Frédéric Leonardi

Mathieu Larochette

Djamel Nasri

Didier Graebling

OPTIMISATION OF EXTRUDED POLYMER FOAM BY THE RESIDENT TIME DISTRIBUTION APPROACH

In this work, we used the Residence Time Distribution (RTD) to study the polystyrene foaming during an extrusion process. The extruder associated with a gear pump is simply and quantitatively described by three continuoustly stirred tank reactors with recycling loops and one plug-flow reactor. The blowing agent used is CO 2 and its obtained by thermal decomposition of a chemical blowing agent (CBA). This approach allows to optimize the density of the foam in accordance with the CBA kinetic of decomposition.

Introduction

The Resident Time Distribution (RTD) is a theoretical frame for studying complex flow networks and is perfectly adequate for describing the polymer flow through an extruder. For reactive extrusion processes where the reaction time is of the same order of the mean residence time, the RTD is of interest, since the length of time that the material remains in the extruder should be closely coupled to the reaction kinetics. The RTD approach has been proved for its efficiency to simulate the twin-screw extruder [1] to [11] .

In this paper, we have studied the processing of polystyrene foam by extrusion in a single screw extruder coupled with a gear pump. The basic principle of foaming is to mix a blowing agent into a polymer melt and induce a thermodynamic instability through a temperature or pressure change to nucleate bubbles of the blowing agent. After nucleation, the bubble growth is controlled by reducing the temperature lower than the glass transition temperature of the polymer [12] . The blowing agent used is CO 2 and its obtained by thermal decomposition of an organic molecule called Chemical Blowing Agent (CBA).

To obtain an optimal foam, i.e. lower density, the process parameters of the extruder must be adapted to the CBA kinetic of decomposition.

Theoretical background

Suppose that an inlet particle concentration C i (t) is applied to the reactor [START_REF] Levenspiel | Chemical Reaction Engineering[END_REF][14] [START_REF] Nauman | Mixing in continuous flow systems[END_REF] . Then we want calculate the outlet particle concentration C o (t). The particles are conveyed by a fluid flowing at a volumetric rate Q. It is assumed that particles do not interact which each other. The number of particles that enter the reactor in the time interval (t ′ , t ′ + dt ′ ) and leave the reactor in the time interval

(t, t + dt) is Q C i (t ′ ) f (t -t ′ ) dtdt ′ . The total outflow dur- ing the time interval (t, t + dt) is Q C o (t)
dt, and thus:

Q C o (t) dt = Q dt t -∞ C i t ′ f t -t ′ dt ′ ⇒          C o (t) = t -∞ C i (t ′ ) f (t -t ′ ) dt ′ C o (t) = ∞ 0 C i (t -t ′ ) f (t ′ ) dt ′ (1)
f (t) is the residence time density function and it represents the density of probability expressed as probability per unit time. This function depends on the characteristics of the system. In the Laplace domain, the equation 1 becomes:

L {C s (t)} = L {C e (t)} × L { f (t)} ⇒ L { f (t)} = L {C s (t)} L {C e (t)} (2)
The function L { f (t)} is known as the transfer function of the reactor. If the inlet signal is a Dirac delta function, the outlet response of the system is identical to the residence time density function.

The cumulative residence time distribution F(t) and the mean residence time of the reactor t are defined by the following equations:

F(t) = t 0 f t ′ dt ′ t = ∞ 0 t ′ f t ′ dt ′ = V Q ( 3
)
where V is the volume of the reactor and Q its flow rate.

The complex flow can be described by the association of two kinds of idealized reactors called the Continuoustly Stirred Tank Reactor or CSTR and the Plug-Flow Reactor or PFR. The residence time density function for each reactor is given by: CSTR :

f (t) = 1 t e -t/t PFR : f (t) = δ (t -t 0 ) (4)
In this article, we use a statistic theory instead of a physical model to related the overall RTD in an single extruder to those in appropriately divided elements. We represent a single extruder by addition of three identical CSTR and one PFR in series (F. 1).

Q o C (t) i Q + q CSTR 1 CSTR 2 CSTR 3 Q + q q q PFR Q Q C (t)
F. 1 The RTD vision of extruder.

Q is the volumetric flow rate passing through the system and q is the recycling volumetric flow rate between two CSTR. We define the recycling parameter α as the ratio q/ Q. For example, this recycling flow is due to the back pressure existing in the extruder. The residence time density function of the three identical CSTR with recycling loops is given by the following equation:

(t) = e t/t 4α t -2 + e -β t/t + e β t/t

with β = 2α 1 + 2α ( 5
)
where t is the mean time residence of one tank. The addition of the PFR implies a simple time shift. The residence time density function of the extruder is given by the following equation:

f (t) = e (t-t 0 )/t 4α t -2 + e -β (t-t 0 )/t + e β (t-t 0 )/t Υ(t -t 0 ) (6)
where t 0 is the mean residence time of the PFR and Υ(t) is the Heaviside step function. Without recycling, the equation 6 becomes:

f 0 (t) = lim α→0 f (t) = (t -t 0 ) 2 2 t3 e -(t-t 0 )/t Υ(t -t 0 ) (7)
In figure 2, we have shown the behaviour of the system given by the equation 5 for differents values of α and t. The relationship between t the mean time residence of one CSTR, t 0 the mean time residence of PFR and tx the mean time residence of the extruder is:

tx = ∞ 0 t f (t) dt = (3 + 4α) t + t 0 (8)
Experimental section

Products

The polystyrene PS 1450N was supplied by Total Petrochemicals. Carbon dioxide is produced by thermal decomposition of the chemical blowing agent: Tramaco NCS 175. The thermal decomposition of this agent is obtained in the temperature range of 135 to 220 • C. The tracer used is a blue dye for polystyrene referenced M120442 SPC from Elian.

Process

We used a single Thermo Haake Rheomex 252p extruder with a length to diameter ratio of 25:1. A gear pump MSDP 090/039 supplied by Xaloy (1.2 cm 3 /rpm), was mounted between the die and the end of the extruder. Usually, gear pumps are solely used to generate pressure ahead of the die. In this case, the pressure differential across the pump is positive. To increase the mean residence time, the melt pump was mounted to obtain a negative pressure differential. Our gear pump is correctly lubricated when the pressure differential is between 10 to 350 bars. The mixing capacity of gear pumps is very limited. The polymer melt is passed through a capillary die, diameter: 2 mm and length: 12 mm, before cooling with four computer fans. The cold extrudate is analyzed by the RTD system. To control the outflow speed of the extrudate a pelletiser Varicut (Thermo Haake) is modified and is used as a speed control pull system. This speed is adjusted to maintain the extrudate diameter equal to the die diameter.

RTD measurement

Many in-line methods have been proposed in the literature for RTD measurement [START_REF] Gendron | [END_REF] to [19] . An optical method based on light transmittance was chosen for our experiments. The RTD is measured by transit experiments by injecting a small quantity of an inert tracer at the feel hopper of the extruder. The dye concentration evolution is analyzed continuously in real time. A cold white light is used as light source. The transmitted light intensity is quantified by a photodiode supplied by Vishay Telefunken. An electronic module amplifies and converts the photodiode current in a voltage compatible with the analog to digital converter. The signal obtained is directly sent to a computer from the data acquisition system, ADC 212 Pico Technology. The RTD measurements were realized without the foaming agent and 100 mg of blue dye was used for each experiment.

Results and discussion

CBA kinetic of decomposition

The CBA decomposition was studied by thermal gravimetry analysis, TA 2950, in the temperature range of 100 to 300 • C for three heating rates: 10, 15 and 20 The kinetic experiments was carried out on a tailor-made system. For each temperature, the release volume of CO 2 produced by thermal decomposition of 100 mg of CBA was measured as a function of time. All results are given for the normal pressure, 1.013 10 5 Pa. The thermal decomposition of AIBN (azo bis isobutyronitrile) was used to validate our experimental approach. The rate of degradation was influenced only by the temperature of the sample (F. 3). The CO 2 release volume is given by the following equation:

V CO 2 = V ∞ 1 -exp k (t -t 0 ) (9)
where V ∞ , t 0 and k are respectively the total volume of CO 2 , the inhibition time and the kinetic constant associated to the decomposition. The F. 4 show the thermal behavior of these paramaters. The thermal variation of the kinetic constant clearly shows the two domains of temperature decomposition. The thermo-dependence of the inhibition time and the kinetic constant is given by an Arrhenius' law:

                 t 0 = 4.82 × 10 -7 exp 8.14×10 3 T (s) k 120→150 = 24.9 × 10 9 exp 99.7×10 3 T (s -1 ) k 150→200 = 5.4 exp 21.2×10 3 T (s -1 )
(10) The total volume of CO 2 variation is given by the following hyperbolic function of temperature:

V ∞ = 32.01 - 8.72 × 10 3 T (mL) (11)
The temperature in the extruder was set to a temperature range of 190-200 • C. In this case, the time to obtain the total decomposition of CBA is 150 s.

RTD for extruder

The gear pump mounted between the extruder and the die was used to increase the pressure gradient in the extruder. The appropriate gear pump lubrication is obtained when the operating pressure is higher than 1 MPa. To limite the polymer leak, the maximum operating pressure is fixed at 35 MPa. The range of pressure necessary for an accurate working of the pump strongly limits the domain of screw rotation speed explored (F. 5). Moreover, the domain size decreases dramatically with the extrusion temperature. In our experiments, the variation of the pressure gradient with the screw rotating speed is similar for all melt pump flow rates studied (Figure 6). The curves are shifted towards the screw rotating speed axis. For each experiment, the model parameters were determined by a non-linear least square method with S (numerical computational package developed by INRIA). In all cases, the standard deviation is less than 10 -3 . The RTD model (E. 6) is in perfect agreement with the experimental data. The theoretical and experimental mean resident times tx were calculated with the E. 8: direct integration for the experimental time and model paramaters for the theoretical time. The comparison between experimental data and the model confirms that the RTD approach is able to describe simply and quantitatively the extrusion process. The results in terms of mean resident times t 0 or tx shown the efficiency of the pump (F. 9 & 10). An increase in pressure gradient in the extruder implies an increase in the mean time residence.

