Charlotte Védère
email: charlottevedere@gmail.com

Manhattan Lebrun
email: lebrun@fzp.czu.cz

Philippe Biron
email: philippe.biron@inrae.fr

Séverine Planchais
email: severine.planchais@sorbonne-universite.fr

Marianne Bordenave-Jacquemin
email: marianne.bordenave_jacquemin@sorbonne-universite.fr

Nicolas Honvault
email: nicolas.honvault@umontpellier.fr

Stéphane Firmin
email: stephane.firmin@unilasalle.fr

Arnould Savouré
email: arnould.savoure@sorbonne-universite.fr

David Houben
email: david.houben@unilasalle.fr

Cornelia Rumpel
email: cornelia.rumpel@inrae.fr

Marianne Bordenave Jacquemin

Nicolas Honvault Bd

The older, the better: Ageing improves the efficiency of biochar-compost mixture to alleviate drought stress in plant and soil

Keywords: Organic amendment, Biochar-compost mixtures, Ageing, Water stress, Water use efficiency, Soil-plant functioning, Plant stress

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Introduction

Water availability is affecting the activity of all living organisms. Under the current climate change, the hydrological cycle will change dramatically leading to increased frequency of extreme events such as flooding and drought (IPCC, 2021). Under the current climate scenarios, water shortage is predicted to be one of the main threats to agricultural production [START_REF] Fao | The State of the World's Land and Water Resources for Food and Agriculture[END_REF]. Indeed, about two third of the worldwide cultivated area is affected by drought, and this proportion is expected to increase due to global warming [START_REF] Farooqi | Regulation of drought stress in plants[END_REF][START_REF] Ullah | Appraisal for organic amendments and plant growth-promoting rhizobacteria to enhance crop productivity under drought stress: A review[END_REF]. In addition, drought events will be not only more frequent, but also longer and more severe [START_REF] Liu | Global drought and severe drought-affected populations in 1.5 and 2 °C warmer worlds[END_REF][START_REF] Hari | Increased future occurrences of the exceptional 2018-2019 Central European drought under global warming[END_REF].

Drought may affect plant growth directly as well as indirectly. Under water deficit, plants generally show reduced growth, water content and nutritious value [START_REF] Kramer | Roots and root systems[END_REF][START_REF] Zia | Plant survival under drought stress: Implications, adaptive responses, and integrated rhizosphere management strategy for stress mitigation[END_REF]. This may be related to physiological drought effects, such as decreased photosynthetic activity following stomata closure to prevent transpiration (Tani et al., 2019;[START_REF] Zia | Plant survival under drought stress: Implications, adaptive responses, and integrated rhizosphere management strategy for stress mitigation[END_REF], increased instantaneous water use efficiency [START_REF] Wang | Effects of biochar amendment, CO2 elevation and drought on leaf gas exchange, biomass production and water use efficiency in maize[END_REF][START_REF] Zhang | The Responses of Plant Leaf CO2/H2O Exchange and Water Use Efficiency to Drought: A Meta-Analysis 13[END_REF], and reduced nutrient uptake. It may also be related to less available soil water inducing a reduction in soil organic matter decomposition and nutrient availability [START_REF] Xue | Soil water content during and after plant growth influence nutrient availability and microbial biomass[END_REF].

Both phenomena have been demonstrated for various crops [START_REF] Król | Changes in the composition of phenolic compounds and antioxidant properties of grapevine roots and leaves (Vitis vinifera L.) under continuous of long-term drought stress[END_REF][START_REF] Mouradi | Effects of water deficit on growth, nodulation and physiological and biochemical processes in Medicago sativa -rhizobia symbiotic association[END_REF][START_REF] Nadeem | Synergistic use of biochar, compost and plant growth-promoting rhizobacteria for enhancing cucumber growth under water deficit conditions: Water deficit stress mitigation in cucumber by PGPR/organic amendments[END_REF][START_REF] Luo | Roots of Lucerne Seedlings are More Resilient to a Water Deficit than Leaves or Stems[END_REF][START_REF] Yang | Biochar Mitigates Combined Effects of Drought and Salinity Stress in Quinoa[END_REF][START_REF] Khan | The application of biochar alleviated the adverse effects of drought on the growth, physiology, yield and quality of rapeseed through regulation of soil status and nutrients availability[END_REF].

One possibility to overcome water deficits is irrigation. However, irrigation has not only an additional cost for the farmers, but it also alters environmental quality by, for instance, promoting soil salinization or increasing soil organic matter mineralisation and thus greenhouse gas emissions [START_REF] Maljanen | Greenhouse gas balances of managed peatlands in the Nordic countries -present knowledge and gaps[END_REF][START_REF] Liu | Water flow and salt transport in bare saline-sodic soils subjected to evaporation and intermittent irrigation with saline/distilled water[END_REF]. Moreover, water resources are far from being available for irrigation everywhere, therefore, there is a need to find a more sustainable way to overcome negative impacts of drought. A recent study indicated that the drought-related yield gaps may be closed by increasing soil organic matter stocks [START_REF] Iizumi | Leveraging drought risk reduction for sustainable food, soil and climate via soil organic carbon sequestration[END_REF].

Thus, adaptation of agricultural systems to climate change and in particular extreme drought may rely on organic matter management and fostering soil organic carbon (SOC) storage [START_REF] Kopittke | Ensuring planetary survival: the centrality of organic carbon in balancing the multifunctional nature of soils[END_REF]. In intensive agricultural systems, organic amendments may be used for this purpose because (1) they can retain water through physicochemical processes [START_REF] Ajayi | Changes in microstructural behaviour and hydraulic functions of biochar amended soils[END_REF][START_REF] Głąb | Fertilization effects of compost produced from maize, sewage sludge and biochar on soil water retention and chemical properties[END_REF] and (2) increase the soil's capacity to retain water by improving its structure and porosity [START_REF] Sisouvanh | Can Organic Amendments Improve Soil Physical Characteristics and Increase Maize Performances in Contrasting Soil Water Regimes[END_REF]. In addition to the beneficial effects on soil water content, organic amendments can improve soil fertility through increasing organic matter content, enhancing nutrient contents and availabilities [START_REF] Diacono | Long-term effects of organic amendments on soil fertility[END_REF].

Finally, many organic amendments are derived from waste materials and their use for soil application is thus a promising option to recycle and divert them from the waste stream thus contributing to the circular economy.

Among the possible organic amendments, biochar and compost have shown potential as soil improvers, able to reduce drought stress [START_REF] Kammann | Influence of biochar on drought tolerance of Chenopodium quinoa Willd and on soil-plant relations[END_REF][START_REF] Tanure | Soil water retention, physiological characteristics, and growth of maize plants in response to biochar application to soil[END_REF][START_REF] Abdelrasheed | Soil Amendment Using Biochar and Application of K-Humate Enhance the Growth, Productivity, and Nutritional Value of Onion (Allium cepa L.) under Deficit Irrigation Conditions[END_REF][START_REF] Ullah | Appraisal for organic amendments and plant growth-promoting rhizobacteria to enhance crop productivity under drought stress: A review[END_REF]. Biochars are solid materials resulting from the pyrolysis of biomass [START_REF] Paz-Ferreiro | Use of phytoremediation and biochar to remediate heavy metal polluted soils: a review[END_REF]. Their application to soil has been proven to have agronomic interest mainly because of their beneficial effects on soil physical and chemical properties [START_REF] Cha | Production and utilization of biochar: A review[END_REF]. They are particularly interesting because of their high porous structure and their high cation exchange capacity that allow them to bind and stabilize water and various elements in soil, in addition to acting as microhabitat for microorganisms [START_REF] Agegnehu | The role of biochar and biochar-compost in improving soil quality and crop performance: A review[END_REF]. Considering their very high stability and carbon content, biochars may allow to contribute to soil carbon sequestration [START_REF] Wang | Biochar stability in soil: meta-analysis of decomposition and priming effects[END_REF]Smith, 2016). In contrast, composts contain a large amount of labile organic matter, which stimulates soil biota, influences microbial community composition, promotes plant growth and, through its effect on microbial activity, improves soil physical and chemical properties [START_REF] Fischer | Synergisms between Compost and Biochar for Sustainable Soil Amelioration[END_REF][START_REF] Eden | Organic waste recycling in agriculture and related effects on soil water retention and plant available water: a review[END_REF]. Some studies unraveled the potential mechanisms of compost and biochar to improve the capacity of plants to sustain drought: (i) improvement of soil moisture [START_REF] Wang | Impact of biochar on water retention of two agricultural soils -A multi-scale analysis[END_REF] through water binding on the surface [START_REF] Jačka | Biochar presence in soil significantly decreased saturated hydraulic conductivity due to swelling[END_REF] and amelioration of soil structure [START_REF] Wang | Impact of biochar on water retention of two agricultural soils -A multi-scale analysis[END_REF] allowing a better development and penetration of plant roots in soil [START_REF] Nadeem | Synergistic use of biochar, compost and plant growth-promoting rhizobacteria for enhancing cucumber growth under water deficit conditions: Water deficit stress mitigation in cucumber by PGPR/organic amendments[END_REF], and (ii) improvement of soil nutrient availability [START_REF] Tanure | Soil water retention, physiological characteristics, and growth of maize plants in response to biochar application to soil[END_REF], especially nitrogen, which is essential for CO2 assimilation and thus plant growth.

The combined use of both materials may induce synergistic effects on SOC storage and plant growth (Agegnehu et al., 2016). For example, [START_REF] Nadeem | Synergistic use of biochar, compost and plant growth-promoting rhizobacteria for enhancing cucumber growth under water deficit conditions: Water deficit stress mitigation in cucumber by PGPR/organic amendments[END_REF], studying the use of biochar and compost mixtures, showed that they allow in combination with rhizobacteria inoculation to enhance cucumber growth under water-stress conditions better than biochar or compost alone. [START_REF] Obadi | Biochar and compost as soil amendments: effect on sweet pepper (Capsicum annuum L.) growth under partial root zone drying irrigation[END_REF] also showed that biochar and compost applied together can alleviate negative effects of water shortage on pepper growth, yield and plant water use efficiency.

