Miguel Angel

Rosales Villegas

Christophe C Maurel

Philippe Nacry
email: philippe.nacry@inra.fr

Miguel A Rosales

Abscisic Acid Coordinates Dose-dependent Developmental and Hydraulic Responses of Roots to Water Deficit

come

Abscisic acid coordinates dose-dependent developmental and hydraulic responses of roots to water deficit

INTRODUCTION

Water deficit (WD) is now recognized as the abiotic stress with the greatest effect on crop productivity (Comas et al., 2013). Thus, understanding how plants use water for optimal biomass production has become a fundamental issue worldwide (Koevoets et al., 2016). Plants are sessile organisms that cannot escape from environmental constraints and, as a result, have evolved numerous adaptive responses at molecular, cellular and physiological levels. When exposed to WD, plants first respond by a strict regulation of stomatal aperture together with rapid changes in root hydraulic conductivity (Lpr) (Maurel et al., 2010;Sutka et al., 2011;[START_REF] Rosales | Physiological analysis of common bean (Phaseolus vulgaris L.) cultivars uncovers characteristics related to terminal drought resistance[END_REF]. Over a longer term, plants change both shoot growth (to restrict water loss) and root growth and differentiation to modulate their capacity to take up soil water [START_REF] Deak | Osmotic regulation of root system architecture[END_REF]Koevoets et al., 2016).

Root system architecture (RSA) refers to the three-dimensional organization of the root system. The model plant Arabidopsis thaliana has been widely used to unravel the molecular and genetic bases of root traits and adaptive responses. In this species, the root system is formed through a reiterative program in which lateral roots (LRs) are produced along the primary root (first-order LRs) or along LRs themselves (second-, third-, etc., order LRs). Despite this apparent simplicity, root development is highly flexible and can adjust to the environment to optimise soil foraging and nutrient and water uptake. More generally, the depth of rooting is an important parameter for foraging for water when deep water is available (Lynch, 1995;[START_REF] Uga | Control of root system architecture by DEEPER ROOTING 1 increases rice yield under drought conditions[END_REF], but the overall distribution of roots has received a lesser attention as it displays a significant degree of plasticity in response to heterogeneous distribution of soil resources (Koevoets et al., 2016). When water availability is limited, plants firstly reduce shoot development leading to a shift in their allometry (metrics of root to shoot relationships) and then reduce root development depending on the constraint extent and duration (reviewed by Comas et al., 2013;Pierick and Testerink, 2014;Koevoets et al., 2016).

However, several studies in maize (Zea mays) (Sharp andDavies, 1979, Dowd et al., 2018) and Arabidopsis [START_REF] Van Der Weele | Growth of Arabidopsis thaliana seedlings under water deficit studied by control of water potential in nutrient-agar media[END_REF], Li et al., 2017) have reported that a mild WD can transiently stimulate root growth. There is, however, no consensus on the mechanisms underlying these responses.

water uptake by roots first requires transport through living tissues that is mainly mediated by aquaporins, which are water channel proteins that facilitate water transport across cell membranes. Many reports show that Lpr is highly dependent on the content of the soil in water, nutrients, or oxygen and on biotic interactions. This control largely relies on the coordination of transcription, post-translational modifications and sub-cellular trafficking of aquaporins [START_REF] Grondin | Aquaporins contribute to ABA-triggered stomatal closure through OST1-mediated phosphorylation[END_REF]. For instance, direct exposure of roots to water stress results in inhibition of aquaporin activity and hydraulic conductivity at the cell or root system levels (Boursiac et al., 2005;[START_REF] Hachez | Short-term control of maize cell and root water permeability through plasma membrane aquaporin isoforms[END_REF]Sutka et al., 2015). However, some plant species or Arabidopsis accessions showed an enhancement of Lpr under moderate stress [START_REF] Hachez | Short-term control of maize cell and root water permeability through plasma membrane aquaporin isoforms[END_REF]Sutka et al., 2015).

Abscisic acid (ABA) has been recognised as the main plant stress hormone playing a major role during drought responses (Parent et al., 2009;Cutler et al., 2010;[START_REF] Wilkinson | Plant hormone interactions: innovative targets for crop breeding and management[END_REF][START_REF] Henry | Drought and abscisic acid effects on aquaporin content translate into changes in hydraulic conductivity and leaf growth rate: a trans-scale approach[END_REF]. Under WD conditions, ABA rapidly accumulates inducing stomatal closure to reduce water loss through transpiration [START_REF] Zhang | Increased synthesis of ABA in partially dehydrated root-tips and ABA transport from roots to leaves[END_REF][START_REF] Wilkinson | Plant hormone interactions: innovative targets for crop breeding and management[END_REF] and, subsequently, a general inhibition of plant growth (Parent et al., 2009;Cutler et al., 2010;[START_REF] Rowe | Abscisic acid regulates root growth under osmotic stress conditions via an interacting hormonal network with cytokinin, ethylene and auxin[END_REF]. Furthermore, high levels of exogenous ABA inhibit shoot and root growth under well-watered conditions [START_REF] Ghassemian | Regulation of abscisic acid signalling by the ethylene response pathway in Arabidopsis[END_REF][START_REF] Van Der Weele | Growth of Arabidopsis thaliana seedlings under water deficit studied by control of water potential in nutrient-agar media[END_REF]De Smet et al., 2003;[START_REF] Deak | Osmotic regulation of root system architecture[END_REF][START_REF] Xiong | Identification of drought tolerance determinants by genetic analysis of root response to drought stress and abscisic acid[END_REF][START_REF] Harris | Abscisic acid: Hidden architect of root system structure[END_REF][START_REF] Rowe | Abscisic acid regulates root growth under osmotic stress conditions via an interacting hormonal network with cytokinin, ethylene and auxin[END_REF]. Besides these well-characterised responses, analysis in Medicago truncatula suggested a positive role for ABA in the establishment and maintenance of root meristem function (Liang et al., 2007) and in stimulation of root elongation [START_REF] Yang | ABA-mediated ROS in mitochondria regulate root meristem activity by controlling PLETHORA expression in Arabidopsis[END_REF]. Similarly, root development of maize plants with reduced endogenous ABA content was more repressed in response to drought than that in control plants, indicating that ABA plays a role in maintaining root elongation under low water potentials [START_REF] Rowe | Abscisic acid regulates root growth under osmotic stress conditions via an interacting hormonal network with cytokinin, ethylene and auxin[END_REF]. Other studies have indicated a complex biphasic effect of exogenous ABA application on root growth under well-watered conditions where low concentrations of ABA stimulated root growth of Medicago [START_REF] Gonzalez | Abscisic acid promotes pre-emergence stages of lateral root development in Medicago truncatula[END_REF], rice (Oryza sativa) and Arabidopsis [START_REF] Xu | Abscisic acid accumulation modulates auxin transport in the root tip to enhance proton secretion for maintaining root growth under moderate water stress[END_REF]. As this response was similar to the biphasic effect of increasing levels of WD, [START_REF] Xu | Abscisic acid accumulation modulates auxin transport in the root tip to enhance proton secretion for maintaining root growth under moderate water stress[END_REF] and Li et al. (2017) proposed that primary root adaptive response to WD was controlled by ABA. More recently, ABA has also been identified as a key component of several major adaptive responses to local WD (reviewed by [START_REF] Scharwies | Water transport, perception, and response in plants[END_REF]. Firstly, [START_REF] Dietrich | Root hydrotropism is controlled via a cortex-specific growth mechanism[END_REF] have shown that local activation of ABA signalling in cortical cells of the elongation zone of Arabidopsis roots controls their hydrotropic response i.e. their growth towards water. Secondly, Orman-Ligeza et al.

(2018) reported that transient water deficit at the tip of cereal roots resulted in xerobranching, a local inhibition of lateral root formation that is dependent on the PYR/PYL ABA signalling pathway. Finally, ABA and auxin signalling pathways have been shown to control hydropatterning i.e. preferential positioning of lateral roots towards higher water availability (Bao et al., 2014, Orsa-Puente et al., 2018[START_REF] Robbins | Growth is required for perception of water availability to pattern root branches in plants[END_REF] ABA also exerts contrasting effects on root hydraulic conductance (Hose et al., 2000;[START_REF] Thompson | Overproduction of abscisic acid in tomato increases transpiration efficiency and root hydraulic conductivity and influences leaf expansion[END_REF]Parent et al., 2009). When applied in the micromolar range (0.1-1 µM), ABA rapidly enhances the hydraulic conductivity of both cortical cells (Hose et al., 2000) and whole roots of maize (Parent et al 2009[START_REF] Li | Pyrabactin regulates root hydraulic properties in maize seedlings by affecting PIP aquaporins in a phosphorylation-dependent manner[END_REF], whereas higher ABA concentrations (5-100 μM) inhibit the Lpr of maize (Aroca et al., 2003) and soybean (Glycine max; Markhart et al., 1979) The hydraulic effects of ABA are largely mediated through tissue-specific regulation of aquaporins. For instance, hydraulic conductance in maize roots closely follows the amount of aquaporin transcripts (Parent et al., 2009;Caldeira et al., 2014) and proteins [START_REF] Li | Pyrabactin regulates root hydraulic properties in maize seedlings by affecting PIP aquaporins in a phosphorylation-dependent manner[END_REF] upon changes in ABA content following water deficit. A key role of phosphorylation in ABA-dependent regulation of aquaporins was also observed in Arabidopsis guard cells [START_REF] Grondin | Aquaporins contribute to ABA-triggered stomatal closure through OST1-mediated phosphorylation[END_REF].

In the present work, we investigated how WD alters the ability of the plant root system to acquire water, by connecting effects on root hydraulics and root growth and development. The latter effects were addressed from an elementary developmental process, LR formation, up to whole-root architecture in Arabidopsis adult plants grown in hydroponics under increasing PEG concentrations to induce a wide range of WD levels. This experimental set-up allowed us to observe a stimulation of both root development and hydraulics under mild WD whereas severe WD had a repressive effect.

Our results showed that ABA controls and coordinates both the developmental and physiological responses. These findings bring further insights into the mechanisms and significance of adaptive control of root hydraulic architecture depending on WD intensity.