The analysis of the three characteristic parameters of the residence time density function curve: t 0 , t and α is not obvious (Figure 11). For the same configuration of the extrusion line, we observe a decrease in the mean time residence and an increase in the recycling parameter with the screw rotating speed of the extruder. The effect of the pressure gradient is clearly shown by the variation of the α parameter. The mean resident time is defined by the ratio volume of the reactor and its flow rate. In the case of the CSTR with recycling loops the flow rate in the reactor is the sum of the global flow rate Q and the recycling flow rate q. Thus, the variation of t can be explained by the increase in the recycling flow while the volume of the reactor is constant. The influence of the addition of the gear pump is not clear. In this case, an increase in the mean resident times and a decrease in the recycling term were obtained. With the foam, the bubbles prevented any light transmission and so the RTD measurements become impossible with our system. The density of the foam provides another way to find the adequate process parameters. The density can be calculated with the mass, the dimensions of the extrudate and the kinetic parameters. The foams were prepared with 0.5 wt % in chemical blowing agent. In the case of the total decomposition of blowing agent, the value of foam density is 587 kg/m 3 . The T. 1 shows the relationship between the density of the foam and the process parameters. The density values given in this table are the 5 samples average. The pressure at the inlet of the gear pump was descreased in presence of the foaming agent. This effect is due to the solubility of CO 2 in the polymer matrix and the viscosity is a function of this solubility [12] . Lowest foam density was only obtained at 55 rpm with the gear pump (26 rpm). This value, 615 kg/m 3 , is close to the optimal density. The mean time residence of the extrusion line is higher than the time to obtain the total decomposition of CBA. In the absence of the pump, the mean time residence of the line is lower than the chemical time and the density foams are too high. The mean time residence of the extrusion line is the critical parameter.

Conclusions

The results obtained confirm that the Residence Time Distribution theory is able to describe simply and quantitatively an extrusion process. An association of three continuoustly stirred tank reactors with recycling loops and one plug-flow reactor was sufficient. In this case, the extrusion line without and with a gear pump could be described by three parameters: t 0 the delay time or the mean time residence of the PFR, t the mean time residence of each CSTR and α the recycling flow between the CSTR. In presence of the CBA, the formation of the bubbles does not allow the RTD measurements on the extrudate. A determination of the foam density shows the importance of the correlation between the chemical time associated to the blowing agent and the mean time residence of the extrusion line.

F. 2

 2 Theoretical RTD for 3 CSTR in series (Eq. 5). Residence time density function vs. time. A) t = 3 s B) α = 1.

F. 4

 4 CBA thermal decomposition. Kinetic parameters vs. reciprocal temperature.

F. 5

 5 Working domain in extrusion. Gear pump rotation speeds vs. screw rotation speeds at 180 and 220 • C.

T. 1

 1 Density of foams and pictures vs. process parameters.

  F. 11 t and α vs. screw rotation speeds at 190 • C for the extrusion line with and without gear pump.

	10 _ t (s)					!	3.0
	8				! without pump	2.5
					! pump 26 rpm
	6				_ t pump 26 rpm _ t without pump	2.0
	4						1.5
	2					n x (rpm)	1.0
	50	60	70	80	90	100	110

Proceedings of the Polymer Processing Society 24th Annual Meeting -PPS-24 -June15-19, 2008 Salerno (Italy)

Acknowledgments

The authors are pleased to acknowledge the Communauté d'Agglomération Pau-Pyrénées and the society Knauf Insulation for a financial contribution to this research.


Jimmy Francky Randrianasoa

Camille Kurtz

Eric Desjardin

Éric Desjardin

Nicolas Passat

AGAT: Building and evaluating binary partition trees for image segmentation

Keywords: binary partition tree, hierarchical modeling, image / graph processing, quality evaluation

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Table 1: AGAT code metadata.

Introduction

Due to the rapid progress in the development of imaging sensors, the produced images are becoming increasingly complex, both in size and in semantics. This is the case for example in medical and biological imaging, remote sensing, material sciences, and more generally, in computer vision applications. In such domains, the data that are now handled require to be processed at various levels of detail, i.e. at various scales, in particular with the purpose of tackling computational and semantic analysis issues.

For tackling these issues, two main paradigms have been investigated over the last decades. On the one hand, the paradigm of multiscale analysis, that intrinsically relies on the underlying notion of scale space [START_REF] Lindeberg | Scale-space for discrete signals[END_REF], consists in observing an image at "different distances", then focusing on the details available at each distance. This led to various multiscale analysis approaches for image description (e.g. SIFT, pyramids [START_REF] Rey-Otero | Anatomy of the SIFT method[END_REF]). On the other hand, the paradigm of image partitioning popularized under the terminology of "superpixels" consists in creating connected clusters of homogeneous pixels of certain size within an image, in order to reduce its space complexity without altering the carried visual information. Superpixels were then developed in many variants, mainly for pre-segmentation purposes (e.g. SLIC [START_REF] Achanta | SLIC superpixels compared to state-of-the-art superpixel methods[END_REF], waterpixels [4]).

At the convergence of these two paradigms, the notion of hierarchical image model was developed, in particular in the field of mathematical morphology, leading to a rich family of graph-based data structures, generally defined as trees (i.e. connected, acyclic graphs), designed for modeling images as hierarchies of partitions. Non-exhaustively, the most frequently used trees are the component-tree [START_REF] Salembier | Anti-extensive connected operators for image and sequence processing[END_REF] (which models a grey-level image as the Hasse diagram of the binary connected components of all the threshold sets, with respect to the inclusion relation) and its multivalued variant [START_REF] Kurtz | Connected filtering based on multivalued component-trees[END_REF]; the tree of shapes [START_REF] Monasse | Scale-space from a level lines tree[END_REF] (which is a self-dual variant of the component-tree, that gathers information obtained by thresholding the image in both top-down and bottom-up ways) and its multivalued variant [START_REF] Carlinet | MToS: A tree of shapes for multivariate images[END_REF]; the watershed tree [START_REF] Santana Maia | Characterization of graph-based hierarchical watersheds: Theory and algorithms[END_REF] (that derives from hierarchical watersheds [START_REF] Najman | Geodesic saliency of watershed contours and hierarchical segmentation[END_REF], and allows to model in a hierarchical way the saliency maps derived from the gradient of an image), the binary partition tree [START_REF] Salembier | Binary partition tree as an efficient representation for image processing, segmentation, and information retrieval[END_REF] (that we consider in this article), and some variants such as the α-tree [START_REF] Havel | Efficient tree construction for multiscale image representation and processing[END_REF] (that derives from the concept of constrained connectivity [START_REF] Soille | Constrained connectivity for hierarchical image decomposition and simplification[END_REF]). Many other hierarchical models (including not only trees but also more complex directed acyclic graph structures, e.g. asymetric hierarchies, braids of partitions, component-graphs or component-hypertrees [START_REF] Perret | Directed connected operators: Asymmetric hierarchies for image filtering and segmentation[END_REF][START_REF] Tochon | Braids of partitions for the hierarchical representation and segmentation of multimodal images[END_REF][START_REF] Passat | Component-graph construction[END_REF][START_REF] Morimitsu | Efficient component-hypertree construction based on hierarchy of partitions[END_REF] that generalize / extend the tree structures beyond their usual topological and/or spectral hypotheses of definition) were provided. Awhole discussion is beyond the scope of this article; the interested reader can refer to [START_REF] Bosilj | Partition and inclusion hierarchies of images: A comprehensive survey[END_REF] for a recent survey.

The construction of the trees mentioned above is generally expressed as a graph partitioning problem. More generally, the induced methods lie in the same family as optimization methods on graphs, which are often involved in imaging problems, but can also tackle a wider family of problems, if the data to be processed are discrete and can be structured via a binary relation (e.g., in mesh-based applications, structured data processing, etc.). In particular, strong links exist between the concepts of hierarchical models, saliency maps and spanning trees in graphs [START_REF] Cousty | Hierarchical segmentations with graphs: Quasi-flat zones, minimum spanning trees, and saliency maps[END_REF].

Most of the hierarchical models (e.g. the component-tree or the tree of shapes) can be built from an image, without considering any additional information. Such trees can be seen as pure image modeling data structures, that embed an image into an alternative space, where it can be handled and modified thanks to image processing paradigms. By contrast, the binary partition tree (BPT, for brief) [START_REF] Salembier | Binary partition tree as an efficient representation for image processing, segmentation, and information retrieval[END_REF], is built from two kinds of information:

(1) the intrinsic information carried by the input image (or, more generally, the input valued graph), and (2) an extrinsic-generally user-defined / application-based-information that determines which criteria should be considered for describing the input data in a multiscale way. This expert / domain-based information is crucial in certain application fields. In other words, the binary partition tree is not only an image-oriented but also a knowledge-based data structure. As a consequence, it can be relevantly involved in image analysis tasks that require the embedding of expert-defined priors and knowledge. For instance, the binary partition tree is quite popular in remote sensing applications [START_REF] Alonso-González | Filtering and segmentation of polarimetric SAR data based on binary partition trees[END_REF][START_REF] Valero | Hyperspectral image representation and processing with binary partition trees[END_REF][START_REF] Alonso-González | Processing multidimensional SAR and hyperspectral images with binary partition tree[END_REF][START_REF] Alonso-González | PolSAR time series processing with binary partition trees[END_REF][START_REF] Veganzones | Hyperspectral image segmentation using a new spectral unmixingbased binary partition tree representation[END_REF][START_REF] Valero | Object recognition in hyperspectral images using binary partition tree representation[END_REF][START_REF] Salembier | Optimum graph cuts for pruning binary partition trees of polarimetric SAR images[END_REF], where the way to decompose an image depends on its content (e.g. an urban area vs. a wild forest zone) but also on the purpose of the analysis (e.g. classifying the buildings vs. observing pollution effects).

Various software programs and libraries are available for hierarchical image model handling. GraphBPT1 [START_REF] Al-Dujaili | GraphBPT: An efficient hierarchical data structure for image representation and probabilistic inference[END_REF] is especially designed for building and using binary partition trees. More general-purposed libraries, for instance scikit-image2 , Higra [START_REF] Perret | Higra: Hierarchical graph analysis[END_REF] or the trees-lib library3 deal with wider issues. In particular the last two mentioned allow for the construction of binary partition trees or α-trees, that can be seen as a variant of binary partition trees.

Other libraries, namely Olena4 or LibTIM 5 (used e.g. in [START_REF] Naegel | Interactive segmentation based on componenttrees[END_REF]) are mainly geared towards the construction of the so-called component-trees and / or trees of shapes, but could probably support further extensions for handling binary partition trees.

In this article, we introduce AGAT, a Java library specifically dedicated to the binary partition tree. Similarly to previous libraries (e.g. GraphBPT) it proposes a construction framework of traditional binary partition trees. In addition, it also proposes a way of building a more general family of binary partition trees, the so-called multifeature binary partition trees [START_REF] Randrianasoa | Binary Partition Tree construction from multiple features for image segmentation[END_REF]. From a structural point of view, these binary partition trees do not differ from the classical ones. They differ actually in the way they are built. Indeed, by contrast to the usual construction algorithm that relies on a single clustering criterion and a single image, the construction of the multifeature binary partition trees relies on the collaboration between various clustering criteria and / or allows to handle many images of a same scene.

