Jérome Ngao
email: jerome.ngao@inrae.fr

Sébastien Martinez

André Marquier

Sylvie Bluy

Brigitte Saint-Joanis

Evelyne Costes

Benoit Pallas

Jérôme Ngao

Sébastien Martinez

Brigitte Saint- Joanis

Benoît Pallas

Spatial variability in carbon and nitrogen related traits in apple trees: the effects of the light environment and crop load

Keywords: Light Harvesting, Leaf Photosynthesis, Light Microclimate, Nonstructural Carbon, Source-Sink Relationships, Spatial Variability

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

INTRODUCTION

Within-plant microclimate gradients, such as those due to incoming light, air temperature, humidity, and wind, locally affect organ function and structure. Leaves respond to multiple constraints in various ways; these responses were gathered into a framework built over a large range of species, the so-called "leaf economics spectrum" [START_REF] Wright | The worldwide leaf economics spectrum[END_REF]Niinements et al., 2015). Leaves acclimate to changing light throughout plant development.

Light acclimation has been intensively studied for decades, as incoming light is one of most important resources for leaf net carbon (C) assimilation (A net ) and energy balance. In trees, numerous studies have reported decreasing A net from the upper to lower layers of forest ecosystems. The authors have linked these photosynthetic profiles to available light and traits involved in light harvesting and photosynthetic capacities, such as nitrogen (N) content per unit area [START_REF] Hollinger | Optimality and nitrogen allocation in a tree canopy[END_REF][START_REF] Makela | Optimal co-allocation of carbon and nitrogen in a forest stand at steady state[END_REF]Mc Murtrie and Dewar, 2011;[START_REF] Niinemets | Within-canopy variation in the rate of development of photosynthetic capacity is proportional to integrated quantum flux density in temperate deciduous trees[END_REF][START_REF] Thornley | Acclimation of photosynthesis to light and canopy nitrogen distribution: an interpretation[END_REF]. These relationships have led to "the optimization hypothesis".

Following this hypothesis, the C and N economy is oriented towards investment of leaf N and leaf biomass for maximum light interception and C return on protein invested [START_REF] Mooney | Environmental and Evolutionary Constraints on the Photosynthetic Characteristics of Higher Plants[END_REF][START_REF] Bloom | Wild and cultivated barleys show similar affinities for mineral nitrogen[END_REF]. This optimization has also been considered in models that account for within-tree N distribution and leaf gas exchanges that depend on incoming radiation at the individual scale (e.g., [START_REF] Roux | Spatial distribution of leaf water-use efficiency and carbon isotope discrimination within an isolated tree crown[END_REF][START_REF] Prieto | A leaf gas exchange model that accounts for intra-canopy variability by considering leaf nitrogen content and local acclimation to radiation in grapevine (Vitis vinifera L.)[END_REF][START_REF] Buckley | What does optimization theory actually predict about crown profiles of photosynthetic capacity when models incorporate greater realism?[END_REF] and in ecosystem models at a larger scale [START_REF] Davi | Modelling carbon and water cycles in a beech forest Part II.: Validation of the main processes from organ to stand scale[END_REF][START_REF] Franklin | Optimal nitrogen allocation controls tree responses to elevated CO2[END_REF]. However, within that framework, both the leaf biochemical parameters driving variations in A net and stomatal conductance are assumed to respond to N allocation and abiotic factors only. Therefore, the influence of endogenous factors such as source:sink relationships on the acclimation of leaves to light gradients has been much less investigated, even if they appear to impact many C-or N-related processes at the plant scale [START_REF] Quilot | Leaf light-saturated photosynthesis for wild and cultivated peach genotypes and their hybrids: A simple mathematical modelling analysis[END_REF][START_REF] Urban | Effect of fruit load and girdling on leaf photosynthesis in Mangifera indica L[END_REF][START_REF] Poirier-Pocovi | Modelling temporal variation of parameters used in two photosynthesis models: influence of fruit load and girdling on leaf photosynthesis in fruitbearing branches of apple[END_REF].

The lack of optimal distribution of A net and its associated traits within trees has been noted in some studies, and nonoptimal distribution is explained by unidentified constraints that could involve source:sink relationships [START_REF] Niinemets | Optimization of foliage photosynthetic capacity in tree canopies: towards identifying missing constraints[END_REF][START_REF] Buckley | What does optimization theory actually predict about crown profiles of photosynthetic capacity when models incorporate greater realism?[END_REF]Hirosaka, 2014). There is a growing body of compelling evidence suggesting that, at the tree scale, leaf C function is strongly sink-driven. This phenomenon is usually observed through the downward regulation of A net when carbon demand is low [START_REF] Sheen | Feedback-control of gene-expression[END_REF][START_REF] Paul | Sink regulation of photosynthesis[END_REF][START_REF] Quentin | Down-regulation of photosynthesis following girdling, but contrasting effects on fruit set and retention, in two sweet cherry cultivars[END_REF][START_REF] Pallas | Growth and carbon balance are differently regulated by tree and shoot fruiting contexts: an integrative study on apple genotypes with contrasted bearing patterns[END_REF]. This decrease in A net is associated with a change in nonstructural carbohydrate (NSC, mostly starch and soluble sugars) turnover, A c c e p t e d M a n u s c r i p t 4 which leads to a global increase in NSC in leaves when the C demand of reproductive organs is low or on girdled branches [START_REF] Nebauer | Photosynthesis down-regulation precedes carbohydrate accumulation under sink limitation in Citrus[END_REF][START_REF] Poirier-Pocovi | Modelling temporal variation of parameters used in two photosynthesis models: influence of fruit load and girdling on leaf photosynthesis in fruitbearing branches of apple[END_REF][START_REF] Urban | Effect of fruit load and girdling on leaf photosynthesis in Mangifera indica L[END_REF][START_REF] Franklin | Optimal nitrogen allocation controls tree responses to elevated CO2[END_REF]. This adjustment of photosynthetic capacity to carbon demand and storage capacity can override the direct short-term control of photosynthesis by light and CO 2 [START_REF] Paul | Sink regulation of photosynthesis[END_REF].