However, following field exposure, properties of organic amendments are changing due to ageing processes. For instance, physical weathering of biochar compost mixtures may alter their material properties, especially through labile compound leaching (Aubertin et al., 2021). The altered mixtures may improve plant biomass production due to increased compost mineralisation when mixed with biochar most probably due to greater ability of aged biochars for nutrient adsorption [START_REF] Chang | A comparative study on biochar properties and Cd adsorption behavior under effects of ageing processes of leaching, acidification and oxidation[END_REF]. Amendment application and their ageing can affect soil, plant and microorganism properties [START_REF] Zhao | Soil microbial biomass and activity response to repeated drying-rewetting cycles along a soil fertility gradient modified by long-term fertilization management practices[END_REF][START_REF] Sun | Effects of organic amendment on soil aggregation and microbial community composition during drying-rewetting alternation[END_REF][START_REF] Paetsch | Effect of in-situ aged and fresh biochar on soil hydraulic conditions and microbial C use under drought conditions[END_REF][START_REF] Rahman | Wetting and drying cycles improving aggregation and associated C stabilization differently after straw or biochar incorporated into a Vertisol[END_REF]. However, up to now, mechanistic studies on amendment effects on the plant-soil continuum are scarce because plant and soil compartments are usually studied separately. To the best of our knowledge, no studies have been carried out to investigate the effect of aged biochar-compost mixtures on plant physiology and soil microbial functioning, although both compartments may be crucial to understand the long-term benefits of this option.

In this study, we carried out a greenhouse experiment with alfalfa plants and a silt-loamy temperate agricultural soil and investigated the effect of biochar-compost mixtures and their natural ageing on the plant-soil system. We aimed to investigate (1) if organic amendment application attenuates negative effects of water stress on plant development and microbial soil functioning and (2) if this effect is changing upon their ageing during field exposure.

To this end, we monitored plant parameters, such as growth, aboveground and belowground biomass, photosynthetic activities, plant stress indicators and their stem water potential during water stress. To examine the contribution of soil processes and plant physiology to water stress responses, we compared plant indicators and soil enzyme activities.

We hypothesised that biochar-compost mixtures affect plant physiological responses to water stress because of their effect on soil water conditions and microbial functioning. We also hypothesised that ageing of biochar-compost mixtures will modify plant responses under water stress due to enhancement of their soil effects.

Materials and Methods

Amendments and soil

Biochar and compost materials originated from a compost platform of the association 'agriculteurs composteurs' in France. At this platform, green waste compost (Fertivert, Seine-Maritime, France) was sampled after green waste composting for six months (four months of fermentation and two months of maturation). To take advantage of non-compostable residues (composed of poplar and conifers branches), with the objective to re-use them to improve compost amendments, they were transformed into biochar with a medium-scale pyrolizer developed by ETIA (Oise, France), by pyrolysis at 450 °C for 10 min.

We sampled the first 5 cm depth of an agricultural soil with amendment mixtures in Beauvais (Oise, France) at the UniLaSalle campus (GPS coordinates 49°25'49''N, 2°04'51''E). This soil is part of a field experiment implemented in 2018, where the effects of long-term amendment application are assessed under a temperate cropping system. The study site is representative of the agricultural region of Northern France. This region is increasingly impacted by climate change and particularly its effects on the water supply of crops. Among others, this includes: drier springs and summers, milder winters but with an increased risk of late spring frosts, more recurrent episodes of high heat and drought, a more random winter recharge of groundwater, which is the source of the majority of irrigation water. In this region, annual precipitations are 669 mm.y -1 on average and average temperatures range from 6.5 to 14.9 °C. The soil was classified as a silt loam Haplic Luvisol, and its physico-chemical characteristics and those of amendments are given in Table 1. Soil was sieved at 5 mm before use.

Experimental design

As the purpose of this study was to evaluate the effect of amendment ageing, we had three treatments: (i) the non-amended soil sampled from our field experiment (control -C), (ii) the same soil as the control amended with fresh biochar-compost mixture (F), composed of biochar applied at 0.39 kg.m -2 dry weight (DW) and compost applied at 0.78 kg.m -2 (DW) respectively (equivalent to 3.9 t.ha -1 and 8.8 t.ha -1 , respectively), and (iii) the soil amended with the same biochar-compost amendment dose (incorporated at 5 cm depth with a rotative harrow), which had been subjected to field ageing for two years (A) and collected on the site at the same time as the non-amended soil. The rate of application of biochar-compost mixtures was based on a previous experiment (unpublished data) and was considered as realistic and economically viable by local farmers. The unamended control and two-year amended soils had been subjected to similar agricultural treatments. The F and A soils, showed similar physicochemical properties, confirming that fresh and aged organic amendments were present in F and A soils in similar amounts (Supplementary Materials, S1, Figure 1).

The soils were placed in 0.9 L pots at a bulk density of 1.3 g.cm -3 , with ten replicates per treatment. After two weeks of acclimatisation at 70 % field capacity (FC), i.e. 25 g H2O for 100 g dry soil, 20 seeds of Medicago sativa L. were sown. Nine days after sowing, the number of plants was reduced to three.

Plants were grown for 64 days under greenhouse conditions (23 °C, natural light with the deployment of a shadow if superior to 70 cd.sr.m -2 , Supplementary Materials, S1, Figure 2).

During the first 41 days, the pots were weighted daily at the end of the day and tap water was added to maintain the treatments at 70 % FC. At the 42 nd day and until the end of the experiment, i.e. during three weeks (22 days), water stress was implemented in half of the pots, randomly selected: the non-stressed pots were still watered at 70 % FC (5 replicates), whereas the stressed pots were watered at 40 % FC i.e. 14 g H2O for 100 g dry soil (5 replicates). The amount of water corresponding to 70 % FC was based on the FC of the control treatment, so that all treatments had the same volumetric water content throughout the experiment. Daily amount of added water was used to calculate the cumulated water supply over the experimental period.

After nine weeks of growth, plants were harvested. Each plant was removed from the pots and soil was gently separated from the roots. Soils were homogenized and an aliquot sample (half) was air-dried, while plants were subjected to root exudate collection followed by separation of shoots and roots. Fresh roots of each plant were photographed and image processed with ImageJ 1.52a (Wayne Rasband, National institutes of Health, USA) and Fiji (ImageJ 1.52i, Wayne Rasband, National institutes of Health, USA) (supplementary materials, S1, Figure 3) in order to analyse root branching (i.e. the number of image detected roots segments). Root nodules were counted. An aliquot of fresh soil was used for enzyme analyses. After three days of drying (50°C), dry mass of plant shoots and roots were recorded.

Plant development

In order to monitor plant growth, we took a photo twice a week at a fixed time during the whole experiment, between 10 am -11 am. Photos were taken at the same place on a table each time in front of a white wall on which was attached a black disk of a known surface. The camera was set on a first fixed distance and height from the pot until they grew too much to fit in the frame. We then replaced it by a new distance until the end of monitoring without changing the height. Three photos were taken per plant with a lateral rotation of 90° each in order to limit the effect of the spatial variability of each plant. After image processing, the average plant surface on these three photos was saved for each plant and expressed in cm². Image processing was performed with the software ImageJ 1.52a (Wayne Rasband, National institutes of Health, USA) by determining the plant surface comparing the number of plant pixels to the number of pixels identified on the disk (Supplementary Materials, S2, Figure 4).

Stem water potential

A Schölander pressure chamber (PMS instrument, model 600) was used to measure the stem water potential in the first and third week of water stress [START_REF] Ritchie | The Pressure Chamber as an Instrument for Ecological Research[END_REF]. In order to allow the leaves to equilibrate with the stem, each leaf was sealed with aluminium foil to be in the dark during 2h prior to measurement [START_REF] Del Pozo | Water relations and use-efficiency, plant survival and productivity of nine alfalfa ( Medicago sativa L.) cultivars in dryland Mediterranean conditions[END_REF]. Data were recorded at solar noon by cutting the leaf from the plant, removing the leaf from the aluminium and placing it in the chamber in which an increasing pressure was applied. From the moment bubbles were observed out of the peduncles of the leave, sap pressure was recorded.

Gas exchange

In the first and last week of the water stress, leaf gas exchanges (net assimilation rate nAR (µmol CO2.m -2 .s -1 ), stomatal conductance gs (mol H2O.m -2 .s -1 ), transpiration rate E (mmol H2O.m -2 .s -1 ) and the resulting instantaneous water use efficiency WUEi, (mmol CO2 .mol -1 H2O) were measured using a Li-6400 Portable Photosynthesis System (Li-Cor Biosciences Inc., Lincoln, NA, USA). Measurements were performed between 10.00 am and 1.00 pm local time, on the 5 th leaf from the top of the plant which is considered as fully developed leaf, on one plant randomly selected in each pot. Inside the measured chamber, temperature was set to 21 °C, and vapour pressure deficit was kept between 0.8 and 1.5 kPa, CO2 concentration in the air (Ca) was regulated at 400 ppm and photosynthetically active radiation (PAR) was 1500 µmol.m -2 .s - 1 . The CO2 concentration value set up to simulate the average CO2 concentration in our atmosphere. The PAR value was decided after realisation of light curves, before induction of the stress, which showed maximum CO2 assimilation at 1500 µmol.m -2 .s -1 . The measure was taken after 20 s of equilibration. The measured leaf was photographed in order to measure leaf area, using ImageJ 1.52a (Wayne Rasband, National institutes of Health, USA), and express the parameter on a leaf area basis (supplementary materials, S3, Figure 5).

Stress indicators

To assess the degree of plant stress following water shortage, we determined the proline content of plant leaves and the carboxylates exudation of plant roots. For proline measurements, we sampled one representative plant leaf, in the first and last week of water shortage. It was immediately frozen in liquid nitrogen and stored frozen until the extraction. Extraction was done based on the method described in [START_REF] Bates | Rapid determination of free proline for water-stress studies[END_REF]. Briefly, 30-40 mg of frozen material was crushed in liquid nitrogen and extracted with 3 % sulfosalicylic acid followed by the addition of ninhydrin buffer and toluene to extract coloration. Then, absorbance at 520 nm was measured using a NanoDrop (NP80, Implen, Germany). Proline concentration was calculated using a seven-point proline standard curve, and expressed in mmoles per kilogram of fresh weight material.

For carboxylates measurements, after whole plant sampling (see section 2.7), its roots were immerged in a CaCl2 solution at 0.2 mol.m -3 for an hour in order to collect plant root exudates. Thereafter, the solution was frozen until it could be filtered and analysed using a HPLC system (Thermo Fisher, San Jose, CA, USA) reverse phase Luna 5µm C18 column 250mm x 4 mm (Phenomenex, 147 Le Pecq, France) as described by [START_REF] Yacoumas | Contrasting Response of Nutrient Acquisition Traits in Wheat Grown on Bisphenol A-Contaminated Soils[END_REF]. We quantified seven carboxylates, i.e. malate, malonate, lactate, acetate, citrate and fumarate (supplementary materials, Figure 6) and calculated their sum as an indicator of total carboxylic acid exudation.

Soil analyses.

