR accessions columella and radial cell walls were visible, as well as outer cell wall fragments (Figure 4F and4I).

The reduction of adherent mucilage in the cesa5 mutant has been associated with a redistribution of RG I sugars to the watersoluble mucilage layer [START_REF] Sullivan | CESA5 is required for the synthesis of cellulose with a role in structuring the adherent mucilage of Arabidopsis seeds[END_REF]. The amount of sugars in water-soluble mucilage was, therefore, determined for the different FMR accessions compared to wild-type Col-0 and cesa5-1 (Figure 5). All four FMR accessions had higher amounts of water-soluble mucilage sugars than wild type, like cesa5-1, indicating that FMR mutants also show redistribution of mucilage to the water-soluble layer.

Discussion

Natural variation between populations is a useful tool for the identification of mutations that produce physiological changes. Previously a visual screen for defective mucilage release from seeds of Arabidopsis accessions had identified Shahdara and Dja-1 as natural mutants affected in the MUM2 and PMEI6 genes, respectively [START_REF] Macquet | A naturally occurring mutation in an Arabidopsis accession affects a b-Dgalactosidase that increases the hydrophilic potential of rhamnogalacturonan I in seed mucilage[END_REF][START_REF] Saez-Aguayo | PECTIN METHYLESTERASE INHIBITOR6 promotes Arabidopsis mucilage release by limiting methylesterification of homogalacturonan in seed coat epidermal cells[END_REF]. Here we have identified a further eight accessions affected in mucilage release and shown that their seeds float on water (Table 1; Table S1; Figure 3). An additional four accessions were also identified whose seeds float, but release mucilage, termed FMR accessions (Figure 4; Table S4).

Seven of the eight accessions affected in mucilage release were mum2 mutants resulting from six different mutations that were distinct from the original Shahdara mutation (Figure 1A). In the accessions that are mum2 mutant alleles, MUM2 transcript abundance and the extent of adherent mucilage swelling were in accord with the mutations identified (Figure 1B and1C; Figure S1). The Sk-1-1 accession was found to contain a non-sense mutation in PER36. The identification of only one natural mutant in PMEI6 and PER36 genes compared to eight variants with 7 causal mutations for MUM2 may be due to the size of the MUM2 gene region, 5751 bp, which would increase the probability of mutation compared to the 816 bp and 1451 bp of PMEI6 and PER36, respectively.

FMR accessions had an extremely reduced layer of adherent mucilage (Figure 4C), whereas soluble mucilage amounts were higher than those of the Col-0 accession (Figure 5). Mutants affected in the synthesis of cellulose present in adherent mucilage, cesa5, fei2 and sos5, have similar mucilage phenotypes. Nevertheless, some cellulose is still observed in the adherent mucilage of these mutants as rays, even in knockout mutants (Figure 4E and 4H) [START_REF] Harpaz-Saad | Cellulose synthesis via the FEI2 RLK/SOS5 pathway and CELLULOSE SYNTHASE 5 is required for the structure of seed coat mucilage in Arabidopsis[END_REF][START_REF] Mendu | Subfunctionalization of cellulose synthases in seed coat epidermal cells mediates secondary radial wall synthesis and mucilage attachment[END_REF][START_REF] Sullivan | CESA5 is required for the synthesis of cellulose with a role in structuring the adherent mucilage of Arabidopsis seeds[END_REF], and these are not observed in the FMR accessions (Figure 4F and4I). Furthermore, seeds of cesa5-1 mutants do not float. This indicates that the mutation(s) in FMR accessions have a more profound effect on the synthesis of cellulose present in seed mucilage. Identification of the gene(s) affected should further our understanding of cellulose production and the interactions between cellulose and pectin.