RESULTS

Root Development Exhibits a Bell-shaped Dose-dependent Response to Water

Deficit

To analyze the adaptive responses of root development to WD, Arabidopsis plants were grown hydroponically under control conditions for 18 days after sowing (18 DAS) and also for an additional 5 days (23 DAS) in the presence of various concentrations of high molecular weight polyethylene glycol (PEG-8000). With respect to experiments in soil or agar plate, this procedure provides access to the RSA of fully developed plants and allows examining the effects of water stress, independently of any ion stress, mechanical impedance, or stress heterogeneity. In addition, the procedure allows a parallel monitoring of root water transport capacity. Whereas a control hydroponic solution shows a water potential of -0.034 MPa, three WD treatments were imposed by addition of 25, 75 or 150 g L -1 PEG yielding water potentials of -0.047MPa (25PEG), -0.103 MPa (75PEG) and -0.332 MPa (150PEG), respectively. Pronounced modifications in root growth and architecture were observed after 5 days of treatment (Fig. 1A). Total root length and root biomass (Fig. 1B-C) showed a bell-shaped dose dependency, with an increase up to 10% in response to 25PEG whereas a reduction was recorded after exposure to 75PEG or 150PEG. To explore the developmental mechanisms underlying this response, we analysed in detail the morphology of root parts developed within the 5 days of PEG treatment, considering independently the primary root and the firstly-formed (oldest) LRs. These parts will be further referred to as Primary Root After Treatment (PRAT) and Lateral Root After Treatment (LRAT), respectively. The PRAT and LRAT were identified based on three criteria: (i) the length of the primary root and oldest LRs before the PEG treatments, (ii) root morphological modifications (i.e. root curvature, root thickening, root hair length, etc.) induced by PEG and visualised under a microscope at the end of the experiment, and (iii) changes in the slope between the position of the LRs and their distance to the root tip (Supplemental Fig. S1) (see Experimental Procedures for more details).

The PRAT length showed a progressive reduction by 18 to 84% with increasing PEG concentrations (Fig. 1D). On the contrary, the LRAT length was stimulated by 12% at 25PEG and repressed by 38 and 67% at 75PEG and 150PEG, respectively (Fig. 1E).

The number and mean length of LRs in both PRAT and LRAT parts also exhibited a bellshaped dose-dependent response to WD (Fig. 1F-I). Yet, we observed both a stronger stimulation and a lower sensitivity for inhibition of LR development in LRAT compared to that for PRAT. For instance, 75PEG caused 47% repression (Fig. 1F) and 20% stimulation (Fig. 1G) of LR number in PRAT and LRAT, respectively. Similarly, 150PEG had no-significant effect on mean LR length in PRAT (Fig. 1H) whereas it induced stimulation by 450% in LRAT (Fig. 1I). We also investigated the LR development in sections of the primary root produced prior to the PEG treatment (Supplemental Fig. S2A). The 75PEG and 150PEG treatments stimulated the mean LR length (up to 86%) in the 0-2 cm section whereas a repression of 60% was induced in the 2-4 cm section (Supplemental Fig. S2B-C). On the contrary, the WD did not change the LR number in these sections (Supplemental Fig. S2F-G). Taken together, our results indicate that RSA exhibits bell-shaped dose-dependent responses to WD, with overall stimulation responses at mild (25PEG) or moderate (75PEG) WD, and a general repression under severe WD (150PEG). In addition, a differential sensitivity to WD was observed between primary and oldest LRs, the former showing lower stimulatory responses associated with a higher sensitivity to WD.

ABA Accumulates under WD and Exerts both Stimulatory and Repressive Effects on RSA

To investigate whether ABA participates in the root growth responses described above, we first quantified ABA accumulation in the same conditions. At the whole-root level, no significant alteration in ABA concentrations was induced by mild or moderate WD whereas a three-fold increase was detected at 150PEG (Fig. 2A). We next analysed the expression of three ABA responsive genes: ras-related small GTPase homologue B18 (RAB18), responsive to desiccation 29A (RD29A) and responsive to desiccation 29B (RD29B) (Leonhardt et al., 2004;[START_REF] Fujii | Identification of two protein kinases required for abscisic acid regulation of seed germination, root growth, and gene expression in Arabidopsis[END_REF]. The mRNA abundance of these genes showed a gradual increase with increasing WD levels, up to 15-fold at 150PEG (Fig. 2B). Therefore, our results suggest that PEG treatments induce an accumulation and gradual response to ABA in relation to WD intensity.

Several studies have shown that exogenous ABA, usually delivered at high concentrations, can dramatically modify root growth and architecture (reviewed in [START_REF] Harris | Abscisic acid: Hidden architect of root system structure[END_REF][START_REF] Rowe | Abscisic acid regulates root growth under osmotic stress conditions via an interacting hormonal network with cytokinin, ethylene and auxin[END_REF]. In order to thoroughly explore the role of ABA in shaping root developmental responses to WD, we investigated the long-term (5 days) effects of low exogenous ABA concentrations (up to 250 nM) in hydroponically grown plants. qRT-PCR showed that the expression levels of RAB18, RD29A and RD29B were gradually enhanced with increasing ABA concentrations to reach a 3 to 4-fold increase in mRNA abundance in response to the 250 nM ABA treatment (Supplemental Fig. S3).

Exogenous ABA application revealed bell-shaped dose-dependent responses of growth, with an increase in the total root length and root biomass at the lowest ABA concentration (15 nM) and an inhibition by up to 25% at the highest ABA concentrations (Fig. 3A-B). These responses were further dissected at the levels of PRAT and LRAT.

Whereas PRAT length essentially showed an inhibition at 250 nM (Fig. 3C), a significant stimulation of LRAT length was recorded along the three lowest ABA treatments (15-100 nM) (Fig. 3D). With respect to LR number, PRAT showed a mild (+22%) stimulation only at 15 nM ABA whereas LRAT exhibited a more pronounced (up to 71%) stimulation at all ABA concentrations investigated (Fig. 3F). Mean LR length was stimulated by ABA in both PRAT and LRAT (Fig. 3G-H), but with a distinct dose-dependency since a stimulation (+116%) or a lack of effect was observed at the highest ABA treatment for LRAT (Fig. 3H) and PRAT (Fig. 3G), respectively. Finally, when considering the primary root formed prior to ABA treatment, a strong stimulation of mean LR length (up to 80%) was induced in the 0-2 cm section by the 50 nM ABA treatment whereas no response was recorded in the 2-4 cm section (Supplemental Fig. S2D-E). LR number was also insensitive to ABA in both sections (Supplemental Fig. S2H-I). Taken together, our results demonstrate that RSA shows bell-shaped responses to exogenous ABA, with stimulation at low ABA concentrations (15-100 nM) and repression at higher concentrations (250 nM). In addition, dose-response curves point to a lower response amplitude but a higher sensitivity for LR formation and elongation in the primary root (PRAT) compared to that in the preformed LRs (LRAT).

ABA Mediates the Effects of WD on RSA

The responses of RSA to exogenous ABA, which largely recapitulate those observed in response to WD (Fig. 1), prompted us to investigate further the involvement of ABA in the root adaptive responses to WD. Our analyses were based on comparison of wild-type plants (Col-0) with mutants deficient in ABA synthesis (aba2-1; [START_REF] Schwartz | Biochemical characterization of aba2 and aba3 mutants in Arabidopsis thaliana[END_REF] or with altered ABA signalling. In the latter case, we used snrk2.2 snrk2.3 [START_REF] Fujii | Identification of two protein kinases required for abscisic acid regulation of seed germination, root growth, and gene expression in Arabidopsis[END_REF] andhab1-1 abi1-2 [START_REF] Saez | Enhancement of abscisic acid sensitivity and reduction of water consumption in Arabidopsis by combined inactivation of the protein phosphatases type 2C ABI1 and HAB1[END_REF] double mutants, which show a lower and higher sensitivity to ABA, respectively. Under control conditions, the root and shoot growth of aba2 was strongly affected with respect to that in Col-0 (Supplemental Fig. S4A-C). A significant but lower shoot and root growth reduction (by approximately 25%) was also observed in snrk2.2 snrk2.3, whereas growth was unchanged in the hab1-1 abi1-2 hypersensitive mutant (Supplemental Fig. S4A-C and Supplemental Table 2).

Under mild WD (25PEG), all mutant lines lost the growth stimulation observed for Col-0 (Supplemental Fig. S4A-C). On the contrary, under severe WD (150PEG), hab1-1 abi1-2 showed a higher growth reduction by up to 50% (under 150PEG) in comparison to that in Col-0, whereas growth of both aba2 and snrk2.2 snrk2.3 was not or only slightly altered (Supplemental Fig. S4A-C). Root development was further dissected at the levels of PRAT and LRAT. Considering PRAT length (Fig. 4A), all genotypes but snrk2.2 snrk2.3 showed qualitatively similar sensitivity to mild WD (Supplemental Table 2). In contrast, when considering LRAT length and LR number in PRAT and LRAT (Fig. 4B-D), both aba2 and snrk2.2 snrk2.3 lacked the stimulation of LR growth and formation that was induced by mild WD (25PEG) in Col-0, whereas a significant LR inhibition was found in hab1-1 abi1-2 (Fig. 4B-D). In response to moderate WD (PEG75), aba2 showed a lower inhibition of the LR growth and formation than that in Col-0, whereas hab1-1 abi1-2 had an enhanced repression of the root development (Fig. 4B-D).

To further investigate these differences in sensitivity, we performed a more detailed analysis of LR growth and development (Fig. 4E-F). As described previously, increasing WD induced a stimulation of the LR elongation in Col-0 PRAT. This response was lost in aba2 and snrk2.2 snrk2.3 and strongly attenuated in hab1-1 abi1-2. However, the latter genotype showed a greater repression for highest WD levels (Fig. 4E). The most striking difference was observed in LRAT, where moderate and severe WD strongly stimulated the LR elongation in Col-0 whereas they dramatically repressed the LR elongation in hab1-1 abi1-2 (Fig. 4F). We also investigated the LR development in sections of the primary root that were produced prior to the PEG treatment (see distinct WD phenotypes of ABA biosynthesis and sensitivity mutants confirm that ABA plays a crucial role in most of the adaptive responses of RSA to WD.

Root Hydraulics Exhibits an ABA-dependent Bell-shaped Dose Response Curve to

WD

To investigate a putative coordination of root developmental and physiological responses to WD, we next investigated the root hydraulics of the same genotypes under PEG and ABA treatments as above. In agreement with these ideas, the whole-root hydraulic conductance (Lo) of Col-0 plants showed a bell-shaped response to increasing PEG concentrations (Supplemental Fig. S5A). The Lpr, as deduced by normalization of Lo to root size (dry weight), exhibited a similar dose-response curve with stimulation and inhibition by 30% and 51% at 25PEG and 150 PEG, respectively (Fig. 5A). When the measured water flow was normalized to the total root length instead of the dry weight, the maximal stimulation and inhibition of Lpr were of 40% and 36%, respectively (Supplemental Fig. S5B). Interestingly, Lpr also showed a bell-shaped dependency to exogenous ABA concentrations with a mild stimulation (12%) at 15 nM and an inhibition down to 20% at 100 and 250 nM ABA (Fig. 5B). Similar effects were observed when considering Lo (Supplemental Fig. S5C) or normalizing Lpr to the root length (Supplemental Fig. S5D).