Enzyme activities were measured on 0.004 kg of fresh soil. We determined β-glucosidase (GLU), urease (URE), β-galactosidase (GAL) and arylamidase (ARN) following the methods developed by [START_REF] Browman | Phosphodiesterase Activity of Soils[END_REF], [START_REF] Sinsabaugh | Rapid assay for amidohydrolase (urease) activity in environmental samples[END_REF] and [START_REF] Acosta-Martínez | Enzyme activities in a limed agricultural soil[END_REF]. Cellulase activity (CEL) was measured following the protocole of [START_REF] Deshpande | An Assay for Selective Determination of Exo-1,4,-beta-glucanases in a Mixture of Cellulolytic[END_REF] and xylanase (XYL) with a method established by [START_REF] Taguchi | A Simple Assay for Xylanase Using o -Nitrophenyl-β -D -xylobioside[END_REF]. Potential nitrification (NIT) was measured by ammonium oxidation according to the ISO 15685:2012 certification. The measure of the nitrate reductase (NITRED) was carried out with the method developed in [START_REF] Abdelmagid | Nitrate reductase activity of soils[END_REF]. The reaction occurs with MUF substrates placed in a 96 wells micro-plates (PS, Nunc, VWR) and a microplate reader (Génius 2 Lector, Safas). Enzyme activities are expressed in mU (nmol of release per minutes).g -1 of dry soil (DW).

Statistics

Normality of the datasets and the homogeneity of the variances were evaluated with the Shapiro-Wilk test (P> 0.05) and Bartlett test (P> 0.05), respectively. If normality and homoscedasticity tests were satisfied, an Analysis of Variance (ANOVA) as well as a Tukey multiple comparison test (with a confidence interval of 5%) were performed. If normality was not achieved, a non-parametric Kruskal-Wallis tests followed by Dunn multiple comparison tests (with a confidence interval of 5%) were carried out. We used principal component analyses (PCA) to analyse whether plant and soil parameters of the different treatments could be distinguished according to their water status. Statistics were performed with RStudio version 1.4.1717.

Results

Cumulative water supply

During the first 41 days of the experiment, when all the pots were watered at 70 % FC, cumulated water supply reached 2.04 L (+/-0.13) for the control treatment without amendments, 2.04 L (+/-0.09) for the F treatment with fresh biochar-compost mixtures and 2.21 L (+/-0.10) for the A treatment with altered biochar-compost mixtures. The pots of the A treatment required 9 % more water than the control pots, while cumulated water supply was not different between the control and F (supplementary materials, Figure 7).

During water stress, cumulated water supply was lower in the stressed condition than the nonstressed pots (Fig. 1). In both cases, the highest cumulated water supply was observed in the A treatment, which received 5.19 L (+/-0.26) under non-stressed conditions and 3.40 L (+/-0.17) under water shortage, while the lowest water supply was measured in F condition, with 4.66 L (+/-0.26) and 2.86 L (+/-0.09) in the non-stressed and stressed conditions, respectively. Cumulated water supply was not different compared to the control both in the treatment receiving fresh amendments and in the treatment receiving aged amendments (F and A), in nonstressed and stressed conditions. However, cumulated water supply was higher in the A treatment compared to the F treatment, by 11 % and 19 % in the non-stressed and stressed conditions, respectively.

Plant development

Five days after seeding, plants grown on soil amended with aged compost-biochar mixtures (A) showed a significantly higher germination rate than the two other treatments (supplementary materials, Figure 8). Before water stress, plant surface linearly increased to reach 258.5 (+/-43.3) cm² for controls (C), 224.1 (+/-31.0) cm² for fresh compost-biochar mixtures (F) and 210.5 (+/-71.8) cm² for aged compost-biochar mixtures (A) (Fig. 2a). Plants of A and F treatments showed a higher plant surface area compared to the control (C) until day 38 (non-significant differences). At 42 days of growth, i.e. the day before water stress application, the control plants show a significant higher surface than F and A (Fig. 2a).

In treatments without water stress (NS), plant surface continued to increase until 52 days after the start of the experiment, thereafter they stabilised around 404.3 (+/-74.3) cm² for NS-C, 380.0 (+/-104.6) cm² for NS-A and 340.2 (+/-56.0) cm² for NS-F (Fig. 2b). NS-C treatments continued to show a higher surface than those amended with mixtures until the end of the experiment (63 days) and plants grown in NS-A treatments showed higher development than those of F-NS treatments, even if the differences were not significant.

Under water stress, plant surface stopped growing from the first day of water stress and a decrease was even observed between 52 and 58 days due to the fall of dead leaves. At the end of the experiment the plants subjected to water stress (S) reached a surface of 215.4 (+/-46.7) cm² for S-C, 167.8 (+/-27.8) cm² for S-F and 191.2 (+/-28.8) cm² for S-A, with no significant differences (Fig. 2b).

Shoot dry masses obtained at the end of the experiment ranged between 3.5 (+/-0.3) and 7.7 (+/-0.5) g and showed a trend following the order C > A > F for both stressed and nonstressed treatments (Fig. 2c). Root dry masses ranged between 3.3 (+/-0.5) and 5.0 (+/-0.4) g following the order C > A > F in well-watered conditions and the order A > C > F in stressed conditions (Fig. 2c). However, the differences among treatments were not significant. In general shoot biomass was significantly higher than root biomass in non-stressed treatments, (p-value < 0.001), while similar root and shoot biomass was recorded under water stress for all treatment. As consequence shoot:root ratio was significantly decreased after water shortage in all treatment (respectively -25, -36 and -43 % in C, F and A) but not significantly different between treatments neither in well-watered or stress conditions.

Several root-related parameters showed significant changes under water stress compared to well watered conditions (Fig. 3): (1) the number of root branching was significantly lower for the C (-61%) and F (-57%) treatments but the difference was not significant in the case of A (-30%), (2) the amount of branches was significantly higher for A than C and F treatments, (3) nodosities were found in significantly lower quantity for C (-85%) and F (-88%) treatments but not for A (-30%), and (4) the amount of nodules was significantly higher in A (49.4 +/-22.8) than C (7.6 +/-7.4) and F (9.0 +/-10.2) treatments.

Stem water potential measurements

During the first week after the implementation of the water stress, significantly more negative stem water potential was found for well watered than water stress conditions for the C, F and A treatments with the latter not being significant (Fig. 4). Considering the same watering conditions, no significant differences were noted among the different amendments (C, F and A). After three weeks of water stress, the F treatment showed statistically significant lower stem water potential than under well watered conditions.

Leaf gas exchange

During the first week of water stress, net assimilation rate (nAR) was significantly lower in stressed than in non-stressed plants, except for the A treatment A (Fig. 5a). In the C treatment, nAR was 20.5 µmol CO2.m -2 .s -1 (+/-5.9) and dropped by 58 % under water stress. Plants in the F treatment had a nAR value of 19.2 µmol CO2.m -2 .s -1 (+/-8.1) under regular watering, and this value was reduced by 66 % under stress. However, the nAR was not different between the control, F and A treatments. After three weeks of stress, nAR was 17.3 µmol CO2.m -2 .s -1 (+/-3.0) in the non-stressed control and was significantly lower in the stressed control treatment (9.4 µmol CO2.m -2 .s -1 +/-1.9). In the two amended treatments, there was contrasting decrease in nAR values between the non-stressed and stressed plants, by 79 % in F and 35 % in A.

Moreover, in the non-stressed conditions, nAR values did not differ between the control, F and A while under stress, nAR was significantly higher in A (13.2 µmol CO2.m -2 .s -1 +/-3.7) compared to F (4.7 µmol CO2.m -2 .s -1 +/-2.6) treatments, while none of the amended conditions differed from the control.

During the first week of stress, the leaf stomatal conductance (gs) of plants grown on the control was 0.56 mol H2O.m -2 .s -1 in the non-stressed condition, and was reduced by 87 % when water supply was reduced (Fig. 5b). Similarly, gs was reduced in the stressed compared to nonstressed plant in the amended treatments F (0.04 mol H2O.m -2 .s -1 +/-0.01 compared to 0.52 mol H2O.m -2 .s -1 +/-0.21) and A (0.12 mol H2O.m -2 .s -1 +/-0.05 compared to 0.71 mol H2O.m -2 .s -1 +/-0.21). The highest reduction in gs was measured in F (92 %), followed by the C (87 %) and A (79 %) treatments. There was no amendment effect on gs in the first week, i.e. no difference between the C, F and A regardless the water stress conditions. During the third week of stress, when plants were watered at 70 % FC, gs was 0.56 mol H2O.m -2 .s -1 (+/-0.20) in the wellwatered C treatment, and reduced by 78 % under stress (0.09 mol H2O.m -2 .s -1 +/-0.03). A significant reduction in gs between non-stressed and stressed plants was also observed for the two other treatments F and A. This reduction was more important in the case of F (89 % reduction) than A (only 65 % reduction). Similarly to what was measured during the first week, no amendment effect on gs value was found.

Transpiration rate (E) did not differ among the treatments in the non-stressed and stressed plants, respectively, in the first week of stress (Fig. 5c), which all showed significantly reduced E under water stress. More precisely, E was 4.34 mmol H2O.m -2 .s -1 (+/-1.03) in non-stressed control and reduced to 0.87 mmol H2O.m -2 .s -1 (+/-0.41) under stress. In F treatment, the E value was 4.16 mmol H2O.m -2 .s -1 (+/-1.80) in non-stressed plants and dropped to 0.58 mmol H2O.m - 2 .s -1 (+/-0.19) under stress, while in A treatment, E was 5.07 mmol H2O.m -2 .s -1 (+/-1.05) and 1.31 mmol H2O.m -2 .s -1 (+/-0.46) in non-stressed and stressed plants, respectively. The highest reduction of E under stress was measured in plants of the F treatment (85 %) followed by those of C (80 %) and A (74 %) treatments. After three weeks of water stress, E was significantly reduced in the C and F treatments by 69 % and 87 %, whereas E of plants of A treatments was unaffected.

As a result, after a week of water shortage, instantaneous water use efficiency (WUEi) was increased under water stress in the C (from 4.7 to 10.0 %), F (from 4.6 to 11.1 %) and A (from 3.9 to 7.4 %) treatments but only significantly for C and F. After the third week of water shortage, WUEi was still increased under water stress in the C (from 5.8 to 9.7 %), F (from 5.3 to 8.1 %) and A (from 4.9 to 7.0 %) treatments significantly only for C. Finally, internal CO2 concentrations (Ci) were not affected by amendment application in the first and third weeks of stress (supplementary material, Figure 9). However, Ci was reduced under water shortage. Specifically, in the first week of water stress, Ci values were 308 (+/-21) µmol CO2.mol -1 , 313 (+/-10) µmol CO2.mol -1 and 327 (+/-10) µmol CO2.mol -1 in plants grown of C, F and A treatments, respectively, which was reduced by 40%, 52% and 24% when water stress was applied. In the third week under water stress, Ci was 294 (+/-27) µmol CO2.mol -1 for non-stressed control and 199 (+/-46) µmol CO2.mol -1 for the stressed control, corresponding to a 32% reduction in Ci, whereas for F and A treatments, Ci was 291 (+/-16) µmol CO2.mol - 1 and 306 (+/-14) µmol CO2.mol -1 in non-stressed condition, and was unaffected by water limitation.