Another contribution of AGAT compared to the already available libraries is the proposal of various tools for evaluating the quality of a binary partition tree (or equivalently, the quality of the meta-parametrization of its construction) with respect to object segmentation purposes. Indeed, evaluating the quality of a hierarchical image model is an important-but infrequently considered-topic as a prerequisite to its actual involvement for real applications [START_REF] Randrianasoa | Evaluating the quality of binary partition trees based on uncertain semantic ground-truth for image segmentation[END_REF][START_REF] Randrianasoa | Intrinsic quality analysis of binary partition trees[END_REF][START_REF] Randrianasoa | Supervised quality evaluation of binary partition trees for object segmentation[END_REF].

Software description

In this section, we describe the structure of the AGAT library and the major functionalities implemented.

Software architecture

AGAT is composed of three modules (Image, BinaryPartitionTree, TreeEvaluation) required for the construction of binary partition trees from images, their handling and their evaluation. The three modules are coded in pure Java 8, taking advantage of the latest language innovations. They also contain some external Java libraries, encapsulated in the projects in the form of .jar files (mainly for input / output).

The Image module is independent. It contains basic tools for manipulating and processing raster images (e.g. equalization, conversion, channel management, inputs / outputs). Images are classically encoded via the BufferedImage class which is part of the Abstract Window Toolkit (AWT), a graphics library commonly used by the Java community.

The BinaryPartitionTree module is dependent on the Image module. It contains various functionalities for building binary partition trees in a usual way, but also to define multifeature trees from consensus of multiple images and / or multiple criteria. This module also allows to handle the trees, for instance by defining / computing tree cuts that can be interpreted in particular as segmentations when dealing with images. In AGAT, binary partition trees are modeled and analyzed through their hierarchical representations.

They are encoded as trees, where each node is a region of the image support.

The main data structures of the library are thus a graph class, implemented as an adjacency list (required for the construction step of the binary partition trees relying on an region adjacency graph), and a tree class, classically implemented with inheritance relationships. To enable the multiple images and / or multiple criteria paradigm, data structures based on ordered lists of valued edges have been also implemented. These data structures are a bit specific because they should allow to choose efficiently the next edges to be selected during the construction of the trees. Multiple index systems and optimized iterators have thus been implemented to make it possible to speed up their scans. In addition, when the number of criteria to be considered is important, the lists are kept sorted sporadically, after a fixed number of modifications, which approximates the expected solution but enables better scaling.

The TreeEvaluation module is dependent on the BinaryPartitionTree module. It provides various classes related to the quantitative evaluation of the quality of a binary partition tree (or its meta-parametrization) with respect to object segmentation purposes. Both intrinsic and extrinsic analyses can be carried out. For a given binary partition tree (an object built from the BinaryPartitionTree module), the user can provide examples of groundtruth (defined as binary regions of interest in the image support) and quality metrics. The main data structures of this module make it possible to manage both information on the ground-truth segments provided by the user (e.g. coordinates of the bounding box, semantic labels, etc.) but also sub-trees of interest on which the analysis is carried out (to make processing faster by restricting it spatially and hierarchically).

Software functionalities

AGAT proposes a large amount of algorithms for the construction, the handling and the evaluation of binary partition trees (complementary technical details regarding the main data structure architecture can be found in [34, Appendix B]):

• BPT construction:

mono-image / mono-criterion [START_REF] Salembier | Binary partition tree as an efficient representation for image processing, segmentation, and information retrieval[END_REF]: tree construction from pixels or flat zones or a given partition, various generic (e.g. color: RGB, LAB, geometric: elongation, smoothness) and thematic (e.g. NDVI, NDWI) criteria are available; multi-image / multi-criteria [START_REF] Randrianasoa | Binary Partition Tree construction from multiple features for image segmentation[END_REF]: efficient process to establish different kinds of consensus among the adjacency lists (e.g. majority vote, most frequent, etc.), visualization of the conflict between metrics.

The construction criteria and the consensus policy are provided by the user as parameters of the (mutltifeature) binary partition tree construction process (an example can be found in the code snippet of Listing 1).

• BPT handling:

definition of tree cuts from partition cardinality: flat or fitting with an input mask of an object of interest; intrinsic analysis: combinatorial, quantitative, node assessment from the notion of pure and impure nodes matching with groundtruth examples [START_REF] Randrianasoa | Intrinsic quality analysis of binary partition trees[END_REF][START_REF] Randrianasoa | Supervised quality evaluation of binary partition trees for object segmentation[END_REF];

extrinsic analysis: home-made evaluation framework [START_REF] Randrianasoa | Evaluating the quality of binary partition trees based on uncertain semantic ground-truth for image segmentation[END_REF][START_REF] Randrianasoa | Supervised quality evaluation of binary partition trees for object segmentation[END_REF], implementation of other existing frameworks from the literature [START_REF] Perret | Evaluation of morphological hierarchies for supervised segmentation[END_REF][START_REF] Pont-Tuset | Upper-bound assessment of the spatial accuracy of hierarchical region-based image representations[END_REF], evaluation metrics: F-measure / Dice, Jaccard index.

Illustrative examples

In this section, we present two illustrative examples of AGAT usage and performances. In the first example (Section 3.1), we show how AGAT can be used for building both traditional and multifeature binary partition trees, that can then be used for image partitioning. In the the second example (Section 3.2), we show how AGAT can be employed for comparing the performances of various binary partition trees, in particular in the context of object segmentation. These illustrations were designed from the source codes and some codes snippets available in the provided GitHub repository.

Building a (traditional or multifeature) binary partition tree

The binary partition tree, such as defined in the pioneering article [START_REF] Salembier | Binary partition tree as an efficient representation for image processing, segmentation, and information retrieval[END_REF], was designed for hierarchically modeling one image with respect to one given criterion. Later on, the notion of multifeature binary partition tree, developed in [START_REF] Randrianasoa | Binary Partition Tree construction from multiple features for image segmentation[END_REF], extended this initial paradigm, by allowing one to build a binary partition tree from one or many image(s) of the same scene with respect to one or many given criteria. The implementation of binary partition trees proposed in AGAT follows the latter paradigm of [START_REF] Randrianasoa | Binary Partition Tree construction from multiple features for image segmentation[END_REF], and allows a fortiori to build traditional binary partition trees as defined in [START_REF] Salembier | Binary partition tree as an efficient representation for image processing, segmentation, and information retrieval[END_REF]. In this first illustrative example, we consider images in the context of remote sensing, and more precisely the analysis of very high spatial resolution (VHSR) satellite images, a domain where the concept of binary partition tree has been quite frequently and successfully involved over the last two decades.

Listing 1: Code snippet for building a binary partition tree using AGAT. These multispectral images are at a spatial resolution of 60 cm with 4 spectral bands (red, green, blue, near infrared).

We considered four criteria for building the binary partition trees, each one modeling either radiometric or geometrical information:

• C colour , defined as the increase of the range of the pixel intensity values for each radiometric band, induced by the putative fusion of incident regions;

• C ndvi , that quantifies the difference of NDVI (Normalized Difference Vegetation Index, a standard indicator for the presence of green vegetation) between two adjacent regions;

• C ndwi , that quantifies the difference of NDWI (Normalized Difference Water Index, a standard indicator for the presence of water) between two adjacent regions;

• C elong , defined as the change of geometrical elongation, potentially induced by the fusion of two regions. A Java code snippet, presented in Listing 1, exemplifies how to obtain such results within AGAT. More extensive experiments related to the construction of various (multifeature) binary partition trees and the impact of these various kinds of trees in the context of remote sensing can be found in [START_REF] Randrianasoa | Intrinsic quality analysis of binary partition trees[END_REF][START_REF] Randrianasoa | Binary Partition Tree construction from multiple features for image segmentation[END_REF].

Assessing / comparing the quality of various binary partition trees

A wide literature has been devoted to segmentation based on binary partition trees. In this context, various criteria were investigated. The design of these criteria strongly influences the resulting trees and, equivalently, the research space for further segmentation, and thus the quality of the subsequent segmentation results. The literature dedicated to the evaluation of the quality of binary partition trees is not abundant. AGAT proposes (variants of) some of the most relevant approaches of the literature:

• an intrinsic quality analysis [START_REF] Randrianasoa | Supervised quality evaluation of binary partition trees for object segmentation[END_REF], that evaluates the relevance of a binary partition tree based on the combinatorial analysis of its nodes and their relationships with a binary ground-truth associated to the input image;

• an extrinsic quality analysis [START_REF] Randrianasoa | Supervised quality evaluation of binary partition trees for object segmentation[END_REF], that evaluates the ability of a binary partition tree to provide a cut that minimizes at best a given quality metric provided as hyperparameter with respect to the ground-truth associated to the input image;

• a framework adapted from [START_REF] Perret | Evaluation of morphological hierarchies for supervised segmentation[END_REF] that provides the F-measure of the segmented object vs. the associated ground-truth, with respect to the size of inside / outside markers generated from the ground-truth associated to the input image;

• a framework adapted from [START_REF] Pont-Tuset | Upper-bound assessment of the spatial accuracy of hierarchical region-based image representations[END_REF] that aims at computing the best cuts composed of k nodes for each k in [0, p] (p > 0), allowing to reconstruct the targeted segmentation. In [START_REF] Randrianasoa | Supervised quality evaluation of binary partition trees for object segmentation[END_REF], extensive experiments were carried out with three commonly used datasets: Grabcut [START_REF] Blake | Interactive image segmentation using an adaptive GMMRF model[END_REF], Weizman [START_REF] Alpert | Image segmentation by probabilistic bottom-up aggregation and cue integration[END_REF] and VOC [START_REF] Everingham | Zisserman, The Pascal Visual Object Classes (VOC) challenge[END_REF]. Examples of partitioning of an image from the Grabcut dataset are illustrated in Figure 2. These partitions are obtained from three different binary partition trees, each one built with a given criterion, noted WSDM, Min-Max and MSE, respectively (see [START_REF] Randrianasoa | Supervised quality evaluation of binary partition trees for object segmentation[END_REF] for their formal definition). [START_REF] Perret | Evaluation of morphological hierarchies for supervised segmentation[END_REF], with respect to the size 2k + 1 of the structuring elements used for erosion (background and foreground) of the ground-truth. Top: Grabcut. Middle: Weizmann. Bottom: VOC. Considering S as the segmentation result and G as the ground-truth, the F-measure / Dice score is defined as 2tp/(2tp+f p+f n) with tp = |S∩G|, f p = |S \ G| and f n = |G \ S|. (In this experiment, we kept the terminology of F-measure as used in the seminal paper [START_REF] Perret | Evaluation of morphological hierarchies for supervised segmentation[END_REF].) The F-measure is related to the ratio of overlapping between two objects. It lies in [0, 1]; the closer to 1, the better the overlapping. binary partition trees (namely the one built with WSDM criterion) over the other two ones. This is characterized by the fact that, in the three different experiments, WSDM leads to better values for the considered measures (the higher these values, the better the results). These results are qualitatively confirmed by the segmentations illustrated in Figure 2.