Under control conditions, and by comparison to that in Col-0, aba2 and snrk2.2 snrk2.3 showed a reduction in Lpr by 56 and 21%, respectively, whereas hab1-1 abi1-2 showed stimulation by 30% (Fig. 5C and Supplemental Table 3). However, Lpr of the three mutant genotypes was insensitive to mild and moderate WD (25PEG and 75PEG) whereas it showed a strong repression in response to 150PEG (Fig. 5C). These combined physiological and genetic approaches indicate that ABA is involved in the stimulation of Lpr by mild WD (25PEG) and can reduce Lpr at the highest concentration investigated. In contrast, ABA plays a minor role, if any, in Lpr inhibition under severe WD (150PEG).

Water uptake in the Arabidopsis root is mediated in large part by aquaporin water channels. To estimate their contribution to the modulation of Lpr by WD and ABA, we applied azide, a well-characterized aquaporin blocker (Sutka et al., 2011), and measured the residual Lpr. Under control conditions, aquaporins accounted for more than 75% of Lpr (Fig. 5A) as described earlier (Sutka et al., 2011). Furthermore, we found a mild effect of WD on residual Lpr specifically at 75PEG (Fig. 5A), whereas none of the ABA treatments altered this parameter (Fig. 5B). Thus, the bell-shaped effects of PEG and ABA application on Lpr can be mostly accounted for by the modulation of root aquaporin function. To address this point further, we analysed the mRNA abundance of all members of the Plasma membrane Intrinsic Protein (PIP) subfamily and of four highly expressed members of the Tonoplast Intrinsic Protein (TIP) subfamily. No significant variation was observed in response to either mild WD (PEG25) (Supplemental Fig. S6A) or exogenous ABA (Supplemental Fig. S6B). In contrast, a moderate or severe WD (PEG75 or150) reduced the mRNA abundance of several aquaporin genes, with the strongest repression observed for PIP1;5, PIP2;4, PIP2;7 and two TIPs (TIP1;1, TIP1;2). Noticeably, PIP1;4 and PIP2;5 expression was induced 2 and 3 fold, respectively.

Interestingly, expression of PIP1,4 but not PIP2,5 was significantly induced by the highest ABA concentration (Supplemental Fig. S6B).

Our results indicate that, similar to its effects on RSA, WD induces a double effect on root hydraulics, with a stimulation of aquaporin-dependent water transport at mild WD (PEG25) and a strong repression of the aquaporin pathway at severe WD (PEG150).

Under mild or moderate WD, these responses seem to be largely mediated by ABA. In contrast, the inhibition of Lpr at 150 PEG is ABA-independent and seems to involve an overall repression of aquaporin expression.

DISCUSSION

Understanding the mechanisms that underlie root development and hydraulics under drought is of major importance to maintain plant growth under suboptimal conditions. However, the analysis of RSA under drying soil conditions is extremely time consuming and not compatible with fine morphological or functional analyses. Thus, many studies have been conducted on Arabidopsis seedlings grown in agar plates and mostly subjected to severe osmotic stress, as induced by high mannitol, sorbitol, NaCl or KCl concentrations. To have a more comprehensive view of adaptive and functional responses of mature plants to WD, we analysed both root architecture and hydraulics of 23-day-old adult plants grown in hydroponics in the presence of a wide range of PEG concentrations. PEG is a non-permeant molecule that can consistently reduce water potential in plates (van der [START_REF] Van Der Weele | Growth of Arabidopsis thaliana seedlings under water deficit studied by control of water potential in nutrient-agar media[END_REF][START_REF] Rowe | Abscisic acid regulates root growth under osmotic stress conditions via an interacting hormonal network with cytokinin, ethylene and auxin[END_REF]. As PEG can also induce anoxia [START_REF] Verslues | Root growth and oxygen relations at low water potentials. Impact of oxygen availability in polyethylene glycol solutions[END_REF], the nutrient solution was constantly oxygenated and circulated around roots. These optimized culture conditions triggered a wide range of highly reproducible responses to WD.

WD Exerts Contrasting Dose-Dependent Effects on Root Development

Inhibition of plant growth and development is a common response to WD [START_REF] Zhu | Overexpression of a Δ1-pyrroline-5-carboxylate synthetase gene and analysis of tolerance to water-and salt-stress in transgenic rice[END_REF][START_REF] Deak | Osmotic regulation of root system architecture[END_REF][START_REF] Xiong | Identification of drought tolerance determinants by genetic analysis of root response to drought stress and abscisic acid[END_REF]Claeys et al, 2014;[START_REF] Thalmann | Regulation of Leaf Starch Degradation by Abscisic Acid Is Important for Osmotic Stress Tolerance in Plants[END_REF]reviewed in Comas et al., 2013). Accordingly, we observed here that a severe WD (150PEG) caused a significant reduction in both shoot and root growth (Fig. 1; Supplemental Fig. S7). Unlike in most fields experiments, no change in shoot:root ratio was observed (Supplemental Fig. S7) probably due to the fact that our culture conditions temperature and hygrometry are tightly controlled and nutrient availability is unchanged under WD whereas it is dramatically reduced when soil water content drops.

In addition, we observed that a mild WD (25PEG) significantly promoted both shoot and root development giving rise to bell-shaped dose-responses to WD. Fine analysis revealed that this type of response was observed for nearly all analysed RSA parameters (Fig. 1; Supplemental Fig. S2 andS7). Such positive effects of mild WD on root development have been punctually reported for the primary root of Arabidopsis (van der [START_REF] Van Der Weele | Growth of Arabidopsis thaliana seedlings under water deficit studied by control of water potential in nutrient-agar media[END_REF]Claeys et al., 2014), or roots of rice [START_REF] Henry | Drought and abscisic acid effects on aquaporin content translate into changes in hydraulic conductivity and leaf growth rate: a trans-scale approach[END_REF] or maize [START_REF] Zhu | Root cortical aerenchyma improves the drought tolerance of maize (Zea mays L.)[END_REF][START_REF] Dowd | Maize lateral root developmental plasticity induced by mild water stress. I: Genotypic variation across high-resolution series of water potentials[END_REF] in soil. Interestingly, our fine analysis showed that the adaptive responses to WD were shifted depending on root order, with the primary root being more sensitive than the oldest LRs (compare for instance root length or LR numbers in PRAT and LRAT in Fig. 1D andE , F and G, and H and I). Differential responses to WD were also recorded for LRs already initiated prior to WD treatment (Supplemental Fig. S2B-C). Thus, elongation of non-emerged or juvenile LRs was stimulated by mild and moderate WD in the 0-2 cm part of the primary root whereas it was repressed for older LRs in the 2 cm section above. We also note that growth stimulation of Col-0 roots by a 25PEG treatment was not unspecific, as this response was lost in ABA mutants (Fig. 4) and could be recapitulated in Col-0 seedlings grown in agar plates using small concentrations (25 mM) of sorbitol (Supplemental Fig. S8).

Taken together, these results highlight a complex response of the root system to WD with different sensitivity depending of root age and branching level (see model in Figure 6). In brief, i) the primary root appears to be more sensitive than LRs to WD, ii) first-order LRs are more sensitive than second-order LRs and, iii) LR elongation is less repressed than LR emergence. Accordingly, combination of these WD responses gives rise to a more compact root system, which is highly branched and carries elongated LRs at its periphery (see PEG75 and PEG150 in Fig. 1A).

A similar differential adaptive response of primary and LR growth has been reported by Julkowska et al. (2014) in Arabidopsis plants under salt stress. In contrast, studies in maize [START_REF] Gao | Reduced crown root number improves water acquisition under water deficit stress in maize (Zea mays L.)[END_REF], rice [START_REF] Uga | Control of root system architecture by DEEPER ROOTING 1 increases rice yield under drought conditions[END_REF][START_REF] Sandhu | Rice root architectural plasticity traits and genetic regions for adaptability to variable cultivation and stress conditions[END_REF] and wheat (Awad et al., 2018) showed that WD dramatically reduced shoot-born roots and LR development whereas it favoured main root elongation. Such difference may reflect distinct adaptive strategies between monocots and dicots. Indeed, the fibrous root system of monocots, with post-embryonic roots developing from the stem provides a unique opportunity for plant foraging of late season precipitations which is absent in dicots.

When considering common drought scenarios, WD usually starts in the upper soil layers and progresses gradually in deeper layers. Our observation that LRs formed in both primary and oldest LRs are more tolerant to WD than their mother root fits with the idea that progression of the primary root in deep soil layers protects it from severe WD and that newly formed LRs experience stronger WD than their genitors as they develop in a soil area already foraged for water by the latter. Thus, when extrapolating our observations under homogenous and constant WD to a developing WD in soil, we can predict a massive stimulation of RSA mainly due to the progressive development of LRs from different orders to explore a larger volume of soil. The observed adaptive responses are also relevant to more severe WD. As surface soil dries, increase of root length and density in the deepest layers significantly contribute to improving the water and nutrient acquisition with a limited carbon investment. This adaptive response to WD agrees with traits found in crops. For instance, cultivars of rice and soybean with increased root length density (root length per soil volume) in the 35-45 cm layer appeared to have increased water uptake and improved resistance to drought (Carter et al., 1999;[START_REF] Henry | Drought and abscisic acid effects on aquaporin content translate into changes in hydraulic conductivity and leaf growth rate: a trans-scale approach[END_REF].

WD also Exerts Contrasting Dose-Dependent Effects on Root Hydraulics

Root hydraulics (Lpr) is known to rapidly respond to environmental cues, such as water availability, supporting its role in plant adaptation to fluctuating environments (Steudle, 2000;[START_REF] Vandeleur | the role of plasma membrane intrinsic proteins aquaporins in water transport through roots: diurnal and drought stress responses reveal different strategies between isohydric and anisohydric cultivars of grapevine[END_REF]. Accordingly, our measurements indicated that a mild WD enhances Arabidopsis Lpr whereas a severe WD had a repressive effect (Fig. 5).

The generally observed decline of Lpr under drought conditions can be interpreted as a means for hydraulically promoting stomatal closure or for limiting a counterflow of water from the root to the drying soil (reviewed in Aroca et al., 2012). Drought-induced increases of Lpr have been reported under more specific conditions, generally under mild drought stress [START_REF] Siemens | Changes in root water flow properties of solution culture-grown trembling aspen (Populus tremuloides) seedlings under different intensities of water-deficit stress[END_REF]. This response is thought to promote water uptake as long as the water potential remains higher in the soil than in the root.