Fruit trees are of major interest for studying the impact of source-sink relationships on carbon metabolism because they are naturally prone to biennial bearing, which leads to contrasting intensities of competition for C between organs, which depends on the year [START_REF] Monselise | Alternate bearing in fruit trees[END_REF]. Moreover, in fruit trees, the local effect of fruit on the A net of nearby leaves has also been noted (e.g., [START_REF] Bairam | Fruit and Leaf Response to Different Source-Sink Ratios in Apple, at the Scale of the Fruit-Bearing Branch[END_REF][START_REF] Gucci | The effect of defruiting at different stages of fruit-development on leaf photosynthesis of golden-delicious apple[END_REF][START_REF] Palmer | Effect of part-tree flower thinning on fruiting, vegetative growth and leaf photosynthesis in cox orange pippin apple[END_REF][START_REF] Saa | Fruit presence negatively affects photosynthesis by reducing leaf nitrogen in almond[END_REF][START_REF] Syvertsen | Fruit load and canopy shading affect leaf characteristics and net gas exchange of 'Spring' navel orange trees[END_REF], even though a tree-scale effect of fruit presence has also been shown [START_REF] Palmer | Effect of part-tree flower thinning on fruiting, vegetative growth and leaf photosynthesis in cox orange pippin apple[END_REF][START_REF] Walcroft | Does variability in shoot carbon assimilation within the tree crown explain variability in peach fruit growth?[END_REF][START_REF] Pallas | Growth and carbon balance are differently regulated by tree and shoot fruiting contexts: an integrative study on apple genotypes with contrasted bearing patterns[END_REF][START_REF] Belhassine | Impact of Within-Tree Organ Distances on Floral Induction and Fruit Growth in Apple Tree: Implication of Carbohydrate and Gibberellin Organ Contents[END_REF]. It is thus still unclear at which spatial scale the downregulation of leaf A net by NSC contents is exerted: the tree scale (via the crop load of the whole tree) or at the local (shoot) scale (through local fruit).

Photosynthetic-associated variables also interact with crop load and C demand at different scales of tree organization [START_REF] Gucci | The effect of defruiting at different stages of fruit-development on leaf photosynthesis of golden-delicious apple[END_REF][START_REF] Urban | Effect of fruit load and girdling on leaf photosynthesis in Mangifera indica L[END_REF][START_REF] Palmer | Effect of part-tree flower thinning on fruiting, vegetative growth and leaf photosynthesis in cox orange pippin apple[END_REF][START_REF] Saa | Fruit presence negatively affects photosynthesis by reducing leaf nitrogen in almond[END_REF]. In that respect, leaf N increases with crop load [START_REF] Urban | Effect of fruit load and girdling on leaf photosynthesis in Mangifera indica L[END_REF][START_REF] Stander | Fruit-load-induced starch accumulation causes leaf chlorosis in "off" 'Nadorcott' mandarin trees[END_REF], presumably because the amount of N absorbed by roots increases [START_REF] Ding | Effects of crop load on distribution and utilization of 13C and 15N and fruit quality for dwarf apple trees[END_REF]. In some cases, competition for N allocation between a growing shoot that bears fruit and a nearby vegetative shoot may decrease A net in the nearby leaves by reducing their N content [START_REF] Saa | Fruit presence negatively affects photosynthesis by reducing leaf nitrogen in almond[END_REF] on almond trees). The light gradient within a single tree is another cause of major variation in leaf N. The latter can be expressed through either the bulk N concentration (per dry mass basis, Nm) or variations in leaf mass per area (LMA, if leaf N is expressed per unit area, Na), with LMA being the ratio between the leaf dry weight (LDW) and the leaf surface area (La). As LMA is also positively correlated with light exposure [START_REF] Poorter | A metaanalysis of plant responses to light intensity for 70 traits ranging from molecules to whole plant performance[END_REF], it is thus considered the main driver for increasing A net among and within species [START_REF] Niinemets | Research review. Components of leaf dry mass per area -thickness and density -alter leaf photosynthetic capacity in reverse directions in woody plants[END_REF]. The influence of LMA is considered greater than leaf N content and is related to seasonal changes in functional and structural A net -related traits [START_REF] Montpied | Seasonal time-course of gradients of photosynthetic capacity and mesophyll conductance to CO(2) across a beech (Fagus sylvatica L.) canopy[END_REF]. However, little is known about LMA variation as a function of crop load. LMA is reduced for fruiting orange trees compared with 50% defruited trees and for leaves of fruiting shoots compared with those of nonfruiting ones [START_REF] Syvertsen | Fruit load and canopy shading affect leaf characteristics and net gas exchange of 'Spring' navel orange trees[END_REF]. This study aims to determine how the spatial variability resulting from local acclimation to intercepted light could be modulated by source-sink relationships. More precisely, we studied "Golden Delicious" apple trees with either high or low crop loads. For these trees, we concomitantly assessed the impacts of intercepted light and crop load on within-tree spatial variability in (i) leaf photosynthesis, (ii) leaf structural traits (LMA, leaf weight), (iii) Nrelated traits (Na, Nm and chlorophyll concentration), and (iv) NSC contents. Furthermore, we analyzed fruiting and nonfruiting shoots to clarify the scale (shoot or tree) at which the source:sink relationships regulate leaf trait acclimation to a light gradient.

MATERIALS AND METHODS

Study site and meteorological conditions

This study was conducted at the SudExpé experimental orchard in Marsillargues, France (43"66′N 4"18′E). The orchard was planted in 1998 with the "Tentation" cultivar grafted on "Pajam2" rootstock, which was then top grafted with "Golden Delicious" in 2005. The experiment was performed on Solaxe trained trees (Lauri and Lespinasse, 1998). The trees were pruned and thinned according to commercial practices until the beginning of the experiment. In both years of the study (2016 and 2017), all the flowers were removed two weeks after full bloom on some of the trees ("OFF" trees), while the others were not subjected to any thinning ("ON" trees).