Seed flotation enables long-distance dispersion on water. A previous study has observed seed dispersion by flotation on run-on rainwater for Plantago coronopus, which inhabits desert highlands. This species also releases mucilage from seeds and it was observed that dry seeds floated for between 10 to 44 minutes before sinking [START_REF] Gutterman | Structure and function of the mucilaginous seed coats of Plantago coronopus inhabiting the Negev desert of Israel[END_REF]. Similarly mucilage retention in the seed coat, or its release as mainly water-soluble mucilage, allowed Arabidopsis seeds to float, and even germinate on the water surface (Figure 3). Mutations causing natural Arabidopsis variants to float could, therefore, be a local adaptation to improve seed dispersal. In effect, the collection sites of Neo-3, Neo-6 and Sus-1 accessions were near to rivers. The external surfaces of seed coats are remarkably diverse and features such as hairs or wings are often used to assist dispersal. Genetic variation in Arabidopsis seed dispersal has previously been observed, but was a maternally inherited trait controlled by plant architecture and expressed in high-density populations [START_REF] Donohue | Genetic basis and consequences of niche construction: plasticity-induced genetic constraints on the evolution of seed dispersal in Arabidopsis thaliana[END_REF][START_REF] Wender | Density-dependent processes influencing the evolutionary dynamics of dispersal: a functional analysis of seed dispersal in Arabidopsis thaliana (Brassicaceae)[END_REF]. This contrasts with the genetic variants identified here that might modify seed dispersal independently of maternal effects. Although the existence of genetic variation for a characteristic that could influence dispersal reveals the potential for evolution of this trait, the advantage of floating due to modified mucilage properties remains to be demonstrated; at the species level, the footprint of natural selection was not observed.

Seed mucilage polysaccharides represent 3% of dry seed weight [START_REF] Sullivan | CESA5 is required for the synthesis of cellulose with a role in structuring the adherent mucilage of Arabidopsis seeds[END_REF] and their production is a significant metabolic investment for the mother plant. Several mucilage release mutants have been identified that accumulate reduced amounts of mucilage and tests using myb5, ttg1, gl2 and mum4 mutants showed that their seeds also floated. Yet, none of the accessions affected in mucilage release were affected in loci that reduce the accumulation of mucilage polysaccharides (Figure 1C) [START_REF] Macquet | A naturally occurring mutation in an Arabidopsis accession affects a b-Dgalactosidase that increases the hydrophilic potential of rhamnogalacturonan I in seed mucilage[END_REF][START_REF] Saez-Aguayo | PECTIN METHYLESTERASE INHIBITOR6 promotes Arabidopsis mucilage release by limiting methylesterification of homogalacturonan in seed coat epidermal cells[END_REF]. This suggested that the nonreleased polysaccharides present in the epidermal cells of the seed coat serve a function. Low-field NMR analysis of water uptake by seeds showed that rates of transfer inside the seed and in interaction with macromolecules in seed tissues were higher in myb5-1 than mum2-11 (Figure 2; Figure S3). The presence of more mucilage polysaccharides in the epidermal cell layer, therefore, decreased the speed with which the tissues within the seed were imbibed and would maintain mum2-11 seed buoyancy, whereas the floating capacity of myb5 seeds would be reduced.

The four FMR accessions present a novel mucilage phenotype with almost no adherent mucilage (Figure 4) while the amounts of soluble mucilage released were higher than those observed in wildtype Col-0 (Figure 5). In these accessions, the mucilage produced could not maintain buoyancy by reducing water uptake by internal seed tissues. Mucilage is also produced by root cap cells and, like seed coat mucilage, it is at the interface between plant cells and the external environment. One of the roles proposed for root cap mucilage has been the structuration of bacterial communities present in the rhizosphere through its metabolism [START_REF] Beniziri | Additions of maize root mucilage to soil changed the structure of the bacterial community[END_REF]. In the same manner, a recent study has implicated the metabolism of seed mucilage by soil microorganisms in the promotion of Artemisia sphaerocephala seedling growth [START_REF] Nguema-Ona | Arabinogalactan proteins in root-microbe interactions[END_REF]. The soluble mucilage from hydrated seeds of FMR accessions would be released into the soil near the mother plant and could aid in the modulation of soil flora as observed for root mucilage [reviewed in [START_REF] Nguema-Ona | Arabinogalactan proteins in root-microbe interactions[END_REF].