A Java code snippet, presented in Listing 2, illustrates how to obtain such results within AGAT. The interested readers can find more extensive experiments related to such natural images in [START_REF] Randrianasoa | Supervised quality evaluation of binary partition trees for object segmentation[END_REF]. In particular, more extensive experiments related to the binary partition tree evaluation framework proposed in AGAT, applied in the context of natural images (Grabcut, VOC and Weizmann datasets) are provided in this reference.

Impact

There already exist libraries dedicated to hierarchical image models in general, and the binary partition trees in particular. However, AGAT is the first library that integrates the construction algorithms for traditional binary partition trees, but also for the recently introduced multifeature binary partition trees. This provides potential users with a unique opportunity to design and to experiment new and richer ways of building hierarchical models from complex / large (sets of) images. The success of the binary partition trees in the field of remote sensing over the last years is the proof of the relevance of this hierarchical model in the case of large and / or semantically complex images. Many domains involving such kinds of images (e.g. biological and (bio)medical imaging) could benefit from the opportunities offered by the binary partition trees, and then from the functionalities offered by AGAT.

Additionally, AGAT also embeds various tools for assessing the quality of binary partition trees. This quantitative evaluation framework can be very useful, for instance in the field of computer vision, where the partitioning of large / complex images is generally a prerequisite for high-level scene analysis tasks (e.g. object detection and recognition). In this regard, providing tools that can be involved in selection / learning of appropriate contextdependent meta-parameters for image decomposition is of great interest for the community. In particular, such frameworks proposed in combination with the binary partition tree construction algorithms could lead to consider the induced image partitioning results as a relevant alternative to the usual, non-hierarchical, image decompositions proposed by super-pixel paradigms.

Finally, it is worth mentioning that the binary partition trees, beyond their usefulness for image analysis task, are first of all a way of building partitions of graph-based structures, independently of their associated semantics. Based on this fact, AGAT may then be used for solving any graph partitioning problem provided that such partitionings are guided by one / many prior knowledge. This opens the way of the use of AGAT in a wide range of machine learning domains where the data are organized as graphs, i.e. with respect to usual binary relations.

Conclusions

We presented AGAT, a library dedicated to the construction, the handling and the evaluation of binary partition trees, which are tree data structures providing hierarchical partitioning of images and, more generally, valued graphs. AGAT contains also many standard and state-of-the-art algorithms in this domain. AGAT is the first library allowing for the construction of multifeature binary partition trees, and it also gathers a large set of evaluation tools for traditional binary partition trees. From this point of view, it constitutes, to our knowledge, the most complete and up-to-date library dedicated to binary partition trees. It is composed of three self-contained Java modules. Code sources are available via GitHub and natively compatible for Linux, Mac, and Windows systems. They can be downloaded with a simple command: git clone https://github.com/yonmi/AGAT2.0.git.

Conflict of Interest

We wish to confirm that there are no known conflicts of interest associated with this publication and there has been no significant financial support for this work that could have influenced its outcome.

-

  backup and restore trees from .h5 files, which is a Hierarchical Data Format (HDF) designed to store and organize large amounts of data and ensures compatibility with external tools; export trees to .xml and .dot files, which allows visualization with external tools. • BPT quality evaluation: management of multiple ground-truth examples per image with potentially different semantic labels; extraction of sub-trees of interest to speed up the analysis by restricting it spatially and hierarchically;

  import java.awt.image.BufferedImage; import java.util.Map.Entry;

Figure 1 :*}

 1 Figure 1: (a, d) Two VHSR satellite images (2 000 × 2 000 pixels) at a spatial resolution of 60 cm sensed by the Pléiades satellite and covering different areas. (b, e) Partitioning results from traditional binary partition trees computed from (a) and (d), respectively (23 500 and 5 000 regions, respectively), using one criterion: C colour . (c, f) Partitioning results from multifeature binary partition trees computed from (a) and (d), respectively (23 500 and 5 000 regions, respectively), using 4 criteria: C colour , C elong , C ndvi , C ndwi .

Figure 1 (

 1 Figure 1(b, e), illustrates the results of partitionings (induced by tree-cuts) obtained from traditional binary partition trees built by considering individually the first criterion. Figure 1(c, f), illustrates the results of partitionings (induced by tree-cuts) obtained from multifeature binary partition trees built by considering collectively these four criteria.

Figure 2 :

 2 Figure 2: Horizontal cuts of different binary partition trees on an image from the Grabcut dataset. First line: initial image, ground-truth and initial superpixel partition. First column: binary partition tree built with WSDM criterion. Second column: binary partition tree built with Min-Max criterion. Third column: binary partition tree built with MSE criterion. From second to fifth rows: horizontal cuts with 40, 50, 60, and 70 nodes. Each node is represented with a false colour, for the sake of visualization.

Figure 3 :

 3 Figure3: F-measure of the segmentations obtained from various kinds of binary partition trees in the evaluation framework[START_REF] Perret | Evaluation of morphological hierarchies for supervised segmentation[END_REF], with respect to the size 2k + 1 of the structuring elements used for erosion (background and foreground) of the ground-truth. Top: Grabcut. Middle: Weizmann. Bottom: VOC. Considering S as the segmentation result and G as the ground-truth, the F-measure / Dice score is defined as 2tp/(2tp+f p+f n) with tp = |S∩G|, f p = |S \ G| and f n = |G \ S|. (In this experiment, we kept the terminology of F-measure as used in the seminal paper[START_REF] Perret | Evaluation of morphological hierarchies for supervised segmentation[END_REF].) The F-measure is related to the ratio of overlapping between two objects. It lies in [0, 1]; the closer to 1, the better the overlapping.

Figure 4 :

 4 Figure4: Normalized (mean) value of the TPFP measure for the optimal cuts of a given size from various kinds of binary partition trees in the evaluation framework[START_REF] Pont-Tuset | Upper-bound assessment of the spatial accuracy of hierarchical region-based image representations[END_REF] Top: Grabcut. Middle: Weizmann. Bottom: VOC. Considering S as the segmentation result and G as the ground-truth, the (normalized) TPFP score is defined as tp-f p |G| , with tp = |S ∩ G|, f p = |S \ G|. The TPFP quantifies the trade-off between true and false positives. It lies in (-∞, 1]; a 0 value means that there are as many true and false positives; the closer to 1, the better the result.

Figure 5 :

 5 Figure 5: Normalized (mean) value of the Dice measure for the (near-)optimal cuts of a given size various kinds of binary partition trees. Top: Grabcut. Middle: Weizmann. Bottom: VOC. Considering S as the segmentation result and G as the ground-truth, the Dice score is defined as 2tp/(2tp+f p+f n) with tp = |S ∩G|, f p = |S \G| and f n = |G\S|. The Dice score is related to the ratio of overlapping between two objects. It lies in [0, 1]; the closer to 1, the better the overlapping.

https://github.com/ash-aldujaili/GraphBPT

https://scikit-image.org

https://github.com/pbosilj/trees-lib

https://www.lrde.epita.fr/wiki/Olena

https://github.com/bnaegel/libtim

Acknowledgements

This work was supported by the French Agence Nationale de la Recherche (Grants ANR-15-CE23-0009, ANR-17-CE23-0015 and ANR-18-CE23-0025) and by the American Memorial Hospital Foundation.

fill in this column C1 Current code version v2.0 C2 Permanent link to code/repository used for this code version https://github.com/yonmi/AGAT2.0 C3 Code Ocean compute capsule NA C4 files are also provided) C8 If available Link to developer documentation/manual https://github.com/

Listing 2: Code snippet for evaluating a binary partition tree using AGAT.


Fanny ; Bordet
email: bordet.fanny@gmail.com

Chloé ; Roullier-Gall
email: chloe.roullier-gall@u-bourgogne.fr

Jordi ; Ballester
email: jordi.ballester@u-bourgogne.fr

Stefania ; Vichi
email: stefaniavichi@ub.edu

Beatriz Quintanilla-Casas
email: beatrizquintanilla@ub.edu

Régis D ; Gougeon
email: regis.gougeon@u-bourgogne.fr

Anne Julien-Ortiz

Philippe Schmitt

Hervé Alexandre

Philippe Schmitt Kopplin

B ; Quintanilla- Casas

Julien-Ortiz

Different wines from different yeasts? "Saccharomyces cerevisiae intraspecies differentiation by metabolomic signature and sensory patterns in wine"

Keywords: yeast, Saccharomyces cerevisiae, Chardonnay wine, metabolomic, volatile compounds, sensory analysis

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Targeted approaches are mostly used for metabolite analysis in oenology. However, they do not enable the study of the diversity of metabolites in a matrix, so only a limited number of compounds is considered. These approaches contribute to answering a specific question, while untargeted approaches allow a holistic perspective. Non-targeted approaches using high-resolution mass spectrometry (uHRMS) provide a more comprehensive view of the metabolome. Thanks to these high-throughput analyses, it is possible to account for the chemical diversity of a complex matrix and bring to light not only known compounds but also previously unidentified compounds. Already frequently used in the fields of medicine, agro-environment, and nutrition, uHRMS has also been applied since the early 2000s to the wine matrix, with the development of the concept of "oenomics" [START_REF] Blow | Biochemistry's New Look[END_REF], which covers different aspects. Vaclavik et al. [START_REF] Vaclavik | The Use of High Performance Liquid Chromatography-Quadrupole Timeof-Flight Mass Spectrometry Coupled to Advanced Data Mining and Chemometric Tools for Discrimination and Classification of Red Wines According to Their Variety[END_REF] were able to discriminate three red wines according to their variety by wine-metabolome analysis. Wines can also be discriminated by their biogeographic origins [START_REF] Roullier-Gall | Integrating Analytical Resolutions in Non-Targeted Wine Metabolomics[END_REF][START_REF] Gougeon | The Chemodiversity of Wines Can Reveal a Metabologeography Expression of Cooperage Oak Wood[END_REF]. Moreover, it was shown that this approach could be used to authenticate wines and evaluate their quality [START_REF] Cuadros-Inostroza | Discrimination of Wine Attributes by Metabolome Analysis[END_REF]. On the other hand, the impact of ageing [START_REF] Gougeon | The Chemodiversity of Wines Can Reveal a Metabologeography Expression of Cooperage Oak Wood[END_REF][START_REF] Castro | Application of a High-Throughput Process Analytical Technology Metabolomics Pipeline to Port Wine Forced Ageing Process[END_REF] and the modification of the matrix by oxidation are topics that are widely addressed by this metabolomic approach [START_REF] Romanet | The Antioxidant Potential of White Wines Relies on the Chemistry of Sulfur-Containing Compounds: An Optimized DPPH Assay[END_REF][START_REF] Bahut | Metabolic Diversity Conveyed by the Process Leading to Glutathione Accumulation in Inactivated Dry Yeast: A Synthetic Media Study[END_REF][START_REF] Roullier-Gall | Sulfites and the Wine Metabolome[END_REF][START_REF] Roullier-Gall | Chemical Messages from an Ancient Buried Bottle: Metabolomics for Wine Archeochemistry[END_REF].