Previous work from our group has shown that aquaporins contribute to approximately 75-80% of Arabidopsis Lpr [START_REF] Tournaire-Roux | Cytosolic pH regulates root water transport during anoxic stress through gating of aquaporins[END_REF]Boursiac et al., 2005;Sutka et al., 2011;[START_REF] Li | Pyrabactin regulates root hydraulic properties in maize seedlings by affecting PIP aquaporins in a phosphorylation-dependent manner[END_REF]. Here, we provide pharmacological evidence that aquaporins can account for most of the stimulation and repression of Lpr under mild and severe WD, respectively (Fig. 5). Yet, no significant change in PIP or TIP gene expression was observed in response to mild or moderate WD (Supplemental Fig. S6). In contrast, severe WD reduced the mRNA abundance of most aquaporin genes, possibly explaining the parallel inhibition of Lpr. These contrasting results are consistent with other studies indicating that numerous post-transcriptional mechanisms can account for aquaporin regulation in roots under stress (reviewed in Aroca et al., 2012;[START_REF] Li | Pyrabactin regulates root hydraulic properties in maize seedlings by affecting PIP aquaporins in a phosphorylation-dependent manner[END_REF].

The observation that both root developmental and hydraulic parameters exhibited similar bell-shaped dose-dependent responses to WD points to an obvious coordination of these responses. Under severe WD (150PEG) for instance, both root development and hydraulics were dramatically repressed to restrict water exchange between roots and their harsh environment. Conversely, a mild WD (25PEG) induced a dual stimulation of root development and root hydraulics to optimize water uptake and support shoot biomass production during the onset of drought. Yet, we found a stimulation of total root length specifically under mild WD (Fig. 1B) whereas Lpr (as under both mild and moderate (75PEG) WD (Supplemental Fig. S5B). Thus, moderate WD represses root development (Fig. 1B) while maintaining root hydraulics (Fig. 5A) to possibly maintain shoot hydration (Suppl. Fig. 4A). These responses illustrate different adaptation strategies to increasing levels of WD with differential carbon investment.

Under mild WD, carbon is invested in the production of new and longer roots, whereas under moderate WD, carbon is invested in the production of second-order LRs and root thickening to prevent water loss. On the contrary, aquaporin-dependent water uptake that mainly recruits pre-existing proteins is stimulated to improve water uptake. Similar responses to moderate and severe WD were also proposed by Parent et al., (2009[START_REF] Vandeleur | the role of plasma membrane intrinsic proteins aquaporins in water transport through roots: diurnal and drought stress responses reveal different strategies between isohydric and anisohydric cultivars of grapevine[END_REF] and Laur and Hacke ( 2013) who suggested that when soil water is scarce, increased aquaporin abundance and activity play a major role in compensating for reductions in root elongation and surface area production.

Another explanation of the increase in Lpr under moderate WD may account for the modification of root architecture that under these conditions present a significant increase in number and elongation of newly formed roots (mainly second-order LRs) that may be more active in water uptake. This hypothesis is supported by several reports suggesting that fine or LRs are the most active portion of root system in water uptake (reviewed in Comas et al 2013). Recently, Ahmed et al. (2016;2018) used heavy water (D2O) labelling to show that, in maize, up to 80% of water absorption can be accounted for by laterals. Improved hydraulic measurements will have to be developed in the Arabidopsis root to directly test this hypothesis.

ABA Acts as an Integrator and Coordinator of Root Responses to WD

It well established that drought and osmotic stress induce an accumulation of ABA in both roots and shoots [START_REF] Schachtman | Chemical root to shoot signalling under drought[END_REF]Wilkinson et al., 2012, Clays andInzé, 2013). Besides stomatal closure (Trejo and Davies, 1995;[START_REF] Schroeder | Guard cell abscisic acid signalling and engineering drought hardiness in plants[END_REF], ABA can positively or negatively act on shoot and root growth depending on its concentration or the plant model investigated [START_REF] Rowe | Abscisic acid regulates root growth under osmotic stress conditions via an interacting hormonal network with cytokinin, ethylene and auxin[END_REF]Hooker and Thorpe, 1998;Barrero et al., 2005;[START_REF] Zhang | ABA promotes quiescence of www.plantphysiol[END_REF]Leach et al., 2011;reviewed by Harris, 2015). Root hydraulics is also controlled by ABA but again stimulatory or inhibitory effects can be observed, depending on the experimental conditions and genotypes (reviewed by Aroca et al., 2012). Our aim here was to evaluate how ABA may coordinate the developmental and hydraulic responses of roots over a wide range of WD.

When quantifying ABA accumulation at the whole-root level, a significant increase was observed under severe WD only, whereas the expression level of ABA responsive genes was enhanced even under mild WD (Fig. 2B). Although this increase remained limited compared to related studies in in vitro grown seedlings [START_REF] Rowe | Abscisic acid regulates root growth under osmotic stress conditions via an interacting hormonal network with cytokinin, ethylene and auxin[END_REF], it potentially reflects a typical response to WD with possibly undetectable and local accumulations of low ABA amounts. These ideas prompted us to analyse the impact of exogenous ABA applications in the nanomolar range instead of the micromolar range as usually used. Interestingly, expression of the ABA reporter genes showed a slight stimulation that was comparable to that measured under mild WD (Supplemental Fig. S3).

When considering RSA, low exogenous ABA concentrations revealed bell-shaped dose-response curves that were reminiscent of those observed under low and moderate WD. Moreover, all developmental parameters positively affected by mild WD were also positively regulated by low ABA concentrations (Fig. 3; Supplemental Fig. S2 andS4).

Finally, the differential developmental responses of roots to WD, with young tissues being more responsive than older ones (Fig. 1 and Supplemental Fig. S4), were also observed in the context of exogenous ABA application (Fig. 3 and Supplemental Fig. S4).

The idea that ABA mediates a large range of RSA responses to WD was further supported by the analysis of ABA mutants with aba2 and snrk2.2 snrk2.3 having an attenuated response of most root developmental parameters to WD whereas the hypersensitive hab1 abi1 mutant showed enhanced responsiveness.

We note, however, that some root responses to WD seem to be ABA-independent (Fig. 6). When considering the primary root (PRAT), its elongation was dramatically repressed by increasing levels of WD (Fig. 1D and Fig. 3A), but to a similar extent in the different ABA mutants (Fig. 4A). Accordingly, exogenous ABA application had little impact on PRAT (Fig. 3C) suggesting that this WD adaptive response is mainly ABA independent. A similar conclusion can be drawn for LRs formed in the 2-4 cm part of the primary root present before transfer (see Supplemental Fig. S2A). On the contrary, elongation of roots in the 0-2 cm part was stimulated by WD (Supplemental Fig. S2C) and this response was typically dependent on exogenous ABA (Supplemental Fig. S2E) and dramatically modified in the ABA mutants (Supplemental Fig. S4E). Taken together, these results suggest that ABA-dependent responses to WD are mainly observed in young roots whereas the adaptive responses of older tissues become ABA independent.

Similar to the adaptive response of RSA to WD, we showed that the response of root hydraulics to WD is in large part mediated by ABA. In brief, Lpr of Col-0 showed a bell-shaped dose-dependent response to both WD and exogenous ABA (Fig. 5A andB) and Lpr response to WD was dramatically attenuated in ABA mutants (Fig. 5C). These results establish that ABA coordinates both root developmental and hydraulic response to mild and moderate WD. The complex interactions between RSA, hydraulics and ABA are summarized in the integrative model presented in Figure 6. When considering severe WDs, both the RSA and hydraulic responses were ABA-independent (as illustrated on Fig. 6 by a large number of red symbols). We speculate that, due to the severity of the stress, strong inhibitory responses are governed by local signals, independent of the overall hormonal status of the plant.

CONCLUSION

In the present study, we showed that mild and somewhat moderate WD stimulate both root growth and root hydraulics. In addition, the fine analysis of root architecture revealed that mild WD mainly stimulates elongation and to a lower extent production of LRs, this response being markedly enhanced in pre-existing LRs. Concomitantly, mild WD significantly stimulates root hydraulics in an aquaporin-dependent manner. Both responses are mediated by ABA. Since under WD, ABA is mainly synthetized in shoots and transported to roots via the phloem (review by Osakabe et al., 2013), we assume that the differential adaptive responses observed in our experiments can be accounted for by either a differential accumulation of ABA due to local regulation of ABA transporters or by differential ABA responses depending on WD level and root tissue types. This non-linear response is well documented for phytohormones and has been extensively studied for auxin. Identifying the molecular basis of these local ABA responses will be critical to better understand how the plant coordinates its RSA and root hydraulic responses, and how these responses can be reshaped to possibly improve the tolerance of crops to water stress. Our work also shows that a severe WD dramatically modifies both RSA and hydraulics and, again, the molecular bases of these ABA-independent regulations remain to be identified. Overall, the experimental framework established in the present work will be crucial to explore the adaptive significance of the multiple responses of roots to WD.

MATERIALS AND METHODS

Plant Materials and Growth Conditions

The Arabidopsis thaliana accession Columbia-0 (Col-0 N60000) and the aba2-1 (Léon-Kloosterziel et al., 1996), snrk2.2 snrk2.3 (Fuji et al., 2007), and hab1-1 abi1-2 [START_REF] Saez | Enhancement of abscisic acid sensitivity and reduction of water consumption in Arabidopsis by combined inactivation of the protein phosphatases type 2C ABI1 and HAB1[END_REF] mutants in Col-0 background were used in this work. Seeds were surface sterilized and sown on 1/2 MS agar vertical plates (2.2 g L -1 MS, 1% w/v sucrose, 0.05% w/v MES, and 0.8% w/v agar, pH 5.7). Plates were incubated for 2 days at 4°C in dark for stratification. Plants were germinated and further grown on these plates for 9-11 days in a growth chamber at 70% relative humidity (RH) and 20°C, with 16 h/8 h light/dark cycles (250 µE m -2 s -1 ). Subsequently, seedlings were transferred to a hydroponic medium containing: 1.25 mM KNO3, 0.75 mM MgSO4, 1.5 mM Ca(NO3)2, 0.5 mM KH2PO4, 0.1 mM MgCl2, 50 µM Fe-EDTA, 50 µM H3BO3, 12 µM MnSO4, 0.7 µM CuSO4, 1 µM ZnSO4, 0.24 µM MoO4Na2, 0.01 µM CoCl2, 100 µM Na2SiO3, 1 mM MES, pH 5.7 adjusted using KOH. At 18 days after sowing (DAS), seedlings were transferred for 5 days to a fresh medium containing different concentrations (25, 75, or 150 g L -1 ) of polyethylene glycol 8000 (PEG-8000) to reduce the water potential (Ψ) of the nutrient solution. To avoid anoxia, culture solutions were constantly bubbled with air and recirculated in each basin. The solution was replaced at the middle of the treatment period (at 2.5 days) to avoid bacterial contamination. Ψ was measured with a vapor pressure osmometer WESCOR 5520 (USA) as described by [START_REF] Turner | Techniques and experimental approaches for the measurement of plant water status[END_REF]. For ABA treatments, 18-day-old plants were transferred for 5 days to a fresh hydroponic solution containing different concentrations of ABA (15, 50, 100 and 250 nM), obtained using ABA stock solutions in ethanol. Control plants grown in the absence of ABA were mocktreated with a same amount of ethanol (final concentration of 0.00033%). The hydroponic solution was replaced once during the treatment period (at 2.5 days). All experiments were performed at least three independent times. All chemicals were provided by Sigma-Aldrich (Saint Quentin, France). Root systems were excised at 23 DAS from plants grown in hydroponics (growth was performed for 18 days under control conditions followed by 5 days in the presence of PEG or ABA, as described above), and immediately used for root hydraulic measurements (see below). Subsequently, roots were washed and stored in 20% v/v ethanol prior to analysis of RSA. For imaging, each root system was manually separated on a 240 × 240 mm Petri dish containing water, and scanned with an Epson Perfection V850 Pro scanner (Epson Europe BV, Netherlands). RSA was analysed using the OPTIMAS image analysis software (Adept Turnkey Pty Ltd, Osborne Park WA, Australia).