Stress indicators

Proline

Two days after the induction of water stress, in well watered C treatments, leaf proline concentration was 0.7 (+/-0.04) mmol.kg -1 fresh weight (FW) (Fig. 6). In the A treatment, a reduction of leaf proline concentration down to 0.3 (+/-0.02) mmol.kg -1 FW was noted. When plants were subjected to water stress, leaf proline concentration of C and F treatments showed a strong proline increase ranging between 3.8-fold and 3.9-fold, while it was not affected in the A treatment. In the third week after stress application, plants from all treatments grown in the well-watered conditions showed a similar leaf proline concentrations of 0.6 (+/-0.07) mmol.kg - 1 FW. Higher values were recorded under water stress conditions for all treatments, ranging between 1.2 (+/-0.08) mmol.kg -1 FW and 2.0 (+/-0.09) mmol.kg -1 FW. Compared to values found in plants of C treatments, lower proline concentrations were measured for plants grown on the two amended substrates (F and A treatments) (Fig. 6).

Root exudation

Total root exudation ranged between 2.4 and 8.7 mmol.kg -1 of dry roots and was not significantly affected by organic amendment addition or water stress treatment (Fig. 7a).

Exudate amounts tended to be higher under water shortage as compared to well-watered treatments. We observed significant increases for malate, which was almost twice as high when released from plant roots grown of the F treatment under water stress as compared to the wellwatered plants (Fig. 7b), while the other two treatments showed no effect (supplementary materials Figure 6).

Enzymes activities

Water limitation induced a change in soil enzyme activities (Fig. 8). Highest enzyme activities were recorded in C treatments with significant differences between water stressed and well watered conditions (β-glucosidase, arylamidase, cellulase and β-galactosidase, all significantly lower under water stress). On the other hand, only one enzyme showed significant differences between well-watered and stressed conditions for F treatments: nitrate reductase which was significantly higher under water stress, and for A treatments: cellulase, which was significantly lower under water stress. Separately most soil enzymes activities were reduced under water stress, but if considering the sum of all enzymes (mU.g -1 dry soil (DW)) water shortage increased soil enzyme activities mainly because of the significantly higher nitrate reductase activity. In soils without water shortage, the two amended treatments F and A showed significant differences in arylamidase, β-galactosidase, potential nitrification and xylanase activities, which were all significantly higher in A than F treatments. In well-watered conditions, no clear difference with the control treatments occurred except for two enzymes: potential nitrification and arylamidase, which showed significantly lower values compared to the control for F (32 % lower) and higher values for A treatment (14 % higher)

Combining plant and soils parameters to analyse responses to water stress

Principal component analyses (PCA) were carried out to investigate whether plant and soil parameters showed contrasting responses to water stress and if this response is influenced by amendment application.

When all soil enzyme activities were analysed together, the first two components of the PCA analysis explained 76% of data variability (Fig. 9). In the PCA plan showing the results for well watered conditions, the amended treatments A and F were not clearly separated from the control treatment C, while A was separated from F along the first axis. Under water stress, the first two components explained 71% of the data variability., All treatments were clearly separated in the PCA plan. Treatment A was distinguished along the first axis from the other two treatments indicating that this treatment showed an overall higher soil enzyme activity than the other two.

PCA analysis of all plant parameters (Fig. 10), indicated that the first two components explained between 47 and 52% of the data variability for well-watered and water stress conditions. In the PCA plan for well watered conditions, the three treatments were separated along the first axis correlated to nodule number, net assimilation rate and proline content at the end of the experiment. These parameters may be increased following mixture addition. In stressed conditions the A treatment was separated from the two others along the first axes correlated to plant biomass, water supply and assimilation. Moreover, treatments were differentiated according to proline concentration and nodulation, being opposed in the correlation plot for water stress conditions.

Discussion

Plant and soil response to compost-biochar mixture application

Amendment application improved germination rate and early biomass production of Alfalfa, but did not show any effect on shoot and root biomass at the end of the experiment, although we observed more nodules in F and A treatments. Moreover, we observed a decreased proline content in amended soils. These results were similar to those of other authors, who showed that biochar and compost might increase germination rate and root penetration by influencing soil physical properties, in particular by reducing soil bulk density [START_REF] Nada | Effect of Wood Compost on Extreme Soil Characteristics in the Lusatian Lignite Region[END_REF][START_REF] Kranz | The effects of compost incorporation on soil physical properties in urban soils -A concise review[END_REF]. Biochar-compost mixtures were sometimes found to increase plant biomass and yield [START_REF] Doan | Impact of compost, vermicompost and biochar on soil fertility, maize yield and soil erosion in Northern Vietnam: A three year mesocosm experiment[END_REF]Agegnehu et al., 2016;[START_REF] Naeem | Combined application of biochar with compost and fertilizer improves soil properties and grain yield of maize[END_REF], but this effect is most probably limited to tropical soils. Absence of plant growth effects in our treatment may be explained by the low amendment application rate and by the nutrient-rich temperate soil, which often does not show plant growth effects after soil amendment [START_REF] Seehausen | Is There a Positive Synergistic Effect of Biochar and Compost Soil Amendments on Plant Growth and Physiological Performance[END_REF][START_REF] Jien | Physical Characteristics of Biochars and Their Effects on Soil Physical Properties[END_REF]Aubertin et al., 2021). In addition, most of studies applied higher amendment rates, which could also explain the lack of effect of the compost-biochar mixture on plant biomass in our study.

On the contrary, biochar-compost mixtures increased the number of nodules on plant roots, which was consistent with previous studies [START_REF] Thies | Characteristics of Biochar: Biological Properties[END_REF][START_REF] Agegnehu | Biochar and biochar-compost as soil amendments: Effects on peanut yield, soil properties and greenhouse gas emissions in tropical North Queensland, Australia[END_REF][START_REF] Hashem | Arbuscular mycorrhizal fungi and biochar improves drought tolerance in chickpea[END_REF][START_REF] Phares | Application of biochar and inorganic phosphorus fertilizer influenced rhizosphere soil characteristics, nodule formation and phytoconstituents of cowpea grown on tropical soil[END_REF]. These findings reflected the overall good plant activity as nodule formation highly depends on carbohydrate and photosynthetic activity [START_REF] Aranjuelo | Nodule performance within a changing environmental context[END_REF]. Indeed, decreased plant proline contents demonstrate that the amendment mixtures reduced plant stress [START_REF] Farooqi | Regulation of drought stress in plants[END_REF]. Amendment addition resulted in a rise in carbon and nitrogen contents in the amended soil, as observed in previous studies (Agegnehu et al., 2016;[START_REF] Mierzwa-Hersztek | Effect of poultry litter biochar on soil enzymatic activity, ecotoxicity and plant growth[END_REF][START_REF] Azeem | Biochar and compost effects on soil microbial communities and nitrogen induced respiration in turfgrass soils[END_REF]. This could lead to changes of the arylamidase synthesis, which catalyses the release of amino acids from SOM (Acosta-Martínez andTabatabai, 2000, 2001). Potential nitrification, considered as the maximum capacity of soil microorganisms to transform NH4 + into NO3 -, was sometimes reduced by the addition of biochar-compost mixture, which could be due to the NH4 + sorption capacity of biochar [START_REF] Abujabhah | The effect of biochar loading rates on soil fertility, soil biomass, potential nitrification, and soil community metabolic profiles in three different soils[END_REF]. However, most enzyme activities were positively affected by amendment application.

Effect of water stress on plant growth and physiological parameters

The monitoring of plants during the water shortage period showed that a reduction of water supply reduced plant growth and biomass production, impaired plant physiological activity (reduction of leaf gas exchange and water potential) and increased oxidative stress inside the plant (increase of proline content in the leaves).

We observed reduced plant growth and biomass production under water stress, which had already been demonstrated previously [START_REF] Mouradi | Assessment of Deficit Irrigation Responses of Moroccan Alfalfa ( Medicago Sativa L.) Landraces Grown Under Field Conditions: Drought responses of Moroccan alfalfa genotypes under field conditions[END_REF]. Similarly, water stress reduced the stem water potential, which results from a higher transpiration associated to lower water uptakes, leading to higher tension in the xylem. This was particularly observed in the first days following the induction of water stress. With time, leaf water potential was less negative, which can be related to the reduction in the transpiration. Moreover, a more negative leaf water potential under water stress demonstrates that plants needed more strength to extract additional water from the soil [START_REF] Bell | Water relations and adaptations to increasing water deficit in three perennial legumes, Medicago sativa, Dorycnium hirsutum and Dorycnium rectum[END_REF]. Finally, as often observed under water shortage conditions, proline content of leaves and malate exudation of roots increased with water shortage [START_REF] Sicher | Responses of growth and primary metabolism of waterstressed barley roots to rehydration[END_REF]. Malate being known to act as a signal for microbial attraction under various stress conditions [START_REF] Ortíz-Castro | The role of microbial signals in plant growth and development[END_REF][START_REF] Blouin | Chemical communication: An evidence for co-evolution between plants and soil organisms[END_REF], might have in turn increased some of the soil enzyme activities [START_REF] Sanaullah | Drought effects on microbial biomass and enzyme activities in the rhizosphere of grasses depend on plant community composition[END_REF].