Light microclimate monitoring, photosynthesis measurements and sampling of plant material were performed during early July 2016, late July 2016, mid-August 2016 and late July 2017 (Table 1). Climatic variables were recorded in the vicinity of the trees by a weather station located at a height of 2.5 m. Climatic conditions were similar in the four periods, with a warm and dry climate. The mean daily temperature and relative humidity were 24.3 °C and 57.7%, respectively, with mean daily maximum and minimum temperatures of 31.5 °C and 17.5 °C and mean daily maximum and minimum relative humidities of 86.1% and 32.9%, respectively (Supplementary material Table S1). The daily photosynthetically active radiation (PAR) intensity slightly differed between periods and ranged from 43.3 to 53.7 mol m -2 day -1 , likely due to variations in photoperiod (Table 1).

Experimental setup

In this experiment, a total of 10 trees (5 ON and OFF trees) were studied. More specifically, during each period, two trees in ON conditions were considered. Only one OFF tree was considered in all periods except the fourth period, for which two trees were used (Supplementary Material Table S2). For ON trees, in 2016, three trees were followed throughout the summer (periods 1, 2 and 3). In 2017 (period 4), two other trees were sampled. These trees differed from those used in 2016 because ON trees in 2016 became OFF trees in 2017 due to biennial bearing. The crop load of each tree was estimated as the ratio of the fruit number to the trunk cross sectional area estimated in autumn. The ON trees displayed high crop loads (14.2 and 18.0 fruits cm -2 in 2016 and 2017, respectively, Supplementary Material Table S2). Conversely, OFF trees had a crop load of 0.

All studied trees were equipped with autoleveling devices for measuring locally transmitted PAR (PAR T ). In each period, 18 and 12 PAR devices were distributed within the crowns of ON and OFF trees, respectively. In total, 120 microclimate conditions were recorded during the experiment. For the ON trees, six shoots were chosen in sunlight (outer crown), six other shoots were located in the middle crown, and the final six shoots were located in shade (inner crown). For these trees, sensors were placed close to fruiting (three sensors per light condition) and nonfruiting shoots (three sensors per light condition). For the OFF trees, the same design was used for contrasting light conditions but with only four shoots per light condition. On all the trees, the devices were placed close to short (spurs, length <5 cm) and medium shoots (elongated shoots, length >5 cm).

The PAR sensors (PAR/CBE 80, Solems, Palaiseau, France) were mounted in aluminum bodies housing batteries and an electronic card dedicated to data storage and wireless communication. These homemade devices were placed on a gyroscopic mount fixed to an aluminum mast inserted into the soil. This setup enabled horizontal autoleveling for correct radiation measurements at any location within the crown. The sensors measured local PAR T every minute and stored 15-minute averages in the internal memory. Prior to each vegetation season, all sensors were calibrated against a Licor 190R Quantum Sensor for 24 hours for one-minute time steps (R 2 > 0.99, data not shown). The PAR sensors were placed less than 2 cm from the leafy shoots.

Leaf gas exchanges and chlorophyll measurements

At the end of each period, just after removing the PAR sensors, the leaf with the largest surface area on each monitored shoot was chosen for gas exchange measurements (n = 120).

Measurements were performed with a Licor 6400 system (Licor, Lincoln, USA) for two to three consecutive days in each period. Measurements were performed under nonlimiting climatic conditions in a measurement chamber (PAR = 1800 µmol m -2 s -1 ; leaf temperature (T leaf ) = 30 °C; vapor pressure deficit = 2 kPa; air CO 2 concentration= 390 ppmv; [START_REF] Massonnet | Stomatal Regulation of Photosynthesis in Apple Leaves: Evidence for Different Water-use Strategies between Two Cultivars[END_REF]). After 5-10 min of stabilization, the net CO 2 assimilation (A net ) was recorded during measurement sessions lasting from 7:00 AM to 12:00 AM (GMT+2). After this period, the air temperature was too high to maintain optimal conditions in the cuvette.

Leaf sampling and biochemical analyses

The shoots for which leaf gas exchange was measured were sampled. We measured the length (L) and width (W) of the leaf on which gas exchange measurements were performed.

Its area (A) was then estimated using an allometric relationship built on the trees used in this study (A= 0.73 × L × W, R²=0.92, n=320). A proxy for chlorophyll content was measured by a SPAD-502 chlorophyll meter (Konica-Minolta, Tokyo, Japan). Then, these leaves were frozen in liquid N and freeze-dried, dry-weighed and finally ground prior to biochemical analyses. The main sugar and starch contents were determined after ethanol extraction by high-performance liquid chromatography (HPLC) and spectrophotometry after enzymatic digestion, respectively [START_REF] Charrier | The timing of leaf fall affects cold acclimation by interactions with air temperature through water and carbohydrate contents[END_REF][START_REF] Quentin | Non-structural carbohydrates in woody plants compared among laboratories[END_REF]. Concentrations of NSC were computed from daily calibration curves and expressed as a % of the dry matter.

The total N concentration (in % of dry matter) was assessed using a CHN analyzer (EA/NA 1110, Thermoquest). In total, 120 leaves were analyzed for NSC and N contents.

The lengths of a subset of shoots (n = 86) were also measured for ON and OFF trees.

Shoot leaf number was estimated from shoot length assuming a linear relationship (shoot leaf number = 0.42 × shoot length + 4.51, R²=0.65, n = 108).

Data processing and analyses

The LMA was computed from the LDW and La. Leaf N content per area unit (Na) was obtained by multiplying the LMA by the N concentration (Nm). SPAD readings were converted into chlorophyll content per area unit (Chl) using a consensus equation published by [START_REF] Cerovic | A new optical leaf-clip meter for simultaneous non-destructive assessment of leaf chlorophyll and epidermal flavonoids[END_REF], and the chlorophyll proportion per Na (Chl:Na) was computed. Mean daily PAR T and incident PAR (PAR i ) were calculated as the average values over the last 15 days before photosynthesis measurements and sampling. Leaves were separated into three classes depending on the actual amount of intercepted radiation. In each period, the ten leaves with the highest PAR T were assigned to the high-light group (H), the ten leaves with the lowest values were assigned to the low-light group (L), and the other ten leaves were assigned to the medium-light group (M).