Released mucilage has been proposed to enhance seed hydration and to enable germination under conditions of reduced water potential [START_REF] Penfield | MYB61 is required for mucilage deposition and extrusion in the Arabidopsis seed coat[END_REF]. Although rapid uptake of water was observed for adherent mucilage polysaccharides in wild-type Col-0 seeds (Figure 2A), water was transferred at a slower rate to internal seed tissues compared to seeds of mucilage release mutants (Figure 3B; Figure S3). This demonstrates that although mucilage polysaccharides are an excellent hydrogel, they do not increase transfer of water into seeds. Accordingly, seed germination on high concentrations of PEG was not consistently different between seeds that released mucilage and those that did not (Figure S2). The more rapid imbibition of internal seed tissues in mucilage release mutants might enable them to germinate more rapidly, but differences in germination reported for certain Arabidopsis mucilage mutants have indicated that the absence of released mucilage causes a germination lag [START_REF] Penfield | MYB61 is required for mucilage deposition and extrusion in the Arabidopsis seed coat[END_REF][START_REF] Witztum | Integumentary mucilage as an oxygen barrier during of Blepharis persica (Burm) Kuntze[END_REF][START_REF] Keijzer | A seed shape mutant of Arabidopsis that is affected in integument development[END_REF][START_REF] Arsovski | MUM ENHANCERS are important for seed coat mucilage production and mucilage secretory cell differentiation in Arabidopsis thaliana[END_REF]. Alternatively, as the adherent mucilage traps water around the seed, this could slow the rate of seed drying. Studies on the desert shrub Artemisia sphaerocephala have shown that DNA repair was improved in achenes with mucilage humidified by desert dew, compared to achenes where mucilage had been removed [START_REF] Yang | The achene mucilage hydrated in desert dew assists seed cells in maintaining DNA integrity: adaptive strategy of desert plant Artemisia sphaerocephala[END_REF]. Seed mucilage could, therefore, prolong the imbibed state, providing more time for repair mechanisms to function and thereby improve seed longevity.

In conclusion, the identification of fourteen natural Arabidopsis mucilage mutants that float has highlighted the occurrence of at least ten independent mutation events, affecting four different loci, in populations in central Asia and Scandinavia. These mutations lead to modifications in seed mucilage production that maintain buoyancy compared to seeds that release a thick adherent layer of mucilage. Whether this is an adaptive trait requires further study, as among the accessions studied here the population genetic signature of local adaptation was not detected. Genetic variation in mucilage properties promises to contribute to our understanding of the ecological relevance of its production and the populations where mucilage release is not a fixed trait will be an important tool for testing potential roles.

