Y Bareha

R Girault
email: romain.girault@irstea.fr

Julie Jimenez

Anne Tremier

A Trémier

Characterization and prediction of organic nitrogen biodegradability during anaerobic digestion: a bioaccessibility approach

Keywords: anaerobic digestion, nitrogen, ammonium, biodegradability, bioaccessibility

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INTRODUCTION

Anaerobic digestion is currently attracting considerable interest for the management of agricultural waste. The main objectives are reducing greenhouse gas emissions, procuring additional income for farmers and autonomy regarding nutrients. But the expansion of anaerobic digestion plants creates new challenges concerning the management of the digestate. Indeed, residues from anaerobic digestion are rich in nutrients, particularly in nitrogen and are therefore of agronomic interest for their value as fertilizer and amendment [START_REF] Bibliography Alburquerque | Agricultural use of digestate for horticultural crop production and improvement of soil properties[END_REF][START_REF] Tambone | Assessing amendment properties of digestate by studying the organic matter composition and the degree of biological stability during the anaerobic digestion of the organic fraction of MSW[END_REF]. Digestates from agricultural plants are mostly spread on fields after storage or post-processing (phase separation, composting, etc.) with the aim of replacing mineral fertilizers. Indeed, anaerobic digestion results in the mineralization of part of the organic nitrogen into ammonium [START_REF] Möller | Effects of anaerobic digestion on digestate nutrient availability and crop growth: A review[END_REF] , enabling short term uptake of nitrogen by crops combined with long term mineralization of slowly biodegradable organic compounds [START_REF] Fouda | Nitrogen availability of various biogas residues applied to ryegrass[END_REF] in the soil. However, the digestate management chain is subject to nitrogen leakages in the form of ammonia emissions during storage [START_REF] Sommer | Ammonia volatilization from farm tanks containing anaerobically digested animal slurry[END_REF] and after spreading on the land, or through nitrate leaching [START_REF] Möller | Effects of anaerobic digestion on soil carbon and nitrogen turnover, N emissions, and soil biological activity. A review[END_REF]. In addition to their environmental impacts, nitrogen losses after digestion reduce the fertilizing value of the digestates and negatively impact the goal of replacing mineral fertilizers. Hence, to mitigate environmental impacts and to optimize nitrogen uptake by crops, the anaerobic digestion process has to be designed taking the characteristics of the digestate into account, i.e. ammonia content and organic nitrogen content, together with short or long-term mineralization kinetics in soils. To this end, a detailed understanding of the nitrogen composition of digestates and anaerobic biodegradability of the organic nitrogen in the substrates is required.

Nitrogen is present in substrates in two main forms: mineralized (e.g. ammonium, nitrates, etc.) and organic. Anaerobic digestion results in the degradation of part of the organic nitrogen into ammonium, a reduced form [START_REF] González-Fernández | Impact of substrate to inoculum ratio in anaerobic digestion of swine slurry[END_REF]. In the substrates, the organic nitrogen is mainly contained in proteins and requires hydrolysis to be converted into monomers. In most cases, the amino acids that result from this transformation are then metabolized through acidogenesis to produce volatile fatty acids and ammonium via Stickland or single amino acid fermentation [START_REF] Ramsay | Protein degradation during anaerobic wastewater treatment: derivation of stoichiometry[END_REF]. However, some authors studied organic nitrogen biodegradation and showed that degradation of the organic nitrogen was not complete during anaerobic digestion, but rather ranged from 18% to 77% depending on the substrate and the hydraulic retention time (HRT), as reported in the different studies [START_REF] Kobayashi | Effect of sludge recirculation on characteristics of hydrogen production in a two-stage hydrogen-methane fermentation process treating food wastes[END_REF][START_REF] Kobayashi | Characterization of Anaerobic Degradability and Kinetics of Harvested Submerged Aquatic Weeds Used for Nutrient Phytoremediation[END_REF][START_REF] Massé | The fate of crop nutrients during digestion of swine manure in psychrophilic anaerobic sequencing batch reactors[END_REF][START_REF] Yang | Degradation properties of protein and carbohydrate during sludge anaerobic digestion[END_REF].

These results highlight the fact that protein biodegradation is strongly constrained by the bioaccessibility of organic nitrogen.

Accessible organic matter refers to the compounds in the substrate that microorganisms can access for intra or extra-cellular degradation. A number of bioaccessibility indicators have been developed using chemical extraction or particle size distribution [START_REF] Dulekgurgen | Size distribution of wastewater COD fractions as an index for biodegradability[END_REF][START_REF] Karahan | COD fractionation of tannery wastewaters-Particle size distribution, biodegradability and modeling[END_REF] to fractionate organic matter according to its degree of bioaccessibility. Better characterization of the bioaccessibility of organic nitrogen in substrates will enable a better understanding of the variability of its anaerobic biodegradability. Methods using successive chemical extractions such as the Van Soest method, or more advanced methods can be used for this purpose.

