domain: sdv spi

text:
François Beaudeau
email: beaudeau@insa-toulouse.fr3aceves@insa-toulouse.fr

Cesar Arturo

Aceves Lara

Josephine Godilllot
email: josephine.godillot@inrae.fr

Jean-Roch Mouret
email: jean-roch.mouret@inrae.fr

Ioan- Cristian Trelea

Carine Bideaux

Modeling the Effects of Assimilable Nitrogen Addition on Fermentation in Oenological Conditions

Keywords: mathematical modeling, oenological fermentation, nitrogen addition

Alcoholic fermentation in oenological conditions is a biological process carried out under significant physiological constraints: deficiency of nitrogen and others nutriments (vitamins, lipids …) and different stresses (pH and osmotic). In literature, few models were proposed to describe oenological fermentations. They are focused on initial conditions and did not integrate nitrogen addition during the fermentation process which is a widespread practice. In this work, two dynamic models of oenological fermentation are proposed to predict the effects of nitrogen addition at two different timings: at the beginning of the process and during the fermentation experiment. They were validated and compared against existing models showing an accurately fit to experimental data for CO2 release and CO2 production rate.

constant of sugar transporter production inhibition by ethanol in gE/L  α2 exponent of ethanol inhibition of sugar transporteur production, dimensionless  Nintra1 constant of sugar transporter limitation by intracellular nitrogen in gN/(10 9 cell)  κ cell activity loss rate in h -1  gS conversion yield of sugar into ethanol in molE/molS  𝑎 number of cells per biomass gram in 10 9 cell/g 1 Introduction

Oenological fermentation is a well-known biological process in which yeasts, mainly Saccharomyces cerevisiae strains, convert hexoses (glucose and fructose) principally to ethanol and carbon dioxide, secondarily to biomass and glycerol and weakly to metabolites produced in low concentrations with major impact on wines organoleptic properties. Oenological fermentation is a process which has several limitations whose main one is deficiency in nitrogen. In industrial conditions, nitrogen is totally consumed in the first two days of fermentation whose "normal" duration is one to two weeks [START_REF] Monteiro | Amino Acid Utilization and Urea Formation During Vinification Fermentations[END_REF]. However nitrogen is an essential nutrient for yeast metabolism and growth during oenological fermentation [START_REF] Agenbach | A study of must nitrogen content in relation to incomplete fermentations, yeast production and fermentation activity[END_REF][START_REF] Bely | Automatic Detection of Assimilable Nitrogen Deficiencies during Alcoholic Fermentation in Enological Conditions[END_REF] and its deficiency can induce sluggish or stuck fermentations [START_REF] Mendes-Ferreira | Growth and fermentation patterns of Saccharomyces cerevisiae under different ammonium concentrations and its implications in winemaking industry[END_REF]. Several studies have been conducted to understand and quantify nitrogen deficiency: Bisson [START_REF] Bisson | Stuck and sluggish fermentations[END_REF] related nitrogen deficiency to stuck and sluggish fermentations, Crépin et al [START_REF] Crépin | Sequential use of nitrogen compounds by Saccharomyces cerevisiae during wine fermentation : a model based on kinetic and regulation characteristics of nitrogen permeases[END_REF] studied the sequential uptake of nitrogen sources by yeasts and Carrau et al [START_REF] Carrau | Production of fermentation aroma compounds by Saccharomyces cerevisiae wine yeasts: effects of yeast assimilable nitrogen on two model strains[END_REF] studies the impact of nitrogen deficiency on aroma compounds. Nitrogen addition during fermentation increases reaction kinetics but this increase depends on addition timing [START_REF] Malherbe | Modeling the effects of assimilable nitrogen and temperature on fermentation kinetics in enological conditions[END_REF]. That is why European legislation allows nitrogen addition at the beginning and during wine oenological fermentation [START_REF] Commission | Commission Delegated Regulation[END_REF]. David et al [START_REF] David | Nitrogenbackboned modeling of wine-making in standard and nitrogen-added fermentations[END_REF] shows that residual growth is observed after the total consumption of nitrogen present initially in the medium which would suggest that the yeasts have a nitrogen reserve to continue their growth. Brou et al [START_REF] Brou | Modelling of S. cerevisiae and T. delbrueckii pure culture fermentation in synthetic media using a compartmental nitrogen model[END_REF] shows that intracellular nitrogen concentration decreases to a minimum during fermentation. It is therefore important to consider the intracellular nitrogen concentration in the yeasts.

The data from David et al [START_REF] David | Nitrogenbackboned modeling of wine-making in standard and nitrogen-added fermentations[END_REF] shows also that a regrowth of biomass is possible after nitrogen addition and that this regrowth is all the stronger the earlier the nitrogen is added. Indeed, yeast physiological state declines during fermentation due to several deficiency and inhibitions such as inhibition by ethanol. Thus, the increase of ethanol concentration during fermentation affects physiological state of yeast cells: activities of nitrogen transporters [START_REF] Bisson | Influence of nitrogen on yeast and fermentation of grapes[END_REF][START_REF] Leão | Effects of ethanol and other alkanols on the ammonium transport system of Saccharomyces cerevisiae[END_REF] and sugar transporters [START_REF] Bisson | Glucose transport in Saccharomyces cerevisiae and the role of potassium in stuck fermentation[END_REF] are decreasing when the ethanol concentration increases. Moreover, a study shows a rapid decrease of cell activity after ethanol addition in the medium [START_REF] Ansanay-Galeote | Stress effect of ethanol on fermentation kinetics by stationary-phase cells of Saccharomyces cerevisiae[END_REF]. Several mathematical models were proposed to simulate fermentation in oenological conditions [START_REF] Aiba | Kinetics of product inhibition in alcohol fermentation[END_REF][START_REF] Boulton | The Prediction of Fermentation Behavior by a Kinetic Model[END_REF][START_REF] Caro | Development of a kinetic model for the alcoholic fermentation of must[END_REF][START_REF] Colombié | Modeling Alcoholic Fermentation in Enological Conditions: Feasibility and Interest[END_REF][START_REF] Marín | Alcoholic Fermentation Modelling: Current State and Perspectives[END_REF][START_REF] Sevely | Modelling, Identification and Control of the Alcohol Fermentation in a Cascade Reactor[END_REF][START_REF] Williams | On-line adaptive control of a fed-batch fermentation of Saccharomyces cerevisiae[END_REF]. They consider time evolutions of concentrations for biomass, sugar, ethanol, carbon dioxide and some of them for nitrogen and glycerol but few models consider the relation between yeast growth and nitrogen concentration:  Cramer's model [START_REF] Cramer | Kinetic model for nitrogen-limited wine fermentations[END_REF] considers nitrogen limitation in the biomass growth with a Monod-type equation and a nongrowth associated conversion of glucose into ethanol. It considers too a cell death rate proportional to ethanol concentration.  Malherbe's model [START_REF] Malherbe | Modeling the effects of assimilable nitrogen and temperature on fermentation kinetics in enological conditions[END_REF] describes the biomass production as a logistic law with a maximum attainable biomass concentration dependent on the initial nitrogen concentration. The authors introduce in their model a state variable representing sugar transporters involved in the sugar consumption rate equation. Moreover, the ethanol inhibition is considered in the equations of sugar and nitrogen consumption rates. Ethanol and CO2 are produced from sugar in an overall yield (1 gram of sugar is converted into 2.17 grams of ethanol and 2.17 grams of CO2).  Brou's model [START_REF] Brou | Modelling of S. cerevisiae and T. delbrueckii pure culture fermentation in synthetic media using a compartmental nitrogen model[END_REF] is based on an intracellular nitrogen compartment divided between the minimum nitrogen necessary to carry out the vital functions of the cells and a storage compartment, which is the only nitrogen available for biomass growth. It considers ethanol inhibition on metabolism of yeasts (production of biomass, ethanol and glycerol) as well as the cell death rate function of ethanol concentration.