Materials and Methods

Plant material and mucilage phenotyping

Accessions were obtained from the Versailles Arabidopsis Stock Centre (http://publiclines.versailles.inra.fr/) except for the Norwegian and Swedish populations in Table 1 and Table S1, which were kindly donated by Odd-Arne Rognli through NARC (Norway). Seeds for new central Asia accessions, including Dja, Sus and Neo, were collected from their natural habitat (Table S1) http://www.inra.fr/vast/collections.htm). Genetic differentiation of MUM2 was examined in 289 lines corresponding to 15 Norwegian, 6 central Asian, 7 Spanish and 13 French populations [START_REF] Kronholm | Influence of mutation rate on estimators of genetic differentiation -lessons from Arabidopsis thaliana[END_REF]. The mum2-10, mum2-11 and cesa5-1 mutants (SALK_011436, SALK_110461 and SALK_125535, respectively; Col-0 background) were obtained in previous studies [START_REF] Macquet | A naturally occurring mutation in an Arabidopsis accession affects a b-Dgalactosidase that increases the hydrophilic potential of rhamnogalacturonan I in seed mucilage[END_REF][START_REF] Desprez | Organization of cellulose synthase complexes involved in primary cell wall synthesis in Arabidopsis thaliana[END_REF]. The ttg1 (GK_286A06), mum4 (SALK_085051), myb61 (SALK_106556) and gl2 (SM_3_16350) mutants, all Col-0 background, were obtained from the Nottingham Arabidopsis Stock Centre ( [START_REF] Tissier | Multiple independent defective suppressor-mutator transposon insertions in Arabidopsis: a tool for functional genomics[END_REF][START_REF] Alonso | Genomewide insertional mutagenesis of Arabidopsis thaliana[END_REF][START_REF] Rosso | An Arabidopsis thaliana T-DNA mutagenized population (GABI-Kat) for flanking sequence tagbased reverse genetics[END_REF]; http://arabidopsis.info). The myb5-1 (SALK_030942) and aba3-1 mutants [START_REF] Gil | Isolation and characterization of abscisic acid-deficient Arabidopsis mutants at two new loci[END_REF] were a gift of C. Dubos and M. Koornneef, respectively. Crosses were performed between mum2-12 (Shahdara accession) and Dja-1, Sus-1, Neo-3, Neo-6, Ale-8, Had-3-1, Lom-3-1, Nfro-1-1, Sk-1-1 and Sku-20, and between Dja-1 and Sk-1-1 accessions. As the seed coat is maternally derived, seed coats of progeny from F 2 and F 3 generations were examined; only seeds from crosses with Dja-1 and Sk-1-1 showed genetic complementation. The gene affecting mucilage release in Sk-1-1 was localised to an interval on the lower arm of chromosome 3 using a mapping population of 176 F2 individuals derived from a cross between Col-0 and Sk-1-1 accessions. DNA was extracted from 33 F2 progeny that did not release mucilage, using 10 seedlings from each. Whole-genome resequencing was carried out on this DNA by Genome Enterprise Ltd (http://www.norwichresearchpark. com/parkdirectory/genomeenterpriselimited.aspx) using an Illumina HiSeq 2000 sequencer. The SHOREmap software package with bwa aligner (http://1001genomes. org/downloads/shore. html) was used to map the Sk-1-1 polymorphisms against those of the Col-0 accession and identify mutations. The output of this pipeline was filtered for mutations in the mapping interval on the chromosome 3. These polymorphisms were then filtered against polymorphisms present in the genomes of 17 accessions available from the 1001 genome project (http://1001genomes.org/index. html) and known to release mucilage; Alc-0, Altai-5; Baz-0, Blh-1, C24, Dja-1, Gol-1, Jea, Ler-0, Neo-6, Oy-0, Qar-8a, Ri-0, Sakata, Sus-1, Ws-2 and Zal-1. These sequence data were produced by the Weigel laboratory at the Max Planck Institute for Developmental Biology, the Ecker laboratory at the Salk Institute [START_REF] Schmitz | Patterns of population epigenomic diversity[END_REF], the Pennacchio laboratory at the DOE Joint Genome Institute, and the Mott laboratory at the Wellcome Trust Center for Human Genetics [START_REF] Gan | Multiple reference genomes and transcriptomes for Arabidopsis thaliana[END_REF]. Of the 258 SNPs that were Sk-1-1 specific only 4 resulted in the introduction of a stop codon; one of these was in PER36, which has been shown to be required for mucilage release [START_REF] Kunieda | Spatiotemporal secretion of PEROXIDASE36 is required for seed coat mucilage extrusion in Arabidopsis[END_REF].

All phenotypic analyses were carried out using seed lots or tissue obtained from plants cultured simultaneously. Phenotyping for mucilage release was carried out as described previously [START_REF] Macquet | A naturally occurring mutation in an Arabidopsis accession affects a b-Dgalactosidase that increases the hydrophilic potential of rhamnogalacturonan I in seed mucilage[END_REF] or by imbibing seeds on filter paper (6 cm dia.) hydrated with 700 mLof water for 1 h followed by staining with 200 mgm L 21 ruthenium red. Wild-type Col-0, mum2-11 and accessions defective for release were treated with 0.05 N HCl then 0.3 M NaOH to release mucilage and stained with ruthenium red as described previously [START_REF] Macquet | A naturally occurring mutation in an Arabidopsis accession affects a b-Dgalactosidase that increases the hydrophilic potential of rhamnogalacturonan I in seed mucilage[END_REF].