The Van Soest fractionation method [START_REF] Van Soest | Use of detergents in the analysis of fibrous feeds. 1. Preparation of fiber residues of low nitrogen content[END_REF] is widely used to fractionate wastes including vegetables, sludges, and plants. It uses different solvents to extract soluble and lignocellulosic compounds. The acidity of the solvents is increased at each step by using hot water, neutral detergent, acid detergent and finally strong acid extraction. The different extraction steps target soluble, proteinlike, hemicellulose-like and cellulose-like compounds, respectively. The residual organic matter is considered as lignin-like compounds. Many studies have explored the correlations between the Van Soest composition of organic matter and its biodegradability [START_REF] Gunaseelan | Regression models of ultimate methane yields of fruits and vegetable solid wastes, sorghum and napiergrass on chemical composition[END_REF][START_REF] Liu | Evaluation of the correlations between biodegradability of lignocellulosic feedstocks in anaerobic digestion process and their biochemical characteristics[END_REF][START_REF] Mottet | Estimating anaerobic biodegradability indicators for waste activated sludge[END_REF]. [START_REF] Gunaseelan | Regression models of ultimate methane yields of fruits and vegetable solid wastes, sorghum and napiergrass on chemical composition[END_REF] demonstrated an inverse relationship between the lignin+cellulose-like content and biodegradability of fruit and vegetables in anaerobic conditions. Despite these promising results, [START_REF] Mottet | Estimating anaerobic biodegradability indicators for waste activated sludge[END_REF] pointed out that this fractionation method is too aggressive to be representative of biological disintegration that occurs during anaerobic digestion, which limits its use for the prediction of biodegradability. [START_REF] Jimenez | A new organic matter fractionation methodology for organic wastes: Bioaccessibility and complexity characterization for treatment optimization[END_REF] then developed a less aggressive fractionation method based on the protocol of [START_REF] Muller | Combining chemical sequential extractions with 3D fluorescence spectroscopy to characterize sludge organic matter[END_REF] that targeted extracellular polymeric substances. This protocol, named EPS protocol, uses increasing alkaline solutions, and targets protein-like substances; it ends with strong acid extraction targeting holocellulosic-like products. This fractionation, combined with 3D-fluorescence to assess the complexity of each fraction, successfully predicted the bio-methanogenic potential (BMP) and carbon biodegradability of various substrates using partial least square (PLS) regressions [START_REF] Jimenez | Methane production and fertilizing value of organic waste: Organic matter characterization for a better prediction of valorization pathways[END_REF]. Hence, EPS fractionation combined with PLS regression enables the fast determination of the BMP value and carbon biodegradability by decreasing the time for analysis from 40-50 days (for a BMP) to 3 days (for EPS fractionation). However, all these studies focused on the biodegradability of volatile solids or carbon compounds. Consequently, no data are available concerning the ability of these accessibility indicators, determined from EPS or Van Soest fractionation, to predict organic nitrogen biodegradability during anaerobic digestion.

The aim of this study was thus (i) to investigate the biodegradability of organic nitrogen in mesophilic anaerobic codigestion and (ii) to develop predictive models using carbon biodegradability and organic nitrogen bioaccessibility as variables, respectively. To this end, we first investigated the bioaccessibility of organic nitrogen on various substrates and compared it with carbon bioaccessibility using two fractionation methods. Next we compared the anaerobic biodegradability of nitrogen and carbon on the same panel of substrates. Finally, we performed PLS regressions to identify possible correlations between organic nitrogen biodegradability and bioaccessibility indicators provided by the two fractionation methods to determine which fractionation method better describes organic nitrogen biodegradability.

MATERIAL AND METHODS

Substrates

Twenty different substrates were collected in France as representative of the diversity of organic wastes used in agricultural anaerobic digestion plants. They included livestock wastes, wastes from agri-industry and municipalities and agriculture residues. Table 1 lists the substrates sampled and their characteristics. Substrate panel was selected to cover a large range of protein content and C/N ratio.

Hence, protein content in this panel ranges from 12 to 67%org-C and C/N ratio from 5.7 to 36.

All the samples were ground in a knife mill (R15 V.V., Robotcoupe®) and stored at -20 °C. Samples for elemental analysis were ground in a ball mill (Dangoumill®, PROLABO®).

Physico-chemical characterization

Total solids (TS), volatile solids (VS), total Kjeldahl nitrogen (TKN) and total ammonia nitrogen were measured using standard methods [START_REF] Apha | Standard methods for the examination of water and waste water[END_REF]. TKN and ammonia concentrations were determined by distillation (TKN after mineralization). Total carbon and total nitrogen were measured in finely ground raw samples by elemental analysis according to the manufacturer's instructions (Thermoflash 2000, Thermoscientific®). Inorganic carbon in the raw samples was determined by calcination at 480 °C and elemental analysis of the ashes. Total organic carbon (TOC) was determined by subtracting inorganic carbon (IC) from total carbon (TC). Protein content in organic carbon was calculated using the following the equation ( 1):

(1) Protein = ((TKN-NH 4 + )*C/N protein )/TOC Where:

-Protein: protein content (% org-C ).

-C/N protein : carbon/nitrogen ratio equal to 4.348 gC.gN -1 based on [START_REF] Ramsay | Protein degradation during anaerobic wastewater treatment: derivation of stoichiometry[END_REF].

Organic matter fractionation

The fractionation methods used in this study to characterize organic matter were based on sequential chemical extractions. The successive steps of the two fractionation methods, derived from EPS [START_REF] Jimenez | A new organic matter fractionation methodology for organic wastes: Bioaccessibility and complexity characterization for treatment optimization[END_REF] and [START_REF] Van Soest | Use of detergents in the analysis of fibrous feeds. 1. Preparation of fiber residues of low nitrogen content[END_REF] sulfuric acid (w/w) at ambient temperature for 3 h. This step used the pellet remaining from the PROT_VS step.

 LIGN_VS: This fraction contained the remaining materials not extracted during the previous extractions.

After the first extraction, the mix was centrifuged at 12100 g for 20 minutes. The supernatant containing the soluble fraction of organic matter was removed and the remaining pellet was then dried at 40°C and then ground to 1 mm. Detergent and strong acid extraction (PROT_VS and HOLO_VS steps) were performed on 1 gram of the dried-ground sample sealed in filter bags (F57 Filter Bags, Ankom Technologies®). Detergent and acid extractions were performed using an automated fiber analyzer (Ankom 2000, Ankom Technologies®). After each extraction step, the content of one bag was used to analyze total organic carbon and total remaining nitrogen using an elemental analyzer (Thermoflash 2000, Thermoscientific®). The organic carbon and nitrogen content in each fraction were determined by the difference between the organic carbon and nitrogen content in the filter bags before and after each extraction.