Analysis of Root

Several parameters were measured. Total root length was quantified on the whole-root system. The PRAT (primary root after treatment) and LRAT (lateral root after treatment) correspond to the parts of primary and lateral roots that were produced during the 5 days treatment. The PRAT and LRAT were precisely observed at the end of the culture using a binocular microscope. Root length measured before transplanting was combined to these microscopic observations in order to identify at the cellular level the morphological changes induced by the PEG or ABA treatment (Supplemental Fig. S1).

Microscopic morphological changes (curvature of the root, changes in cell size and a transient increase in distance between lateral roots) were not only observed in response to PEG or ABA but also, though at a much lower extend, in plants grown on a control medium. These morphological changes were found to be very reproducible, probably due to a transient stress induced by manipulating the plants. Finally, plants with no clear differentiation between the initially formed root parts and the PRAT and/or LRAT were discarded for the RSA analysis. Overall, the length of PRAT and LRAT as well as the number and mean length of lateral roots formed in these parts during the treatment were measured. The number and mean length of lateral roots were also determined in the 0-2cm and 2-4 cm parts of the primary root that was produced before treatment application (see Fig. 1A andS2A).

ABA Quantification

For ABA quantification, root and shoot tissues were frozen in liquid nitrogen and ABA was extracted and quantified by the Metatoul platform (https://www6.toulouse.inra.fr/metatoul_eng/, Toulouse, France). Three biological replicates from three independent experiments were used.

Measurement of Root Hydrostatic Hydraulic Conductivity (Lpr)

the same hydroponic medium as used for each treatment. The hypocotyl was tightly sealed inside a combination of plastic and metallic seals using a low-viscosity dental paste (President Light, Coltene, Switzerland). The rate of pressure (P)-induced sap flow (Jv) exuded from the hypocotyl section was recorded using high-accuracy flow meters (Bronkhorst, France) in an automated manner using a LabVIEW-derived application. In practice, roots excised at 23 DAS from plants grown in standard conditions were subjected to a pre-treatment at 350 kPa for 10 min to attain flow equilibration, and Jv

was measured successively at 320, 160, and 240 kPa for about 5 min. For PEG treatments, pressure increments corresponding to the Ψ of the hydroponic solution were applied in order to counteract osmotically-induced water efflux from the root. Root dry weight (DWr) was analysed after measurement of Jv and RSA. The Lpr (mL g -1 h -1

MPa -1 ) of an individual root system was calculated using the following equation:

Lpr = Jv / (DWr • P)
In NaN3 experiments, Lpr was derived from continuous Jv measurement at 320 kPa as described in Sutka et al. (2011).

Total RNA Isolation and Analysis

Root samples were frozen in liquid nitrogen and disrupted for 1 min at 30 Abauzit, and C. Baracco; and the informatics assistance of H. Afonso.

Figure 1 .

 1 Figure 1. Changes of root system architecture in response to water deficit. Plants were grown until 18 days after sowing (DAS) in hydroponics under standard conditions and subjected for 5 additional days (23 DAS) to the indicated PEG-8000 treatments. A, Representative images showing the whole root system architecture, the parts of the primary root grown after treatment (PRAT), and the oldest lateral root grown after treatment (LRAT) used for specific analyses. B and C, Whole root systems were used to determine total root length (B) and biomass production (C) per plant. D to I, The length of the PRAT (D) and the LRAT (E), the number of LRs formed in the PRAT (F), the number of second-order LRs formed in the LRAT (G), the mean length of LRs formed in the PRAT (H), and the mean length of second-order LRs formed in the PRAT (I) per root are shown. Mean values ± SE were obtained from plants grown in three independent experiments (n = 20-25). 'Homogeneous group' statistics were calculated through ANOVA, where mean values with different letters are significantly different according to LSD test at P ≤ 0.001.

Figure 2 .

 2 Figure 2. Effects of water deficit on ABA abundance and expression of ABAregulated genes. A and B, ABA concentrations (A) and transcript abundance of ABA-regulated genes RAB18, RD29A and RD29B in roots (B) of plants subjected from 18 days after sowing to a 5-day-long treatment with the indicated PEG concentrations. The dotted line in (B) represents the normalized expression level in control conditions. Mean values ± SE were obtained from 15 plants grown in three independent experiments (n = 3). 'Homogeneous group' statistics were calculated through ANOVA where mean values with different letters are significantly different according to LSD test at P ≤ 0.05 (A). FW, fresh weight.

Figure 3 .

 3 Figure 3. Effects of exogenous ABA on root system architecture.

Figure 4 .

 4 Figure 4. Effects of water deficit on root system architecture of ABA biosynthesis (aba2) and response (snrk2.2 snrk2.3; hab1 abi1) mutants. A to F, Plants grown in hydroponics were subjected at 18 days after sowing (DAS) for 5 additional days (23 DAS) to the indicated PEG concentrations. Three mutants including aba2 (an ABA biosynthesis deficient mutant), snrk2.2 snrk2.3 (an ABA signaling mutant) and hab1 abi1 (an ABA signaling hypersensitive mutant), were used in addition to the Col-0 WT control. The root system architecture was analysed by several parameters: the length of the primary root grown after treatment (PRAT; A) and the oldest lateral root grown after treatment (LRAT; B), the number of lateral roots (LRs) formed in PRAT (C), the number of second-order LRs formed in the LRAT (D), the mean length of LRs formed in the PRAT (E), and the mean length of second-order LRs formed in the LRAT (F) per root. Open boxes, light grey, dark grey and black boxes represent values for plants grown in PEG25, PEG75 and PEG150 conditions, respectively. Mean values ± SE were obtained from plants grown in three independent experiments (n = 10-20).'Homogeneous group' statistics were calculated through ANOVA for each genotype, where mean values with different letters are significantly different according to LSD test at P ≤ 0.05, representing n.s. as not significant (P > 0.05).

Figure 5 .

 5 Figure 5. Effects of water deficit and exogenous ABA on root hydraulic properties of wild-type and ABA biosynthesis (aba2) and response (snrk2.2 snrk2.3; hab1 abi1) mutants.

Figure 6 .

 6 Figure 6. Integrative model of root developmental and hydraulic responses to representative water deficit intensities. The different water deficit (WD) treatments are represented by four plants. The root system is schematically represented by a primary root, an old lateral root (LR) and first and second-order LRs on the primary and the old LR. The root parameters analyzed are schematically represented and their response to WD is represented by an arrow or a bar for stimulation or repression, respectively. The intensity of the responses is shown by the thickness of the line. PRAT is the part of the primary root grown after treatment, LRAT is the part of the old LR grown after treatment, L and # stand for mean LR length and LR number, respectively. Lpr stands for root hydraulic conductivity. The blue and red color codes represent ABA-dependent or -independent responses, respectively. The thickness of blue and red lines and arrows represent the intensity of response (thicker line represents stronger response). The three yellow boxes at the bottom of the model represent the root ABA content. Color intensity and number of arrows are a schematic representation of ABA concentrations.

System Architecture (RSA)

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ACKNOWLEDGMENTS

This work was supported by the AgreenSkills fellowship programme (M.A.R.), which has received funding from the EU's Seventh Framework Programme under grant agreement Nº FP7-26719, and the EU's Horizon 2020 research and innovation programme under the individual fellowship Marie Sklodowska-Curie grant agreement No 657374 (M.A.R.).

We thank to Dr Pedro L. Rodriguez (IBMCP-UPV-CSIC, Spain) for providing the ABA mutant lines. We fully acknowledged all former and current members of Aquaporins' team at B&PMP (CNRS/INRA/SupAgro/Univ Montpellier, France) for the exciting discussions and inputs on this work. We want to thank the technical and logistical assistance of X. Dumont, H. Baudot, T. Dessup, J. Garcia, R. Picaud, and F. Lecocq; the

This project was funded by the EU within the AgreenSkills (FP7-26719) and Marie Sklodowska-Curie (H2020-657374) programs (to M.A.R.), as well as by the Institut National de la Recherche Agronomique and the Centre National de la Recherche Scientifique.

13

Supplemental Fig. S2A for illustration). Whereas increasing WD stimulated the mean LR length in the 0-2 cm section of Col-0 as described above (Supplemental Fig. S2B-C and Supplemental Table S2), this bell-shaped response was lost in ABA mutants (Supplemental Fig. S4E). By contrast, the WD-induced inhibition of the LR length observed in the 2-4 cm section of Col-0 (Supplemental Fig. S2F) was unaffected in the mutant genotypes (Supplemental Fig. S4F and Supplemental at an annealing temperature of 57°C according to the manufacturer's instructions. SYBR Green Primer efficiencies for each pair were evaluated from the analysis of dilution series of 1, 1:5, 1:10, 1:100 and 1:1000 of a mix of all the diluted first strand cDNA samples and derived from Cp values calculated according to the second derivative maximum method (LightCycler® LC480 II, Hoffmann-La Roche AG, Basel, Switzerland).

Three to six biological replicates from three independent plant cultures and two technical repeats were used per treatment in every run. Expression data were normalized to expression of three housekeeping genes, TIP41-like protein (At4g34270), CLATHRIN (At4g24550), and SAND family protein (At2g28390), which were selected as reference genes according to (Czechowski et al., 2005). Data from mutant and control plants were compared using a two-tailed Student's t-test. The primer sequences used are listed in Supplemental Table S1.