These effects of water shortage may be explained by a reduction of photosynthetic activity resulting from a reduced leaf gas exchange indicated by lower transpiration rates (assimilation, stomatal conductance, and transpiration) [START_REF] Ahmed | Biochar amendment of fluvio-glacial temperate sandy subsoil: Effects on maize water uptake, growth and physiology[END_REF]Tani et al., 2019;[START_REF] Baccari | Linking Leaf Water Potential, Photosynthesis and Chlorophyll Loss With Mechanisms of Photo-and Antioxidant Protection in Juvenile Olive Trees Subjected to Severe Drought[END_REF], stomata closure to prevent water loss (Tani et al., 2019;[START_REF] Baccari | Linking Leaf Water Potential, Photosynthesis and Chlorophyll Loss With Mechanisms of Photo-and Antioxidant Protection in Juvenile Olive Trees Subjected to Severe Drought[END_REF][START_REF] Zia | Plant survival under drought stress: Implications, adaptive responses, and integrated rhizosphere management strategy for stress mitigation[END_REF] and increased WUEi. Moreover, reduction of photosynthesis can also be attributed to a reduction of carboxylation efficiency, since internal Ci concentration decreased concomitantly with assimilation (supplementary materials, Figure 9) [START_REF] Xu | Effect of drought and heat stresses on photosynthesis, pigments, and xanthophyll cycle in alfalfa (Medicago sativa L.)[END_REF]. Also, the increased WUEi under water deficit is commonly found [START_REF] Naidoo | Drought stress effects on gas exchange and water relations of the invasive weed Chromolaena odorata[END_REF][START_REF] Guo | Biochar amendment improves shoot biomass of tomato seedlings and sustains water relations and leaf gas exchange rates under different irrigation and nitrogen regimes[END_REF], and is an adaptive response to water stress, in order to improve resource use efficiency under stress [START_REF] Naidoo | Drought stress effects on gas exchange and water relations of the invasive weed Chromolaena odorata[END_REF]. More precisely, plants can produce more assimilates while consuming lower amounts of water (Swann, 2018). The decrease of nodules can be related to lower photosynthesis activity and thus carbohydrate production by the plant [START_REF] Aranjuelo | Nodule performance within a changing environmental context[END_REF]. In accordance with a reduction of their physiological functions, leaf proline content was found to be increased, [START_REF] Liu | Physiological and Comparative Proteomic Analysis Reveals Different Drought Responses in Roots and Leaves of Drought-Tolerant Wild Wheat (Triticum boeoticum)[END_REF][START_REF] Luo | Roots of Lucerne Seedlings are More Resilient to a Water Deficit than Leaves or Stems[END_REF][START_REF] Mouradi | Assessment of Deficit Irrigation Responses of Moroccan Alfalfa ( Medicago Sativa L.) Landraces Grown Under Field Conditions: Drought responses of Moroccan alfalfa genotypes under field conditions[END_REF][START_REF] Kiani | Morphological, Physiological, and Biochemical Impacts of Different Levels of Long-Term Water Deficit Stress on Linum album Ky. ex Boiss[END_REF]. Such accumulation of proline helps prevent cell damage, stabilizes molecules, maintains osmotic potential and stores carbon and nitrogen for a potential use after stress removal [START_REF] Szabados | Proline: a multifunctional amino acid[END_REF][START_REF] Ben Rejeb | How reactive oxygen species and proline face stress together[END_REF][START_REF] Luo | Roots of Lucerne Seedlings are More Resilient to a Water Deficit than Leaves or Stems[END_REF][START_REF] Kiani | Morphological, Physiological, and Biochemical Impacts of Different Levels of Long-Term Water Deficit Stress on Linum album Ky. ex Boiss[END_REF][START_REF] Khan | The application of biochar alleviated the adverse effects of drought on the growth, physiology, yield and quality of rapeseed through regulation of soil status and nutrients availability[END_REF]. In the rhizosphere, overall reduction of microbial enzyme activities under water stress was already observed in previous studies [START_REF] Sanaullah | Drought effects on microbial biomass and enzyme activities in the rhizosphere of grasses depend on plant community composition[END_REF][START_REF] Zaheer | Potential Effects of Biochar Application for Improving Wheat (Triticum aestivum L.) Growth and Soil Biochemical Properties under Drought Stress Conditions[END_REF].

Decreasing the water supply increased plant stress expression, resulting in a decrease of the plant activity toward an improvement of their water use efficiency. In consequence, shoot and root development was stopped. Soil enzyme activities were also affected by water shortage most probably due to stress induced modification of exudate release by plants, indicating the importance to study both plant and soil functioning simultaneously.

Can water shortage effects be alleviated by soil amendment with biochar compost mixtures?

Few significant amendment effects were noted for plant physiological parameters. However, amendment addition affected the overall plant response to (water) stress as shown by PCA analysis (Fig. 10). Indeed, plant stress seems to be reduced by amendment addition as indicated by the significantly lower proline contents in plant leaves of amended treatments. In addition, even if the differences between well-watered and stressed plants were not significant, organic acid exudation increased more between well-watered and stressed plants under fresh mixture application mainly because of malate production which is involved, among others, in plant nutrition and N2 fixation through nodule activity [START_REF] Irigoyen | Phosphoenolpynivate carboxylase, malate and alcohol dehydrogenase activities in alfalfa (Medicago sativa) nodules under water stress[END_REF][START_REF] Schulze | Malate plays a central role in plant nutrition[END_REF][START_REF] Aranjuelo | Nodule performance within a changing environmental context[END_REF]. This could have participated to the improvement of plant resistance to water stress and is in accordance to the lower level of proline found in treatments with fresh mixture addition.

Lower proline content after biochar or compost amendment was already observed in previous studies [START_REF] Kammann | Influence of biochar on drought tolerance of Chenopodium quinoa Willd and on soil-plant relations[END_REF][START_REF] Abdelrasheed | Soil Amendment Using Biochar and Application of K-Humate Enhance the Growth, Productivity, and Nutritional Value of Onion (Allium cepa L.) under Deficit Irrigation Conditions[END_REF][START_REF] Hafez | Minimizing hazard impacts of soil salinity and water stress on wheat plants by soil application of vermicompost and biochar[END_REF][START_REF] Khan | The application of biochar alleviated the adverse effects of drought on the growth, physiology, yield and quality of rapeseed through regulation of soil status and nutrients availability[END_REF].

These results could be explained by a higher nutrient content and availability in amended soils [START_REF] Din | EFFECT OF BIORICHAR AMENDMENT ON GROWTH, NUTRITIONAL PROPERTIES AND BIOCHEMICAL CHANGES OF BANANA (Musa acuminata) cv[END_REF][START_REF] Hafez | Minimizing hazard impacts of soil salinity and water stress on wheat plants by soil application of vermicompost and biochar[END_REF]. Our data showed that these improvements affected plant physiology without altering plant growth.

In water-stressed soil, PCA analysis showed that enzymes activity differed between the control and F treatments (Fig. 9). The use of fresh mixture (F) allowed alleviating the negative effect of water shortage on β-glucosidase, arylamidase, cellulase and β-galactosidase enzyme activities and increased nitrate reductase activity, an enzymatic complex able to catalyse the nitrate reduction during denitrification.

Does field ageing alter amendment effects on plant responses to water stress?

Compared to fresh mixtures, the aged biochar-compost mixture increased root branch numbers and nodule formation under water stress. In addition, the internal CO2 concentration and transpiration rates were maintained with aged amendments despite the negative impacts of water shortage on these parameters. Leaf proline content also increased less during water stress with aged mixtures. In agreement with the maintenance of the assimilation rate in treatment with aged amendments, this might indicate an improvement of the plants' water stress resistance.

Mixture ageing may also have a positive effect on soil functioning under water stress, as indicated by increased enzyme activities. Under well-watered conditions, the nitrification potential activity decreased by the application of the fresh biochar-compost mixture, but the activity was recovered to its initial level, with the ageing of the mixture. Under water shortage conditions the β-galactosidase decreased in F and C treatments, and increased only in A treatments with the aged mixtures. PCA analysis of soil enzyme activities under water shortage (Fig. 9) illustrated that, soil enzyme activity is favoured when soil is amended with aged mixtures. Plants favoured root development over shoot development under water stress (Fig. 10), to prevent water loss through transpiration and allowing to expand the volume of soil where they can reach water and nutrients. Thereby plants of A treatments were able to increase soil water consumption together with photosynthetic activity leading to a decrease of their WUEi. This shows that water shortage had a lower impact on plant functioning in A treatments. WUEi has been shown to be related to root development as observed in our study [START_REF] Li | Changes in root characteristics, gas exchange and water use efficiency following water stress and rehydration of Alfalfa and Sorghum[END_REF].

Effects of amendments ageing might be explained by alterations of their material properties. Indeed, with maturation in soil, the surface of biochar may become more hydrophilic, their specific surface area may decrease, its CEC may increase, and the minerals on the biochar surface may dissolve, and provide nutrients for microorganisms and plants [START_REF] Mia | Long-Term Aging of Biochar[END_REF][START_REF] Wang | Biochar Aging: Mechanisms, Physicochemical Changes, Assessment, And Implications for Field Applications[END_REF][START_REF] Liu | Effect of ageing on biochar properties and pollutant management[END_REF], while compost when applied alone mineralizes once in the soil, leading to the release and leaching of nutrients (Aubertin et al., 2021). During cocomposting, biochar ageing can be accelerated when brought with fresh organic matter in result of an enhanced microbial activity induce by the microhabitat provided by biochar, the comineralisation of biochar and biochar surface adsorbed organic matter [START_REF] Mia | Long-Term Aging of Biochar[END_REF]. In their review, [START_REF] Gorovtsov | The mechanisms of biochar interactions with microorganisms in soil[END_REF] stated that around biochar particles, microorganism's mycelia could favour the formation of aggregates; which could further enhance microbial activities, especially those related to water, nutrient and organic matter cycling [START_REF] Agegnehu | The role of biochar and biochar-compost in improving soil quality and crop performance: A review[END_REF][START_REF] Gorovtsov | The mechanisms of biochar interactions with microorganisms in soil[END_REF]. The development of such properties is occurring after prolonged field exposure [START_REF] Mukherjee | Physicochemical changes in pyrogenic organic matter (biochar) after 15 months of field aging[END_REF] and one year of soil ageing of biochar was found to lead to preservation of microbial activities under water stress [START_REF] Paetsch | Effect of in-situ aged and fresh biochar on soil hydraulic conditions and microbial C use under drought conditions[END_REF]. In the same line, our results indicate that ageing of organic amendments containing biochar is beneficial not only for maintaining soil microbial activity but also to ameliorate plant functioning under water shortage.

Finally, our experiment highlighted that if plant resistance to water limitation was improved by amendment ageing in soil, WUEi of plants decreased and their water consumption was not reduced. We can thus consider that aged mixtures allowed improved plant functioning under low water contents, without reducing their water requirements. To investigate the use of organic amendments to reduce water requirements and plant survival under water stress, no water additions should have been made. However, soil water content was maintained at a low but stable level during the duration of the experiment. We suggest that that to investigate the effects of organic amendments, future experiments should consider two different types of water stress experiments: (1) maintenance of a low soil water content throughout the experiment or (2) a finite pool of applied water in soil. This could allow to obtain a more complete understanding of the effects of organic amendments on plant and soil functioning.

Conclusion

Drought event frequency is forecasted to increase in the near future, with potential negative impacts on plant growth, soil microorganisms, and soil microbial activity. In this study, we investigated whether water shortage effects might be alleviated by soil amendment with fresh and aged biochar-compost mixtures. We conclude that application of mixtures of biochar and compost have few significant effects on plant physiological parameters, while they seem to alter the response pattern of soil microbial enzyme activities and also plant response to water shortage. Amendment presence could reduce the stress imposed to plants and microorganisms by the reduction of water supply, especially after their ageing in soil. These effects might be explained by a combination of their influence on water, nutrient and carbon cycling. Our results suggest that the use of a biochar-compost mixture reduces water stress in plants especially after their aging in soil. However, organic amendments may not be suitable to increase plant water use efficiency.