However, these models were not developed nor calibrated for fermentations with nitrogen addition during the fermentation process. Cramer's and Brou's models can allow regrowth of biomass after nitrogen add. Malherbe's model could simulate nitrogen addition with a complicated algorithm: model is simulated using initial conditions and it is stopped before nitrogen addition instant and new simulation is started with the new initial conditions. This is a difficult task if we try to apply the model for online optimization purposes.

In this work, two models derived from Malherbe and Brou's models are proposed to allow the simulation of nitrogen addition during fermentation without stopping the simulation at nitrogen addition instant (section 3). These models have been calibrated on experimental data from fermentations with different initial nitrogen concentrations and different nitrogen amount addition at an add timing corresponding to 20g/L of CO2 release allowing biomass regrowth (section 4). A sensitivity analysis of the two models is presented in section 5. Then, the two models have been validated and compared to Malherbe's and Brou's models on experimental data from others fermentations with various initial nitrogen conditions and nitrogen addition at 20 and 35g/L produced CO2 (section 6).

2 Materials and Methods

Yeast strain

The fermentations, which are used in this study, are performed with the commercial strain of Saccharomyces cerevisiae Lalvin EC-1118 (Lallemand SA, Montreal, Canada). Fermentation tanks are inoculated with 100 mg/L active dry yeast, i. e. 10 9 cells/L, which are rehydrated for 30 minutes at 37°C in a 50 g/L glucose solution.

Fermentation media

The fermentations are carried out in synthetic musts exhibiting the characteristics of a standard grape juice [START_REF] Bely | Description of alcoholic fermentation kinetics-its variability ad significance[END_REF]. The sugar concentration of all musts is 180g/L evenly split between glucose and fructose and the pH is at 3.3. Three initial concentrations of assimilable nitrogen (ammonium chloride and mixture of amino acids) are used: 70, 140 and 210 mgN/L, corresponding respectively to MS70, MS140 and MS210. The three media present the same proportions of the different nitrogen sources [START_REF] Mouret | Kinetic analysis and gas-liquid balances of the production of fermentative aromas during winemaking fermentations: Effect of assimilable nitrogen and temperature[END_REF]. The concentrations of others nutrients are the same as in [START_REF] Mouret | Kinetic analysis and gas-liquid balances of the production of fermentative aromas during winemaking fermentations: Effect of assimilable nitrogen and temperature[END_REF].

Fermentation conditions

The fermentation are carried out in 1.2 L glass fermenters with 1 L of medium regulated at 24°C. CO2 release is accurately measured from an automatic online monitoring of weight loss [START_REF] Sablayrolles | Design of a laboratory automatic system for studying alcoholic fermentations in anisothermal enological conditions[END_REF].

Nitrogen addition is carried out with three concentrations: 50, 100 and 150 mgN/L in the form of mineral nitrogen (diammonium phosphate) and different timings: at 20 g/L produced CO2 for calibration fermentations and at 20 g/L and 35g/L produced CO2 for validation fermentations. Nitrogen additions are performed automatically by means of a pump [START_REF] Godillot | The Timing of Nitrogen Addition Impacts Yeast Genes Expression and the Production of Aroma Coumpounds During Wine Fermentation[END_REF].

Cell population

The total cell population is measured using a Beckman Coulter counter (Model Z2, Beckman-Coulter, Margency, France) fitted with a 100 µm aperture probe.

Measurement of Assimilable Nitrogen

Ammonium concentration is measured enzymatically (R-Biopharm, Darmstadt, Germany). The free amino acid concentrations are measured by cation exchange chromatography with post-column ninhydrin derivatization (Biochrom 30, Biochrom, Cambridge, United Kingdom) as presented by Crépin et al [START_REF] Crépin | Sequential use of nitrogen compounds by Saccharomyces cerevisiae during wine fermentation : a model based on kinetic and regulation characteristics of nitrogen permeases[END_REF] .

Fermentation conditions of data used for models' calibration and validation

The conditions of the cultures used for the calibration and the validation of the models are presented in Table 1.

Models formulation

Two structured models were developed based on nitrogen-limited biomass growth to simulate nitrogen addition without discontinuities, one based on Malherbe's model and another on Brou's model. These new models allow to simulate the fermentation variables: biomass (X in 10 9 cell/L), sugar (S in g/L), nitrogen (N in g/L) and ethanol (E in g/L), the cumulative production of carbon dioxide (CO2 in g/L) and also the dynamic of state variables representative of yeast physiological state which are intracellular nitrogen (Nintra in g/10 9 cell), sugar transporter (NST in gN/10 9 cell) and cell activity (A dimensionless).

Introduction of intracellular nitrogen and cell activity

As reported in the literature, a residual growth is observed after the end of nitrogen consumption present in the medium [START_REF] David | Nitrogenbackboned modeling of wine-making in standard and nitrogen-added fermentations[END_REF]. So, as in the Brou's model, an intracellular nitrogen compartment (Nintra) is considered in the models. The intracellular nitrogen is formed by entry of nitrogen into the yeast and is used for biomass growth and sugar carrier production as shown in the Erreur ! Source du renvoi introuvable.. As in the Malherbe's model, the sugar transporters (NST) are considered. They are synthetized from intracellular nitrogen. The sugar transporters are involved in the sugar equation and depict the sugar affinity and the ethanol inhibition of sugar transporter on sugar consumption.

Figure 1 Diagram of nitrogen forms

As it is also known that the physiological state of yeasts declines during the fermentation [START_REF] Bisson | Influence of nitrogen on yeast and fermentation of grapes[END_REF][START_REF] Leão | Effects of ethanol and other alkanols on the ammonium transport system of Saccharomyces cerevisiae[END_REF][START_REF] Bisson | Glucose transport in Saccharomyces cerevisiae and the role of potassium in stuck fermentation[END_REF][START_REF] Ansanay-Galeote | Stress effect of ethanol on fermentation kinetics by stationary-phase cells of Saccharomyces cerevisiae[END_REF] , the term of cell activity was introduced in the models to consider enzymatic activity decrease due to nitrogen deficiency and ethanol production. Its evolution is described in equation [START_REF] Monteiro | Amino Acid Utilization and Urea Formation During Vinification Fermentations[END_REF].

𝑑𝐴 𝑑𝑡 = µ (1 -𝐴) -𝜅 𝐴 (1)
µ (h -1 ) is the specific growth rate and 𝜅 (h -1 ) a constant.