Seeds for 53 accessions (Table S4) were obtained from 2 independent series of plants cultured in compost (Tref Substrates, http://www.jiffygroup.com/) in a growth chamber (21uC day, 17uC night, 150 mmol m 22 s 21 light intensity, 16 h photoperiod, 65% relative humidity). A seed lot from each culture was examined for seed flotation by imbibition of seeds for 10 min in water, followed by staining in 500 mgm L 21 ruthenium red and observation with a light microscope (Axioplan 2; Zeiss; http:// www.zeiss.fr/).

DNA extraction and obtaining MUM2 sequences

DNA for PCR analysis was extracted from flower buds as described by Doyle and Doyle [START_REF] Doyle | Isolation of plant DNA from fresh tissues[END_REF]. The full sequence of MUM2 in a subsample of 28 accessions was retrieved from public databases [START_REF] Cao | Wholegenome sequencing of multiple Arabidopsis thaliana populations[END_REF]. Otherwise, sequencing of the MUM2 gene was performed as described by Sullivan et al. [START_REF] Sullivan | CESA5 is required for the synthesis of cellulose with a role in structuring the adherent mucilage of Arabidopsis seeds[END_REF]. The Arabidopsis lyrata sequence of MUM2 was obtained from the public database and used as outgroup (http://www.phytozome.net/alyrata) [START_REF] Hu | The Arabidopsis lyrata genome sequence and the basis of rapid genome size change[END_REF]. Genotyping with the MUM2 Sha marker was carried out by PCR amplification of either a 162 bp (wild-type) or 118 bp (mum2-12) DNA fragment with forward primer 59-TGGTCGTTATTGG GTCTCGT-39 and reverse primer 59-TTAAGAACGCCCGAG-GAATA-39. Two fragments of MUM2 were re-sequenced for 41 Arabidopsis accessions collected worldwide and for the 110 individuals collected in Norway and central Asia; the 59 portion of ,1000 bp was amplified using forward primer 59-GAAG-GAGGCATCGATGTGAT-39 and reverse primer 59-GGTGAG TTTGGTCCAGGAAA-39 and the 39 portion of ,600 bp was amplified using forward primer 59-CTGGAGCTTACATGGA-GAGGA-39 and primer 59-CAAGAGGATCACCTTCC-39.

Expression analysis

Developing siliques at 8 to 12 days after pollination were pooled and total RNA extracted and reverse transcribed as described previously [START_REF] Saez-Aguayo | PECTIN METHYLESTERASE INHIBITOR6 promotes Arabidopsis mucilage release by limiting methylesterification of homogalacturonan in seed coat epidermal cells[END_REF]. Quantitative real-time PCR reactions were performed as described by Plessis et al. [START_REF] Plessis | New ABAhypersensitive Arabidopsis mutants are affected in loci mediating responses to water deficit and Dickeya dadantii infection[END_REF]. MUM2 specific primers were as follows, forward primer 59-CAGCGG-CATGGTTGGTCT-39 and reverse primer 59-CCAAG-CAAACCCACCGAGT-39, and had been tested for their efficiency rates and sensitivity on a dilution series of cDNAs. EF1a4 primers have been described previously [START_REF] Plessis | New ABAhypersensitive Arabidopsis mutants are affected in loci mediating responses to water deficit and Dickeya dadantii infection[END_REF].

Extraction and analysis of water-soluble mucilage

Water-soluble mucilage extracts were obtained from 200 mg of intact seeds as described previously [START_REF] Sullivan | CESA5 is required for the synthesis of cellulose with a role in structuring the adherent mucilage of Arabidopsis seeds[END_REF] The uronic acid (as GalA) and total neutral sugar (as Rha) contents were determined by the automated m-hydroxybiphenyl and orcinol methods, respectively [START_REF] Thibault | Automatisation du dosage des substances pectiques par la me ´thode au me ´tahydroxydiphe ´nyle[END_REF][START_REF] Tollier | Adaptation de la me ´thode a `l'orcinol sulfurique au dosage automatique des glucides neutres totaux: conditions d'application aux extraits d'origine ve ´ge ´tale[END_REF].