Figure 1 .

 1 Figure 1. Cumulated water supply from the beginning of the water stress until the end of the experiment for pots with control soil (C), fresh (F) and aged (A) mixtures of amendments in well-watered (NS) and under water stress (S) conditions. Statistics were performed at day 63 of the experiment.

Figure 2 .

 2 Figure 2. Surface of plant biomass before water stress (10 replicates per treatments) (a), after the application of the water stress (5 replicates per treatments) (b) and shoot (c) and root (d) biomasses after the harvest for control soil (C), fresh (F) and aged (A) mixtures of amendments in well-watered (NS) and under water stress (S) conditions. Statistics were performed at 41 days (a) and at the end of the experiment (b, c and d).

Figure 3 .

 3 Figure 3. Number of branches (a) and nodulation observed on roots after the harvest.

Figure 4 .

 4 Figure 4. Water potential during the first (lighter colours) and third weeks (darker colours) of the water stress for control soil (C), fresh (F) and aged (A) mixtures of amendments in wellwatered (NS) and under water stress (S) conditions. Statistics were performed each week separately.

Figure 5 .

 5 Figure 5. Net assimilation rate, nAR (a), stomatal conductance, gs (b), transpiration rate, E (c) and instantaneous water use efficiency (d) during the first (darker colour) and third weeks (lighter colour) of the water stress for control soil (C), fresh (F) and aged (A) mixtures of amendments in well-watered (NS) and under water stress (S) conditions. Statistics were performed each week separately.

Figure 6 .

 6 Figure 6. Proline concentration during the first (darker colour) and third (lighter colour) weeks of the water stress for control soil (C), fresh (F) and aged (A) mixtures of amendments in well-watered (NS) and under water stress (S) conditions. Statistics were performed each week separately.

Figure 8 .

 8 Figure 8. Enzymes activities, i.e. β-glucosidase (GLU) (a), cellulase (CEL) (b), β-galactosidase (GAL) (c), xylanase (XYL) (d), urease (URE) (e), arylamidase (ARN) (f), nitrate reductase (NITRED) (g) and potential nitrification (h), in soil according to soil without amendment (C) or amended with fresh (F) or altered (A) mixture of biochar + compost and in well-watered (NS) or water stress (S) conditions.

Figure 9 .

 9 Figure 9. PCA of soil enzyme activities for control soil (C), fresh (F) and aged (A) mixtures of amendments in well-watered (top) and under water stress (bottom).

Figure 10 .

 10 Figure 10. PCA of plant parameters for control soil (C), fresh (F) and aged (A) mixtures of amendments in well-watered (top) and under water stress (bottom).

Table 1 .

 1 Soil, biochar and compost chemical characteristics. 1 :5 ratio NF ISO 10390 ; b NF ISO 10693; c dry combustion NF ISO 14235; d Dumas method; e Metson NFX 31-130; f NFX 31-108; g aqua regia NF EN 13650 followed by ICP MS NF ISO 17294.

	Soil	Biochar Compost

a

Acknowledgements

The authors acknowledge funding from FUI through the project BIOCHAR21, which led to establishment of the collaboration between UniLaSalle, CNRS and INRA.

In addition, the authors wish to thank Dr. Regis Fichot (Université d'Orléans, France) for his help with the leaf gas exchange measurements.


Timothée Fages

Franck Jolibois

Romuald Poteau
email: romuald.poteau@univ-tlse3.fr

Recognition of the three-dimensional structure of small metal nanoparticles by a supervised artificial neural network

Keywords: Artificial Intelligence, Artificial Neural Network, Transition Metal Nanoparticles, Structure Descriptors LPCNO (IRSAMC),

published or not. The documents may come

Recognition of the three-dimensional structure of small metal nanoparticles by a supervised artificial neural network

Introduction

The structure of nanomaterials can directly influence their physical and chemical properties, that can be of interest for applications in various fields ranging from biology, medicine, optoelectronics, catalysis, energy, etc [START_REF]Nanoparticles. From theory to application[END_REF]. Among nano-objects, colloidal transition metal nanoparticles (TMNPs) exhibit unique properties, often located between those of bulk materials and small clusters [START_REF] Burda | [END_REF]3], and related to their size, shape, surface composition, surface or core defects. Thanks to the art of chemical synthesis, the metal core of TMNPs exhibit a fascinating variety of shapes, most of them being in fact Platonic (Figure 1), Archimedean, or Catalan solids, or even concave or convex polyhedra. Magic numbers and other structural characteristics of such NPs are listed for example in refs. 4 or 5. Noble-metal nanocrystals can be considered as a paragon of this structural versatility, which is ruled out by kinetic or thermodynamic effects involved by synthesis conditions [6,7].

Nanocatalysis has now become a major application which involves the use of nanomaterials of metals, oxides or semiconductors for transforming molecules into addedvalue compounds [START_REF]Nanoparticles. From theory to application[END_REF][START_REF]Nanomaterials in Catalysis[END_REF]. TMNPs are valuable complement to conventional homogeneous and heterogeneous catalysts [START_REF] Polshettiwar | [END_REF], potentially showing high activities and selectivities. The interest in colloidal TMNPs not only relies on their high surface area-to-volume ratio [3], but also on the high concentration of potential and different active metal sites. It is not only a matter of global shape, apexes, edges, and of diversity of crystallographic planes within the same nanocrystal, but a special site can also be related to the very nature of the surface species (hydrides, ligands, ...) that stabilize the NP [10]. In other words, and in line with the so-called Sabatier principle, it is possible to modulate the catalytic activity of a nanocatalyst by a modification of its surface composition [START_REF] Del Rosal | Nanoparticles in Catalysis: Advances in Synthesis and Applications[END_REF]. In this context, and in opposition with trial-and-error approaches, the rational design of heterogeneous or nano-catalysts relies on correlations between descriptors and catalytic performance data like activity and selectivity. Thanks to density functional theory (DFT), it is possible to derive electronic structure descriptors and atomic structure descriptors. Catalytic activities and selectivities can be understood and predicted by associating DFT energy descriptors with microkinetic models, in the framework of the Sabatier-Balandin volcano plots [START_REF] Chorkendorff | Concepts Of Modern Catalysis And Kinetics[END_REF][START_REF] Nørskov | [END_REF][14], using Brønsted-Evans-Polanyi and scaling relationships [15]. This is for example the case of the search for alternatives to platinum electrodes for the hydrogen evolution reaction (HER). According to the seminal study of Nørskov and co-workers [16], the best catalysts are characterized by a dissociative hydrogen adsorption standard Gibbs free energy close to zero, i.e. the closer to zero ∆ d G • (H 2 ), the higher the measured exchange current i 0 involved by hydrogen evolution. A lot of recent studies still rely on this strategy, which involves to multiply expensive electronic structure calculations on a wide variety of materials and active sites.

Yet, a new paradigm has emerged, based upon machine learning (ML) approaches. It is especially the case in the heterogeneous catalysis domain, with approaches transferable to nanocatalysis [17]. Regarding HER, and still in the framework of the Sabatier principle which states in this case that hydrogen should neither bind too weakly nor too strongly, it has been shown on MoS 2 and AuCu nanoclusters that it is possible to train a model to predict ∆ d G • (H 2 ) energies for an arbitrary site based on its structural description [18]. Most of ML applications to atomistic systems need to use relevant structural local or global descriptors, such as Coulomb Matrices (CM) [19], Many-Body Tensor Representation (MBTR) [20], Atom-centered Symmetry Functions (ACSF) [21] and the Smooth Overlap of Atomic Positions (SOAP) [22] (see also ref. 23 for a comparison and discussion). The CM index is appealing by its simplicity. However, it is not invariant with respect to permutation of atomic indices, and different numbers of atoms result in different dimensionalities of the Coulomb matrices. The Radial Distribution Function (RDF) g(r) is another good fingerprint for materials science that encodes information about the whole atomic structure. It is experimentally obtained from high energy X-ray diffraction. It is particularly well suited to discriminate in situ different crystalline structures and different shapes of NPs (see refs. 24, 25 and references therein). It is unique, continuous, differentiable with respect to atomic coordinates, invariant with respect to rotation, translation and nuclear permutation. It is however unable to distinguish between chiral compounds and it depends on the inter-atomic distances, i.e. it depends upon atom types. An implementation has been proposed by von Lilienfeld and coll. for machine learning models of molecular species [26]. X-ray absorption near-edge structure (XANES) spectroscopy can also be used to determine particle sizes, structural motifs, and shapes in NPs. A recent coupling of XANES with a supervised artificial neural network (ANN) showed that the ANN extends the sensitivity of XANES by enabling the determination of particle sizes and shapes [27]. The present work is related to the classification tasks in ML. It requires the use of ML algorithms that learn how to assign a class label to examples from the problem domain. It finds several remarkable applications, such as mastering the game of Go [28], image classification [29], or even cancer classification [30]. We present here an application of ML to the structural analyzis of metal NPs. After a presentation of the methods and of the various data sets, we will apply four supervised ANNs, namely one CM ANN and three RDF ANNs, to classify the shape of nanoparticles described as 3D models, such as those plotted in Figure 1.

2 Methods and training set 3D models. All cartesian coordinates of the various NPs considered in this work were generated using the in-house polyhedra software [24].

Energy potentials. Sutton-Chen potentials [31] and analytical gradients are implemented in polyhedra, with parameters optimized for platinum [32] and silver [33]. It has been used in some cases to relax the geometries generated from geometrical considerations.

Coulomb Matrix (CM). The matrix elements of a Coulomb matrix C [19] are given by:

C ij = 0.5Z 2.4 i ∀ i = j ZiZj |Rj -Ri| ∀ i = j (1)
where Z i is the nuclear charge of element i. Off-diagonal elements correspond to the Coulomb repulsion between atoms i and j, while diagonal elements encode a polynomial fit of atomic energies to nuclear charge. To avoid large values on the diagonal, all nuclear charges were set up to 1. To partially overcome the ill-defined ordering of atoms, first they were sorted in two subsets of subsurface and surface atoms, second the matrix is permuted in such a way that its rows and columns in each subset are ordered by their norm [19,34]. In order to have the same dimensionality d for all systems, matrices are completed with zeros, up to the number of atoms of the largest NP (d CM = 189 in this study).