Mass balance

The bioreactor is assumed to be infinitely mixed with a constant volume without any transfer limitation. Then the temporal evolution of variables is only linked to the biological kinetics. Based on these assumptions, unsteady-state mass balances for cells, sugar, nitrogen, ethanol, CO2, intracellular nitrogen and sugar transporter are given by Eqs ( 2)-( 8):

𝑑𝑋 𝑑𝑡 = 𝑟 𝑋 (2) 𝑑𝑆 𝑑𝑡 = 𝑟 𝑆 (3) 𝑑𝑁 𝑑𝑡 = 𝑟 𝑁 (4) 𝑑𝐸 𝑑𝑡 = 𝑟 𝐸 (5) 𝑑𝐶𝑂 2 𝑑𝑡 = 𝑟 𝐶𝑂2 (6) 𝑑𝑁 𝑖𝑛𝑡𝑟𝑎 𝑑𝑡 = 𝑟 𝑁 𝑖𝑛𝑡𝑟𝑎 - 𝑁 𝑖𝑛𝑡𝑟𝑎 𝑋 𝑑𝑋 𝑑𝑡 (7) 𝑑𝑁 𝑆𝑇 𝑑𝑡 = 𝑟 𝑁 𝑆𝑇 - 𝑁 𝑆𝑇 𝑋 𝑑𝑋 𝑑𝑡 (8)
With rX, rE and rCO2 the production rate of respectively biomass, ethanol and CO2 and rS and rN the consumption rate respectively of sugar and nitrogen, rNintra and rNST the net rate of respectively Nintra NST. The term-

Model 1 derived from Malherbe's model

Malherbe's model [START_REF] Malherbe | Modeling the effects of assimilable nitrogen and temperature on fermentation kinetics in enological conditions[END_REF] has to be modified to integrate effect of nitrogen addition and potential regrowth of biomass after nitrogen addition as biomass depends only on initial nitrogen in this model. Model 1 includes 18 parameters against 16 for the Malherbe's model.

The sugar consumption rate [START_REF] Malherbe | Modeling the effects of assimilable nitrogen and temperature on fermentation kinetics in enological conditions[END_REF] is expressed by:

𝑟 𝑆 = -𝜈 𝑆𝑇 (𝑆, 𝐸)𝑁 𝑆𝑇 X (9)
In which 𝜈 𝑆𝑇 (𝑆, 𝐸) represent the activity of a sugar transporter (facilitated mechanism diffusion) with ethanol inhibition:

ν 𝑆𝑇 (𝑆, E) = 𝑘 2 𝑆 𝑆 + 𝐾 𝑠 + 𝐾 𝑆1 𝑆𝐸 α 𝑆 ( 10
)
With k2 the maximum specific rate in gS/( gN.10 9 cells.h), KS the affinity constant in gS/L, KSI the inhibition constant in (L/gE) αS and αS dimensionless.

Assuming a constant yield of CO2 released and ethanol produced during fermentation, the ethanol and CO2 productions rates are described by Eq [START_REF] Brou | Modelling of S. cerevisiae and T. delbrueckii pure culture fermentation in synthetic media using a compartmental nitrogen model[END_REF] and ( 12):

𝑟 𝐸 = - 1 𝑌𝐸 𝑆 𝑟 𝑆 (11)
𝑟 𝐶𝑂 2 = -1 𝑌𝐶𝑂2 𝑆 𝑟 𝑆 [START_REF] Bisson | Influence of nitrogen on yeast and fermentation of grapes[END_REF] YE/S and YCO2/S are the conversion yields respectively of sugar to ethanol and of sugar to CO2. they are set to 2.17 [START_REF] Malherbe | Modeling the effects of assimilable nitrogen and temperature on fermentation kinetics in enological conditions[END_REF].

It is assumed that the sugar transporter synthesis depends on intracellular nitrogen and that sugar transporters can be degraded.

The net rate of sugar transporter is defined by:

𝑟 𝑁 𝑆𝑇 = 𝑘 𝑛𝑠𝑡 (1 - 𝑄 0𝑛𝑠𝑡 𝑁 𝑖𝑛𝑡𝑟𝑎 ) -𝑘 𝑑𝑛𝑠𝑡 𝑁 𝑆𝑇 𝐾 𝑁𝑆𝑇 + 𝑁 𝑆𝑇 ( 13
)
In which knst is the maximum specific production rate in gN/(10 9 cell.h), Q0nsst is the minimal intracellular nitrogen content for sugar transporter production in gN/(10 9 cell), KNST is the affinity constant in gN/10 9 cell and kdnst is the maximum specific degradation rate in gN/(10 9 cell.h).

The specific rate of nitrogen consumption of Malherbe's model is modified by introducing the notion of cell activity:

𝑟 𝑁 = -𝜇 𝑁 (𝑁, 𝐸). 𝑋. 𝐴 [START_REF] Bisson | Glucose transport in Saccharomyces cerevisiae and the role of potassium in stuck fermentation[END_REF] μN (gN/(10 9 cell.h) correspond to specific nitrogen consumption rate which is limited by nitrogen and inhibited by ethanol. It is defined by:

μ 𝑁 (𝑁, 𝐸) = 𝑘 3 𝑁 𝑁 + 𝐾 𝑁 + 𝐾 𝑁𝐼 𝑁𝐸 α 𝑁 (15)
With k3 the maximum specific consumption rate in gN/(10 9 cell.h -1 ), KN the affinity constant in gN/L, KNI the inhibition constant and αN dimensionless.

For the net production rate of intracellular nitrogen (eq 16). Three phenomena are considered: the consumption of nitrogen by yeast cell, the biomass production and the production and degradation of sugar transporters.

𝑟 𝑁 𝑖𝑛𝑡𝑟𝑎 = 𝜇 𝑁 (𝑁, 𝐸) -𝛼 1 𝑟 𝑋 - 1 𝑌 𝑛𝑠𝑡 (𝑘 𝑛𝑠𝑡 (1 - 𝑄 0𝑛𝑠𝑡 𝑁 𝑖𝑛𝑡𝑟𝑎 ) -𝑘 𝑑𝑛𝑠𝑡 ) (16)
With α1 the nitrogen yield in cell in gN/(10 9 cell), Ynst the nitrogen yield of sugar transporter in gN/gN.

The biomass production rate (eq 17) is function of intracellular nitrogen concentration and cell activity to consider, respectively, the residual growth after nitrogen depletion in the medium and the lower capacity of the yeast to regrow after nitrogen addition for a longer period of nitrogen depletion. It considers also a linear inhibition by ethanol:

𝑟 𝑋 = 𝑘 1 (𝑇)𝑋 (1 - 𝑄 0 𝑁 𝑖𝑛𝑡𝑟𝑎 ) (1 - 𝐸 𝐸 𝑚𝑎𝑥 ) 𝐴 (17)
In which k1(T) is the maximum specific growth rate depending on temperature (h -1 ): 𝑘 1 (𝑇) = 𝛼 𝑘1 𝑇 -𝛽 𝑘1 , that relation comes from the Malherbe model [START_REF] Malherbe | Modeling the effects of assimilable nitrogen and temperature on fermentation kinetics in enological conditions[END_REF], 𝑄 0 the minimum intracellular nitrogen content of biomass for biomass growth in gN/(10 9 cell) and Emax the critical ethanol concentration for biomass growth in gE/L. Reaction rates 𝑟 𝑖 * are in mol/(L.h). The stoichiometric coefficients g3 and g4 can be deduced from g1 and g2. gS is the yield of conversion of sugar into ethanol and CO2. gS is slightly lower than 2 mol/mol, the theoretical yield of ethanol production, because sugar is also converted into other metabolites like glycerol and aromas. The biomass composition is taken from [START_REF] Brou | Modelling of S. cerevisiae and T. delbrueckii pure culture fermentation in synthetic media using a compartmental nitrogen model[END_REF].

Model equations

The model 2 includes 19 parameters against 18 for the Brou's model. The rates of consumption or production of each species can be expressed as a weighted sum of the four stoichiometric equation rates (eq 18 to 24). All these rates are expressed in g/(L.h) except for biomass whose rate is expressed in 10

 Sugar transporter :

𝑟 𝑁 𝑆𝑇 = 𝑟 4 * 𝑀 𝑁 ( 24
)
With MX, MS, ME, MCO2 and MN the molar mass, respectively, of biomass, sugar, ethanol, CO2 and nitrogen in g/mol and 𝑎 the number of cells per biomass gram in 10 9 cell/g.