Statistical Analyses

Statistical analysis was performed using the STATGRAPHICS Centurion XVI software (StatPoint Technologies, Warrenton, VA, USA). One-way ANOVA was performed to determine significant differences between groups of samples, as indicated S1. Sequences of gene primer pairs used for RT-qPCR. S2. Statistical analysis of the effects of WD on RSA of wild-type and ABA 2 biosynthesis (aba2) and response (snrk2.2 snrk2.3; hab1 abi1) mutants. S3. Statistical analysis of the effects of WD on root hydraulic properties of wild-8 type and ABA biosynthesis (aba2) and response (snrk2.2 snrk2.3; hab1 abi1) mutants.

Supplement Table

Supplement Table

Supplement Table


Jonathan Rupp

Benoît Corraze

Marie-Paule Besland

Laurent Cario

Julien Tranchant

Dirk Wouters

Rainer Waser

Etienne Janod

Control of stoichiometry and morphology in polycrystalline V2O3 thin films using oxygen buffers

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

Introduction:

The binary system of vanadium and oxygen consists of various Magnéli V n O 2n-1 -and Wadsley V n O 2n+1 phases [START_REF] Wriedt | The O-V (Oxygen Vanadium) System[END_REF]. Most of these phases show remarkable electronic and magnetic phase transitions [START_REF] Stefanovich | Electrical switching and Mott transition in VO 2[END_REF]. Amongst them, corundum-type V 2 O 3 undergoes an Insulator-to-Metal transition (IMT) at 155 K. This transition occurs between an antiferromagnetic (insulating) monoclinic phase at low temperature and a paramagnetic (conducting) rhombohedral corundum phase at high temperature [START_REF] Word | Spin waves in vanadium sesquioxide V 2 O 3[END_REF]. Upon decreasing temperature, the phase change is accompanied by a drop of the c/a ratio as well as an increase in volume of about 1.2 % [START_REF] Mcwhan | Metal-Insulator Transition in (V 1-x Cr x ) 2 O 3[END_REF]. At room temperature, substituting vanadium with more than 1.1 at. % chromium induces a transition from paramagnetic metal to paramagnetic Mott insulator while retaining the same corundum structure. Applying physical pressure on (V 1-x Cr x ) 2 O 3 leads to the inverse IMT and restores the metallic state. More interestingly, the Mott insulator-to-metal transition can not only be driven by pressure or temperature [START_REF] Mcwhan | Metal-Insulator Transition in (V 1-x Cr x ) 2 O 3[END_REF] but also by an electric field [START_REF] Stoliar | Universal Electric Field-Driven Resistive Transition in Narrow-Gap Mott Insulators[END_REF]. Therefore, this archetype Mott-Hubbard-insulator is of strong interest for application in resistively switching devices [START_REF] Querré | Metal-insulator transitions in (V 1-x Cr x ) 2 O 3 thin films deposited by reactive direct current magnetron co-sputtering[END_REF] and neuromorphic circuits [START_REF] Stoliar | A Leaky-Integrate-and-Fire Neuron Analog Realized with a Mott Insulator[END_REF] [START_REF] Adda | Mott insulators: A large class of materials for Leaky Integrate and Fire (LIF) artificial neuron[END_REF]. However, very accurate control of stoichiometry is required to achieve a well-defined Mott-insulating state that matches the required halffilling criteria [START_REF] Janod | Resistive Switching in Mott Insulators and Correlated Systems[END_REF]. Such a control of the vanadium-oxygen ratio is crucial in thin films on which further electrical applications will be based. For instance, deviations of stoichiometry in V 2-y O 3 as low as y = 0.03 indeed lead to an absence of the low temperature IMT [START_REF] Shivashankar | Preparation and Electrical Properties of V 2 O 3 Single Crystals of Controlled Stoichiometry[END_REF]. To reach low oxygen content compounds under thermodynamic control, reduction experiments can be performed in reducing atmospheres such as CO/CO 2 or Ar/H2 [START_REF] Harold | Transition Metal Oxides: Surface Chemistry and Catalysis[END_REF], usually at high temperatures above 1000 K. For instance, Shivashankar et al. investigated the controlled formation of non-stoichiometric V 2-y O 3 across the pure-phase window at a reduction temperature of 1473 K in CO/CO 2 atmosphere with subsequent quenching [START_REF] Shivashankar | Preparation and Electrical Properties of V 2 O 3 Single Crystals of Controlled Stoichiometry[END_REF]. A huge reduction of the vanadium point defect density (decreasing y from 0.02 down to 0.007) with a concomitant increase of transition temperature from 10 K to 155 K could be achieved by lowering the oxygen partial pressure towards the equilibrium line of VO/V 2 O 3 . An alternative method to control the oxygen partial pressure can be achieved by an oxygen buffer method [START_REF] Tilley | Principles and Applications of Chemical Defects[END_REF] that similarly imposes an oxygen partial pressure with a metal -metal oxide buffer couple (see experimental part). Here we show that reduction with an oxygen buffer can be successfully applied to control the stoichiometry of polycrystalline V 2 O 3 thin films even for low annealing temperatures such as 873 K. Four different buffer couples (BC) have been chosen to aim at four different stoichiometry values in the range of phase-pure V 2 O 3 . Based on thermochemical data [START_REF] Reed | Free Energy of Formation of Binary Compounds[END_REF], one might expect that the vanadium vacancies y in V 2-y O 3 decreases with the BC's according to y Ni NiO > y Fe-Fe3O4 > y Cr-Cr2O3 > y Mn-MnO . On the contrary, we found that for thin films, reduction annealing with the mentioned oxygen buffers does not follow the thermodynamic principle of single crystals reduced at high temperatures anymore.

Experimental:

One promising way to succeed a very precise control of oxygen point defects is to exploit the condition of thermodynamic equilibrium for metal-oxide reactions. Each dynamic equilibrium between a metal and a corresponding oxide is defined by its Gibbs free energy ∆𝐺 that consists of an enthalpy 𝛥𝐻 and entropy 𝛥𝑆 terms. In this case, referring to the Ellingham approximation, both are considered temperature-independent. The change in ∆𝐺 can then be related to the oxygen partial pressure 𝑝 O in a direct way :

∆𝐺 𝛥𝐻 𝑇𝛥𝑆 R𝑇 ln 𝑝 O (1)
where R denotes the gas constant, 𝑇 the temperature and 𝑝 O the oxygen partial pressure in thermodynamic equilibrium between the two solids. With given reaction enthalpies and entropies from literature (Table 1), the equilibrium oxygen partial pressure was straightforwardly calculated for four different oxygen buffer associations within the window of off-stoichiometric V 2 O 3 . Amorphous vanadium oxide thin films (thickness 300 nm and 100 nm) have been deposited on silica by RF-reactive sputtering from a one inch vanadium target. The oxygen partial pressure p(O 2 ) was adjusted by the flux ratio of two mass flow controllers: one with pure argon (90 sccm) and one with a mixture of argon and oxygen in the ratio 99:1 (10 sccm). This allowed control of the p(O 2 ) in a few 10 nbar range. The relatively low oxygen partial pressure value of 10 nbar was used to reach a V:O ratio close to 2:3 in the amorphous films prior to reducing annealing (where the measured average value constituted 2:4 [14] ). The used power of P = 50 W and the process pressure of p = 10 µbar resulted in a deposition rate of q = 3.3 nm/min. Thin films were subsequently placed inside silica tubes with a metal and oxide powder couple at a pressure of p < 10 -3 mbar to provide a constant V:O stoichiometry ratio independent of temperature. After sealing, the tubes were annealed in a tubular furnace at a temperature of 873 K, with a heating rate of 300 K / h, an annealing time of 1h at 873 K, and finally passive free cooling down to room temperature with a rate of ~100 K / h. Figure 1 displays the theoretical equilibrium oxygen partial pressures for the four selected buffer couple reactions between metals and oxides with respect to temperature.

Buffer couples were chosen to introduce an increasing concentration of vanadium defects as a result of an increase of oxygen partial pressure from Mn-based to Cr-/Fe-/Ni-based BCs.

Metal and oxide quantities were weighted according to the reaction equation's mole masses.

Morphology was determined by scanning electron microscopy (SEM) images with a Zeiss "DSM982 GEMINI" microscope. Lateral grain sizes were determined by the line section method. Surface vacancy area (100 nm layers) and surface crack area (300 nm layers) were determined by ImageJ 1.51d with a contrast filter. X-ray diffraction (XRD) patterns were recorded in Bragg-Brentano geometry with a Bruker X-Ray diffractometer. Lattice parameters were extracted by le Bail refinement with JANA software from X-ray diffraction (XRD) patterns. To investigate electrical transport characteristics at low temperatures in four-point configuration, a closed-cycle helium circuit cryostat "Omniplex DE210" from ARS was used.

Transition temperatures of the IMT were determined for the cooling and heating branch at the turning point of the derivative logarithmic resistance versus inverse temperature (d(lnR)/d(1/T)).

Results:

Morphology

Figure 2 shows morphological changes of V 2 O 3 thin films throughout the stoichiometry window. As-deposited amorphous 100 nm thick films already present a rough surface with relatively large particles up to 36 nm in diameter (Figure 2a1&2) whereas 300 nm thick films show a relatively dense columnar structure (Figure 2a3&4). The 100 nm thick film annealed with BC Ni/NiO exhibits a grain size of d Ni,100 = 39±14 nm with visible surface pinholes (Figure 2b1&2). The grain size is comparable to the pristine amorphous state (Figure 2a1&2).

For a higher thickness of 300 nm (Figure 2b3&4), grain size increases slightly (d Ni,300 = 44±18 nm) compared to 100 nm thick thin films and the cross section image shows a more porous bulk morphology as compared to the pristine amorphous dense columnar structure (Figure 2a3&4). For BC Fe/Fe 3 O 4 (Figure 2c1&2) and a thickness of 100 nm, grain size (d Fe,100 = 23±7 nm) as well as pinhole size decreases compared to Ni/NiO, quantitatively described by Figure 2f&g. With respect to the 100 nm films reduced by Fe/Fe 3 O 4 , an increased grain size is obtained for 300 nm (d Fe,300 = 36±15 nm) thick layers (Figure 2c3&4). In addition, a considerable part of the surface is covered with formed cracks (Figure 2c3). Layers synthesized with a BC Cr/Cr 2 O 3 (Figure 2d1&2) show a smaller average grain size (d Cr,100 = 20±8 nm) with few smaller pinholes for 100 nm layers as compared to 100 nm thick layers annealed with BC Fe/Fe 3 O 4 (Figure 2c1&2). Corresponding 300 nm thick layers (Figure 2d3&4) still form cracks to a lesser extent compared to BC Fe/Fe 3 O 4 (Figure 2c3&4) and present only a slightly higher grain size than 100 nm layers (d Cr,300 = 23±7 nm). Lastly, BC Mn/MnO (Figure 2e1&2) results in a very fine grain size of (d Mn,100 = 15±2 nm) with a considerably higher roughness compared to BC Cr/Cr 2 O 3 which is reflected by a spatial variation in contrast. For 300 nm layers (Figure 2e3&4), a flatter surface with increased grain size is visible compared to 100 nm thin films (d Mn,300 = 26±10 nm). Yet, in this case, broad hills grow on the surface (instead of cracks as found for BCs Fe/Fe 3 O 4 and Cr/Cr 2 O 3 ). To sum up, grain sizes (Figure 2f) and free volume (Figure 2g) decreases equally with the sequence of buffer couples for both thicknesses.