Modified "EPS" fractionation

EPS fractionation [START_REF] Jimenez | A new organic matter fractionation methodology for organic wastes: Bioaccessibility and complexity characterization for treatment optimization[END_REF] is based on successive alkaline extractions ending with strong acid extraction. This fractionation method is similar to the Van Soest method including the use of strong acid extraction at the end. Sequential extractions were performed on raw samples (0.5 gram of dry matter) using the method described by [START_REF] Jimenez | Methane production and fertilizing value of organic waste: Organic matter characterization for a better prediction of valorization pathways[END_REF]. This method separates the organic matter into four fractions:

 SOL_EPS: The first step of the protocol consists of two successive extractions of the sample with 30 mL of a saline solution of CaCl 2 10mM at 30 °C under stirring (300 rpm) for one hour.

 PROT_EPS: The pellet remaining from the first step is washed four times with 30 mL of a basic solution of NaOH 10mM + NaCl 10mM at 30 °C and under stirring (300 rpm) for 15 minutes. The remaining pellet is washed four times with 30 mL of a strong basic solution of NaOH 0.1M at 30 °C and under stirring (300 rpm), for one hour.

 HOLO_EPS: The pellet remaining from the previous step is washed three times with 25 ml of a strong acid solution of H 2 SO 4 72% (w/w) at 30 °C under stirring at 300 rpm for three hours.

This step is equivalent to the final extractions carried out in Van Soest protocol used to extract holocellulose materials,  LIGN_EPS: This fraction contains the most recalcitrant material and is calculated by subtracting the total mass extracted from the original mass of the sample.

The organic carbon and total nitrogen content in each fraction (except LIGN_EPS fraction) were measured in the extracts using a TOC-L analyzer (Shimadzu®) and by carbon and nitrogen balance for LIGN_EPS fraction between the raw sample and the sum of the extractible fractions. All extractions and measurements on extracts were performed in triplicate.

Organic carbon and nitrogen biodegradability

Anaerobic biodegradability of organic carbon and nitrogen were analyzed on each substrate studied.

The substrate was prepared in the same way as the one used before the extraction protocol (described in section 2.1). The inoculum used for both experiments was obtained from a continuous mesophilic anaerobic digester that is used to process pig slurry and horse feed. Carbon biodegradability was assessed in processing biochemical methanogenic potential (BMP) experiments according to [START_REF] Vedrenne | The effect of incubation conditions on the laboratory measurement of the methane producing capacity of livestock wastes[END_REF]. These batch biodegradability experiments were performed in triplicate with an inoculum:substrate ratio of 1 gVS.gVS -1 and were incubated at 38 °C for 40 days. TC and biogas production were used to determine carbon mass balance continuity during the monitoring. Whatever the test, mass balance error is between -8 and 10%.

ANMP (Apparent nitrogen mineralized potential) tests were carried out to determine the maximum apparent organic nitrogen mineralized during anaerobic digestion. This method allows the determination of the organic nitrogen part of the substrate converted into soluble ammonium which is the result of organic nitrogen mineralization from substrate, biomass growth and biomass decay. The experimental conditions were similar to the BMP experiments and the ammonium concentration was monitored during the test. However, the inoculum used for ANMP tests was previously centrifuged at 12100 g for 20 minutes at ambient temperature and the supernatant was removed in order to reduce the initial ammonium concentration in the batch reactors. The remaining pellet was suspended in a KHCO 3 10 g.L -1 + NaHCO 3 10 g.L -1 solution to preserve sufficient buffering capacity in the batch and to prevent inhibitions due to acidification during incubation. A blank experiment was performed without the addition of substrate to assess the apparent organic nitrogen mineralization due to the inoculum. The AMNP of each substrate was determined by difference between apparent mineralization in the batch experiment with a substrate and the control experiment, as described by equation ( 2).

(2)

Where:

- ).

Ammonium and TKN contents were measured before and after each incubation test using the distillation method to check nitrogen mass balance. The ammonium distillation method is aggressive enough to solubilize ammonium precipitates such as struvite and these ammonium forms are included in total ammonium. Hence, ANMP value considers organic nitrogen mineralization into ammonium which can be soluble or precipitated in the digestate. Whatever the test, difference between initial and final total nitrogen content is between -4% and 5%.

ANMP is an apparent mineralization potential which considers organic nitrogen from substrate mineralization and ammonium immobilization for biomass growth. To quantify the impact of ammonium immobilization for biomass growth on ANMP value, a control batch experiment was performed following the ANMP protocol with a volatile fatty acid solution as substrate. This experiment highlights an immobilization rate of 0.006 gN-NH 4

+ immobilized .gC degraded -1
. This value is lower than the references found in the literature that range from 0.017 to 0.009 gN-NH 4 + immobilized .gC degraded -1 [START_REF] Batstone | The IWA Anaerobic Digestion Model No 1(ADM 1)[END_REF][START_REF] Ramsay | Protein degradation during anaerobic wastewater treatment: derivation of stoichiometry[END_REF].However, these constants only consider growth, while in this study, the constant is the result of both growth and partial decay during 40 days.

This constant was applied to the panel of substrate. Hence, 6 ±3% of the TKN brought by the substrate can be immobilized for biomass growth after 40 days of incubation.

All the biodegradability tests were performed in triplicate to determine uncertainties due to the operator and the measuring equipment.

Statistical analysis

In order to sort substrates according to their biodegradation rate and investigate the relationship between organic nitrogen biodegradability and organic nitrogen bioaccessibility, hierarchical cluster analysis (HCA) and partial least square (PLS) regressions were performed on the data set using Xlstat® for Excel®. Substrates were sorted depending on their organic carbon and organic nitrogen biodegradability by using HCA.

Models based on fractionation methods were developed to describe and predict organic nitrogen biodegradability using PLS regression. PLS regression is an extended multiple linear regression that include principal component analysis principles in the regression structure. This technique build model to link one dependent variable to different explanatory variables by minimizing their covariance. Here, the dependent variable (data to predict) was organic nitrogen biodegradability (gN-NH 4 + .kgTS -1 ) and the explanatory variables (predictor variables) were the organic nitrogen content in each fraction for, in one case modified Van Soest fractionation (expressed in gN.kgTS -1 ), and in another case, modified EPS fractionation (expressed in gN.kgTS -1 ). In this study, model robustness was investigated using the following quality parameters:

 The coefficient of determination R², which is the proportion of the dependent variable variance that can be explained by the explanatory variable set and varies between 0 and 1.