Reactions rates

We define Xn the biomass concentration in C-molX/L by the equation:

𝑋 𝑛 = 𝑋 𝑎𝑀 𝑋 ( 25
)
with X the biomass concentration in 10 9 cell/L. The value of 𝑎 and MX are those of Brou's model [START_REF] Brou | Modelling of S. cerevisiae and T. delbrueckii pure culture fermentation in synthetic media using a compartmental nitrogen model[END_REF]: 37.6 10 9 cell/g and 25.0689g/C-mol respectively.

First stoichiometric equation rate (Yeast growth rate (𝑟 1 * )) is limited by intracellular nitrogen (Nintra) and by sugar (S). It depends of biomass (Xn) and cell activity (A) and can be expressed by the equation 26:

𝑟 1 * = 𝑘 𝑋 𝑋 𝑛 ( 𝑁 𝑖𝑛𝑡𝑟𝑎 𝑁 𝑖𝑛𝑡𝑟𝑎 + 𝑁 𝑖𝑛𝑡𝑟𝑎0 ) ( 𝑆 𝐾 𝑆1 + 𝑆 ) 𝐴 (26)
With kX the maximum specific growth rate in h -1 , KS1 the affinity constant for substrate in gS/L and Nintra0 the constant of growth limitation by intracellular nitrogen in gN/L. Ethanol production rate (𝑟 2 * ) is inhibited by ethanol (E) and is limited by sugar (S) and sugar transporter (NST):

𝑟 2 * = 𝑘 𝐸 𝑋 𝑛 ( 𝑆 𝑆 + 𝐾 𝑆2 ) (1 - 𝐸 𝐸 𝑙𝑖𝑚1 ) 𝛼 1 ( 𝑁 𝑆𝑇 𝑁 𝑆𝑇 + 𝐾 𝑆𝑇 ) (27)
With kE the maximum specific ethanol production rate in molE.molX.h -1 , KS2 the affinity constant for sugar in gS/L, Elim1 the critical concentration of ethanol in gE/L for which there is no more ethanol production and KST the constant of ethanol production limitation by sugar transporter in gN/10 9 cell.

Nitrogen absorption rate (𝑟 3 * ) is limited by nitrogen (N) and depends of biomass (Xn) and cell activity (A):

𝑟 3 * = 𝑘 𝑁 𝑋 𝑛 ( 𝑁 𝑁 + 𝐾 𝑁1
) 𝐴 [START_REF] Shampine | The MATLAB ODE Suite[END_REF] With kN the maximum specific nitrogen absorption rate in molN.molX.h -1 , KN the affinity constant for nitrogen in gN/L. Sugar transporter rate (𝑟 4 * ) is inhibited by ethanol (E) and limited by intracellular nitrogen (Nintra):

𝑟 4 * = 𝑘 𝑁𝑆𝑇 𝑋 𝑛 (1 - 𝐸 𝐸 𝑙𝑖𝑚2 ) 𝛼 2 ( 𝑁 𝑖𝑛𝑡𝑟𝑎 𝑁 𝑖𝑛𝑡𝑟𝑎 + 𝑁 𝑖𝑛𝑡𝑟𝑎1 ) ( 29
)
With kNST the maximum specific sugar transporter rate in molN.molX.h -1 , Elim2 the critical concentration of ethanol in gE/L and Nintra1 the constant of sugar transporter limitation by intracellular nitrogen.

Equations of the two models developed are summarized in Table 2.

Computing

Matlab R2017b software was used for calibration and simulation of the models: ode15s function [START_REF] Shampine | The MATLAB ODE Suite[END_REF] to solve differential equations and pattern search and Rosenbrock algorithms to calibrated models.

Statistical analysis

Models quality was analysed with experimental data using the Normed Root Mean Square Error (NMRSE) [START_REF] Armstrong | Error measures for generalizing about forecasting methods: Empirical comparisons[END_REF] and the Akaike Information Criterion (AIC) [START_REF] Akaike | A New Look at the Statistical Model Identification[END_REF]. The NRMSE is defined as:

𝑁𝑅𝑀𝑆𝐸 = √ ∑ (𝑥 𝑖 -𝑦 𝑖 ) 2 𝑇 𝑖=1
𝑛 𝑦 𝑚𝑎𝑥 -𝑦 𝑚𝑖𝑛 [START_REF] Akaike | A New Look at the Statistical Model Identification[END_REF] With 𝑛 the number of experimental data, 𝑥 𝑖 the experimental data corresponding to time ti, 𝑦 𝑖 the data simulated by model for the same time ti, 𝑦 𝑚𝑖𝑛 and 𝑦 𝑚𝑎𝑥 the minimum and maximum data values.

the NRMSE is used for several variables, with the following formula:

𝑁𝑅𝑀𝑆𝐸 𝑡𝑜𝑡 = ∑ 𝑁𝑅𝑀𝑆𝐸 𝑖 √𝑛 𝑖 𝑚 𝑖=1 √∑ 𝑛 𝑖 𝑚 𝑖=1 (31)
m is the total number of variables, NRMSEi are the NRMSE value for the i th variable and ni is the number of values of the i th variable.

The AIC is defined by:

𝐴𝐼𝐶 = 2𝑝 + 𝑛(𝑙𝑛(2𝜋) + 𝑙𝑛(𝑆𝑆𝐸) -𝑙𝑛(𝑛) + 1 ) (32)
With 𝑝 the number of parameters, 𝑛 the n number of experimental data and 𝑆𝑆𝐸 the Sum Square Error.

The SSE is defined by:

𝑆𝑆𝐸 = ∑(𝑥 𝑖 -𝑦 𝑖 ) 2 𝑛 𝑖=1 (33)
With 𝑛 the number of experimental data, 𝑥 𝑖 the experimental data corresponding to time ti, 𝑦 𝑖 the data simulated by model for the same time ti..

Sensibility analysis

The robustness of the models 1 and 2 to its parameters has been studied using the sensitivity coefficient 𝜎 𝑦 Δ𝑝 (Eq 32) for the variable y and the parameter p [START_REF] Bernard | Dynamical model development and parameter identification for an anaerobic wastewater treatment process[END_REF].

𝜎 𝑦 𝛥𝑝 = ∫ 𝑦(𝑝 + 𝛥𝑝, 𝑡) -𝑦(𝑝, 𝑡) 𝑦(𝑝, 𝑡) 𝑡 𝑓 0 𝑑𝑡 ( 34
)
With tf the final fermentation time, y(p,t) the simulated value of the variable y at the time t and for the vector of optimized parameters and Δp the modification of a parameter.

4 Models calibration

Parameters calibration

The two models are calibrated using the four fermentations presented in Table 1 of paragraph 2.6. Each fermentation present between 10 and 18 data of nitrogen and of biomass and about 460 data of CO2 (one data each 20 minutes).

The Table 3 shows Model 1 and model 2 calibrated parameters, and the confidence intervals for these parameters. It could be seen that calibrated Model 1 have values close to those reported in the literature [START_REF] Malherbe | Modeling the effects of assimilable nitrogen and temperature on fermentation kinetics in enological conditions[END_REF].

The confidence intervals are small for almost all parameters of both models, which means that the parameters values are reliable. For the Model 1, only three parameters (KS, knst and Knst) present a great confidence interval compared to their values. For the Model 2, only the parameter α2 present a great confidence interval compared to its value.