Low-field NMR

1 H NMR measurements were performed using a Time-Domain spectrometer (Minispec BRUKER; http://www.brukeroptics. com/) operating at a resonance frequency of 20 MHz. The NMR system was equipped with a temperature control device connected to a calibrated optic fibre (Neoptix Inc.; http://www. neoptix.com/) allowing for 60.1uC temperature regulation. For the assignment of T 2 relaxation times to different water compartments, measurements were firstly obtained for three different wild-type Col-0 samples; intact imbibed seeds, intact dry seeds and imbibed seeds pre-treated to remove soluble mucilage, but with adherent mucilage; water-soluble mucilage was extracted from wild-type Col-0 seeds as described previously [START_REF] Sullivan | CESA5 is required for the synthesis of cellulose with a role in structuring the adherent mucilage of Arabidopsis seeds[END_REF] and after lyophilisation, seeds without soluble mucilage were resuspended in water and analysed by NMR. The mature, ''dry'' Arabidopsis seeds (approximately 8% water content) were introduced into NMR tubes (10 mm dia.). In order to fill tubes to a 10 mm height, corresponding to the homogeneous region of the NMR radiofrequency, 200 to 220 mg of Arabidopsis seeds were used and imbibed with 150 to 220 ml of deionised water, tubes were then weighed and hermetically sealed. Acquisitions of T 2 were carried out from 5 min to 24 h of imbibition and samples were analysed at ambient temperature (20uC). Two types of pulse sequences were used; proton free induction decays (FID) were acquired using the following parameters: a 90u pulse of 2.6 ms, a dwell time of 0.4 ms between two successive data points, 16 scans of 150 data points, and a recycle delay of 9 s between each scan, and the Carr-Purcell-Meiboom-Gill (CPMG) pulse sequence with a time echo of 0.2 ms. Sixteen scans were acquired for each genotype with 8000 or 16000 data points [START_REF] Meiboom | Modified spin-echo method for measuring nuclear relaxation times[END_REF].

Transverse relaxation data were analysed with the following model:

I CPMG (t)~X ? i~1 A i |exp({ t T 2i )
where T 2i are the relaxation times of the mobile populations and A i is the intensity of the mobile populations [START_REF] Meiboom | Modified spin-echo method for measuring nuclear relaxation times[END_REF]. To ensure the accuracy of the data treatment, spin-spin relaxation decay curves were fitted using MEM [START_REF] Mariette | Continuous relaxation time distribution decomposition by MEM[END_REF] and a discrete method [START_REF] Marquardt | An algorithm for least squares estimations of nonlinear parameters[END_REF].

In imbibed intact seeds five T 2 components were identified which could be assigned to protons of water populations with different mobility and ratio (expressed in relative percentage) (Table 2). The first and second components, T 2 (1) and T 2 (2), were also observed in dry seeds and could be assigned, respectively, to the solid phase of the seed, notably macromolecules such as polysaccharides and proteins, and protons in exchange with the hydroxyl groups found in these macromolecules. The latter two components (T 2 (3) and T 2 (4)) were assigned to oil with a superposed contribution from water in both as intracellular water in the former and in adherent mucilage in the latter. Comparison of T 2 (3) and T 2 (4) values for dry seeds with those obtained in imbibed seeds with water-soluble and adherent mucilage or only adherent mucilage confirmed the latter attributions (Table 2). A fifth component, T 2 [START_REF] Windsor | Arabidopsis seed coat development: morphological differentiation of the outer integument[END_REF], was identified in imbibed wild-type seeds that corresponded to water in soluble mucilage. This component was also present in imbibed mutant seeds where it was attributed to water outside seeds (Table 2).

In order to verify the assignment given to the multi-exponential NMR signals for water in seed compartments, at the end of NMR measurements, the water content of samples was estimated by weighing before and after drying in an oven at 103uC for 24 h. The amplitudes of the NMR signals from the seeds before and after imbibition were compared to the amplitude of the signal expected from distilled water. The signals expected from water were calculated for each sample and each compartment as the product of its mass, its water content and the signal of the distilled water per unit mass. The water content of each compartment was then calculated by deducing the signal contribution from oil.