Theoretical Radial Distribution Functions (RDF). The RDF function g(r) has been calculated from atomic coordinates, i.e. directly in the real space, using (it is different from von Lilienfeld's approach [26]):

g(r) = A i j b i b j < b > 2 δ(r -r ij ) (2)
where r ij is the interatomic distance between two atoms i and j belonging to the model crystal, b i is the scattering power of atom i, < b > is the average scattering power of the sample and A is a parameter for the amplitude of the signal. In the case of X-rays, b i is simply the number of electrons of atom i [35]. Eq. 2 is the so-called chemists definition [36] (another formula is often used, where g (r) = g(r)/r). The delta function, δ(r -r ij ) is replaced by a Gaussian distribution function of the form:

δ(r -r ij ) = 1 √ 2πσ(r ij ) exp - 1 2 r -r ij σ(r ij ) 2 (3)
We have considered the r-independent formulation of the peak width σ(r ij ), which has been is set up to a constant value σ 0 = 0.2 Å. Note that in its usual definition, and for the purpose of comparison with the experimental RDF function g exp (r) -which is the sine Fourier transformation of the normalized scattering intensity S(Q) provided by X-Ray or neutron diffraction -the 4πr 2 ρ 0 term is subtracted from eq. 2, where ρ 0 is the average number density of the material. Since we were only interested in a global fingerprint of TMNPs for structural analyzis, this term has not been taken into account in the present study. RDF profiles of two identical structures made of different atom types (e.g. Ag and Pt) will not coincide given that equilibrium bond lengths differ. To circumvent this issue, we considered g(r) where r = r/R NN1 , and R NN1 is the position of the first peak of the RDF profile that characterizes nearest neighbours. g(r) is then discretized, with a r-step of 0.002 for r ≤ 3, which is increased to 0.02 for r > 3. It means that a strong weight is put on the bonding scheme of an atom with its neighbors that belong to a sphere of radius 3R NN1 centered on each atom. Moreover, the intensity of the first peak is normalized to 1 in order to make the intensity of the first peaks weakly dependent on the NP size. To reinforce the information, the first derivative, g (r) = dg(r)/dr, was also used to train two ANNs, namely RDF2-ANN and RDF3-ANN (vide infra).

Training set. Eleven classes were considered, with two to four different sizes according to the class. For some of them, the sizes correspond to the well-known structural magic numbers in cluster science [5,[37][38][39]. The 30 resulting compounds are shown in Figure 2. Each class is identified by an acronym, with -C and -S that stand for cubic and spherical shapes. The training set is made of (i) Platonic NPs: fcc and bcc cubes (FCC-C and BCC-C), fcc octahedra (OH), fcc regular tetrahedra (RTD), dodecahedra (DD), Mackay icosahedra (IC) [40]; (ii) Archimedean NP: fcc cuboctahedra (CB); (iii) spherical fcc, hcp and β-Mn NPs (FCC-S, HCP-S, BMN-S); (iv) pentagonal bipyramid decahedron (DC). On the contrary to the ten other classes made only from building principles, dodecahedra were fully optimized given the very low packing efficiency of such structure before optimization. The resulting geometries are concave (see also Figure 1). As evidenced by high-energy X-Ray diffraction technique, several NPs exhibit a β-Mn-type crystal structure [41,42], which turns out to be a very interesting polytetrahedral packing of atoms. They are for example encountered in Frank-Kasper phases [43,44] and in some bare transition metal clusters, such as 55-atoms species [45].

Characteristics of the ANNs. The supervised neural network models are multi-layer perceptrons (MLP) imple-Fig. 2 Training set made of 30 structures divided into eleven classes. Core atoms appear in magenta below surface facets. CB: cuboctahedron; FC: decahedron; FCC-C: cubic fcc shape; FCC-S: spherical piece of fcc system; HCP-S: spherical piece of hcp system; IC: icosahedron; BMn-S: spherical piece of β-Mn system; OH: octahedron; RTD: regular tetrahedron; BCC-C: cubic bcc shape; DD: regular dodecahedron (optimized). Core atoms appear in dark magenta, beneath the triangular and square facets. mented in the scikit-learn project [46], which trains using back-propagation. The Adam stochastic optimizer was chosen given its robustness for relatively large datasets [START_REF] Kingma | A method for stochastic optimization[END_REF]. For classification, MLP minimize the cross-entropy loss function. For a given compound j, ANNs returns P j (C k ) -with k = 1, 11 -, the probability number per class C k . After an adjustment stage, the ANNs' architecture was set up to three hidden layers of 40 neurons each. It appeared appropriate to avoid overfitting or underfitting.

Four different implementations for the recognition of the shape of 3D models of NPs have been achieved: (i) CM-ANN, based on flattened Coulomb matrices (schematized in Figure S1 for the 105-atoms decahedron); (ii) RDF1-ANN, based on discretized g(r) RDF profiles; (iii) RDF2-ANN based on the discretized first derivate g (r) of RDF profile; (iv) RDF3-ANN based on concatenated -and still discretizedg(r) and g (r) fingerprints (schematized in Figure S2). RDFi-ANNs are designed in the same spirit as the shape recognition based on XANES experimental spectra [27], the machinery of this application being also based on the discretization of the continuous and differentiable experimental XANES signal I(E) as well as on the discretization of its theoretical counterpart.

Data augmentation and training of the ANN.

The training set summarized in Figure 2 is obviously too small to train an ANN, a process which usually requires several thousands of data. To enlarge the datasets, 1000 structures, together with their CM, their RDF function g(r) as well as g (r), have been generated for each of the 30 nanoclusters used for training. Each new geometry is obtained by a random displacement by 0.1 Å in all directions of each atom of the parent geometry.

Ten structures per class were separated to make the test set. The remaining 990 structures were randomly split in a 80%-structures per class subset, used to train the ANN, and in a 20%-structures per class subset, used to validate the ANN performance. g(r) RDF profiles of selected fully symmetric and randomly modified fcc structures are plotted in Figure S3. One can see that these random displacements preserve the structural fingerprint of the structures. Such training will also make the ANNs able to classify the shape of the metal core of ligand-protected NPs, which interatomic metal-metal bond lengths, sensitive to electron donation or back-bonding effects of ligands and to surface coverage, differ from bare NPs. Cross-validation. The stratified 5-folds cross-validator of scikit-learn was used [START_REF] Kohavi | Intl. Jnt. Conf. AI[END_REF]. It provides an average perfor-mance of the models, with folds made by preserving the percentage of samples for each class.

Challenging dataset and scoring of the related performance of the ANNs. Another dataset will be presented in section 3. It aims at evaluating the performance of the ANNs when confronted with structures that significantly differ from the training set: truncated NPs, alloys, other metal than Pt with different interatomic bond lengths, coalesced NPs, new bcc shape different from the only learned bcc cubic shape, oblate and prolate structures whereas the training set is made of structures that exhibit only small deviations from spherical shape, NPs larger than those of the training set, closely-related structures (cuboctahedra vs. truncated octahedra). Some of them can be seen as decoys, made to deceive the optimized ANNs. In other words, the capability of the ANNs to identify some a priori non obvious structural patterns is evaluated through this dataset, hereafter named a challenging dataset. It is not straightforward, in this context, to evaluate the performance of the ANNs defined and optimized in this study. Performance is often conveniently assessed through RMS deviations between target and estimated values. It is less obvious to define in such structure recognition application. This is why a gross scoring has been defined by considering for each compound s = j P j (C x )/N , where N is the total number of compounds submitted to the ANN (CM-ANN: N = 27; RDF-ANNi: N = 32) and P j (C x ) is the probability associated to the expected class C x .

Results

Validation of the ANN performance. It is done on the 11 × 20% validation subsets. The cross-validation and test scores for each of the three schemes are reported in Table 1. The RDF-based ANNs perform very well. They never fail to identify the classes the structures of the validation sets belong to. After analysis, it turns out that the CM-ANN is unable to classify 13-atoms cuboctahedra and icosahedra in the appropriate CB and IC classes. So far, it can be considered as an insignificant disagreement. Given the similarity of g(r) and g (r) for fcc structures (see examples in Figure S4 and Figure S5), the ability of all RDF-based ANNs to discriminate between classes CB, FCC-C, FCC-S and OH is quite rewarding. On the contrary, the patterns of their CM (see Figure S6) seem different enough to unambiguously assign these compounds to our shape classification on the basis of this descriptor.

Other scores obtained with CM-ANN and RDF3-ANN are reported in Table S1 The expected classification of the 32 compounds to the eleven classes known by the ANNs is subjectively colorcoded in Figure 5 (green for a priori easy classifications, orange for less obvious classifications, red for challenging classifications). We did not include shapes that can be assigned to all eleven learned classes. As already said in section 2, some of these classes (CB, HCP-S, BMN-S, DD) are decoys that may deceive ANNs. Compounds 1-4, 7-8 should be easily identified as icosahedra. Given their elongated shape and the repetition pattern, it may be uneasy for the CM-ANN to assign them to the IC class. Although the ANNs have only been confronted with cubic shapes, it should not be uneasy to assign compound 9 to the FCC-C class. The number of atoms of this species (n: 147), identical to the IC and CB magic numbers, should not be a problem. Whereas compound 10 is just another FCC-S shape, the significantly oblate and prolate shapes of 11 and 12 may perturb the ANNs. It is obvious for a reader fa-miliar with polyhedra that the trigonal bipyramids 13 and 14 are three-fold twinned regular tetrahedra (RTD class). However, it could be less easy for the CM-ANN, and even for the RDFi-ANNs that may wrongfully assign them to another fcc class. Ino's decahedra (15)(16)(17) and Marks' decahedra (18)(19)(20)(21) are five-fold twinned nanoparticle built by appropriate truncations of the edges of parent decahedra. Let us remind that NPs that exhibit decahedra shapes are five-fold multiply twinned (MTP) fcc NPs [START_REF] Hofmeister | [END_REF]. Similarly to icosahedra, they are composed of tetrahedral sub-units joined along twin boundaries and sharing axes of five-fold symmetry. In both types or structures, tetrahedra are inherently strained due to twinning. The illustration that five regular fcc tetrahedra form an imperfect decahedron with a gap of 7.35°is provided in Figure S7. Given these comments, Ino's and Marks' decahedra may not be that easy to assign to the DC class. By the way, a reader unfamiliar with MTPs could also hesitate between the DC and IC classes. But a conveniently trained ANN is expected to do better than that. If you visualize the quite long Pt 126 BCB helix (22) with a molecular viewer and even if you zoom in enough and if you rotate this compound, you will see that it is not that easy to identify that this structure is an helical stacking of Pt 10 regular tetrahedra. Given also that the present ANNs have been faced to several fcc classes that do not differ that much from each other, this RTD assignment could be challenging (it is marked in red in Figure 5). The larger one, 23, is less elongated, and the Pt 35 RTD pattern is probably more obvious in RDF profiles. The excavated fcc cube 26 is a concave structure that misses a lot of atoms. On top of that, its cubic core is also reduced to a very low number of atoms. An ANN could thus be confused with other fcc classes that are significantly different from a cube. Given that 27 has a Pt 55 IC core, its classification to the IC class should not be a problem. On the contrary, 28 does not have an IC core, and that could make its classification to the IC class very challenging. It is not immediately evident that compound 29 is an excavated icosahedron. However, it could be more obvious on the basis of its RDF profile. Its core is nothing else than 27 and the numerous surface atoms probably reinforce the IC pattern. Compounds 30 and 31 are highlighted in red in Figure 5, given the structural proximity between these truncated octahedra and cuboctahedra. The assignment could fall in either of the CB and OH classes. Finally, given that the apexes of the parent regular tetrahedron of 32 were moderately truncated, its assignment to the RTD class is expected to be obvious. Given this biased analysis, a gross score s between ∼0.5 and ∼0.8 would be acceptable, whereas s 0.8 would be a remarkable outcome.