Models comparison

The Figure shows the comparison of the two calibrated models' simulation with experimental data and simulation of Brou's and Malherbe's models. The Brou's and Malherbe's models were calibrated with the same data as models 1 and 2 to better compare them. Graphically, models 1 and 2 fit experimental data well and simulate slightly better experimental data than Brou's and Malherbe's models. Models 1 and 2 fit less on MS70+100 than for other fermentations on CO2 production Brou's model underestimates the final CO2 production for the four fermentations. The Malherbe's model simulates well the CO2 production for two fermentations (MS70+100 and MS140+50). However, Malherbe's model simulates badly the CO2 production after nitrogen addition for the other two fermentations (MS140+150 and MS210+100), where added nitrogen is important. Models 1 and 2 fit the CO2 production rate better before nitrogen addition than after nitrogen addition especially for maximum value of CO2 production rate. Model 1 seems to be slightly better than model 2 for CO2 production and for CO2 production rate. Model 1 and 2 simulate better CO2 production rate than Malherbe's and Brou's models after nitrogen addition. Model 1 and 2 simulate well nitrogen consumption during the first part of fermentation unlike the Malherbe's model but, after nitrogen addition, the simulated consumption is faster than experimental data. Brou's model simulates also the nitrogen consumption too quickly after the nitrogen addition. Models 1 and 2 seem to have equivalent performance on nitrogen. Concerning simulation of biomass dynamics, Model 1 underestimates the biomass production rate while model 2 tends to overestimate this rate after nitrogen addition. Both models overestimate maximum biomass produced for MS210+100 and for MS70+100 but estimate well maximum biomass produced for MS140+50 and MS140+150. Brou's model overestimates the biomass whereas Malherbe's model underestimates the biomass production.

Figure 2 Dynamic evolution of biomass, nitrogen, CO2 and CO2 production rate for the experimental data (in red) and data simulated by models 1 (in black), model 2 (in blue), Malherbe's model (in pink) and Brou's model (in green) for the four calibration fermentatations

The Table 4 shows the NRMSE values for each variable for all fermentations for Models 1 and 2. Model 1 is slightly better than model 2 for the whole fermentations and for the whole variables (NRMSE values of 0.208 for model 1 and 0.241 for model 2 cf. Table 4) and for each variable. Model 1 better describes kinetic evolution of experimental data than model 2 for nitrogen for the four fermentation and for biomass for three fermentations (not for MS140+50). Regarding the NRMSE for CO2, rCO2 and for the whole variables for MS140+150 and for MS70+100, Model 1 is closer to the data than the model 2 while model 2 is slightly better for MS210+100 and for MS140+50.

Table 4 NRMSE values applied to each variable for each fermentation, to all of the variables for each fermentation, to each variable for all of the fermentations and to all of the variables for all of the fermentations and for Models 1 and 2.

Model

Fermentations CO2 in g/L rCO2 in g/(L.h) Biomass in 10 According to the AIC values (Table 5), Models 1 and 2 are better than Malherbe's and Brou's Models with higher nitrogen addition: for instance, for MS+150 the AIC value for Brou's Model and Malherbe's Model are approximately two times the value for Model 1 and for Model 2. Models 1 and 2 are slightly better than Brou's and Malherbe's Models for fermentations with a lower nitrogen addition. Models 1 and 2, Malherbe's and Brou's Models are equivalents for the biomass and for nitrogen. Models 1 and 2 present better performance than Brou's and Malherbe's Model for CO2 production rate.

Model sensitivity

Sensitivity analysis was done to find parameters that play the main role in the models. Moreover, as the model will be used for online optimization, the model sensitivity to parameter variations must be studied. In this work the sensitivity coefficients are calculated for biomass, nitrogen, CO2 and rCO2 and for a modification of each parameter value between -10% and 10% with a step of 0.5%. For the model 1, the sensitivity analysis was not applied to parameter k1 because this parameter depends on temperature and we use only one temperature. For the model 2, the sensitivity analysis was not applied to the parameter g3 because this parameter is calculated from the parameter g1 (𝑔 3 = 6𝑔 1 -1). Figure 3 and Erreur ! Source du renvoi introuvable. represent the sensitivity coefficients calculated for CO2 release and for each parameters of model 1 and 2 respectively. Model 1 is sensitive to variations of four parameters (k2, Nintra0, Q0nst, Ynst). Model 2 is sensitive to variations of three parameters (k2, k3 and g2) and diverges for some modifications of two parameters (Elim2 and gS). Model 1 seems to be less sensitive than model 2 because model 2 diverges for some modifications of two parameters values (Elim2 and gS).

For the model 1, nitrogen is the most sensitive variable to changes in parameters as for all parameters the sensitivity coefficient takes an absolute value of more than 1 for at least one variation of the parameter. Increasing Q0 or decreasing Q0nst result in the greatest variation of the sensitivity coefficient for nitrogen. Biomass is not very sensitive to the variation of the parameters: only two parameters modifications leads to a sensitivity coefficient of more than 1 in absolute value: Q0 and Q0nst. The CO2 production rate rCO2 is not sensitive to the modification of the value of most of the parameters except for the diminution of k2, Q0 and Ynst that can lead respectively to a sensitivity coefficient of -8.88, -4.21 and -2.90 for a diminution of 10% of the three parameters values. CO2 is the variable least sensitive to variations in parameters values: for only five parameters, the value modification can lead to a sensitivity coefficient more than 0.1 in absolute value but none of them induce a sensitivity coefficient more than 1 in absolute value.

For the model 2, increasing gS by more than 7% or decreasing Elim2 by more than 6.5% lead to the divergence of model 2. As for model 1, nitrogen is very sensitive to parameters value modification: most of the modification lead to a sensitivity coefficient more than 1 in absolute value. Nitrogen is most sensitive to modification of g2: sensitivity coefficient can be more than 100. Biomass is not very sensitive to parameters value modification: no modification leads to a sensitivity coefficient of more than 1 in absolute value. Concerning rCO2, the modifications of 6 parameters lead to a sensitivity coefficient more than 1 in absolute value especially the modification of k2, Elim2 and g2 that lead to a sensitivity coefficient more than 20 in absolute value. CO2 is not sensitive to the modification of any parameters: no parameters value modification lead to a sensitivity coefficient more than 0.5 in absolute value. Malherbe's model estimates well CO2 production for three fermentations (MS140+50 and MS210+100 with a nitrogen addition at 20 g/L of CO2 released and MS140+100 with a nitrogen addition at 35 g/L CO2 released) but estimates poorly the CO2 production for MS70+100 with a nitrogen addition at 20 g/L of CO2 released during the whole fermentation and MS140+150 with a nitrogen addition at 20 g/L of CO2 released after nitrogen addition. Brou's model estimates well CO2 production before nitrogen addition but underestimates CO2 production after nitrogen addition and the final CO2 production. Models 1 and 2 simulate well CO2 production all around the fermentation but they slightly overproduce CO2 after nitrogen addition.

Malherbe's model does not predict very well the CO2 production rate before the nitrogen addition. Malherbe's model overestimates the Vmax. Brou's model simulates poorly the CO2 production rate for the five fermentations. The nitrogen addition has no effect on CO2 production rate simulated by Brou's and Malherbe's models. Models 1 and 2 simulate well CO2 production rate during the whole fermentation. Models 1 and 2 predict well the CO2 production rate during the whole fermentations. Models 1 and 2 predict well the Vmax value during the first phase of growth and the time at which Vmax are reached before and after nitrogen addition but during the second growth phase after nitrogen addition, Vmax is less well estimated than before nitrogen add by models 1 and 2.

Globally models 1 and 2 simulate the five validation fermentations of calibration better than Malherbe's and Brou's models. Models 1 and 2 simulate very well the fermentation with a nitrogen add at 35 g/L of CO2 released and can be extended to fermentations with different nitrogen adds timings.