Crystal Structure and Lattice Parameters

All films were characterized by XRD analysis. XRD records from 100 nm thick films exhibit diffraction peaks with weak intensity, not suitable to accurately resolve lattice parameters.

Thus, cell parameters were extracted from XRD patterns obtained for 300 nm thick V 2 O 3 thin films (Figure 3a). For the V 2 O 3 thin film obtained by buffer couple Ni-NiO, black arrows denote an (unknown) formed secondary phase. Table 2 summarizes the obtained lattice parameter values and fitting parameters. In Figure 3b, the variation of unit cell parameters as function of BC type is plotted (where bulk V 2 O 3 values are indicated by horizontal lines). For all buffer couples, the c/a ratios (orange star) deviate from the bulk value except for Mn/MnO where the c/a ratio matches the ideal c/a ratio of V 2 O 3 . Furthermore, with BC Ni/NiO for offstoichiometric V 2-y O 3 , c parameter (green triangle) and cell volume (blue hexagon) are compressed by 0.05 Å and 1 Å 3 , respectively, whereas the a parameter (red square) is slightly expanded by 0.01 Å. With BC to lower p(O 2 ) (left to right in Figure 3b), c-parameter and cell volume relax to bulk values whereas the a-parameter expands even more up to the BC Cr-Cr 2 O 3 . For BC Mn/MnO, parameters a and c as well as the cell volume are reduced compared to bulk.

Electrical Transport Characteristics

With low temperature electrical transport measurements, the insulator-to-metal transition of V 2 O 3 was investigated for 300 nm thick films (Figure 4a) as well as 100 nm thick films (Figure 4b). For all buffer couple combinations, both thicknesses exhibit exactly the same trends with sharp transition behaviour as well as an increase of room temperature resistivity towards the equilibrium line of V 2 O 3 /VO, indicating a high reproducibility of the reduction process in this thickness range. The lowest transition temperatures between 90 K and 140 K were found for the two extreme BC's, namely Mn-MnO and Ni-NiO. Besides, Fe-Fe 2 O 3 and Cr-Cr 2 O 3 revealed the highest transition temperatures between 110 K and 157 K. In the case of a 300 nm thick V 2 O 3 film annealed with BC Fe-Fe 3 O 4 , the largest resistance change is observed with five to six orders of magnitude, in good agreement with the transition magnitude obtained for single crystals [START_REF] Mcwhan | Metal-Insulator Transition in (V 1-x Cr x ) 2 O 3[END_REF]. In these experiments, 300 nm thick films exhibit a slightly broader hysteresis than the 100 nm ones. While varying the nature of the BC, room temperature resistivity increases continuously by roughly one order of magnitude from 4.7•10 - 4 Ω•cm (300 nm Ni/NiO) to 3.0•10 -3 Ω•cm (300 nm Mn/MnO). To be able to identify the differences between reduction processes in the transition region in more detail, the negative differential resistance versus inverse temperature is plotted versus temperature (Figure 4c).

Interestingly, one can identify two maxima for each branch in the 300 nm thick film reduced by BC Ni+NiO (blue plot) and even three maxima for the two samples reduced by BC Fe+Fe 3 O 4 (green plot). Generally, for each thickness, one would expect only one maximum for cooling as well as heating owing the hysteresis linked to the first order transition, as found for BCs Cr+Cr 2 O 3 and Mn+MnO. Figure 4d summarizes the development of transition temperatures for used buffer couples and thicknesses. Lower thicknesses of 100 nm exhibit higher transition temperatures with an increase between 5 K and 25 K. An increasing transition temperature can be found in the case of Mn, Ni to Fe and Cr, with split transition temperatures into multiple maxima for Fe and Ni.

Discussion:

As can bee seen in the experimental section, highly stoichiometric thin films have been obtained for all oxygen buffer combinations. Clearly, by changing the Gibbs free energy of the reduction process with BCs, an (equivalently associated) decrease in vanadium deficiency does not hold for polycrystalline thin films as observed in single crystals [START_REF] Shivashankar | Preparation and Electrical Properties of V 2 O 3 Single Crystals of Controlled Stoichiometry[END_REF]. In the following sections, results are interpreted in more detail for each oxygen buffer couple individually.

Buffer Couple Ni-NiO

As determined by SEM imaging (Figure 2b), thin films obtained by BC Ni-NiO revealed the largest grain size for 100 nm thick films as well as the largest void volume among the investigated samples (Figure 2b1&2). In addition, 300 nm thick thin films preserve the same rather large grain sizes and exhibit a porous microstructure (Figure 2b3&4). XRD-patterns of 300 nm thick thin films (Figure 3a) confirm a corundum-type V 2 O 3 structure. From the phase diagram [START_REF] Wriedt | The O-V (Oxygen Vanadium) System[END_REF], one could also expect V 3 O 5 to be a stable phase during the reduction process, since only a slightly higher p(O 2 ) is needed to stabilize such phase. Apparently, a secondary phase is formed (marked by arrows) which could not be indexed by a single known vanadium oxide phase. Thermodynamically, the most stable phase in ambient atmosphere after completion of the reduction process would be VO 2 [START_REF] Andersson | Crystal structure studies on the homologous series Ti n O 2n-1 , V n O 2n-1 , Ti n-2 Cr 2 O 2n-1[END_REF] on large time scales (and oxides with comparable stoichiometry such as V 6 O 11 ). Through a deeper analysis of the XRD-pattern, slight impurity phase is found with weak diffraction peaks at 29.2 °, 47.3 ° and 48.3 ° that may correspond to (-126), ( 2010) and (-136) planes of a minor phase fraction of V 6 O 11 [START_REF] Horiuchi | Crystal structures of V n O 2n-1 (2≤n≤7)[END_REF]. Yet, additional peaks at 57.1° and 58.6° cannot be associated to this phase. In any case, a higher oxidized phase is to be expected for the given BC Ni-NiO. Both phases V 3 O 5 and V 6 O 11 belong to the family of Magnéli phases V n O 2n-1 and differ only by a change in sheared crystallographic planes [START_REF] Horiuchi | Crystal structures of V n O 2n-1 (2≤n≤7)[END_REF]. The exposure to air after reduction might lead to a surface oxidation and appearance of V 2 O 3 grains exhibiting a shell constituted of oxide phases close to VO x~2 (such as V 6 O 11 ) as already detected in the case of epitaxially grown V 2 O 3 [17][18]. Indeed, the high porosity (as observed in SEM images) can further promote surface oxidation more deeply within the "bulk" thin film with a larger surface area exposed to air. Lattice parameter values of V 2 O 3 crystallites (Figure 3b, left) show a c-parameter, c/a ratio as well as cell volume V lower than the bulk value; only the a-parameter is slightly higher than the corresponding bulk value [START_REF] Ueda | Phase diagram and some physical properties of V 2 O 3+x (0≤x≤0.080)[END_REF] (straight line). Since the c/a ratio deviates from bulk values (which should be constant if related only to the deviation in vanadium deficiency [START_REF] Ueda | Phase diagram and some physical properties of V 2 O 3+x (0≤x≤0.080)[END_REF]), one can conclude that compressive internal stress is present in the thin film. Low temperature electrical transport measurements (Figure 4a) reveal a broad transition temperature range between 100 K and 165 K for 300 nm thick films with two sharp variations (better visible in the derivative of the resistance in Figure 4c dark blue). For 100 nm thin films (Figure 4b), only a single slope maximum is present (Figure 4c light blue). A possible explanation for the two maxima could be the difference between grain boundaries and void regions in 300 nm thin films where different stress states exist between more relaxed grains in vicinity of voids and more compressed grains in denser regions. However, one may not expect two sharp maxima but rather a continuous distribution of the transition temperature region. Another explanation favoured by the authors refers to the possible formation of a V 6 O 11 phase, which has a bulk transition temperature of 177 K [START_REF] Okinaka | Electrical Properties of V 6 O 11 and V 7 O 13 Single Crystals[END_REF].

In combination with the V 2 O 3 transition temperature at 155 K [START_REF] Mcwhan | Metal-Insulator Transition in (V 1-x Cr x ) 2 O 3[END_REF], theory would predict two maxima separated by a temperature shift of 22 K where we observe a variation of 18 K and 25 K, for cooling and heating curve, respectively. Then, the shift of both transition temperatures of V 2 O 3 and V 6 O 11 could be related to a compressive stress within the film as revealed by the compressed cell volume (Figure 3b). The fact that an (almost) ideal stoichiometric V 2 O 3 phase with a quite high transition temperature can be synthesized with BC Ni-NiO (inducing a relatively high oxygen partial pressure) is rather surprising since thermodynamics would predict a highly non-stoichiometric thin film with a transition temperature close to 10 K [START_REF] Shivashankar | Preparation and Electrical Properties of V 2 O 3 Single Crystals of Controlled Stoichiometry[END_REF]. Like many other binary metal oxides, NiO is known to provide a non-stoichiometry regime that changes with temperature [START_REF] Dubey | The effect of stoichiometry on the structural, thermal and electronic properties of thermally decomposed nickel oxide[END_REF]. Therefore, this effect may shift the iso-composition line towards more reducing conditions. Apparently, the deviation towards reducing conditions occuring during the iso-compositional cooling process with BC Ni-NiO favours a nearly stoichiometric V 2 O 3 phase (in contrast to a quenching process of single crystals after the use of high reduction temperatures [START_REF] Shivashankar | Preparation and Electrical Properties of V 2 O 3 Single Crystals of Controlled Stoichiometry[END_REF]). Consequently, one could also relate the two maxima in transition slope to a change in BC conditions with a stoichiometric NiO phase at the maximum reduction temperature (belonging to the lower maximum) and a final Ni 2+ 1-3x Ni 3+ 2x O phase at room temperature (belonging to the higher maximum). However, no color change could be observed after the reduction process, i.e. from green colour of a stoichiometric NiO towards grey/black colour of a nonstoichiometric compound. Moreover, this explanation would need to rely on strongly deviating reduction conditions between the two thicknesses since no peak splitting was observed for the thinner film (100 nm thick) reduced by BC Ni/NiO.