Besides oenomics, metabolomics have been applied for over a decade to understand the metabolism of microorganisms [START_REF] Van Der Werf | Microbial Metabolomics: Toward a Platform with Full Metabolome Coverage[END_REF][START_REF] Mashego | Microbial Metabolomics: Past, Present and Future Methodologies[END_REF]. Metabolomics can provide, at a given moment, a representation of the cell phenotype according to genetic background and its expression under specific environmental conditions, offering indications of possible biochemical regulations that cannot be quantified by other omics approaches [START_REF] Pinu | Grape and Wine Metabolomics to Develop New Insights Using Untargeted and Targeted Approaches[END_REF]. High-resolution mass spectrometry (HRMS) is used to profile and globally describe the non-volatile metabolome changes associated with metabolic conditions based on the simultaneous measurement of several thousand signals due to high sensitivity, resolution, and mass accuracy [START_REF] Schmitt-Kopplin | Systems Chemical Analytics: Introduction to the Challenges of Chemical Complexity Analysis[END_REF].

The impact of microorganisms on different matrices, including wine, was addressed in studies by Schmitt-Kopplin et al. and Garcia et al. [START_REF] Garcia | Separation and Mass Spectrometry in Microbial Metabolomics[END_REF][START_REF] Tang | Microbial Metabolomics[END_REF]. Thus, metabolomics has made it possible to discriminate between wines produced by different yeasts or yeast couples. Roullier-Gall et al. were able to distinguish several finished wines with a characteristic composition, strain, or mix of strains used for fermentation [START_REF] Roullier-Gall | Exploring Yeast Interactions through Metabolic Profiling[END_REF]. This approach also allowed us to highlight differences in metabolism between different species, as well as within the same species of yeast, under specific conditions. For example, different strategies developed by two Saccharomyces species for cold resistance were observed on the level of various metabolisms, such as lipid metabolism and the shikimate pathway [START_REF] López-Malo | Metabolomic Comparison of Saccharomyces Cerevisiae and the Cryotolerant Species S. Bayanus Var. Uvarum and S. Kudriavzevii during Wine Fermentation at Low Temperature[END_REF]. Additionally, differences were reported within the Saccharomyces cerevisiae species, notably in the volatile compounds formed [START_REF] Mendes | Integrating Transcriptomics and Metabolomics for the Analysis of the Aroma Profiles of Saccharomyces Cerevisiae Strains from Diverse Origins[END_REF][START_REF] Carrau | Production of Fermentation Aroma Compounds by Saccharomyces Cerevisiae Wine Yeasts: Effects of Yeast Assimilable Nitrogen on Two Model Strains[END_REF][START_REF] Eder | QTL Mapping of Volatile Compound Production in Saccharomyces Cerevisiae during Alcoholic Fermentation[END_REF]. These differences probably reflect differences in the metabolism of the strains that have not been explored. The innovative aspect of our study is to investigate, for the first time, the metabolomic differences among different strains belonging to the same species. Indeed, we demonstrated that each of the twelve studied strains possess a specific non-volatile metabolomic signature that allows us to discriminate them and address intraspecific diversity. We novelly combined uHRMS, a powerful tool, with different targeted approaches to develop an integrative vision of this intraspecific diversity within the species. Furthermore, the monitoring of oenological parameters and of the growth of yeasts in fermentation were associated with a targeted approach to identify the volatilome expressed at the end of alcoholic fermentation. Additionally, a sensory analysis of each of the associated wines was performed.

Materials and Methods

Yeast Strains

Twelve commercial strains of Saccharomyces cerevisiae (Lallemand Inc., Montreal, QC, Canada) were selected for this study. Each strain was supplied as an ADY and stored at 4 • C once opened. These strains were coded S1 to S12.

Growth and Fermentation Conditions

Each strain was rehydrated from ADY stock and then diluted at 0.1% (v/v) concentration in 150 mL of YPD medium (0.5% (w/v) yeast extract, 1% (w/v) bactopeptone, 2% (w/v) glucose, and 0.02% (w/v) chloramphenicol) in 250 mL Erlenmeyer flasks. After incubation at 28 • C with stirring (150 rpm) for 18 h, the second culture, in 150 mL of pasteurized Chardonnay must, filtered on a 0.22 µm membrane was performed in Erlen-meyer flasks (250 mL) at 28 • C in static mode for 18 h. These later cultures were used to inoculate pasteurized Chardonnay must containing 226.6 g/L glucose/fructose, pH 3.92, and 343.1 mg/L total assimilable nitrogen, at 1 × 10 6 viable cells/mL. These fermentations were performed in 2 L bottles containing 1 L of inoculated must covered with sterile cotton wool. For each strain, assays were conducted in four biological replicates at 20 • C without stirring. The end of fermentation was considered as the total depletion of sugars.

Monitoring of Biomass Growth

Cell viability in preculture and during fermentation was determined by flow cytometry. The fluorochrome used was cFDA (5-6 carboxyfluorescein diacetate) (Invitrogen, Molecular Probes, ThermoFisher Scientific, Illkrich, France) dissolved in acetone at a concentration of 1500 µM [START_REF] Longin | Application of Flow Cytometry to Wine Microorganisms[END_REF]. We added 3 µL of cFDA to 100 µL of diluted yeast suspension in Mc Ilvain buffer (100 mM citric acid, 200 mM Na 2 HPO 4 , pH 4). Samples were incubated in the dark 20 min before measurement. Flow cytometry was performed with a BD Accuri C6 flow cytometer, and the resulting data were processed using the BD Accuri C6 software. For each sample, 20 µL was analyzed at 34 µL/min. The FSH threshold used was 80,000. A 488-nm wavelength argon laser was used to excite the cells (autofluorescence) and dye them. CFDA fluorescence was measured on the FL1-H long pass filter (533/530 nm) and side-scatter light (SSC)/fluorescence intensity data were analyzed. Daily sampling of all the samples was carried out.

Analytical Methods

Enological Analysis

Samples were centrifugated at 28,000× g for 5 min at 4 • C. Sugar concentration and ethanol degree were monitored daily by FTIR (Fourier-transformed infrared) spectroscopy (OenoFOSS TM , FOOS, Hilleroed, Denmark). Daily sampling of all the samples was carried out.

Volatilome Analysis

Headspace solid-phase microextraction gas chromatography/mass spectrometry, as reported previously [START_REF] Gobert | Non-Saccharomyces Yeasts Nitrogen Source Preferences: Impact on Sequential Fermentation and Wine Volatile Compounds Profile[END_REF][START_REF] Petitgonnet | Influence of Cell-Cell Contact between L. Thermotolerans and S. Cerevisiae on Yeast Interactions and the Exo-Metabolome[END_REF], was used to quantify volatile compounds at the end of alcoholic fermentation for three of four biological replicates. In brief, 2 mL of sample was placed in a 10 mL vial with a silicone septum and then placed in an oil bath at 40 • C with a magnetic stirrer (700 rpm) for 10 min. A divinylbenzene/carboxene/polydimethylsiloxane (DVB/CAR/PDMS) fiber (Supelco, Bellefonte, PA, USA) was exposed to the sample headspace for 30 min and then subjected to direct desorption in the injector of the gas chromatograph set at 260 • C. Volatile compounds were analyzed by gas chromatography coupled to a quadrupolar mass-selective spectrometer. GC-MS analysis was performed in complete scanning mode (SCAN) in the 30-300 mass-unit range. The comparison of mass spectra and retention times with standard compounds allowed for the identification of compounds. In a few cases, a tentative identification was carried out based on the mass spectra using Wiley's library 6-reference spectral databank. The quantitative assessment of volatiles was based on calibration curves obtained analyzing different concentrations of reference compounds in 10% hydroethanolic solution. The results were processed by performing an ANOVA (p-value < 0.01), followed by a Tukey test. All the results were processed using R software (R-4.0.4).

Non-Volatile Metabolome Analysis

Ultra-high-resolution mass spectra were acquired using an FT-ICR-MS (SolariX, Bruker Daltonik, Bremen, Germany) equipped with a 12 Tesla superconducting magnet (Magnex Scientific Inc., Kidlington, UK) and an Apollo II electrospray ionization source (Bruker Daltonik, Bremen, Germany) operated in negative ionization mode. Samples were collected at the end of alcoholic fermentation and diluted at 5:100 v/v in pure methanol (LC-MS grade, Fluka, Germany). Quality controls (QC) were prepared by pooling equal amounts of all samples. QCs were analyzed at the beginning and end of the run and every ten samples to validate the repeatability of the measurement. The diluted samples and QC samples were injected at a flow rate of 120 µL/h into the electrospray ion source. Spectra were acquired with a time domain of 4 megawords within a mass range of m/z 147-2000. At total of 300 scans was accumulated for each sample. All the samples were injected randomly in the same batch to avoid batch variability. A resolving power of 400,000 at 300 m/z was achieved. All the spectra were calibrated externally on a methanol solution of arginine clusters (10 mg/L), and accuracy reached values of less than 0.1 ppm in day-to-day measurements. Additionally, internal calibrations were performed on a list composed by recurrent compounds in wine to keep only m/z peaks with a signal-to-noise (S/N) ratio of 4. Matrix Generator software (v. 0.4, Helmholtz-Zentrum Muenchen) was used to align each peak with a mass-accuracy window of 1 ppm. The quality of the analysis was controlled before any data processing (Supplementary Figure S1). Features were annotated using the in-house software NetCalc 2015 (v.1.1a, Helmholtz-Zentrum Muenchen). Finally, van Krevelen diagrams were generated by an Excel file according to the H/C versus O/C ratio of annotated metabolites. Annotation levels were in line with Viant et al., 2017 [25]. Perseus 1.5.1.6 (Max Planck Institute of Biochemistry, Germany) was used to perform principal-component analysis (PCA), hierarchical cluster analysis (HCA), and analysis of variance (ANOVA). For HCA, the Euclidean distance and average linkage were chosen, and a threshold p-value of 0.05 was chosen for ANOVA. Multidimensional Stoichiometric Compounds Classification (MSCC) have been used to elucidate extracted biomarkers categories commonly defined as lipids, peptides, amino sugars, carbohydrates and polyphenols derivatives compounds [START_REF] Ballester | The Odor of Colors: Can Wine Experts and Novices Distinguish the Odors of White, Red, and Rosé Wines?[END_REF].