Statistical analyses were performed with R software (R Core Team, 2017). Three-way ANOVA considering light conditions (high, medium, low), crop status (ON, OFF), periods of measurements (accounting for both possible temporal and tree effects) and an interaction between light conditions and bearing status were performed for the A net , Na, Chl, Chl:Na, and NSC contents. These analyses were followed by Tukey-HSD tests for pairwise comparison considering all the crop status-light combinations. Two-way ANOVA was used to analyze the consistency of light condition and crop load effects among periods by considering each period separately. The impact of local fruit on these variables was analyzed by comparing leaves belonging to fruiting and nonfruiting shoots on ON trees by two-way ANOVA considering shoot type and period effects. To estimate the effect on individual trees for each crop status, two-way ANOVAs considering tree and light conditions were performed on each date. The effect of the type of shoots (spur or elongated shoots) was tested, and no major significant differences were detected (data not shown).

Correlation analyses were conducted to assess the relationships between A net , Na and NSC concentration, between the subvariables involved in Na variation (LMA, LDW, Nm, La) and between all NSC forms. These correlation analyses were performed considering the whole dataset or ON and OFF trees separately.

Structural equation modeling (path analysis, Shipley 2016) was performed to analyze

the relationships between NSC forms and A net . Previous studies (e.g., [START_REF] Tisné | Combined Genetic and Modeling Approaches Reveal That Epidermal Cell Area and Number in Leaves Are Controlled by Leaf and Plant Developmental Processes in Arabidopsis[END_REF][START_REF] Shipley | The AIC model selection method applied to path analytic models compared using a d-separation test[END_REF] have sought the best models in terms of performance and parsimony, testing different sets of variables and structures. In our study, we chose to fit the same model structure employing the same variables to demonstrate the effects of crop status on the coefficients. This approach considers covariations among variables for computing these coefficients, in contrast to usual correlation matrix approaches. We used a model assuming (i) causal relationships between A net and each of the reserve and transported NSCs, i.e., starch, sorbitol and sucrose, and (ii) causal relationships between each of the reserve and transported NSCs and hexoses (i.e., mainly glucose and fructose), and (iii) free correlations (covariations) between starch, sorbitol and sucrose and between fructose and glucose. This analysis was performed with the Lavaan package of R.

RESULTS

Light variation with treatments and testing period

In comparison to its value under high-light conditions, the average daily PAR T was reduced by approximately one-third and two-thirds in medium-and low-light conditions, respectively, regardless of the testing period (Table 1). In 2016, the highest PAR T values were observed in periods 1 and 2, while they were slightly lower in period 3, likely due to the shorter photoperiod. In 2016, PAR T in high-light conditions represented more than 60% of the PARi, while it represented between 15 and 30% in low light conditions. In 2017 (period 4), PAR T values were lower than those in 2016 for all light conditions. PAR T represented 32% and 13% of the incoming PAR in high-and low-light conditions, respectively. This reduction in the proportion of PAR T compared with that of the periods in 2016 was likely associated with (1) a lack of pruning in winter 2016-2017, thus leading to greater self-shading within the canopy and (2) a deeper location of the sensors in the canopy in 2017. Finally, no major difference in PAR T was observed between the two crop statuses (ON and OFF trees). Only a slight but significant difference (P=0.032) was observed under high-light conditions due to the higher PAR T for OFF trees.

Effect of crop status and light on carbon-and nitrogen-related variables

A net was strongly affected by the crop status, with greater values for ON trees than for OFF trees regardless of the local light conditions (Fig. 1A, mean values = 13.2 and 7.6 µmol m -2 s - 1 for ON and OFF trees, respectively). The impact of light was lower but still significant. These differences were associated with a significant decrease in A net for low-light conditions.

The effect of light was significant for ON trees only. Nevertheless, the interaction between crop status and light conditions was statistically insignificant, meaning that this general trend of A net variation with light intensity was similar regardless of the crop status. A significant period effect was observed, but the effect of the crop status and light condition remained similar if each measurement period was considered separately (Supplementary Fig. S1). No significant individual tree effect on A net was observed in any period (Supplementary Fig. S1).

A c c e p t e d M a n u s c r i p t 10 Moreover, A net was similar for fruiting and nonfruiting shoots of ON trees (Fig. 1B), showing the absence of any effect of local fruit.

Na was significantly lower in OFF trees than ON trees (Fig. 2). This difference was quite small (1.79 and 1.59 g m -2 for ON and OFF trees) and was significant in period 1, but only if the analysis was performed for each period separately (Supplementary Fig. S2). Light also had a significant effect on Na. This effect was associated with lower values in ON trees under low light (Fig. 2). If the four periods were considered separately, these significantly lower values were observed in periods 1 and 2 (Supplementary Fig. S2). Conversely, the decreased Na under low-light conditions was not observed for OFF trees, leading to a significant crop status × light effect. For ON trees, local fruit had no effect on Na, consistent with the results for A net (Fig. 2A). Furthermore, as for A net , no significant individual tree effect on Na was observed regardless of the period (Supplementary Fig. S2).

Chlorophyll contents (Chl) were higher for ON trees than for OFF trees (0.55 vs 0.36 g m -2 , Fig. 3A) regardless of the light. These higher values resulted from higher Na values but also from a significantly higher proportion of Chl per Na (Chl:Na) for ON trees (26.3 and 23.3% for ON and OFF trees, respectively, P<0.01, Fig. 3B). The effect of crop status on Chl was significant in all periods, while crop status affected Chl:Na in period 4 only (Supplementary Figs. 3 and4). This increase in Chl:Na for ON trees was significant under only low light. A slight but significant effect of light was also observed for Chl and Chl:Na. Specifically, Chl had greater values under medium light than under low light, while Chl:Na had higher values under low light in ON trees only. The effects of light were observed in periods 1 and 3 for Chl and Chl:Na, respectively. Once again, the individual tree effect remained low and was significant for Chl in ON trees during period 1 only (Supplementary Figs. S3 andS4).