Based on previous studies using PLS for biodegradability prediction [START_REF] Jimenez | Methane production and fertilizing value of organic waste: Organic matter characterization for a better prediction of valorization pathways[END_REF], a coefficient of determination superior to 0.8 is required to ensure a good fitting of the experimental data.

 The cross validated coefficient of determination Q², which is the variation rate of the dependent variable predicted by the model by cross validation. Q² makes it possible to judge the quality of the fit between the predicted and measured output variables and the ability of the model to predict new data. This coefficient varies between -and 1. A Q² value above 0.5 indicates good predictability of the model [START_REF] Jimenez | Prediction of anaerobic biodegradability and bioaccessibility of municipal sludge by coupling sequential extractions with fluorescence spectroscopy: Towards ADM1 variables characterization[END_REF]. Cross-validation was done using the jackknife method by excluding 1 out of 4 values in the data set chosen at random.

External model validation was done by applying the models to another set of data covering a wide range of biodegradability and substrate origin. The predicted organic nitrogen biodegradability was compared with the measured values.

RESULTS AND DISCUSSION

Organic carbon and nitrogen distribution in bioaccessibility based fractionation.

Modified Van Soest and modified EPS fractionation were compared on 20 substrates representing the diversity of feedstock in agricultural anaerobic digestion plants. Figure 1 shows the results of Van Soest and EPS fractionations for carbon content (1a) and organic nitrogen content (1b).

Fractionation using the modified Van Soest method

Figure 1a shows that the distribution of organic carbon in modified Van Soest fractions differed considerably from one substrate to another, with SOL_VS ranging from 13% TOC to 48% TOC , PROT_VS from 5% TOC to 37% TOC and HOLO_VS from 9% TOC to 66% TOC . Only LIGN_VS showed limited distribution, ranging from 1% TOC to 11% TOC . The wide range of values shows that the carbon distribution obtained with this fractionation method is strongly substrate dependent. In figure 1b, organic nitrogen distribution shows that nitrogen was present in all fractions and, like carbon, is strongly substrate dependent. Indeed, the ranges of nitrogen contents were wide in each fraction. On average, only about 30% org-N was contained in the NPROT_VS fraction. The remaining organic nitrogen was mainly spilt between the NSOL_VS (35% org-N on average) and NHOLO_VS fractions (30% org-N on average). The range of nitrogen contents was wide in all fractions except NLIGN_VS.

Only a small proportion of organic nitrogen (between 1 and 15% org-N ) was contained in LIGN_VS.

Other authors have reported the presence of nitrogen in all the fractions, even in those that are hard to extract like HOLO_VS and LIGN_VS, using the Van Soest method for organic matter characterization before composting [START_REF] Denes | Numerical simulation of organic waste aerobic biodegradation: A new way to correlate respiration kinetics and organic matter fractionation[END_REF] or soil mineralization of organic waste [START_REF] Chalhoub | Increased nitrogen availability in soil after repeated compost applications: Use of the PASTIS model to separate short and long-term effects[END_REF][START_REF] Garnier | Modelling carbon and nitrogen dynamics in a bare soil with and without straw incorporation[END_REF].

Fractionation using the modified EPS method

Figures 1a and1b show that variability of the carbon and nitrogen content of all EPS fractions was also wide. Extractible fractions SOL_EPS, PROT_EPS and HOLO_EPS ranged from 2 to 31% TOC , 3

to 20% TOC and 10 to 45% TOC , respectively, for organic carbon. Non-extractible LIGN_EPS ranged from 29 to 59% TOC . The distribution of organic nitrogen ranged from 2 to 36% org-N for NSOL_EPS, 3 to 41% org-N for NPROT_EPS, 3 to 29% org-N for NHOLO_EPS and from 17 to 67% org-N for NLIGN_EPS. The wide range of variability obtained shows that the carbon distribution in the EPS fractions is strongly substrate dependent. In addition, organic carbon and nitrogen are largely present in the non-extractible fraction LIGN_EPS and NLIGN_EPS reflecting that the extraction method uses soft extractants to target organic compounds. These soft extractants are supposed to solubilize specific molecules in organic matter, but organic nitrogen, which is mainly present in protein, was also detected in HOLO_EPS and a large proportion in the LIGN_EPS fraction. According to [START_REF] Jimenez | A new organic matter fractionation methodology for organic wastes: Bioaccessibility and complexity characterization for treatment optimization[END_REF], HOLO_EPS and LIGN_EPS are mainly composed of lignocellulosic materials and other materials entrapped by them. Lignocellulosic materials are hardly biodegradable and biodegradable molecules which are entrapped by them are hardly biodegradable as well (Monlau et al., 2012). Thus, the organic nitrogen contained in HOLO_EPS and LIGN_EPS fractions is the result of the organic nitrogen entrapment by lignocellulosic materials that are not disintegrated by alkali solvents.

Consequently, this fractionation method not only takes into account the nature of the extracted molecules, but also their bioaccessibility due to physical structure.

Comparison of carbon and nitrogen distribution obtained with the modified Van Soest and modified EPS fractionation methods

The distributions of organic carbon and nitrogen obtained with modified EPS and modified Van Soest fractionation methods differed significantly. Indeed, the percentage of organic carbon contained in extractible fractions was higher using modified Van Soest fractionation than the modified EPS fractionation: HOLO_VS was 36% TOC higher than HOLO_EPS and PROT_VS was 66% TOC higher than PROT_EPS. In contrast, the non-accessible fraction was noticeably higher with the modified EPS method than with the modified Van Soest method. The LIGN_EPS fraction reached 41% TOC on average while LIGN_VS represented only 6% TOC . The same kinds of results were obtained for organic nitrogen fractionation even if the trend of distribution between extractible fractions differed significantly. These observations show that a significant part of the organic carbon and nitrogen extracted with the Van Soest method solvents was not extracted by EPS solvents but remained in the non-extractible fraction LIGN_EPS.