Buffer Couple Fe-Fe 3 O 4

In contrast to BC Ni-NiO, grain sizes of thin films reduced by BC Fe+Fe 3 O 4 become smaller (Figure 2f) along with the decrease of "void" volume for 100 nm thick films in form of pin holes (Figure 2c1&2). The smaller grain size obtained at lower oxygen partial pressure is likely to be a side effect of stronger out-diffusion of oxygen from the initially amorphous film. The stronger excorporation of oxygen could favor the nucleation density during crystallization which may hinder grain growth and recrystallization in the reduction process. At the same time, for 300 nm thick films (Figure 2c3&4), no void regions are visible anymore. Instead, "free volume" is revealed by extended cracks at the surface. These cracks typically reach several hundred nanometers deep into the thin film (Figure 2c2 for a 300 nm film). Contrary to BC Ni-NiO, the 300 nm thick films do not show any XRD-resolvable secondary phases except corundum R3 c V 2 O 3 (Figure 3a). Cell parameters are similar to those obtained with BC Ni-NiO with compressed values except for a slight tensile strained as revealed by the a-parameter value (Figure 3b). However, the resistance jump observed at transition is roughly one order of magnitude higher for 300 nm thick films (five orders of magnitude instead of four orders of magnitude for BC Ni/NiO, Figure 4b) and the transition itself shows three maxima in slope (Figure 4c). A possible explanation for this slight dispersion of the transition temperature is an inhomogeneous distribution of vanadium vacancies y within grains of the V 2-y O 3 phase. This would happen if the trajectory of the p(O 2 ) -temperature imposed by the Fe-Fe 3 O 4 couple (indicated by the green line in Figure 1), does not strictly correspond to a constant y value in V 2-y O 3 . As a consequence, a gradient between the grain core and its shell would arise during the cooling part of the annealing process (see inset in Figure 1), which can be "frozen" at low temperature as soon as the kinetics of vanadium diffusion becomes too slow. Such a coreshell gradient in vanadium vacancies y could therefore easily explain the distribution of transition temperature shown in Figure 4c. Moreover, this scenario is consistent with the different transition temperatures observed in 100 nm and 300 nm thick films annealed with Fe-Fe 3 O 4 , since their strongly different grain size (23 nm for the 100 nm thick film, against 37 nm for the 300 nm thick one) could lead to a different final distribution of vanadium vacancies within each grain.

Buffer Couple Cr-Cr 2 O 3

Thin films reduced by BC Cr-Cr 2 O 3 exhibit the same trend towards smaller grain size and void & crack volume compared to BC Ni-NiO or Fe-Fe 3 O 4 (Figure 2d,f,g). As checked by XRD pattern, only pure phase corundum R3 c V 2 O 3 is detected (Figure 3a). In contrast to all other BCs, the cell volume is expanded and the c parameter only exhibits a slight compression. Thus, one expects the transition temperature to be raised which is confirmed by the highest transition temperature for 300 nm thick films (147 K in Figure 4a). In analogy, 100 nm thick films exhibit a transition temperature similar to the one obtained after reduction by Fe-Fe 3 O 4 (Figure 4b).

However, the resistivity jump at transition is reduced by over one order of magnitude.

Apparently, the quite dense nanostructure with small crystallites (average size < 20 nm) might not be sufficient to provide the required space of 1 % free volume that is necessary to enable the volume expansion of the low temperature phase transition [START_REF] Mcwhan | Metal-Insulator Transition in (V 1-x Cr x ) 2 O 3[END_REF]. Only surface-related grains might provide enough free volume close to cracks and pinholes (Figure 2g). For both thicknesses of 100 nm and 300 nm, a sharp single maximum of the transition slope is present (Figure 4c) which resembles a pure and dense corundum V 2 O 3 phase as well as a uniform distribution of stress. The very controlled conditions are likely to be a consequence of the Cr-O phase diagram where only pure Cr 2 O 3 is a thermodynamically stable phase [22] . Lacking intermediate phases thus prevents any shift of the iso-composition line.

Buffer Couple Mn-MnO

An obvious difference of 100 nm thick films reduced by BC Mn-MnO is an increased roughness (Figure 2e1) and a highly dense thin film with smallest grain diameters of ~12 nm. In contrast to the previously discussed BCs, 300 nm thick films do not exhibit any cracks or pinholes in surface. Instead, hill growth is visible at the surface. Grain sizes and "void" volume drop to the minimum for both thicknesses compared to all other BCs. XRD analysis confirm the presence of a pure V 2 O 3 phase belonging to R3 c-type (Figure 2a) where diffraction peaks are significantly broadened and fully coherent with a small grain size of 26±10 nm. Compared to stoichiometric bulk V 2 O 3 , this film displays the same c/a ratio, but a lower unit cell volume, i.e. a compressive internal stress. According to ref. [START_REF] Ueda | Phase diagram and some physical properties of V 2 O 3+x (0≤x≤0.080)[END_REF], this could indicate an "oxygen nonstoichiometry": z = 0.044 in the (erroneous) formulation V 2 3+z , or rather to vanadium deficiency y = 0.029 in the correct V 2-y O 3 description. (Figure 2b). This would lead to a transition temperature as low as 10 K and thus a metallic behavior [START_REF] Shivashankar | Preparation and Electrical Properties of V 2 O 3 Single Crystals of Controlled Stoichiometry[END_REF]. Obviously, this scenario is not coherent with the observed transition temperature above 100 K and the resistivity jump at transition of three to four orders of magnitude, respectively (Figure 4a&b).

Another possible explanation could be the extreme reducing conditions imposed by the Mn-MnO buffer couple leading to oxygen vacancies and an effective composition V 2 O 3+x (x > 0). As for the case of well-established vanadium vacancies in V 2-y O 3 , such oxygen vacancies would lead to the reduction of the unit cell volume, without changing the c/a ratio, as we observed experimentally.

On the Effect of Buffer Couples

The discussion above shows that thermodynamic principles of high temperature reduction of bulk samples cannot easily be transferred to thin films with relatively low reduction temperatures. For instance, the calculated oxygen partial pressures along the cooling path are below any countable static oxygen partial pressures. Apart from the four studied buffer couples, another oxide-oxide combination Ce 2 O 3 -CeO 2 (where the equilibrium line of oxygen partial pressure lies between BCs Fe and Cr) resulted in comparable electrical transport properties (transition temperature of 100 K and resistance jump at transition of five orders of magnitude, not shown) even though unknown CeO x phases could be detected in the oxygen buffer after the annealing process. These results raise the need of further theoretical investigations for these technologically relevant synthesis conditions, especially due to the astonishing broad success of the method.

Conclusion

Polycrystalline diagram [21] (compare Table 1). Dashed line describes maximum reduction temperature used in this work. Inset: Sketch of the annealing procedure.

Compliance with ethical standards

Table 1: Quantity of metal and oxide powder used for annealing of layers with the four BC combinations. Enthalpy ΔH and Entropy ΔS extracted from Reed et al. [13] .

Reaction Equation Metal Mass

[mg]

Oxide Mass

[mg] ΔH [kJ/mole] [13] ΔS [J/K/mole] [13] 2 𝑁𝑖 𝑂 ↔ All thin films exhibit a corundum R3 c structure corresponding to V 2 O 3 lattice planes [23] c-parameter (green), a-parameter (red), cell volume V (blue), c/a ratio (orange). Horizontal lines correspond to bulk values [4] .

Figure 1 :

 1 Figure 1: Equilibrium oxygen partial pressures p(O 2 ) associated to of the different oxygen

Figure 2

 2 Figure 2 (a): SEM images (top view and cross section) for V 2 O 3 thin films on silica substrates

Figure 3

 3 Figure 3 (a): X-ray diffraction patterns in Bragg-Brentano geometry for 300 nm thick V 2 O 3 films.

  (vertical dashed lines) with an unknown secondary phase indicated by black arrows. (b) Unit cell parameters of 300 nm thick V 2 O 3 films after annealing process with different buffer couples:

Figure 4

 4 Figure 4 (a)&(b): Low temperature electrical transport characteristics of annealed V 2 O 3 thin

  V 2 O 3 thin films (thickness 300 nm and 100 nm) have been synthesized under controlled thermodynamic conditions at low temperatures and strongly deviate from high temperature reduction experiments on single crystals. Changing the Gibbs free energy by different buffer couples affected morphological features but resulted in comparable electrical properties. Oxygen buffers close to the equilibrium line of VO/V 2 O 3 (Mn-MnO) andV 2 O 3 /V 3 O 5Finally, the Fe-Fe 3 O 4 and Cr-Cr 2 O 3 oxygen buffers led to the strongest changes in resistance at the IMT's up to five orders of magnitude and highest transition temperatures close to the one of stoichiometric V 2 O 3 . The Cr-Cr 2 O 3 buffer couple is particularly appealing since it leads to very homogeneous V 2 O 3 films with abrupt insulator to metal transitions. 100 nm thick films exhibited identical trends with slightly reduced hysteresis width, higher transition temperature and a smaller change of resistance at the transition. These results may have a strong impact on design rules for the miniaturization of resistive Mott-switching devices towards their physical limits. been perfomed at the Insitute des Matériaux (IMN Nantes/FR). Furthermore, J. A. J. Rupp greatly acknowledges the Deutsche Forschungsgemeinschaft DFG for funding this project in the Sonderforschungsbereich (SFB) 917.

(Ni-NiO) induced a possible oxygen deficiency and secondary phase precipitation, respectively. By lowering of the Gibbs free energy with different oxygen buffers, grain sizes and void regions shrink which is explained by a stronger removal of oxygen during the reduction process.

Table 2 :

 2 Le Bail fitting parameters for 300 nm thick films with buffer couple type BC, reliability factors R p , weighted reliability factors wR p , goodness of fit GOF, cell parameters a and c, cell parameter ratio c/a and cell volume V.

	BC	R p [%] wR p	GOF	a [Å]	c [Å]	c/a [Å] V [ų]
	[nm]		[%]
	Ni+NiO	4.93	6.66	1.18	4.9511 13.9570 2.8190 296.3
	Fe+Fe 3 O 4 4.96	6.63	1.20	4.9515 13.9587 2.8191 296.4
	Cr+Cr 2 O 3 4.54	5.97	1.03	4.9539 13.9865 2.8233 297.3
	Mn+MnO 4.70	6.14	1.03	4.9450 13.9828 2.8277 296.1

Acknowledgements

J. A. J. Rupp would like to thank M. Querré and T. Hennen for fruitful discussions. Low temperature electrical transport measurements as well as X-ray diffraction experiments have

Conflict of Interest

The authors declare no conflict of interests.