The classification of structures 1-32 to the eleven classes are summarized in Figure 6 and more detailed in Tables S2 to S5. The performance of each ANN can be caught at a glance: the higher the number of dark green cells, the better the performance. With a gross score s : 0.16, the CM-ANN miserably fails. The inability to identify compounds 2 and 3 as belonging to the IC class or compound 10 to the FCC-S class are among the most prominent failures of CM-ANN. This optimized neuron network actually shows a propensity for the DC and BMN-S classes. With gross scores between s : 0.56 (RDF2-ANN) and s : 0.67 (RDF3-ANN), the RDFi-ANNs are by far more adapted to this recognition task. They all succeed in assigning icosahedral species 1-7 to the IC class, excepted for the biggest one, 4. This may be because long-range information of the g(r) and g (r) profiles perturb the recognition. The coreshell icosahedron 8 is identified as a decahedron by RDF1-Fig. 6 Classification of structures 1-32 to the eleven classes learned by the ANNs (columns: classes index, same as in Figures 2 and4; CM and RDFi ANNs are defined in section 2, see also Table 1). Green: expected result; dark green: right class identification by the ANN; burgundy: wrong identification. The probabilities P i (C k ) calculated for each class C k by the ANNs are given in the SI, Tables S2-S5. Cx: biased expectation on ANNs' performance, same color code as in Figure 5. Blue cells highlight answers that were not expected but that can be considered as acceptable. and RDF2-ANNs, whilst it is -luckily ? -assigned to the IC class by RDF3-ANN. Yet, the RDF profiles of decahedra and icosahedra are significantly different, and the RDF fingerprint of the core-shell AgPtNP is close to the single metal Pt 147 NP, optimized or not (see Figure S8). It is hard to understand the failure of RDF1-ANN. It is probably a data-fitting issue of the training process, that led to a bad weighting of some neural connections. It also turns out that among the compounds allegedly easy to assign, 29 is never well identified and g (r) seem to alter the assignation of 9 to the FCC-C class (RDF2-ANN: P 9 (FCC -C) : 0.24, RDF3-ANN: P 9 (FCC -C) : 0.02).

Let us now consider the challenging species (in red in Figure 5). As expected, no ANN is able to assign the long BCP helix 22 to the RTD class, although a nonzero P 22 (RTD) is found by RDF1-ANN and RDF2-ANN (0.026 and 0.020). But RDF-ANN assigns it to the HCP-S class, which has nothing in common with RTDs. Interestingly, RDF1-ANN and RDF3-ANN classify it in the DC or IC classes. Given the similar twinning patterns of tetrahedra in RTDs, ICs and DCs, it can be considered as a quite relevant identification. The RDF first derivative helps identifying the drilled icosahedron 28 to the IC class, whilst RDF1-ANN assigns it to the DC class. Finally, none of these RDFi-ANNs is able to see that compounds 30 and 31 are made from octahedra. They all agree to say that it is a spherical piece of an fcc packing (FCC-S class), which is after all an acceptable answer. With this tolerance being shown, the s score increases to 0.20, 0.67, 0.63 and 0.73 for CM-, RDF1-, RDF2-and RDF3-ANNs, respectively.

Conclusion and outlook

We built the geometries of 30 fcc, bcc, hcp and polytetrahedral metal clusters and nano-clusters M n (n = 13-189). Four different ANNs, based on Coulomb matrices or RDF profiles and their first derivative, learned to classify each compound j in eleven different classes C k with a given probability P j (C k ). The CM-ANN and RDFi-ANNs all brilliantly passed the validation test, i.e. they successfully classified shapes very close to the training set. We then assessed the ability of the 4 ANNs to properly assign 32 additional structures to the eleven classes. Let us attempt to introduce an analogy with the cats vs. dogs classification, although true image recognition is usually best achieved in the framework of convolutional neural networks, a specialized kind of neural network for processing data that have a known grid-like topology [START_REF] Goodfellow | Deep Learning[END_REF]29]. With some of these new 32 shapes, to some extent we checked the ability of the ANNs to extrapolate to other felines, big cats and canids, some of them having significant physical disabilities or wearing camouflages. Regarding the fcc-type NPs, we also evaluated the ability these ANNs to discriminate between very similar structures such as cuboctahedra and truncated octahedra. Despite such strong requirement, the RDF-based ANNs do well, with scores close to 0.6 or even 0.7 -a somewhat acceptable performance -, whereas the CM-based ANN is not adapted at all to this task, even in the "easy" cases. Given that such scoring is not related to the test set but to the challenging test, it shall be underlined that it cannot be analyzed as an overfitting or underfitting evidence.. With very few exceptions, such as compound 8, the mistakes made by the RDFi-ANNs can usually be rationalized in terms of atomic arrangements, a further indication that ANNs do not suffer from pathological over-or underfitting. The best ANN, namely RDF3-ANN, uses both discretized RDF profiles and their first derivative counterpart. May be owing to the explicit identification of critical points.

With this application of ANNs to structural chemistry, we are far from any DFT-based and descriptors-based assistance by machine learning to the rational design and optimization of NPs with tailored-made properties. This is a first step, that could easily find a direct application to the analysis of experimental RDF, obtained by in situ high-energy synchrotron X-ray diffraction or other WAXS experiments [25,41], after taking the average number density of the material, ρ 0 , into account [24]. Experimental RDFs would be submitted to ANNs trained on theoretical RDF profiles, possibly supplemented with a collection of well-resolved and identified experimental RDF profiles. The RDF3-ANN could also take part to the in silico optimization of nanocatalysts, among other descriptors (coordination numbers, chemical hardness, d -band center, adsorption energies, etc...). Other structural descriptors are needed to introduce coordination modes (on-top, face capping, edge-bridging...) of the surface species that stabilize metal NPs. We are currently working along these lines.

Fig. 1

 1 Fig. 1 Platonic solids : 286-atoms fcc regular tetrahedron, a; 666atoms fcc cube, b; 670-atoms fcc octahedron, c; 427-atoms dodecahedron, d; 561-atoms icosahedron, e; optimized 427-atoms dodecahedron, f (geometries a-e are not relaxed, interatomic distances are set to 2.7 Å, a typical metal-metal bond length; Sutton-Chen potential for Pt used to optimize compound f).

Fig. 3

 3 Fig. 3 RDF functions g(r) and coulomb matrices for the largest NP in each class. Same labels as in Figure 2.

Fig. 4 5 Fig. 5

 455 Fig.4Structures of the challenging dataset. All structures marked with a * were fully optimized with Sutton-Chen potentials optimized for Pt and Ag (see Methods and datasets section). Core atoms appear in dark magenta, beneath the triangular and square facets.

Table 1

 1 as a function of their architecture, i.e. the number of hidden layers and the number of neurons per hidden layer. A good validation is already obtained with 1 hidden layer made of 11 neurons, whereas 2 neurons is obviously not enough. Regarding CM-ANNs, increasing the number of neurons does not help improving the 0.96 test score. Test and cross-validation (cv) scores of the four considered ANN (CM and RDFi ANNs are defined in section 2). of similar or new shapes. The 32 structures submitted to the four ANNs are reported in Figure4. On the contrary to the training and validation sets, most of the structures were fully optimized without any symmetry constraints, using Sutton-Chen potentials. This is what makes structure 1 (Pt 147 ) different from the IC-147 compound shown in Figure2. The 32 structures are classified in nine new classes, that we shall now briefly review. Concave cubic and icosahedral NPs 26, 27 and 29 were made with square-pyramidal and icosahedral tips, respectively. Compound 28 is made by digging through a Pt 147 icosahedron with a cylinder.

		CM	RDF1 RDF2	RDF3
	cv score	0.97	1.00	1.00	1.00
	test score 0.96	1.00	1.00	1.00
	Classification

The 1-8 Mackay icosahedra-based structures are either magic number clusters, i.e. with closed atomic shells (1, 4, 7, and the bimetallic core-shell 8) or partially filled atomic shells (2 and 3). Compounds 5 and 6 are short metal rods made of bound icosahedral Pt 13 and Pt 55 clusters. Structures 9-12 are rectangular cuboid, spherical, oblate and prolate spheroid fcc clusters, respectively. Two trigonal bipyramids, 13 and 14, were also added to the challenging dataset. Structures 15-21 are five-fold twinned NPs

[START_REF] Hofmeister | [END_REF]

. These so-called Ino's

[50]

and Marks'

[51]

decahedra have non spherical shapes, built from decahedra. Two Boerdijk-Coxeter-Bernal (BCB) helices

[52][START_REF] Coxeter | Regular Complex Polytopes[END_REF][START_REF] Bernal | [END_REF][55]

, 22 and 23, were also added to the challenging dataset. They are made of linearly stacked regular fcc tetrahedra, they are chiral, and they experimentally appear as either left-handed spirals or right-handed ones. Compounds 24 and 25 are bcc rhombic dodecahedra. Such structures are Catalan solids. The in-house polyhedra software also allows to excavate polyhedra with emporte-pièces.

Acknowledgements We acknowledge the CALcul en MIdi-Pyrénées HPC (CALMIP-Olympe, grant P0611) for generous allocations of computer time. Université Paul Sabatier-Toulouse, INSAT and CNRS are also thanked for financial support. FJ and RP also thank Béatrice Laurent-Bonneau and Olivier Roustant for helpful and stimulating discussions. This article is dedicated to Fernand Spiegelmann on the occasion of his retirement. Short private message from RP: "Fernand, je ne te remercierai jamais assez de m'avoir donné la passion de ce métier, d'avoir su aiguiser ma curiosité scientifique, d'avoir contribué à ma formation large en chimie physique et théorique, et de m'avoir appris que développer à bon escient ses propres outils est une démarche féconde".