The crop status significantly affected starch, sorbitol and sucrose concentrations but in different ways (Fig. 4). Indeed, starch and sorbitol concentrations increased in OFF trees compared with ON trees, while sucrose concentrations slightly decreased. Moreover, the impact of crop status was greater on starch (+78% for OFF trees) than sorbitol (+19%). These effects of crop status on starch, sorbitol and sucrose concentrations were observed in almost all periods if considered separately (Supplementary Figs. S5, S6 and S7). The impact of light on NSC concentrations appeared lower. Light did not modify sorbitol concentration and slightly but significantly affected starch and sucrose concentrations, with a decrease under low light. These effects of light were found for almost all the measurement periods. Finally, the interaction between crop status and light was not significant for these three NSC forms. The effect of light was observed in some periods only (Supplementary Figs. S5, S6, and S7).

Again, individual effects were not significant for these NSC forms. Regarding glucose and fructose concentrations, no significant crop status, light or interaction effects were observed (Supplementary Fig. S8). For A net and Na, NSC concentrations were similar between fruiting and nonfruiting shoots of ON trees (Supplementary Fig. S9).

Analysis of relationships between photosynthesis, light harvesting traits and NSC contents

When the datasets from both crop statuses were considered together, a negative correlation between A net and starch was observed (Fig. 5A). Nevertheless, this relationship was not significant for OFF trees. In contrast, the relationship was significant and positive for ON trees. Na and A net were positively but slightly correlated when datasets for both crop statuses were considered together and for ON trees. This relationship was not significant when OFF trees were considered separately (Fig. 5B).

Crop status affected all the variables explaining variations in Na (LDW, LMA, Nm and La) (Fig. 6) but had an opposite effect on Na. Indeed, slightly lower La (which increased LMA and Na) and LDW (which decreased LMA and Na) values were observed for ON trees.

Nevertheless, the crop status had a smaller effect on La (-14%) than on LDW (-32%), resulting in lower LMA for ON trees than for OFF trees (Fig. 6B, 93.5 and 81.1 g cm -2 for OFF and ON trees, respectively). Similarly, lower LMA (decreasing Na) and higher Nm (increasing Na) were observed for ON trees than for OFF trees. Crop status had a smaller effect on LMA (-17%) than on Nm (+30%), consistent with a slightly higher Na for ON trees (Fig. 2). The crop status also affected the mean number of leaves per shoot, with greater values for OFF trees than for ON trees (8.2 vs 5.7 leaves, data not shown).

Regarding correlations with PAR T , large variability was observed, but it depended on the variables and the crop status (Fig. 6). If data from both crop statuses were considered together, PAR T was not significantly correlated with La or Nm concentration but was significantly positively correlated with LMA and LDW. Moreover, PAR T was significantly correlated with LDW, LMA and Na concentration for ON trees, while a small significant correlation was found with LMA for only OFF trees.

Relationships between NSC forms and A net strongly depended on the crop status (ON vs OFF trees, Fig. 7). First, A net was strongly positively associated with sucrose and starch concentrations in ON trees, whereas the path coefficients related to A net were only slightly significant (P=0.036) with sucrose in OFF trees. In ON trees, the starch concentration covaried with sucrose and sorbitol, but this result was not observed in OFF trees. Conversely, for OFF trees, sorbitol and sucrose covaried significantly. For ON trees, the impact of sucrose concentration on hexoses was quite low, and sorbitol and starch concentrations had no impact. For OFF trees, sorbitol, sucrose and starch concentration influenced (P<0.001) the hexose concentrations. The correlations were positive between sorbitol, starch and hexoses and negative between sucrose and hexoses. Finally, for both crop statuses, glucose and fructose concentrations covaried. Correlation analyses (Table 2) confirmed most of the relationships observed in the path analysis. Nevertheless, for ON trees, the relationships between starch and the other NSCs (sucrose, starch) observed in the path analysis were not observed in the correlation analysis. Similarly, for OFF trees, the relationships between sucrose and glucose and between sorbitol and fructose highlighted by the path analysis were no longer observed in the correlation matrix. This phenomenon likely resulted from the structure of the path analyses, which accounted for partial correlations between the NSC forms.

DISCUSSION

A net is not determined by the local fruit on highly fruited trees

Previous results for apple trees have shown that fruit proximity can affect photosynthesis on branches subjected to different girdling practices [START_REF] Poirier-Pocovi | Modelling temporal variation of parameters used in two photosynthesis models: influence of fruit load and girdling on leaf photosynthesis in fruitbearing branches of apple[END_REF]. In mango, [START_REF] Urban | A biochemical model of photosynthesis for mango leaves: evidence for the effect of fruit on photosynthetic capacity of nearby leaves[END_REF] also observed an effect of fruit presence on nearby leaf photosynthesis due to changes in Na. In our study, local fruit presence had no effect regardless of the measured variables, consistent with results other studies [START_REF] Belhassine | Impact of Within-Tree Organ Distances on Floral Induction and Fruit Growth in Apple Tree: Implication of Carbohydrate and Gibberellin Organ Contents[END_REF]. Such a discrepancy is likely associated with the very high crop loads under our conditions (more than 10 fruit cm -2 ) compared with those under usual orchard management (Wünsche et al. 2000). Under high crop load, maximal investment in C assimilation and rapid export of photoassimilates from all leaves are required to sustain fruit growth at the tree scale, thus explaining the lack of differences between leaves. Thus, our results suggest a sink strength above which the global C demand requires maximizing A net at the canopy scale. This maximization can be achieved by optimizing both light capture and C assimilation, and by modifying C allocation as observed in this study and further discussed.

Effect of crop load status on photosynthesis optimization by acclimation of leaf Nrelated variables within trees

Different leaf traits are key variables for describing leaf C function and acclimation to light gradients across a various range of plant species and are part of the so-called leaf economics spectrum [START_REF] Wright | The worldwide leaf economics spectrum[END_REF]Niinements et al., 2015[START_REF] Onoda | Physiological and structural tradeoffs underlying the leaf economics spectrum[END_REF]. Nevertheless, the combined effects of crop load and light were not investigated in previous studies. Our study thus challenges the general applicability of that framework for systems with two contrasting source-sink relationships.