Metabolites were identified by ultra-high-performance liquid chromatography (Dionex Ultimate 3000, ThermoFischer, Waltham, MA, USA) coupled to a MaXis plus MQ ESI-Q-ToF mass spectrometer (Bruker, Bremen, Germany). A reversed-phase liquid-chromatography (RP-LC) separation method was applied by injecting 5 µL in an Acquity UPLC BEH C18 1.7 µm column 100 × 2.1 mm (Waters, Guyancourt, France) to separate metabolites according to their polarity. Buffer A (acetonitrile 5% (v/v) with 0.1% (v/v) formic acid) and buffer B (acetonitrile with 0.1% (v/v) formic acid) were employed to elute metabolites. Detection was implemented in negative ionization mode with the following parameters: an electrospray (Nebulizer pressure = 2 bars and nitrogen dry gas flow = 10 L/min), ion transfer (end plate offset at 500 V) capillary voltage (at 4500 V), and acquisition (100-1500 m/z mass range).

A mix of standard peptides and polyphenols was used for the UHPLC-Q-ToF-MS quality control. Experimental quality control (mix of samples) was used to guarantee system repeatability. All the samples were injected randomly in the same batch to avoid batch-to-batch variability. Calibration was processed with 1 /4 diluted ESI Tuning Mix (v. 4.3, Bruker Daltonik GmbH). Features (couple of m/z-values and retention times) were fragmented using the AutoMS/MS function on the most intense features, with a frequency of 2 Hz. Fragmentation was done at three different collision energies: 15, 25, and 35 eV. After acquisition, MS/MS spectra were manually extracted using Bruker Data Analysis 4.4 (Bruker Daltonic, Bremen, Germany).

Descriptive Sensory Analysis

In order to have enough volume per sample to carry out descriptive sensory analysis, the four biological replicates of each yeast modality were pooled. The twelve post-alcoholic fermentation wines were then filtered and sulfited to 40 mg/L before bottling. These samples were stored in the cellar at a constant temperature for one month until sensory analysis.

The assessors were recruited from among the enology students at the Dijon School of Enology at the Institut Universitaire de la Vigne et du Vin. They all attended 56 h of training in winetasting. The 33 candidates were subjected to a selection process during which their ability to identify the main white wine attributes and their reproducibility was checked. The final descriptive panel was composed of 22 assessors (14 males, 8 females, average age of 26).

The final sensory measure was carried out in a single session divided into two series of twelve samples (about 45 min per series). The session was conducted in a sensory evaluation room with individual boxes. Each sample was coded by a three-digit random number. Thirty mL of each wine was served at room temperature in standard ISO black glasses and covered with a plastic Petri dish. The samples were assessed in a specific order for each panelist following a Latin square. Samples were described according to the frequency-of-citation method [START_REF] Cadière | Evolutionary Engineered Saccharomyces Cerevisiae Wine Yeast Strains with Increased in Vivo Flux through the Pentose Phosphate Pathway[END_REF]. The panel was asked to describe the odor of each sample by checking the associated descriptors within a pre-established list of 33 terms corresponding to odor attributes related to white wines. The list was adapted from previous research [START_REF] González-Ramos | A Saccharomyces Cerevisiae Wine Yeast Strain Overproducing Mannoproteins Selected through Classical Genetic Methods[END_REF] and is presented in Supplementary Material, Table S1. Two blank lines were added to the list in order to allow the participants to use descriptors that were missing from the list, so they could add their own descriptors. For each term, the frequency of citation was established for each wine. Only the descriptors mentioned at least 4 times for at least one wine were kept for statistical analysis. The other descriptors were removed. The sensory data were subjected to correspondence analysis (CA) (α = 0.05), followed by hierarchical cluster analysis on the wine coordinates of the most relevant CA factors. Sensory statistical analyses were performed using R software (R-4.0.4).

Results and Discussion

Twelve Saccharomyces cerevisiae strains were screened. All these strains were selected for their phenotypic diversity, diverse origins, and genetic backgrounds. The twelve strains were commercial stains widely used in the wine industry. For example, S2 was obtained by an adaptative evolution from strain S1 [START_REF] Brice | Assessing the Mechanisms Responsible for Differences between Nitrogen Requirements of Saccharomyces Cerevisiae Wine Yeasts in Alcoholic Fermentation[END_REF]. Strain S7 was a natural hybrid of strain S10 that had been crossed with another Saccharomyces cerevisiae strain, and S6 was a hybrid obtained by UV mutagenesis [START_REF] Julien | Comparison of Nitrogen and Oxygen Demands of Enological Yeasts: Technological Consequences[END_REF]. All the strains exhibited different nitrogen requirements [START_REF] Barbosa | The Nitrogen Source Impacts Major Volatile Compounds Released by Saccharomyces Cerevisiae during Alcoholic Fermentation[END_REF][START_REF] Edgardo | Selection of Thermotolerant Yeast Strains Saccharomyces Cerevisiae for Bioethanol Production[END_REF], which can be associated with different profiles of aromatic compound formation [START_REF] Blanco | Modulation of Chemical and Sensory Characteristics of Red Wine from Mencía by Using Indigenous Saccharomyces Cerevisiae Yeast Strains[END_REF].

Fermentation Kinetics and Yeast Viability

Alcoholic fermentation of Chardonnay must inoculated by 12 different yeast strains was monitored by IRTF spectroscopy (OenoFoss) and flow cytometry every day until the end of fermentation. All twelve strains showed similar growth and fermentation kinetics or patterns. The results of some fermentation parameters are expressed in the Supplementary Data (Table S2). The strains all showed a rapid exponential phase (48 h). No residual sugars remained at the end of the monitoring period, except for strain S8 (Supplementary Table S2). This last yeast reached dryness at 264 h. The maximum population was within the range of 7.95 × 10 7 to 1.46 × 10 8 viable cells/mL. The ethanol yield was whatever the strains, which was in accordance with previous studies [START_REF] Synos | Effect of Yeast Strain on Aroma Compounds in Cabernet Franc Icewines[END_REF][START_REF] Redzepovic | Differential Malic Acid Degradation by Selected Strains of Saccharomyces during Alcoholic Fermentation[END_REF][START_REF] Rossouw | Linking Gene Regulation and the Exo-Metabolome: A Comparative Transcriptomics Approach to Identify Genes That Impact on the Production of Volatile Aroma Compounds in Yeast[END_REF]. S12 consumed 20% of initial malic acid, which had already been described earlier [START_REF] Camarasa | Phenotypic Landscape of Saccharomyces Cerevisiae during Wine Fermentation: Evidence for Origin-Dependent Metabolic Traits[END_REF]. Comparable kinetics were observed between the strains, which was expected since all the strains belonged to the same species and were selected for their alcoholic fermentation performances [START_REF] Rivas-Ubach | Moving beyond the van Krevelen Diagram: A New Stoichiometric Approach for Compound Classification in Organisms[END_REF][START_REF] Ribéreau-Gayon | Observations related to the causes and consequences of stuck fermentation in vinification[END_REF].

Specific Footpinting of Strains

In our experiment, the twelve strains fermented the same must; thus, in these conditions, our metabolomic analysis reflected the specific traits of each strain. Indeed, statistical analysis of our data revealed a unique footprint for each of the strains studied.

A principal-component analysis (PCA) was performed on the FT-ICR-MS data to display the differences in the metabolomic composition of wine by representing the biological replicates of each strain. The PCA score plot of the two first components (Figure 1A) explained 37.9% of the metabolic variation. This representation highlighted the great proximity of the replicates for a given strain. At the strain level, this projection on these two axes allowed for separation of strains based on the metabolite produced and revealed high metabolic diversity. Our non-targeted analysis allowed us to report, for the first time, considerable metabolic differences between strains within the same species. The first principal component accounted for 25.6% of the variation and enabled the clear differentiation of the related strain as S1 and its adaptative evolution as S2. This first study of the exometabolome of twelve strains of the same species under fermentative conditions also reflected metabolically different strains that are associated with phenotypic differences. For example, the relevant separation, according to axis 1 of strain S8 to the other strains, may be related to the sluggish fermentation described earlier. A significant change in the exometabolome seemed to contribute to this phenomenon, consistent with the impact of various known metabolites already described [START_REF] Alexandre | Biochemical Aspects of Stuck and Sluggish Fermentation in Grape Must[END_REF][START_REF] Viant | How Close Are We to Complete Annotation of Metabolomes?[END_REF].

A total of 58,392 masses detected in FT-ICR-MS was extracted. Of these, the unique masses were excluded for further data processing. As a result, 2685 masses (Level 4) were retained. Then, among these masses, 2179 could be associated with a molecular formula (Level 3). Among them, it was possible to distinguish molecular formulas that were unique to a strain from a molecular formula whose abundance varied significantly, depending on the strain. Molecular formulas that presented significant differences in their mean intensity between all twelve strains were extracted by performing ANOVA statistical analyses (p-value < 0.05) and were considered as biomarkers. For each of these, their mass was subjected to different databases (KEGG, MassTrix, Metlin, YMDB) for putative annotation (Level 2).

Despite a similar metabolic background shown in the representation of common masses (Supplementary Figure S2), the strains were differentiated from each other by a pool of specific compounds extracted statistically (Table 1). Out of the 2179 molecular formulas, 1380 were common to all strains. Thus, 36.7% of the detected non-volatile composition was different, depending on the strain. As stated above, this proximity could be explained by the fact that all the strains belong to the same species and have very close genetic backgrounds [START_REF] Borneman | Whole-Genome Comparison Reveals Novel Genetic Elements That Characterize the Genome of Industrial Strains of Saccharomyces Cerevisiae[END_REF] S8, which stood out with PCA, unsurprisingly had the highest number of specific markers (1162) (Table 1). Looking further ahead, it was very interesting to know the nature of the differences in chemical composition of biomarkers for each strain. The set of biomarkers for a given strain matched their metabolomic footprint, which was previewed by van Krevelen diagrams. The van Krevelen diagrams were based on their O/C and H/C ratios (Figure 1). The wide range of biomarkers of each strain and its composition highlighted the diversity of metabolisms among these strains. Differences in both quantitative and chemical composition could be observed. This metabolic diversity was also illustrated by associated histograms of proportion-marker composition for each strain (Figure 1, Supplementary Figure S3). Thus, S3 was predominantly associated with CHO markers in the area of the van Krevelen diagram where carbohydrate-and polyphenol-derivative compounds were expected. On the contrary, the S4 profile appeared distinctly different from the other strains, with markers mainly composed of CHON and CHONS. The latter were located in the area associated with peptides on the van Krevelen diagram and whose composition is in agreement with Rivas-Ubach et al., 2018 [START_REF] Ballester | The Odor of Colors: Can Wine Experts and Novices Distinguish the Odors of White, Red, and Rosé Wines?[END_REF]. S5 and S7 were characterized by a large number of CHO, closely followed by CHON, and finally, CHONS.