To explain these results, the composition of solvents used for each fractionation method has to be considered. In particular, as stated by [START_REF] Jimenez | A new organic matter fractionation methodology for organic wastes: Bioaccessibility and complexity characterization for treatment optimization[END_REF] and [START_REF] Muller | Combining chemical sequential extractions with 3D fluorescence spectroscopy to characterize sludge organic matter[END_REF], EPS fractionation aims to describe the bioaccessibility of organic matter considering the impact of its chemical composition and physical structure. However, Van Soest fractionation only considers the impact of chemical composition on bioaccessibility (the ability of exoenzymes to reach active sites on organic compounds considering its chemical complexity but with no limitation caused by the physical structure of the organic matter). Indeed, as observed by [START_REF] Jimenez | A new organic matter fractionation methodology for organic wastes: Bioaccessibility and complexity characterization for treatment optimization[END_REF], Van Soest solvents are more aggressive than EPS solvents. In particular, the NDF solvent used for the second step of the Van Soest fractionation is a detergent and results in strong disintegration of complex structures composed by lignin and holocellulose. Thus, this extraction step allows the extraction of physically inaccessible organic matter at this and subsequent steps. As a consequence, few carbon and nitrogenous compounds were present in LIGN_VS. On the other hand, the alkaline solvents used for EPS fractionation did not disintegrate the organic matter and extracted only the physically and chemically accessible compounds. These results indicate that, on average, 38% org-N of the organic nitrogen and 35% TOC of the organic carbon (estimated by difference between non-extractible fractions obtained for EPS and Van Soest fractionation respectively) are contained inside complex physical structures containing lignocellulose compounds which strongly limits its bioaccessibility.

Organic carbon and nitrogen biodegradability under anaerobic conditions

Influence of substrate origin on biodegradability

Organic nitrogen biodegradability and carbon biodegradability were determined using the AMNP test and the BMP test. The results are presented in table 3.

Organic nitrogen biodegradability is strongly substrate dependent, ranging from 14% org-N of degradation to 82% org-N in the substrate panel, with an average value of 48% org-N . In comparison, organic carbon biodegradability varied less, from 36 to 74% TOC , with a mean value of 54%.

Biodegradability of organic nitrogen and carbon was shown to be partial, which is in accordance with the results previously obtained with the EPS fractionation method, which showed that a significant part of the organic nitrogen and carbon is not bioaccessible. Indeed, the EPS method showed that, on average, 41% TOC and 43% org-N cannot be extracted.

To further investigate the variability of organic nitrogen and carbon biodegradability, substrate categories can be defined using a statistical method. To this end, three indicators were used that include the biodegradation rate for carbon and nitrogen, respectively, along with the NH 4 + /TKN ratio in the raw substrate. Hierarchical cluster analysis was performed on these variables for all substrates.

The dendrogram (fig. 2a) highlights two groups of substrates based on the variables.

Comparison between organic carbon biodegradability and organic nitrogen biodegradability.

As highlighted in figure 3a, the first group G1 is mainly composed of substrates that present a slight difference between organic carbon biodegradation and organic nitrogen biodegradation with high biodegradability (57% on average for organic carbon and nitrogen). Figure 2b shows that G1 is also composed by substrates with a low NH 4 + /TKN ratio (< 30%) and includes all crop residues, non-stored agro-industrial wastes and one silage sample out of three. As the biodegradability values for organic carbon and nitrogen are very close for these kinds of substrates, which contain less than 30% of mineralized organic nitrogen (fig. 3a), predicting organic nitrogen biodegradation from organic carbon mineralization is possible with a mean absolute error of 12%. Indeed, some exceptions remain, like supermarket vegetable wastes as well as drain screenings from slaughterhouses with a percentage difference 39% and 37%, respectively between organic carbon and nitrogen biodegradability.

As shown in figures 2a, 2b and 3b, the second group, G2, is the opposite and is composed of substrates with a marked difference in the biodegradability of organic carbon and nitrogen, and with a high NH 4 + /TKN ratio (> 30%). Livestock manure is the most representative of this group but silage and stored agro-industrial waste show the same behavior. The biodegradation levels of these substrates containing large amounts of nitrogen in mineralized form are lower than for G1, with average carbon and nitrogen biodegradability of 43% and 30%, respectively. In addition, the biodegradability of organic carbon and nitrogen are not correlated in this type of substrate, making it impossible to accurately predict organic nitrogen biodegradability from the value obtained for organic carbon.

The NH4+/TKN ratio indicates if organic nitrogen mineralization occurs before anaerobic digestion or not. As highlighted by the results, these transformations can occur during long storage (supermarket vegetable waste), animal digestion (livestock manures) or silage fermentation process (crop silage samples). During these processes, carbon and nitrogen mineralization can differ. As an example, during crop silaging, fermentation produces organic acids. These organic acids such as lactic acid lead to a pH decrease and an inhibition of methanogenic activity [START_REF] Palmisano | Microbiology of Solid Waste[END_REF]. Hence, transformations of organic carbon (partial hydrolysis and acidogenesis) occur but without significantly reaching mineralization and most of the BMP is preserved. However, as highlighted by Teixeira

Franco et al. ( 2016), the proteolytic activity can continue and a large amount of ammonia can be produced indicating a significant organic nitrogen mineralization. This process can significantly impact AMNP value. Hence, the impact of silage fermentation process on BMP and ANMP values can significantly differ. Even if processes differ, animal digestion and spontaneous transformations during storage can have a differential impact on BMP and ANMP values. Therefore, the prediction of organic nitrogen biodegradability from the value obtained for organic carbon (derived from BMP values) is not relevant for most of the substrates belonging to the second group G2. Hence, depending on transformations that can occur before anaerobic digestion, a substrate can move from G1 (fresh substrates) to G2. In the results, this phenomenon is observed for oat that belongs to G1 after harvest and to G2 after silage fermentation process.