Several studies reported enhanced A net in ON trees compared with OFF trees (as shown by [START_REF] Wunsche | Effects of crop load on fruiting and gas-exchange characteristics of 'Braeburn'/M.26 apple trees at full canopy[END_REF]on apple, Vaast et al. 2005on coffee, and Wu et al. 2008 on peach). Enhancing A net implies that leaves need more energy for both photochemical and biochemical processes of photosynthesis. At the leaf level, enhancing light harvesting and use can be achieved by increasing light absorption efficiency through increasing the content of light-absorbing molecules such as chlorophyll. Among the covariables that could explain the increase in A net depending on the crop status, Na values were higher in ON trees than OFF trees. The apparent effect of the crop status (ON vs OFF trees) on Na might be attributed to variations in Nm. Lower Nm values have been reported for trees with low crop loads than for trees with high crop loads [START_REF] Stander | Fruit-load-induced starch accumulation causes leaf chlorosis in "off" 'Nadorcott' mandarin trees[END_REF] for mandarin; [START_REF] Syvertsen | Fruit load and canopy shading affect leaf characteristics and net gas exchange of 'Spring' navel orange trees[END_REF] for orange; and [START_REF] Urban | Effect of fruit load and girdling on leaf photosynthesis in Mangifera indica L[END_REF] for mango). If we consider ON trees only, our results are in agreement with those of these previous studies and consistent with the optimization hypothesis [START_REF] Hollinger | Optimality and nitrogen allocation in a tree canopy[END_REF], Thornley, 1998[START_REF] Thornley | Acclimation of photosynthesis to light and canopy nitrogen distribution: an interpretation[END_REF]). Nevertheless, one original aspect of our study is that such an impact of light was poorly observed for OFF trees despite the strong PAR T gradient. Our results thus suggest that, under the growing conditions of the study, optimal allocation of N within trees to maximize light harvesting and photosynthesis occurs only above a certain fruit C demand. This implies that trees adjust N absorption and further N allocation to leaves depending on the crop load [START_REF] Ding | Effects of crop load on distribution and utilization of 13C and 15N and fruit quality for dwarf apple trees[END_REF]. For a better understanding of the impact of C demand on plant C and N functions [START_REF] Paul | Sink regulation of photosynthesis[END_REF], N partitioning into light harvesting, bioenergetics and biochemistry pools might require analysis. This partitioning has been documented based on the model of Niinemets and Tenhnunen (1997) for different plant functional types (see the review of [START_REF] Niinemets | A worldwide analysis of within-canopy variations in leaf structural, chemical and physiological traits across plant functional types[END_REF] for nonfruiting species, Frak et al. 2006 on walnut, andUrban et al. 2003 on mango). In that framework, our results reveal a higher concentration of Chl in high cropping trees (as reported by Wünsche et

Effect of crop load status on photosynthesis optimization by acclimation of leaf structural characteristics within trees

Leaf structural traits such as LMA are central players in the leaf economics spectrum [START_REF] Wright | The worldwide leaf economics spectrum[END_REF]Niinements et al., 2015[START_REF] Onoda | Physiological and structural tradeoffs underlying the leaf economics spectrum[END_REF], but the combined effects of crop load and light on these variables have been poorly investigated. In our study, significant relationships between PAR T and LMA were found for ON trees only, and mean LMA values were lower in ON trees. Few studies have investigated the impact of crop load on LMA [START_REF] Schechter | Apple Fruit Removal and Limb Girdling Affect Fruit and Leaf Characteristics[END_REF][START_REF] Urban | Effect of fruit load and girdling on leaf photosynthesis in Mangifera indica L[END_REF], but they did not evaluate the variation in La and LDW, which are used to calculate LMA, as performed in this study. Our results show that the relationship between PAR T and LMA for ON trees was related to variations in LDW. The decrease in LMA due to crop load could also be attributed to a stronger decrease in LDW than in La for ON trees. A smaller investment in leaf dry matter in ON trees could be an adaptive trade-off to achieve satisfactory light interception efficiency, i.e., a minimal amount of biomass is invested when the fruit C demand is high on the plant scale. In parallel, LMA can also be considered the product of leaf thickness and leaf density; higher thickness and lower density could result in higher A net due to higher photosynthetic compound content and greater internal CO 2 diffusion to chloroplasts, respectively [START_REF] Niinemets | Research review. Components of leaf dry mass per area -thickness and density -alter leaf photosynthetic capacity in reverse directions in woody plants[END_REF]. Hence, in the present study, the increased A net in ON trees coupled with lower LMA in ON trees was likely to be associated with lower density.

Consistent with other studies in fruit trees (e.g., [START_REF] Palmer | Effects of varying crop load on photosynthesis, dry-matter production and partitioning of crispin/m.27 apple-trees[END_REF][START_REF] Inglese | Crop Load and Rootstock Influence on Dry Matter Partitioning in Trees of Early and Late Ripening Peach Cultivars[END_REF], a negative relationship between vegetative primary growth and crop load was observed as the outcome of a high level of competition for C between vegetative and reproductive growth. This lower C allocation to the vegetative compartment can result in decreased light interception in high cropping trees (Wünsche et al., 2000). At the tree scale, the carbon demand of fruits in ON trees having this decrease in light interception could be sustained by improved radiation use efficiency through increased Nm and chlorophyll content and optimization of the N allocation to sunny leaves [START_REF] Zanotelli | Effect of fruit load on the photosynthetic capacity and on the ecological light use efficiency of an apple orchard[END_REF]. Several studies have reported the impact of light gradients on the spatial variability of NSCs [START_REF] Lichtenthaler | Photosynthetic activity, chloroplast ultrastructure, and leaf characteristics of high-light and low-light plants and of sun and shade leaves[END_REF][START_REF] Roux | Spatial distribution of leaf dry weight per area and leaf nitrogen concentration in relation to local radiation regime within an isolated tree crown[END_REF]. In contrast, our results showed nearly no effect of light on the different NSC concentrations. These results suggest similar C statuses and/or export rates across the crown despite significantly different A net values. Such a result is likely related to the homogeneous distribution of the fruit within the trees for both crop statuses in our study, resulting in a homogeneous distribution of the leaf export rate.