Furthermore, to determine the impact of each strain on their biomarkers, we extracted biomarkers that were significantly more intense (Figure 2A) and less intense (Figure 2B) for each strain. The histogram proportions show the differences in qualitative elemental composition, and the pie charts support the prediction of the families of compounds that can be attributed to each feature. A diagram representing the H/C ratio as a function of the m/z ratio combined with the intensity of each of the features according to their m/z was used. This alternative representation provided additional information on the molecular weight of the biomarkers. All the features were in the mass range of 150 to 650 m/z. We found that the features extracted showed a large variability in composition between those that were less and more intense (Figure 2 and Supplementary Figure S4). For example, we observed that for strain S1, the significantly more intense markers were mainly composed of nitrogen-containing compounds (potential peptides and polyphenolderivative compounds), while the less intense ones were mostly associated with CHO markers in the area of the van Krevelen diagrams where carbohydrate compounds were expected. Biomarkers of S2, whether they were more or less intense, presented peaks with lower intensity in comparison with the other strains.

Once the markers were extracted and their nature assumed, it was possible to assign a hypothetical annotation (Level 3) to each of them using databases (KEGG, YMDB, Metlin, Lipidmap, Oligonet). In our case, only 10 to 15% of the specific markers could be annotated in the databases, confirming previous conclusions that evoked the complexity of wine composition and the lack of knowledge on it in the current databases [START_REF] Roullier-Gall | Integrating Analytical Resolutions in Non-Targeted Wine Metabolomics[END_REF][START_REF] Roullier-Gall | Exploring Yeast Interactions through Metabolic Profiling[END_REF][START_REF] Roullier-Gall | High Precision Mass Measurements for Wine Metabolomics[END_REF]. This step also allowed for the determination of the metabolic pathways associated with the metabolic modifications expressed by the specificity of the markers of each strain (Supplementary Figure S5). Thirty-two metabolic pathways were involved in exometabolome changes and include from 1 to 105 biomarkers. Among the most represented pathway, central metabolic pathways were found, such as carbon metabolism (67 biomarkers) or pyruvate metabolism (67 biomarkers). Moreover, there were also metabolic pathways involved in the synthesis of amino acids, such as phenylalanine (94 biomarkers). This last pathway is one of the many examples highlighting the importance of nitrogen metabolism, which appeared to be the most affected pathway. Indeed, most of the strain differentiation was associated with nitrogen-containing compounds. The significantly less intense biomarkers associated with the S2 strain, an adaptive evolution of the S1 strain, were predominantly nitrogen compounds, unlike S1. S1 was previously described by overexpression of genes coding amino-acid metabolism [START_REF] Barbosa | The Nitrogen Source Impacts Major Volatile Compounds Released by Saccharomyces Cerevisiae during Alcoholic Fermentation[END_REF]. The adaptive evolution leading to the stimulation of the pentose phosphate pathway would therefore have fewer intermediate metabolites. This was confirmed by the absence of intermediate biomarkers of this metabolic pathway. To confirm the structure of the previously annotated compounds, we performed an LC-MS/MS analysis and a comparison with the METLIN fragmentation database. A total of eight structures was confirmed (Level 2) (Supplementary Table S3) among the annotated masses.

The power of this approach made it possible to extract metabolites according to the strains used to conduct alcoholic fermentation. Thus, it was possible to determine the unique impact of each strain on the different types of metabolites and the related metabolic pathways. This also revealed intraspecific diversity through the non-volatile exometabolome. The non-targeted metabolomic approaches in the literature are mainly focused on secondary metabolism and therefore on the volatile exometabolome [START_REF] Roullier-Gall | High Precision Mass Measurements for Wine Metabolomics[END_REF]. To our knowledge, this is the first time that a non-targeted approach focused on the main metabolism was conducted on a large panel of strains used in the wine industry. Metabolic diversity was mainly observed at the level of nitrogenous metabolism, which plays a major role in the synthesis of volatile compounds. Therefore, it seemed important to investigate the intraspecific diversity on the secondary metabolism scale.

Impact of Strains on the Volatilome

HS-SPME-GC/MS was used to dose 35 volatile compounds in our fermentations. The volatile composition of each sample is presented in detail in Supplementary Table S4. A one-way ANOVA with strain as main effect was performed for each compound. The results showed that 31 compounds out of 35 showed significant differences between yeast strains. The four compounds showing non-significant differences were nonanol, benzyl alcohol, nonanoic acid, and benzaldehyde. For our study, only the discriminant compounds were considered for further statistical analyses. The ester group was most represented, with 20 esters identified and quantified. PCA and HCA were applied to volatilome data and allowed for the differentiation of five groups of strains based on Euclidean distance and the Ward method (Figure 3). The PCA score plot of the first two components explained 52.5% of the variation (Figure 3), with the first principal component (Dim1) accounting for 30.6% and the second (Dim2) accounting for 21.9%. The five clusters of samples from the HCA were projected onto this PCA using different colors.

The S8 and S2 strains appeared to form separate groups. The sluggish fermentation of S8 observed was also associated with a distinct volatilome and was in line with a contrasting metabolomic signature. This strain correlated with 1-hexanol and linalool. S2 is associated with isoamyl acetate, ethyl myristate, and phenylethyl acetate. On the other hand, other groups, like S5 and S7, were related to ethyl nonanoate and decanoate, while S1, S3, S6, and S12 were associated with three medium-chain fatty acids (MCFA) (hexanoic, octanoic, and decanoic acids). Finally, S4, S9, and S10 were correlated with higher alcohols, such as 1-octanol and 1-heptanol.

Another representation made it possible to highlight that across our twelve strains, an overexpression of certain families of VOCs by some strains (Figure 4), in addition to the significant diversity of expression of volatile compounds, was observed. S5 and S7 overexpressed the same six esters, and S4 overexpressed mostly higher alcohols. S2 resulted from an adaptative evolution by orientation of the carbon flow towards the pentose phosphate pathway, overexpressing 8 of the 20 quantified esters, confirming previous studies [START_REF] Alves | Exploring the Saccharomyces Cerevisiae Volatile Metabolome: Indigenous versus Commercial Strains[END_REF][START_REF] Cadière | Pilot-Scale Evaluation the Enological Traits of a Novel, Aromatic Wine Yeast Strain Obtained by Adaptive Evolution[END_REF]. On the contrary, parental strain S1 predominantly overexpressed intermediates of these esters as MCFA. Indeed, Cadière et al., 2012 [44] reported an increase in the concen-tration of some acetate esters by strain S2 evolved from parental strain S1. For example, the concentration was 2.5, 3.2, and 3.2 times higher for isoamyl acetate, isobutyl acetate, and phenylethyl acetate, respectively.

The initial composition of the matrix in nitrogenous sources [START_REF] Rollero | Combined Effects of Nutrients and Temperature on the Production of Fermentative Aromas by Saccharomyces Cerevisiae during Wine Fermentation[END_REF], as well as the preferential nitrogenous sources [START_REF] Vilanova | Assimilable Nitrogen Utilisation and Production of Volatile and Non-Volatile Compounds in Chemically Defined Medium by Saccharomyces Cerevisiae Wine Yeasts[END_REF], could lead to this modulation of the concentration of the volatile compounds according to the strain of Saccharomyces cerevisiae involved. Furthermore, this variety of production of these compounds is subject to the expression of several genes and variations in the expression level of several transcription factors [START_REF] Hazelwood | The Ehrlich Pathway for Fusel Alcohol Production: A Century of Research on Saccharomyces Cerevisiae Metabolism[END_REF][START_REF] Verstrepen | Yeast Flocculation: What Brewers Should Know[END_REF][50]. Eder et al., 2020 [51] also recently highlighted the involvement of loci and genes in nitrogen metabolism and its assimilation, influencing the formation of these volatile compounds, using the QTL mapping approach. This confirms the key role of nitrogen metabolism, the expression of related genes, and their regulation in the diversity of Saccharomyces cerevisiae strains at different scales. Our exometabolomic study underlined those differences in nitrogen metabolism and explained differences between strains, which supports previous findings using molecular approaches.

As described above, our results showed that it is possible to discriminate samples, thereby confirming intraspecific diversity in Saccharomyces cerevisiae species [START_REF] Roullier-Gall | High Precision Mass Measurements for Wine Metabolomics[END_REF] and the considerable metabolic diversity of our strains. The latter reflected the intraspecific metabolic diversity observed during the study of the non-volatile exometabolome. Indeed, primary metabolism participates in the expression of secondary metabolism and thus in its diversity. However, these two approaches remain complementary. Chemical diversity was therefore observed from another angle. Indeed, FT-ICR-MS targeted a range of analyzed masses corresponding to the non-volatile metabolome of yeast. Furthermore, 35 volatile compounds were targeted for quantification, but this is not fully representative of the diversity of non-volatile compounds present in wines. Therefore, sensory analysis is still a valuable means of obtaining a comprehensive view of this intraspecific diversity.

Sensory Impact of Intraspecific Diversity

At the end of the alcoholic fermentation, the wines from the organic replicates of each yeast modality were pooled, sulfited, filtered, bottled, and stored for one month. Frequency citations of each attribute were computed for each sample.

The resulting contingency matrix was subjected to a correspondence analysis (CA), shown in Figure 5. The first two principal components of this CA, Dim1 and Dim2, explained 50.32% of the variance. The distribution of wine samples displayed a considerable separation between wines made with distinct yeast strains. Hierarchical cluster analysis (HCA) was carried out on wine coordinates on the two first dimensions of the CA. The samples were separated into three main groups, represented in various colors (Figure 5).