The links between substrate typology and substrate characteristics (protein content, C/N ratio, organic nitrogen fractionation following modified Van Soest and EPS methods) were investigated. C/N ratio, protein content and organic nitrogen fractionation following modified Van Soest method are not significantly different for G1 and G2 (data not shown). However, as presented in figure 4, significant differences are observed on EPS fractionation obtained for G1 and G2. Indeed, carbon fractionation results are close for both groups (fig. 4a), but, organic nitrogen fractionation shows significant differences between substrates belonging to G1 and G2, respectively (fig. 4b). Hence, NSOL_EPS fraction for G2 (7% org-N in average) is significantly inferior to the average value obtained for G1 (27% org-N ). In addition, the relative part of NLIGN_EPS for G2 (51% org-N in average) is higher than for G1 (39% org-N in average). Differences between G1 and G2 are less significant for NPROT_EPS and NHOLO_EPS fractions. These results highlight that for substrates belonging to G2, transformations prior to anaerobic digestion (silage fermentation, storage or animal digestion) led to the mineralization of most of the bioaccessible organic nitrogen (NSOL_EPS fraction). Resulting substrates contain more hardly bioaccessible organic nitrogen (NLIGN_EPS fraction). These changes in bioaccessibility of organic nitrogen explain why average ANMP for G2 is significantly inferior to the average value obtained for G1. In addition, results highlight that the impact of transformations taking place before anaerobic digestion (silage fermentation, storage or animal digestion) impact differently organic carbon and nitrogen bioaccessibility, which can explain why prediction of organic nitrogen biodegradability from the value obtained for carbon is impossible for G2. These results highlight that the modified EPS fractionation allowed the determination of accessibility indicators which can explain biodegradability variations for organic nitrogen. Thus, using a fractionation method and especially modified EPS fractionation could help predict organic nitrogen biodegradability.

Prediction of organic nitrogen biodegradability from bioaccessibility indicators

Partial least squares (PLS) regression for the prediction of organic nitrogen biodegradability

PLS analysis was first carried out on the whole set of substrates. Secondly, the same analysis was performed on previously determined substrate groups (G1 end G2, see section 3.2), respectively.

Development of the statistical model considering the whole substrate set

Two PLS analysis were carried out to investigate correlations between organic nitrogen biodegradability and the bioaccessibility indicators obtained with the modified Van Soest and modified EPS fractionations, respectively, considering the whole set of substrates. Two statistical models were obtained (see Table 4): Model N EPS , which considers modified EPS fractions of organic nitrogen as explanatory variables, and model N VS , which considers modified Van Soest ones as explanatory variables. Both models show good model structure according to the cross validated coefficient of determination Q² (Q² > 0.5) with Q²(N EPS ) = 0.736 and Q²(N VS ) = 0.571. However, the proportion of the organic nitrogen biodegradability variance that can be explained by the bioaccessibility indicators is higher with the N EPS model (R² = 0.789) than with the N VS model (R² = 0.640). The N EPS model using modified EPS fractionation thus enables better simulation of the variation in nitrogen biodegradability, but R² is inferior of 0.8 so taking into account the typology determined in section 3.2. could improve the predictability of the models.

Statistical models for the prediction of organic nitrogen biodegradability considering the set of substrates and associated quality parameters considering substrate group G1 and G2

As mentionned in section 3.2., the substrates can be divided into two groups, G1 (ratio of NH 4 + /NTK < 30%) and G2 (ratio of NH 4 + /NTK > 30%) whose organic nitrogen mineralization patterns differ. PLS analyses were thus performed to take them into account. Models considering modified EPS fractions as explanatory variables are N EPS_G1 for G1 and N EPS_G2 for G2 and are detailed in Table 5. Quality parameters shows that the models considering the two typologies are better than for the model N EPS 2001)). These results reveal that substrate typology enables better accuracy and predictability with models using EPS fractionation as explanatory variables.

Models considering modified Van Soest fractions as explanatory variables (N VS_G1 for G1 and N VS_G2

for G2, see Table 5) present no real improvement of the R² with 0.668 and 0.455 for respectively N VS_G1 and N VS_G2 . These results showed that the variance of organic nitrogen biodegradability is not well described considering the typology of substrate by models using modified Van Soest variables.

Also, the cross-validation parameter Q² obtained for N VS_G1 (0.551) and for N VS_G2 (0.057) were below the value obtained for model N VS (0.571) which took the whole set of substrates into account. These results indicate that the substrate typology does not improve the robustness of statistical models considering Van Soest variables. Consequently, prediction of organic nitrogen biodegradability with models using the modified Van Soest fractionation as explanatory variables is not accurate. This result is due to the lack of information about the physical structure of substrates even though this data strongly impacts bioaccessibility. This statement is mainly due to the use of detergents during extractions that lead to the complete disintegration of the physical structure of the organic matter as stated by [START_REF] Mottet | Estimating anaerobic biodegradability indicators for waste activated sludge[END_REF].

External model validation on models considering modified EPS variables

For external model validation, the ability of each model developed to predict organic nitrogen biodegradability of four substrates not used for model development was investigated. Predicted organic nitrogen biodegradability and prediction errors were only determined for models that showed satisfying robustness in the previous sections (N EPS , N EPS_G1 , N EPS_G2 ). Results are presented in Table 6.

Regarding the prediction of organic nitrogen biodegradability by models using modified EPS fractions as explanatory variables, the prediction errors of the N EPS model that considers the whole set of substrates, range from 5% to 37%. These results are better than those obtained with models using modified Van Soest fractions as explanatory variables but nevertheless underline the poor predictibility of the N EPS model. However, models that were specifically designed for each group of substrates, G1 and G2, produced much better results. The N EPS_G1 and N EPS_G2 models that predict organic nitrogen biodegradability for substrates belonging to the groupe G1 and G2 respectively, produced very accurate predictions with a maximum prediction error of 2% and 10%, respectively.