Regulation of photosynthesis by the fruit or seed C demand has been previously observed, and two main mechanisms, i.e., stomatal closure and end-product saturation, have been discussed [START_REF] Andrade | Differential source-sink manipulation affects leaf carbohydrate and photosynthesis of early-and late-harvest nectarine varieties[END_REF][START_REF] Gucci | The effect of defruiting at different stages of fruit-development on leaf photosynthesis of golden-delicious apple[END_REF]Wünsche et al., 2005). In our study, the most marked effect was the strong depletion in leaf starch for high crop load regardless of the light [START_REF] Naschitz | Internal management of non-structural carbohydrate resources in apple leaves and branch wood under a broad range of sink and source manipulations[END_REF][START_REF] Quilot | Leaf light-saturated photosynthesis for wild and cultivated peach genotypes and their hybrids: A simple mathematical modelling analysis[END_REF]. In addition, the difference in the relationships between A net and starch content highlights differences in C function between the two crop statuses. In ON trees, the synthesized photosynthates are rapidly exported to sustain fruit growth [START_REF] Breen | Revisiting the role of carbohydrate reserves in fruit set and early-season growth of apple[END_REF][START_REF] Génard | Changes in fruit sugar concentrations in response to assimilate supply, metabolism and dilution: a modeling approach applied to peach fruit (Prunus persica)[END_REF], with C even being imported from nonbearing shoots [START_REF] Walcroft | Does variability in shoot carbon assimilation within the tree crown explain variability in peach fruit growth?[END_REF], thus leaving a minimal amount of starch in leaves.

The positive correlation observed in ON trees between A net and the starch content was more surprising. The positive correlation can be interpreted as resulting from the starch pool that is likely refilled proportionally to both the source capacity and fruit importation rate, advocating for it being considered a priority sink under high crop load, which is very scarcely observed in trees (Lescouret et al., 1998;[START_REF] Silpi | Carbohydrate reserves as a competing sink: evidence from tapping rubber trees[END_REF]. Conversely, in OFF trees, the photosynthates are oriented towards only vegetative growth. In these trees, the leaf starch pool was filled due to low C demand at the tree scale. This starch pool was likely dedicated to reserves for sustaining further organ primary and/or secondary vegetative growth (root, shoots, and branches). Finally, this starch accumulation might downregulate A net [START_REF] Nebauer | Photosynthesis down-regulation precedes carbohydrate accumulation under sink limitation in Citrus[END_REF][START_REF] Poirier-Pocovi | Modelling temporal variation of parameters used in two photosynthesis models: influence of fruit load and girdling on leaf photosynthesis in fruitbearing branches of apple[END_REF][START_REF] Urban | Effect of fruit load and girdling on leaf photosynthesis in Mangifera indica L[END_REF][START_REF] Franklin | Optimal nitrogen allocation controls tree responses to elevated CO2[END_REF], thus canceling its spatial variability.

Similar to starch, light had nearly no effect on leaf sucrose and hexose contents.

Nevertheless, sorbitol content was lower in ON trees than OFF trees, suggesting a higher use rate for fueling fruit growth [START_REF] Pallas | Growth and carbon balance are differently regulated by tree and shoot fruiting contexts: an integrative study on apple genotypes with contrasted bearing patterns[END_REF]. Moreover, the relationships among the NSC and A net differed between the ON and OFF trees, as shown by the path and correlation analyses, revealing different C allocation patterns for the two crop loads. In ON trees, the pattern that could be drawn was a major allocation of photosynthates to transport to outside A c c e p t e d M a n u s c r i p t 16 the leaf, especially for sucrose and, to a lesser extent, sorbitol. The relationships among sucrose, glucose and fructose were also consistent with the known pathway of sucrose biosynthesis. The relationships between A net and starch and among starch, sorbitol and sucrose reveal the central role of the latter group as an intermediary pool directly fueled by photosynthesis. In contrast, in OFF trees, the path model showed a feedback loop between sucrose and sorbitol, with the latter being related to both glucose and fructose, which in turn were related to sucrose. Such cyclic interactions might reflect other roles of sucrose and sorbitol as temporary storage forms when the leaf starch pool has likely reached high levels for further use in vegetative growth or storage (Escobar-Gutierrez and Gaudillère, 1996;Genard et al., 2003).

CONCLUSIONS

Although previous studies have investigated the impact of light microclimate and fruit load on leaf traits (functional and structural), none of them have analyzed their combined effects.

In this context, our study reports original results and demonstrates that crop status has a greater influence than local light or local fruit on all the measured traits. Moreover, our study clearly shows that the intensity of leaf acclimation to light strongly depends on the carbon demand at the tree scale. Indeed, acclimation of photosynthesis to light was mainly observed for ON trees, which was achieved mainly by increased light capture efficiency, implying higher leaf N and lower LMA. Conversely, low C demand, as in OFF trees, is thought to disrupt the optimal distribution of resources by modifying the interplay among NSCs. These experimental results have potential implications for shifting modeling approaches towards a more mechanistic representation of optimal strategies between C and N within-tree allocations depending on the crop load. Our study also supports a consistent description of the possible role of starch in regulating photosynthetic activity and its spatial variability according to crop load. Under high crop loads, starch could be one of the priority sinks.

Under high crop loads, high starch levels promote the optimization of photosynthesis and related traits, while under low crop load, high starch levels tend to downregulate photosynthetic activity. Moreover, sorbitol and sucrose play major roles in the transport of carbohydrates when fruit demand is high, while they serve as temporary reserves under low crop loads in apple trees. 1. Mean values of daily incoming photosynthetically active radiation (PARi, +/-standard deviation among days) and mean values of transmitted PAR for the two crop statuses ("ON" and "OFF") and the three light environments in the four measurement periods (+/standard deviation among leaves of each light/crop load environments).