Analysis of the evolution of signal amplitudes for the different components allowed the water transfer rates between different compartments to be determined. The total water content was calculated using the T 2 amplitude and was coherent with results using a gravimetrical method before and after drying seeds.

Calculation of water content for each compartment confirmed that even after 24 h of imbibition, approximately 40% of water associated with wild-type seeds was trapped outside in mucilage (Table 2).

Cytochemical staining of adherent mucilage

Seeds were imbibed in water for 3 h then rinsed twice prior to staining. The released adherent mucilage was stained with ruthenium red as previously described [START_REF] Macquet | A naturally occurring mutation in an Arabidopsis accession affects a b-Dgalactosidase that increases the hydrophilic potential of rhamnogalacturonan I in seed mucilage[END_REF] or Pontamine Fast Scarlet S4B in 150 mM NaCl [START_REF] Anderson | Real-time imaging of cellulose reorientation during cell wall expansion in Arabidopsis roots[END_REF]. Observations were carried out with a light microscope for ruthenium red (Axioplan 2; Zeiss) or a Zeiss LSM710 confocal microscope using a 561 nm diode laser line to excite Pontamine and detecting fluorescence emission between 570 and 650 nm. For comparison of signal intensity within a given experiment laser gain values were fixed.

Figure 1 .

 1 Figure 1. Characterization of natural mum2 mutants. (A) Schematic representation of the MUM2 gene indicating the positions of the causal mutations in the different accessions and their effect on the encoded protein in capital letters. Boxes represent exons; black shading shows coding sequence; grey shading indicates 59 and 39 untranslated regions. (B) Steady state MUM2 mRNA levels in developing siliques of indicated accessions, 8-12 days after pollination, represented as a percentage of the constitutive EF1a-4a (EF) gene abundance. Error bars represent SE (n = 6). (C) Ruthenium red stained seeds of indicated accessions after forced mucilage release by sequential treatment with HCl and NaOH. WT, wild type. doi:10.1371/journal.pgen.1004221.g001

Figure 2 .

 2 Figure 2. mum2 seeds float at the water surface. (A) After placing in contact with water the majority of mum2-11 seeds float, in contrast to wild-type Col-0 (WT) seeds that sink to the bottom of the tube. (B) Floating mum2-11 seeds germinate after 48 h of imbibition at the water surface. doi:10.1371/journal.pgen.1004221.g002

Figure 3 .

 3 Figure 3. Maintenance of seed buoyancy in mum2 seeds is associated with delayed water uptake. Evolution of water uptake by adherent mucilage and internal seeds tissues as determined by lowfield NMR. Variation of the amplitude of T 2 values (A) for, water in adherent mucilage and oil (component 4), and (B) water in internal seed tissues (component 3), during imbibition of seeds of wild type, mum2-11 and myb5-1. Standard errors are estimated at 3.4% and 1%, respectively. Results from two experiments with seeds from independent cultures gave similar results. WT, wild type. doi:10.1371/journal.pgen.1004221.g003

Figure 4 .Figure 5 .

 45 Figure 4. Adherent mucilage width and cellulose labelling are reduced in floating mucilage-releasing (FMR) accessions. Ruthenium red staining of pectins (A)t o( C) and Pontamine S4B staining of cellulose (D)t o( I) in the adherent mucilage released from imbibed seeds of wild-type Col-0 (A), (D) and (G), cesa5-1 (B), (E) and (H), and the FMR accession Rak-1 (C), (F) and (I). (G)to(I) are magnifications of regions in (D)t o( F), respectively. Images (D)t o( G) are shown using the Rainbow2 look-up table. Bars = 150 mm( A)to(F)or20mm(G)to(I). C, Columella; o, outer cell wall; r, radial cell wall. doi:10.1371/journal.pgen.1004221.g004

Table 2

 2

	, A(3)+A(4)) confirmed this finding (46.1%60.71
	for myb5-1, 40.34%61.35, wild type and 42.62%60.73, mum2-11).

Table 1 .