Conclusions

Two models of fermentation in oenological conditions were proposed in this work. They are based on a storage compartment of nitrogen in yeast cells and simulate the macroscopic temporal evolution of biomass, sugar, ethanol, carbon dioxide, nitrogen, intra-cellular nitrogen and cell activity by differential equations. They consider effect of nitrogen addition during fermentation on growth and production kinetics of CO2 and ethanol. The two models are robust for most parameters and have been validated on experimental data with good fitting on CO2 release and production rate. Even though both developed models have good performance on the validation fermentations, Model 1 is slightly better than Model 2 on CO2 and CO2 production rate (NRMSE average value respectively of 0.0365 and 0.0404) whereas model 2 are slightly better for CO2 production rate and biomass than model 1 (NRMSE average value respectively of 0.0804 and 0.0756 for CO2 production rate and of 0.235 and 0.371 for biomass. The Models 1 and 2 present better performance than Malherbe's and Brou's Models according to AIC values even if they have been calibrated with the same data as models 1 and 2. In addition, Model 1 is less sensitive than Model 2 to changes in parameters.

  of dilution of respectively sugar transporter and intracellular nitrogen due to biomass growth.

Figure 3

 3 Figure 3 Sensitivity coefficients for each model 1 parameters and for CO2 release

Figure 4

 4 Figure 4 Sensitivity coefficients for each model 2 parameters and for CO2 release 6 Models validation Models 1 and 2 are validated and compared with Malherbe's [8] and Brou's [11] models recalibrated with the same calibration data as models 1 and 2 on data from 5 fermentations with nitrogen addition. The fermentations are made with three initial nitrogen concentrations (70, 140 and 210 mg/L), three added nitrogen concentrations (50, 100 and 150 mg/L) and two timing of nitrogen addition (20 and 35 g/L of CO2). Erreur ! Source du renvoi introuvable. shows data generated by the four models and experimental data for the five calibration fermentations. Graphically Malherbe's model simulates well the maximal biomass concentration and Brou's model overestimate maximal biomass concentration before nitrogen addition. Malherbe's model does not predict biomass regrowth because its biomass equation does not take into account a nitrogen add. Brou's model simulates a biomass regrowth after nitrogen addition but overestimates strongly the biomass production. Model 2 predicted well the maximal biomass after the first part of the biomass growth whereas model 1 simulates too slowly biomass production in the first part of biomass growth. After nitrogen addition model 2 is closer to the experimental biomass measure than the model 1.Malherbe's model estimates well CO2 production for three fermentations (MS140+50 and MS210+100 with a nitrogen addition at 20 g/L of CO2 released and MS140+100 with a nitrogen addition at 35 g/L CO2 released) but estimates poorly the CO2 production for MS70+100 with a nitrogen addition at 20 g/L of CO2 released during the whole fermentation and MS140+150 with a nitrogen addition at 20 g/L of CO2 released after nitrogen addition. Brou's model estimates well CO2 production before nitrogen addition but underestimates CO2 production after nitrogen addition and the final CO2 production. Models 1 and 2 simulate well CO2 production all around the fermentation but they slightly overproduce CO2 after nitrogen addition.Malherbe's model does not predict very well the CO2 production rate before the nitrogen addition. Malherbe's model overestimates the Vmax. Brou's model simulates poorly the CO2 production rate for the five fermentations. The nitrogen addition has no effect on CO2 production rate simulated by Brou's and Malherbe's models. Models 1 and 2 simulate well CO2 production rate during the whole fermentation. Models 1 and 2 predict well the CO2 production rate during the whole fermentations. Models 1 and 2 predict well the Vmax value during the first phase of growth and the time at which Vmax are reached before and after nitrogen addition but during the second growth phase after nitrogen addition, Vmax is less well estimated than before nitrogen add by models 1 and 2.Globally models 1 and 2 simulate the five validation fermentations of calibration better than Malherbe's and Brou's models. Models 1 and 2 simulate very well the fermentation with a nitrogen add at 35 g/L of CO2 released and can be extended to fermentations with different nitrogen adds timings.

Figure 5

 5 Figure 5 Dynamic evolution for CO2 production, biomass production and CO2 production rate for the experimental data (in red) and data simulated by models 1 (in black), 2 (in blue), Malherbe's model (in green) and Brou's model (in magenta). The first line represents the CO2 production, the second line the biomass production and the third line the CO2 production rate.

Table 1

 1 Experimental conditions of calibration fermentations

		Fermentations	Initial nitrogen	Added nitrogen	CO2 produced at nitrogen	time at nitrogen
			(mg/L)	(mg/L)	addition (g/L)	addition (h)
		MS70+100	70	100	20	71.412
	Calibration	MS140+50 MS140+150	140 140	50 150	20 20	37.51 37.52
		MS210+100	210	100	20	33.72
		MS70+100	70	100	20	67.2
		MS140+50	140	50	20	34.94
	Validation	MS140+150 MS210+100	140 210	150 100	20 20	35.97 29.85
		MS140+100	140	100	35	57.88
	3

  𝑔 1 𝐶 6 𝐻 12 𝑂 6 + 𝑔 2 𝑁 𝑖𝑛𝑡𝑟𝑎 → 𝐶𝐻 1.741 𝑂 0.632 𝑁 0.097 + 𝑔 3 𝐶𝑂 2 + 𝑔 4 𝐻 2 𝑂  (r2 * ) 𝐶 6 𝐻 12 𝑂 6 → 𝑔 𝑆 𝐶 2 𝐻 6 𝑂 + 𝑔 𝑆 𝐶𝑂 2

	3.4	Model 2 derived from Brou's model

3.4.1 Stoichiometric equations

Model 2 is based on four stoichiometric reactions (expressed in mol) that represent the major phenomena considered in this model of oenological fermentation i.e. biomass production (r1 * ), ethanol production (r2 * ), nitrogen consumption (r3 * ) and sugar transporter production (r4 * ):

 (r1 * )  (r3 * ) 𝑁 → 𝑁 𝑖𝑛𝑡𝑟𝑎  (r4 * ) 𝑁 𝑖𝑛𝑡𝑟𝑎 → 𝑁 𝑆𝑇

  9 cell/(L.h) considering the molar mass of each species:

	 Sugar:
	𝑟 𝑆 = -(𝑟 2 * + 𝑔 1 𝑟 1 * ) 𝑀 𝑆	(18)
	 Ethanol:
	𝑟 𝐸 = 𝑔 𝑆 𝑟 2 * 𝑀 𝐸	(19)
	 CO2:
	𝑟 𝐶𝑂 2 = (𝑔 𝑆 𝑟 2 * + 𝑔 3 𝑟 1 * ) 𝑀 𝐶𝑂2	(20)
	 Biomass:
	𝑟 𝑋 = 𝑟 1 * 𝑎 𝑀 𝑋	(21)
	 Nitrogen:
	𝑟 𝑁 = -𝑟 3 * 𝑀 𝑁	(22)
	 Intracellular nitrogen:
	𝑟 𝑁 𝑖𝑛𝑡𝑟𝑎 = (𝑟 3 * -𝑔 2 𝑟 1 * -𝑟 4 * )𝑀 𝑁