Hence, to accurately estimate organic nitrogen biodegradability, models have to consider modified EPS fractions as explanatory variables and G1 and G2 as validity domains.

The EPS fractionation method has been used to develop accurate models for BMP prediction on various substrates [START_REF] Jimenez | Methane production and fertilizing value of organic waste: Organic matter characterization for a better prediction of valorization pathways[END_REF]. These models were completed with complexity variables acquired with 3D fluorescence spectrometry and reach a R² of 0.818 and a Q² = 0.689. The performance of the models developed in this study were similar without considering complexity, which can be explained by sampling before extraction and the type of substrate considered. Indeed, the preparation of the sample by [START_REF] Jimenez | Methane production and fertilizing value of organic waste: Organic matter characterization for a better prediction of valorization pathways[END_REF] (freeze-drying + grinding to 1 mm) modifies the physical structure and complexity, but using 3D fluorescence spectrometry makes it possible to track the recalcitrant materials released in the different fractions. The samples in the present study were used raw with only light pretreatment as described in section 2.3.1 which saved the structure of organic matter, and only bioaccessible materials were released during the different extraction steps. These results highlight the fact that EPS fractionation allows the determination of bioaccessibility indicators that take the impact of physical structure of the substrate organic matter into account in its biodegradability.

Analysis of the impact of bioaccessibility indicators on nitrogen biodegradability

The normalized coefficient of each variable of the model can be determined from the correlation between the explanatory variable and the dependant variable, hence, based on these coefficients, the contribution of each fraction to biodegradability was investigated. As model N VS was not validated in the previous section, only normalized coefficients associated with models N EPS_G1 and for N EPS_G2 are considered in this section and are presented in Figure 5. Errors bars associated to the normalized coefficients in figure 5 are from uncertainty estimation considering 95 % confidence interval. The impact of each fraction is considered significant if the obtained confidence interval does not contain 0.

For both models, the fractions that had the most significant impact on nitrogen biodegradability were NSOL_EPS and NHOLO_EPS. This result is in agreement with the organic fractions targeted by this fractionation method. Indeed, PROT_EPS targets the protein present in extrapolymeric substances [START_REF] Jimenez | A new organic matter fractionation methodology for organic wastes: Bioaccessibility and complexity characterization for treatment optimization[END_REF] which are recalcitrant to biodegradation. Neither does NLIGN_EPS contribute significantly, due to the strongly limited bioaccessibility of the compounds contained in this fraction.

In comparison with a similar study investigating the link between EPS fractionation and carbon biodegradability, our results corroborate the observation made by [START_REF] Jimenez | Methane production and fertilizing value of organic waste: Organic matter characterization for a better prediction of valorization pathways[END_REF] concerning the contribution of the non-extractible fraction (LIGN_EPS). Indeed, LIGN_EPS on carbon did not contribute to the model like NLIGN_EPS to nitrogen based models. However, the extractible fractions of organic nitrogen (NSOL_EPS, NPROT_EPS and NHOLO_EPS) do not contribute at the same level as organic carbon, which is explained by the difference in the distribution of organic nitrogen and carbon discussed in section 3.1.2. Hence, for that substrate group, the organic nitrogen contained in the PROT_EPS fraction is not significantly biodegradable under anaerobic digestion.

CONCLUSION

Our results highlight the fact that the organic nitrogen in substrates is contained in fractions with different bioaccessibility ranging from highly accessible to inaccessible. The distribution of organic nitrogen depends to a great extent on the substrate. Therefore, like for carbon, organic nitrogen biodegradability strongly depends on the substrate and can be predicted using statistical models that use bioaccessibility indicators as variables. These models enable the fast determination of ammonium and organic nitrogen in the digestate and help to optimize anaerobic digestion plants aimed at advancing the substitution of mineral fertilizers by digestates and preventing ammonia inhibition.

AKNOWLEDGMENTS

This study was part of the MéthaPolSol and Concept-dig projects which are supported by the French Environment and Energy Agency (ADEME).

(

  Q² = 0.736 and R² = 0.789). Hence, model N EPS_G1 describing the biodegradability of the organic nitrogen for G1 shows Q² = 0.802 and R² = 0.843. Model N EPS_G2 which considers substrates from G2 shows Q² = 0.771 and R² = 0.943. Considering models found in literature developed using PLS regression, N EPS_G1 and N EPS_G2 models have satisfying R² values (0.818 for Jimenez et al. (2017), 0.88 for Monlau et al. (2012) and 0.925 for Wold et al. (

Figure 1 :

 1 Figure 1: Organic carbon (a) and organic nitrogen (b) distribution according to Van Soest and EPS fractionation (Fraction abbreviations are explained table 2).

Figure 2 :

 2 Figure 2: Hierarchical Cluster Analysis of the panel of substrates (a) and (b) the distribution of the ratio NH4+/TKN according to the substrate typology (Substrate abbreviations are explained in table1).

Figure 3 :

 3 Figure 3: Box plots of the distribution of organic carbon and nitrogen biodegradability for G1 (a) and G2 (b).

Figure 4 :

 4 Figure 4: Organic carbon (a) and organic nitrogen (b) content for G1 and G2substrates according to modified EPS fractionation (Fraction abbreviations are explained table 2).

Figure 5 :

 5 Figure 5: Normalized coefficient for model N EPS_G1 (a) and N EPS_G2 (b) explaining organic nitrogen biodegradation on G1 and on G2 (Fraction abbreviations are explained table 2).