 1 List of Arabidopsis accessions analysed for seed mucilage release in this study.

				Number of
				individuals
				affected in
	Population	Geographic region	N	mucilage release
	Ale	Scandinavia	19	1
	Dja	Central Asia	9	9
	Eid-1	Scandinavia	5	0
	Had-3	Scandinavia	5	5
	Kar	Central Asia	11	0
	Kon-2	Scandinavia	5	0
	Kvi-2	Scandinavia	5	0
	Kyr	Central Asia	8	0
	Lod-2	Scandinavia	5	0
	Lod-3	Scandinavia	5	0
	Lom-3	Scandinavia	5	5
	Neo	Central Asia	25	25
	Nfro-1	Scandinavia	5	5
	Ro ¨d	Scandinavia	16	0
	Sk-1	Scandinavia	5	5
	Sku	Scandinavia	15	8
	Sus	Central Asia	7	7
	Tje-1	Scandinavia	5	0
	Veg-1	Scandinavia	5	0
	Veg-2	Scandinavia	4	0
	Vgn-1	Scandinavia	5	0
	Zal	Central Asia	5	0
	N, number of individuals sampled in population.

doi:10.1371/journal.pgen.1004221.t001

Table 2 .

 2 Attribution, value and amplitude of T 2 relaxation signals obtained in low-field NMR analyses of dry and imbibed Arabidopsis seeds.

		Component
		12			3			4			5
	Signal attribution in dry seeds Solid phase (macromolecules)	Exchangeable protons	Oil			Oil			-
	Attribution in imbibed (imb) seeds	Solid phase (macromolecules)	Exchangeable protons	Water within seeds and oil	Water within adherent mucilage and oil	Water outside seeds
		%A(1)	T 2 (1)	water (%)	%A(2)	T 2 (2)	water (%) %A(3)	T 2 (3)	water (%)	%A(4)	T 2 (4)	water (%)	%A(5)	T 2 (5)	water (%)
	WT Col0 WSM imb 1 h	12.5	0.0240	0	26.2	3.487	19	29.6	43.9	10.39	31.8	223	12.52	-	-	-
	WT Col0 dry	49.1	0.0164	0	11.5	0.231	8.46	20.2	35.2	0	19.2	138	0-	-	-
	WT Col0 imb 24 h	10.5	0.0249	0	18.4	2.466	15.59	33.0	19.8	17.29	38.1	114	22.16	9.9	457	8.39
	mum2-11 dry	45.6	0.0165	0	11.2	0.211	8.5	22.1	35.2	0	21.0	140	0-	-	-
	mum2-11 imb 24 h	14.0	0.0239	0	15.4	1.068	12.30	46.5	11.7	21.05	20.3	78	0.99	3.9	319	3.09
	myb5-1 dry	42.9	0.0165	0	10.5	0.176	8.10	23.9	35.8	0	22.7	141	0-	-	-
	myb5-1 imb 24 h	11.6	0.0231	0	15.5	1.212	12.66	37.3	13.5	15.92	29.9	67	10.67	5.7	266	4.61

Water contributions to components 3 and 4 in imbibed seeds were calculated based on oil contents in dry seeds. WSM, without soluble mucilage. doi:10.1371/journal.pgen.1004221.t002

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March 2014 | Volume 10 | Issue 3 | e1004221

PLOS Genetics | www.plosgenetics.org

Acknowledgments

We thank M.-J. Cre ´peau and P. Delagarde for technical aid, F. Mariette for advice on NMR data analyses and M. Anjue `re and H. Ferry for assistance with plant culture. NMR analyses were performed on the PRISM platform, Rennes, France.

This work was supported in part by the INRA Plant Biology and Amelioration section (grant number BAP2013_22-ExMu), the ANR-program (grant number ANR-08-BLAN-0061) that included a doctoral fellowship to SSA, and by a doctoral fellowship from the French Ministry of Education and Research to AM. The Zeiss 710 confocal microscope in the IJPB Observatoire du Ve ´ge ´tal was cofinanced by a grant from the Conseil Ge ´ne ´ral des Yvelines. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Supporting Information

Author Contributions