Table 2

 2 Two models equations

	Variable	Model 1

Table 3

 3 Model 1 and 2 and Malherbe's model parameters

	Parameters	Model 1	Malherbe's model	Parameters	Model 2
			[8]
	k1	𝛼 𝑘1 𝑇 -𝛽 𝑘1	𝛼 𝑘1 𝑇 -𝛽 𝑘1	kX	0.4036±0.0113
	αk1	0.0287	0.0287	Nintra0	(9.059±0.0000).E-6
	βk1	0.3	0.3762	KS1	1.565±0.0358
	k2	0.0386±0.00038	0.035	kE	0.2215±0.0047
	KS	20.67±18.3341	15	KS2	1.955±0.0624
	KSI	0.006299±0.00087	0.012	Elim1	100.2±1.1988
	αS	0.9355±0.2671	1.25	α1	0.7505±0.0205
	YE/S	2.17	2.17	Kst	0.0007528±0.0000
	YCO2/S	2.17	2.17	kN	0.03373±0.0004
	k3	0.001033±0.0001	0.001	KN1	0.008628±0.0003
	KN	0.04105±0.0147	0.03	g1	0.2018±0.0034
	KNI	0.02635±0.0096	0.035	g2	0.1243±0.0027
	αN	1.195±0.295	1.5	g3	6g1-1
	Q0	0.0001347±0.000	-	kNST	(7.661±0.0046).E-5
	Emax	94.67±8.1371	-	Elim2	90.55±2.6018
	knst	1.0024±0.5750	-	α2	(4.71±2.857)
	kdnst	1.987±0.5	-	Nintra1	0.0005719±0.0000
	Knst	10.76±7.1421	-	κ	0.35002±0.0015
	Ynst	694.8±118.2153	-	gS	1.909±0.0035
	Q0nst	0.0001334±0.000	-
	α1	0.0004795±0.0001	-
	κ	0.03±0.0057	-

Table 5

 5 AIC values applied to each variable for each fermentation and for Models 1, 2, of Brou and ofMalherbe.

	Model	Fermentations	CO2 in g/L rCO2 in g/(L.h)	Biomass in 10 9 cell/L Nitrogen in g/L
	Model 1	MS210+100	2234	-437	254	272
		MS140+150	1012	-718	242	274
		MS140+50	1597	-1000	233	273
		MS70+100	1948	-1020	104	184
		MS210+100	1761	-834	262	274
		MS140+150	1839	-301	250	276
	Model 2
		MS140+50	637	-1159	233	275
		MS70+100	2653	-409	136	186
		MS210+100	3147	-142	237	268
		MS140+150	3027	-59	241	270
	Brou's Model
		MS140+50	3082	245	240	269
		MS70+100	3037	433	124	180
		MS210+100	1736	-416	240	272
		MS140+150	3230	446	220	274
	Malherbe's Model
		MS140+50	1486	-462	220	27
		MS70+100	3250	295	129	184

Table 6

 6 NRMSE calculated for CO2, CO2 production rate and biomass for models 1 and 2, Brou and MalherbeAccording to AIC values, Models 1 and 2 predict better than Brou's and Malherbe's Models the CO2 production rate: the AIC values goes from -766 to -90.1 for Model 1, from -630 to -215 for Model 2, from 123 to 638 for Brou's Model and from -44.0 to 239 for Malherbe's Model. Models 1 and 2 are better than Brou's Model for all fermentations and than Malherbe's Model to predict CO2 for almost all fermentations: Malherbe's Model is better than Models 1 and 2 for MS210+100 with a nitrogen addition at 20 g/L of CO2 released.

	Fermentation

Table 7

 7 AIC values calculated for CO2, CO2 production rate and biomass for models 1 and 2, of Brou and of Malherbe

	Fermentation

This research project was funded by the French National Research Agency (ANR) under grant agreement STARWINE (ANR-18-CE10-0013).

Funding

This research project was funded by the French National Research Agency (ANR) under grant agreement STARWINE (ANR-18-CE10-0013).

The datasets presented un this study can be found in online repositories. The names of the repository/repertories and accession number(s) can be found below: https://www.ncbi.nlm.nih.gov/geo., GSE189010.

Data availability

The datasets presented in this study can be found in online repositories. The names of the repository/repertories and accession number(s) can be found below: https:// www. ncbi. nlm. nih.gov/ geo., GSE189010.

Conflict of interest

The authors declare that they have no conflict of interest.


Clement Jonquet
email: jonquet@lirmm.fr

Syphax Bouazzouni
email: syphax.bouazzouni@lirmm.fr

State-of-the-art browsing of SKOS resources in AgroPortal

Keywords: SKOS thesauri, semantic artefacts, ontology browsing, ontology repository, vocabulary service, SKOS schemes and collections, mappings

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

1

Context and motivations

In the realm of semantic artefacts -a broader term to include ontologies, terminologies, taxonomies, thesauri, vocabularies, metadata schemas and standards-developed with semantic web technologies, SKOS resources are becoming more and more prominent. Typically, since its release in 2009, SKOS (Simple Knowledge Organization System) [START_REF] Miles | SKOS simple knowledge organization system reference[END_REF] , the W3C Recommendation for thesauri and vocabularies, has been widely adopted in multiple domains from environmental sciences e.g., GEMET, to ecosystems research e.g., ANAEE Thesaurus, to agriculture e.g., AGROVOC, social sciences e.g., TheSoz, cultural heritage e.g., UNESCO Thesaurus, or even institutional standardization e.g., EuroVoc Thesaurus. SKOS resources can be semantically very rich -not at the same level that OWL ontologies-especially in the way they regroup and classify concepts with sub-schemes and collections; therefore, specific software needs to be developed to handle and valorize this richness and complexity. One challenge is also to facilitate the cohabitation, interoperation and appropriate use of each type of semantic artefact (SKOS/OWL) in a common shared platform.

Often specific "terminology/vocabulary services" are designed to support a given SKOS thesaurus or set of thesauri such as the NERC vocabulary server, the CESSDA Vocabulary service or Humanum OpenTheso.1 SKOSMOS [START_REF] Suominen | Publishing SKOS vocabularies with Skosmos[END_REF]was certainly the first, and for sure is the most adopted, generic technology to easily deploy vocabulary services for SKOS (multiple) resources. For instance, Loterre, Finto, SHOC Vocabs services, BARTOC (original version) are services based on this technology. 2 Since 2013, the BioPortal ontology repository [START_REF] Noy | BioPortal: ontologies and integrated data resources at the click of a mouse[END_REF] offers basic support for SKOS and now hosts around one hundred of such resources. However, because SKOS was not really adopted in biomedicine, we have not seen a full support of this format in BioPortal. 3Handling SKOS in BioPortal and in the generic version of the OntoPortal technology provided by the OntoPortal Alliance (https://ontoportal.org) being limited, we wanted to enhance this support especially in the context of AgroPortal -a reference vocabulary and ontology repository for agri-food [START_REF] Jonquet | AgroPortal: A vocabulary and ontology repository for agronomy[END_REF] based on the OntoPortal technology-as SKOS is a representation language that has been widely adopted in agri-food. The vision was to also extend this to other projects relying on the OntoPortal technology such as EcoPortal (ecology/biodiversity) and the coming EarthPortal (earth sciences).

Related work and objectives

One limitation of the BioPortal technology was not supporting schemes, collections and SKOS-XL. The portal also is not multilingual [START_REF] Jonquet | Roadmap for a multilingual BioPortal. 4th Workshop on the Multilingual Semantic Web[END_REF] and not capable of integrating mappings between semantic artefacts declared with SKOS mappings properties in the multiple mapping services offered by the technology. The main strength of BioPortal is really to offer a wide range of services (from indexing to browsing, versioning, visualizing, annotation, recommendation, mappings, community notes, etc.) for various types of semantic artefacts, but because the portal was originally developed "for ontologies" with OWL at its core, it was not trivial to make it more SKOS compliant. The richness of supporting multiple formats in addition to OWL (e.g., OBO, UMLS RRF and SKOS) came with some limitations in how these formats were supported. For instance, BioPortal is built to handle classes (owl:Class) and instances but was not necessarily ready to support resources in SKOS where this distinction does not exist (everything is an instance of skos:Concept).