Table 1 :

 1 Characterization of the panel of substrates.

	lass	Sample	TS (g TS .kg -1 )	VS (g VS .kg -1 )	NH 4 (gN .kg -1 ) +	TKN (gN.kg -1 )	TOC (gC.kg -1 )	Protein (% org-C
	residues	Faba beans	140.2	125.6	0	6.4	72.4	38%
		Vetch	174.5	158.6	0	8.4	86.5	42%
		Phacelia	216.6	197.7	0	2.8	49.9	24%
		Mustard	178.1	158.7	0	5.2	89.2	25%
		Oat	157.1	141.1	0	4.8	106.7	20%
		Rye	207.6	195.6	0	3.6	128.9	30%
		Barley	246.5	221.3	0	4.0	149.1	12%
		Corn silage	298.2	275.6	0.3	6.2	133.4	19%
		Grass silage	267.4	234.0	0.7	7.7	138.8	22%
		Oat silage	161.9	134.0	1.9	4.2	85.6	12%
	ck manure	Cattle manure	133.7	103.8	1.3	4.3	71.0	18%
		Pig slurry	50.3	37.1	2.3	3.2	25.1	17%
		Cattle slurry	92.4	73.4	0.9	2.4	48.3	14%
		Poultry manure	328.1	252.2	5.5	13.8	148.4	24%
	agroindustry and	Screening refusal from slaughterhouse (SRS)	294.1	282.7	0.2	7.8	165.4	20%
	cipalities	Grass clippings (GC)	261.4	213.3	0.4	8.1	112.0	30%
		Cattle feed waste (CF)	698.1	628.1	3.4	34.0	321.9	41%
		Kitchen Waste (KW)	259.1	206.2	0.1	11.5	139.7	36%
		Waste from yeast production (ELVI)	587.7	465.0	4.9	43.9	251.3	67%
		Vegetable waste from supermarkets (SVW)	107.4	95.7	0.7	2.7	62.6	14%

Table 2 :

 2 Fractions and extractions steps in the modified Van Soest and EPS methods. In addition to targeted molecules, other compounds are also liberated by modifying accessibility. ** If N prefix is added prior to the fraction name, organic nitrogen content in the fraction is considered, otherwise, organic carbon content is considered.

	Modified Van Soest method	Modified EPS method
	Fraction name**	Extraction step	Fraction name**	Extraction step
	SOL_VS	Water extraction	SOL_EPS	CaCl 2 extraction
	PROT_VS	Neutral detergent extraction (NDF)	PROT_EPS	NaOH, NaCl 10mM + NaO 0.1M extractions
	HOLO_VS	Acid detergent (ADF) + H 2 SO 4 72% extraction	HOLO_EPS	H 2 SO 4 72% extraction
	LIGN_VS	Non-extractible	LIGN_EPS	Non-extractible

*

Table 3 :

 3 Results of carbon and nitrogen biodegradability 674

	Sample	BMP (Nm 3 .kgTS -1 )	%CH 4	Organic carbon biodegradability gC.kgTS -1 % org-C	gN-NH 4	AM .kgTS -1 +
	Faba beans	267.9	53%	291.6	54%	21.3
	Vetch	297.8	56%	289.1	58%	36.3
	Phacelia	167.8	54%	171.0	74%	11.7
	Mustard	241.7	45%	321.8	61%	19.7
	Oat	325.2	52%	360.0	51%	19.1
	Rye	301.0	44%	271.8	45%	5.4
	Barley	272.5	44%	262.1	43%	4.4
	Corn silage	220.9	45%	225.9	56%	3.1
	Grass silage	320.5	46%	310.3	58%	13.3
	Oat silage	365.9	60%	323.0	63%	2.2
	Cattle manure	212.0	56%	196.4	36%	6.8
	Pig slurry	235.3	70%	182.8	36%	3.4
	Cattle slurry	251.9	64%	242.7	41%	3.7
	Poultry manure	221.2	65%	182.8	41%	13.1
	Screenings refusal from slaughterhouse (SRS)	299.2	60%	249.8	40%	6.0
	Grass clippings (GC)	270.6	54%	230.4	54%	17.1
	Cattle feed waste (CF)	396.6	65%	329.8	72%	35.7
	Kitchen waste (KW)	220.9	54%	391.0	72%	20.4
	Waste from yeast production (ELVI)	320.5	55%	248.1	58%	31.0
	Supermarket vegetable waste (SVW)	365.9	41%	384.9	70%	7.6

Table 4 :

 4 Statistical models for the prediction of organic nitrogen biodegradability considering the 677 whole set of substrates and associated quality parameters.

	678
	actionation method	Explanatory variables	Biodegradability (BD) equation	Model quality Q²
	odified EPS	NSOL_EPS, NPROT_EPS, NHOLO_EPS, NLIGN_EPS	BD(orgN_N EPS ) = -5.14 + 1.48*NSOL_EPS + 0.07*NPROT_EPS + 1.76*NHOLO_EPS + 0.12*NLIGN_EPS	0.736
	odified Van Soest	NSOL_VS, NPROT_VS, NHOLO_VS, NLIGN_VS	BD(orgN_N VS ) = -1.91 + 0.80*NSOL_VS + 0.72*NPROT_VS + 0.44*NHOLO_VS -0.178*NLIGN_VS	0.571

Table 6 :

 6 Comparison of organic nitrogen biodegradability values obtained from experiments and models.

	Mod el used	Q² R²	Livestock feed waste (G1) Predic tion Prediction (g/kg error (%)	Oat (G1) Predic tion Prediction (g/kg error (%)	Cattle slurry (G2) Predic tion Prediction (g/kg error (%)	Oat silage (G2) Predic tion Prediction (g/kg error (%)
				TS -1 )		TS -1 )		TS -1 )		TS -1 )
	N EPS	0.7 36	0.7 89	34.1	5%	15.2	20%	2.4	37%	1.8	19%
	N EPS _G1	0.8 02	0.8 43	35.7	2%	18.7	2%	n.t.	n.t.	n.t.	n.t.
	N EPS _G2	0.7 71	0.9 43	n.t.	n.t.	n.t.	n.t.	3.9	5%	2.0	10%
	n.t.: not tested

 Organic nitrogen is contained in materials with various bioaccessibility levels.

 Organic nitrogen bioaccessibility differs from organic carbon bioaccessibility.

 Organic nitrogen biodegradability cannot be estimated from carbon biodegradability.

 Van Soest fractionation does not predict organic nitrogen biodegradability.

 Models using bioaccessibility data from EPS fractionation show good predictability.