The first group (in blue), located in the positive values of the first dimension, included samples S1, S7, S10, S11, and S3, which can be described by the attributes: "grapefruit", "wet mop", "rancid", "vegetal". The second cluster (in green) was composed of wines from fermentations conducted with the S5, S9, S2, and S12 strains and were located on the negative side of the first dimension. Within this cluster, S2 and S12 were characterized as "banana" and "English candy", while S5 and S9 were "chemical" and "fruity". The last group (in pink), composed of strains S4, S6, and S8, was characterized by oxidation terms as "quince paste", "honey", "butter". Our results showed quite distinctive aroma profiles among the strains studied, demonstrating intraspecific diversity at the sensory level [START_REF] Eder | QTL Mapping of Modelled Metabolic Fluxes Reveals Gene Variants Impacting Yeast Central Carbon Metabolism[END_REF][START_REF] Blanco | Inoculation of Treixadura Musts with Autochthonous Saccharomyces Cerevisiae Strains: Fermentative Performance and Influence on the Wine Characteristics[END_REF]. It was even possible to discriminate finished wines fermented by certain related strains. The S2 strain, resulting from the evolutionary adaptation of the S1 strain, belonged to different sensory classes, and hence, led to distinct sensorial profiles. Nevertheless, this was not the case for the S7 hybrid and the parental S10 strains. Despite the significant role of volatile compounds, their presence could not simply explain the sensory differences [START_REF] Vararu | Fermentative Volatilome Modulation of Muscat Ottonel Wines by Using Yeast Starter Cultures[END_REF][START_REF] Tempère | The Complexity of Wine: Clarifying the Role of Microorganisms[END_REF]. Moreover, despite a complex matrix, interactions between volatile compounds, and important differences in the perception threshold between the different aromatic volatile compounds, some descriptors could be related to volatile organic compounds. A high concentration of isoamyl acetate for strains S2 and S12 was significantly associated with very fruity terms, including "banana" and "English candy", as mentioned in previous studies [START_REF] Alves | Exploring the Saccharomyces Cerevisiae Volatile Metabolome: Indigenous versus Commercial Strains[END_REF][START_REF] Gammacurta | Impact of Yeast Strain on Ester Levels and Fruity Aroma Persistence during Aging of Bordeaux Red Wines[END_REF]. Concerning the vegetal term, we found a significant correlation with 1-hexanol, 1-heptanol, which has also been reported by other authors [START_REF] Ferreira | Investigation on the Role Played by Fermentation Esters in the Aroma of Young Spanish Wines by Multivariate Analysis[END_REF][START_REF] Álvarez-Pérez | Sensory and Chemical Characterisation of the Aroma of Prieto Picudo Rosé Wines: The Differential Role of Autochthonous Yeast Strains on Aroma Profiles[END_REF]. Moreover, 1-propanol was significantly linked to the term "rancid", which had already been related to pungent flavors [START_REF] Carrau | Production of Fermentation Aroma Compounds by Saccharomyces Cerevisiae Wine Yeasts: Effects of Yeast Assimilable Nitrogen on Two Model Strains[END_REF]. As for the two other approaches, it was possible to distinguish the finished wines produced thanks to the different strains of Saccharomyces cerevisiae used. The metabolic differences were, in fact, expressed in distinct phenotypes with regard to volatilome and sensory properties. We could see that the groups established based on the volatile composition analysis of the metabolome did not correspond exactly to the classes established from the sensory analysis. Furthermore, we observed that only a few sensory descriptors could be correlated to volatile compounds, as previously stated. Thus, this confirms previous studies, which revealed the difficulty of correlating the sensory aspect and the dosage of volatile compounds. Synergetic phenomena were observed between volatile compounds [START_REF] Callejon | Volatile and Sensory Profile of Organic Red Wines Produced by Different Selected Autochthonous and Commercial Saccharomyces Cerevisiae Strains[END_REF]. Conversely, the masking of a volatile compound by another was demonstrated [START_REF] Ferreira | Investigation on the Role Played by Fermentation Esters in the Aroma of Young Spanish Wines by Multivariate Analysis[END_REF][START_REF] Grosch | Evaluation of the Key Odorants of Foods by Dilution Experiments, Aroma Models and Omission[END_REF][START_REF] Ferreira | Quantitative Determination of the Odorants of Young Red Wines from Different Grape Varieties[END_REF]. Thus, the interactions between volatile compounds lead to diverse aromatic profiles. Moreover, in this study, the dosage of volatile compounds remained non-exhaustive and therefore not representative of the aromatic profile of wine at the sensory level.

To our knowledge, this was the first time that these three complementary approaches were combined for a comparative study.

Conclusions

This work reported the metabolic diversity within the Saccharomyces cerevisiae species under fermentative conditions from different perspectives. Ultra-high-resolution mass spectrometry (uHRMS) proved to be a powerful tool for the discrimination of yeast strains of the same species-in this case, Saccharomyces cerevisiae. A wide range of non-volatile metabolites belonging to different families of compounds, such as carbohydrates, peptides, lipids, aminosugars, polyphenols, and derivatives, was detected. Each of the strains could be associated with a specific metabolomic fingerprint, including unique markers and biomarkers that varied significantly in intensity. Thus, using this technique, we were able to highlight metabolic differences between strains of the same species that presented the same technological performances. Furthermore, the significant involvement of nitrogen metabolism in this differentiation was considered. It was also possible to show that the modulation of metabolism observed at the level of the non-volatile exometabolome was observed from the perspective of the volatilome and sensory aspect. Therefore, phenotypic differences within the same species revealed metabolic differences that resulted in the diversity of the volatile fraction that participates in the palette of the sensory pattern.

UHRMS analysis may be used for discriminating strains within yeast species after the alcoholic fermentation process and used in combination with other approaches to establish an integrative view of intraspecific diversity.

Supplementary Materials:

The following are available online at https://www.mdpi.com/article/10 .3390/microorganisms9112327/s1, Figure S1 S3: Table of extracted, annotated, and identified metabolites according to wine fermented by each strain of Saccharomyces cerevisiae (S1 to S12). Levels of annotations were derived from Viant et al., 2017 [26], Table S4: Table of extracted, annotated, and identified metabolites according to wine fermented by each strain of Saccharomyces cerevisiae (S1 to S12). Levels of annotations were derived from Viant et al., 2017 [26].

Figure 1 .

 1 Figure 1. (A) Principal-component analysis of twelve Saccharomyces cerevisiae strains based on FT-ICR-MS data using direct methanol dilution. ANOVA (p < 0.05) was used to extract specific markers for each of the twelve strains: S2, S3 and S4 are represented as examples. For each strain, H/C vs. O/C van Krevelen diagrams (B), histogram proportions that show their elemental compositions (C), and a pie chart (D) representing the distribution of these markers by hypothetical families of common wine compounds are presented. Bubble sizes indicate relative intensities of corresponding masses. Color code: CHO, blue; CHON, orange; CHONS, red; CHOS, green.

Figure 2 .

 2 Figure 2. H/C vs. m/z van Krevelen diagrams combined with intensity vs. m/z diagrams coupled to histogram proportions of the elemental formula compositions exhibit specific strain markers significantly less (B) and more (A) intense in each fermentation. Bubble sizes indicate relative intensities of corresponding masses. Color code: CHO, blue; CHON, orange; CHONS, red; CHOS, green. The pie chart represents the distribution of these markers by hypothetical families of common wine compounds.

Figure 3 .

 3 Figure 3. Biplot of PCA (Dim1 vs. Dim2) analysis applied to significantly different volatile compounds found in the twelve fermentations carried out by the different strains of Saccharomyces cerevisiae. Colored samples represent different classes obtained from HCA.

Figure 4 .

 4 Figure 4. Heat map of volatile compounds produced by the different strains of Saccharomyces cerevisiae. Columns correspond to volatile compounds that presented significant differences between twelve strains. Colored samples represent different class obtained from HCA.

Figure 5 .

 5 Figure 5. Biplot of the correspondence analysis of the general description of the twelve wines. Colors indicate the clusters obtained by HCA (using Ward's criterion) on the two first CA dimensions.

  : (A) Time series plot of the first principal component (t(1) vs. sample run order) (B) Plot representing the maximum, mean, and minimum peak intensity for each of the 9 QCs. (C) Histogram of all coefficients of variation values computed from the peak intensities from all the detected molecular compositions in the FT-ICR-MS data. (D) Extracted ion chromatograms of m/z 149.00917 in 9 sequential QCs samples., TableS1: Ballot used for the general odor description (translated from French), TableS2: Cell viability and fermentation parameters for the 12 strains of Saccharomyces cerevisiae (S1 to S12), FigureS2: Compounds common to all samples detected after methanol dilution. H/C vs. O/C van Krevelen diagrams, histogram proportion showing their elemental compositions; H/C vs. m/z van Krevelen diagrams combined with intensity vs. m/z diagrams coupled to histograms proportions of the elemental formula compositions, and pie chart representing the distribution of these markers by hypothetical families of common wine compounds adapted from Rivas and Ubach et al., 2018 [23]. Bubble sizes indicate relative intensities of corresponding masses. Color code: CHO, blue; CHON, orange; CHONS, red; CHOS, green.

Figure S3 :

 S3 Foot printing of twelve Saccharomyces cerevisiae strains based on FT-ICR-MS data using direct methanol dilution. ANOVA (p < 0.05) was used to extract specific markers for each of the twelve strains. For each strain, H/C vs. O/C van Krevelen diagrams (B), histogram proportion (C) that show their elemental compositions and pie chart (D) representing the distribution of these markers by hypothetical families of common wine compounds adapted from Rivas and Ubach et al., 2018 [23]. Bubble sizes indicate relative intensities of corresponding masses. Color code: CHO, blue; CHON, orange; CHONS, red; CHOS, green., Figure S4: H/C vs. m/z van Krevelen diagrams combined with intensity vs. m/z diagrams coupled to histograms proportion of the elemental formula compositions exhibits specific strains markers significantly less and more intense in each fermentation. Bubble sizes indicate relative intensities of corresponding masses. Color code: CHO, blue; CHON, orange; CHONS, red; CHOS, green. The pie chart represents the distribution of these markers by hypothetical families of common wine compounds adapted from Rivas and Ubach et al., 2018 [23], Figure S5: Number of biomarkers that could be associated with the different metabolic pathways of Saccharomyces cerevisiae using MassTrix and Kegg, Table

Author

  Contributions: Conceptualization, F.B., C.R.-G., J.B., A.J.-O. and H.A.; methodology, F.B., C.R.-G., J.B., A.J.-O., P.S.K. and H.A.; validation, F.B., C.R.-G., A.J.-O. and H.A.; formal analysis, F.B., C.R.-G. and J.B.; investigation, F.B., S.V. and B.Q.-C.; resources, C.R.-G., J.B., S.V., B.Q.-C., R.D.G.,

Table 1 .

 1 Table of extracted, annotated, and identified metabolites according to wine fermented by each strain of Saccharomyces cerevisiae (S1 to S12).

	Strains

Number of Extracted Masses Number of Biomarkers (Level 4) Unique Molecular Formulas Tentative Structure (Level 3)

					Fragmented
					Biomarkers	Validated
					(Putative	Identification
					Identification	(Level 2)
					Level 2)
	S1	133	0	6	1	0
	S2	208	0	16	5	1
	S3	127	0	8	4	2
	S4	289	0	15	3	0
	S5	128	0	5	0	0
	S6	165	0	7	5	0
	S7	130	0	7	1	0
	S8	1162	34	37	10	4
	S9	222	0	17	3	1
	S10	402	0	21	2	0
	S11	309	0	15	0	0
	S12	668	3	32	0	0

Microorganisms 2021, 9, 2327. https://doi.org/10.3390/microorganisms9112327 https://www.mdpi.com/journal/microorganisms

Acknowledgments:

The authors thank Rémy Romanet and Florian Bahut for their help in processing the data.

Funding: This work is a part of the METABOLOM (BG0022832.) project supported by the Conseil Régional de Bourgogne-Franche-Comté and the European Union through the PO FEDER-FSE Bourgogne 2014/2020 programs.

Institutional Review Board Statement: Not applicable.

Informed Consent Statement: Not applicable.

Conflicts of Interest:

The authors declare no conflict of interest.