On its side, the SKOSMOS technology, certainly the most advanced for browsing/using SKOS resources at this time supports schemes, collections and SKOS-XL. Plus, its multilingual and the interface simply displays SKOS mappings (but no other mapping services are supported by SKOSMOS). The main strength of SKOSMOS is definitely to support SKOS very well -as it is design for this language-but it comes with the biggest limitation that it is impossible to use SKOSMOS to store and serve semantic artefacts in various representation languages, typically OWL. In some SKOSMOS installations e.g., Loterre, additional possibilities to browse concepts by temporality were added (based on dates metadata at the concept level). This is especially helpful when knowledge resources editors -such as VocBench doesdirectly incorporate dct:created or dct:modified properties when concept are edited.

One big limitation (in BioPortal but also SKOSMOS) that we wanted to address was the capability to browse concepts in an intuitive and easy manner when thesauri would make an extensive use of both schemes and collections. Indeed, there was no innovative way to browse concepts taking into accounts the multiples schemes and collections constructs that are inherently at the core of SKOS.

In the SKOS specification, a scheme (skos:ConceptScheme) is "an aggregation of one or more SKOS concepts" and is typically used to group concepts together with a specific hierarchy (integration to the scheme is done at the concept level with the property skos:in-Scheme). Typically, the thesaurus itself is a concept scheme but it can also include subschemes that would be only part of the thesaurus that one could browse and interact with as with the main thesaurus. SKOS collections "are labeled and/or ordered groups of SKOS concepts" and are typically used to group concepts that "share something in common" (integration to the collection is done at the collection level with the skos:member property). From these constructs and other aspects in the SKOS specification, several questions raised:

• How to distinguish the main concept scheme from other sub-schemes in a unique SKOS source file? This is absent from the SKOS specification but is require typically to extract the right metadata and to distinguish schemes.

•

How to display the hierarchies of any scheme independently or mixed? Considering some hierarchy paths could go through concepts that are not necessarily included in the scheme(s) being browsed.

•

How to display concepts in collections (especially non ordered one)? The typical alphabetical approach (e.g., the approach proposed by SKOSMOS) is not necessarily sufficient when a collection contains a large number of members.

•

How to browse concepts in a thesaurus (or even classes in an OWL ontology) ordered by their dates of creation/modification? So that someone can have a quick look at the temporal evolution of the content of a semantic artefact.

•

How to include SKOS mappings in the "mapping repository" service offered by ontology repositories? We wanted to address these needs while staying as close as possible to the official SKOS specification and not developing any extension or new constructs. Our vision was really to stay as generic and standard as possible. For instance, Loterre has addressed the issue of browsing multiple collections by relying on SKOS resources that would use constructs from SKOS extensions such as ISO-THES or UNESKOS. 4

SKOS browsing in AgroPortal

For SKOS resources, we have completed the AgroPortal model and API to include all the objects in the SKOS specification such as skos:ConceptScheme, skos:Collection, and skosxl:Label. [START_REF] Jonquet | Roadmap for a multilingual BioPortal. 4th Workshop on the Multilingual Semantic Web[END_REF] We have created new user interfaces to visualize these objects in AgroPortal and re-invented how to browse concepts. 6 In summary, users can now:

• Visualize the list of schemes defined in a SKOS resource.7 AgroPortal will also distinguish one main scheme from the others. We recommend developers to use the SKOS resource URI to identify the "main" skos:ConceptScheme and also to type it with owl:Ontology to allows us to distinguish it from the other schemes and extract metadata.

•

Visualize the lists of collections defined in a SKOS resource and count the numbers of concept members. (Fig. 1).

•

Jump to concepts with a autocomplete search box (pre-existing) and visualize concepts with 3 different approaches: o Hierarchical, by selecting the scheme(s) to browse. The hierarchy tree will always refresh to display only the selected scheme(s) and selected collection members will be displayed with specific colors (Fig. 2). Plus, concepts traversed by a hierarchy path that are not necessarily included in the selected scheme(s) are displayed in italic. o By collections, showing alphabetically all the concept members of a selected collection. o Temporal, showing all concepts/classes sorted by date of creation or modification (using dcterms properties). This feature is also available for OWL ontologies (if the source file provides the information). • Visualize SKOS-XL labels to provide information about a reified label (Fig. 3).

• See for every concept, which scheme and collection the concepts belong to. This is trivial for schemes (as defined in the resources by skos:inScheme property) but needs to be computed for collections (we use the property uneskos:memberOf to encode this additional information in our triple-store). • See inside the class/concept mappings tab (Fig. 4) the SKOS mappings explicitly defined in the source file, aside of the other ones in the mapping repository (automatically generated e.g., SAME_URI, LOOM or uploaded by users e.g., REST). They are retrieved in the triple-store and also available in the API as any other mappings.

Conclusion and perspectives

A complete technical trace of what was implemented is available in AgroPortal documentation (releases 2.3 and 2.4). 8 We are currently working with the OntoPortal Alliance to include these features in the main code branch so they become available for other semantic artefact catalogues based on this technology. All together, these features make AgroPortal a fully SKOS compliant platform which is certainly one of the most advanced SKOS browsing technology. Plus, it does that in a platform that can seamlessly handle a large variety of semantic artefacts (typically OWL and SKOS) enabling use cases where multiple knowledge resources are needed. One big step now for AgroPortal is to become multilingual (planned for 2023) as this is required in various communities, especially the ones developing (SKOS) thesauri.

Supplementary Figures

Fig. 1 .

 1 Fig. 1. Collections defined in the Biodiversity Thesaurus (https://agroportal.lirmm.fr/ontologies/BIODIVTHES/?p=collections).

Fig. 2 .

 2 Fig. 2. Hierarchy of the main scheme in BIODIVTHES while highlighting concepts in 6 different collections with colors.

Fig. 3 .

 3 Fig. 3. The SKOS-XL label "gaeabionta" (synonym of "organisms") in AGROVOC.

Fig. 4 .

 4 Fig. 4. Mappings from different sources (including declared in the source file with skos:exact-Match) for the concept "hydrosphere" in BIODIVTHES.

Respectively: http://vocab.nerc.ac.uk ; https://vocabularies.cessda.eu ; https://opentheso.huma-num.fr.

https://www.loterre.fr ; https://finto.fi ; https://vocabs.sshopencloud.eu/vocabularies ; https://skosmos.bartoc.org.

See for details: https://www.bioontology.org/wiki/SKOSSupport

Respectively http://purl.org/iso25964/skos-thes and https://skos.um.es/TR/uneskos

See AgroPortal's API documentation: https://data.agroportal.lirmm.fr/documentation.

The following features are illustrated in the Supplementary Figures section or can be consulted in the AgroPortal release notes (https://doc.jonquetlab.lirmm.fr/share/d77f1b99-60fb-4fdb-982b-927204f1c1e3).

Good resources in AgroPortal to illustrate are BIODIVTHES, AGROVOC or INRAETHES (available very soon).

https://github.com/agroportal/project-management. Corresponding GitHub issue for traceability and reproducibility is: https://github.com/agroportal/project-management/issues/262.

Acknowledgement

This work has been supported by the Data to Knowledge in Agronomy and Biodiversity project (D2KAB -www.d2kab.org -ANR-18-CE23-0017) and the NUMEV Labex (grant ANR-10-LABX-20).