Periods

Starting A c c e p t e d M a n u s c r i p t

Figure 1. A. Boxplot representation of net carbon assimilation (A net ) for the two crop statuses ("ON" and "OFF") and the three light conditions (H: High, M: Medium, L: Low) considering together the four measurement dates. B. Boxplot representation of A net in the fruiting and non-fruiting shoots in "ON" trees considering together the four measurement dates. In A, a three-way ANOVA with crop status, light condition and period effects, and the light condition × crop status interaction was performed. This analysis was followed by a pair-wise Tukey test considering all the crop status-light condition combinations and letters indicate significant differences among groups at P<0.05. In B, a two-way ANOVA with fruit presence and period effects was performed. *** significant at P<0.001, ** significant at 0.001<P<0.01 and ns non-significant.

Figure 2. A. Boxplot representation of leaf nitrogen concentration per area unit (Na) for the two crop statuses ('ON' and 'OFF') and the three light conditions (H: High, M: Medium, L: Low) considering together the four measurement dates. B. Boxplot representation of Na in the fruiting and non-fruiting shoots in "ON" trees considering together the four measurement dates. In A, a three-way ANOVA with crop status, light conditions and period effects, and the light condition × crop status interaction was performed. This analysis was followed by a pairwise Tukey test considering all the crop status-light condition combinations and letters indicate significant differences among groups at P<0.05. In B, a two-way ANOVA with fruit presence and period effects was performed. *** significant at P<0.001, ** significant at 0.001<P<0.01, * significant at 0.05<P<0.01 and ns non-significant.

Figure 3. Boxplot representations of chlorophyll concentration per area unit (Chl) and of chlorophyll proportion per leaf nitrogen area (Chl:Na) for the two crop statuses ("ON" and "OFF") and the three light conditions (H: High, M: Medium, L: Low) in the four measurement periods. For each period, a two-way ANOVA with crop status, light conditions and the interaction between light condition and crop status was performed. *** significant at P<0.001, ** significant at 0.001<P<0.01, * significant at 0.01<P<0.05, and ns nonsignificant. This analysis was followed by a pair-wise Tukey test considering all the crop status-light condition combinations and letters indicate significant differences among groups at P<0.05. ), sorbitol (B), sucrose (C) concentrations in leaves for the two crop statuses ("ON" and "OFF") and the three light conditions (H: High, M: Medium, L: Low) considering together the four measurement dates. In A, B and C threeway ANOVA with crop status, light conditions and period effects, and the light condition × crop status interaction was performed. These analyses were followed by pair-wise Tukey tests considering all the crop status-light condition combinations and letters indicate significant differences among groups at P<0.05. *** significant at P<0.001, ** significant at 0.001<P<0.01, * significant at 0.05<P<0.01 and ns non-significant. (La, D). Dotted lines represent the linear regression considering both crop statuses ("ON" and "OFF"), blue lines represent the linear regression considering ON trees, only and red lines represent the linear regression considering "OFF" trees, only. R² values and the level of significance of the correlations are represented in each sub-figure legend. *** significant at P<0.001, ** significant at 0.001<P<0.01 and ns non-significant. Dashed red and blue lines represent the mean values observed for "OFF" and "ON" trees, respectively. A one-way ANOVA was used to estimate the significance of the crop status effect. The level of significance of the effect of the crop status is represented in the first line of the sub-figures legend.

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  al. 2005) and a higher proportion of Chl in Na in shaded leaves (as reported byNiinemets et

  ). Our study thus suggests that high fruit C demand might promote optimization of A net by increasing N investment in the light harvesting pool in response to a light gradient.

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A

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Figure 4 .

 4 Figure 4. Boxplot representations of starch (A), sorbitol (B), sucrose (C) concentrations in leaves for the two crop statuses ("ON" and "OFF") and the three light conditions (H: High, M: Medium, L: Low) considering together the four measurement dates. In A, B and C threeway ANOVA with crop status, light conditions and period effects, and the light condition × crop status interaction was performed. These analyses were followed by pair-wise Tukey tests considering all the crop status-light condition combinations and letters indicate significant differences among groups at P<0.05. *** significant at P<0.001, ** significant at 0.001<P<0.01, * significant at 0.05<P<0.01 and ns non-significant. Figure5. Correlations between net carbon assimilation (A net ) and starch concentration in leaves (A) and between A net and leaf nitrogen concentration per area unit (Na, B). Dotted lines represent the linear regression considering both crop statuses ("ON" and "OFF") and blue lines represent the linear regression considering "ON" trees, only. R² values and the level

Figure 5 .

 5 Figure 4. Boxplot representations of starch (A), sorbitol (B), sucrose (C) concentrations in leaves for the two crop statuses ("ON" and "OFF") and the three light conditions (H: High, M: Medium, L: Low) considering together the four measurement dates. In A, B and C threeway ANOVA with crop status, light conditions and period effects, and the light condition × crop status interaction was performed. These analyses were followed by pair-wise Tukey tests considering all the crop status-light condition combinations and letters indicate significant differences among groups at P<0.05. *** significant at P<0.001, ** significant at 0.001<P<0.01, * significant at 0.05<P<0.01 and ns non-significant. Figure5. Correlations between net carbon assimilation (A net ) and starch concentration in leaves (A) and between A net and leaf nitrogen concentration per area unit (Na, B). Dotted lines represent the linear regression considering both crop statuses ("ON" and "OFF") and blue lines represent the linear regression considering "ON" trees, only. R² values and the level

  the correlations are represented in the top left corner of each graph. *** significant at P<0.001, ** significant at 0.001<P<0.01 and ns non-significant.

Figure 6 .

 6 Figure6. Correlations between locally transmitted photosynthetically active radiation (PAR T ) and leaf dry weight (LDW, A), leaf mass area (LMA, B), nitrogen concentration per mass unit in leaves (Nm, C) and individual leaf area (La, D). Dotted lines represent the linear regression considering both crop statuses ("ON" and "OFF"), blue lines represent the linear regression considering ON trees, only and red lines represent the linear regression considering "OFF" trees, only. R² values and the level of significance of the correlations are represented in each sub-figure legend. *** significant at P<0.001, ** significant at 0.001<P<0.01 and ns non-significant. Dashed red and blue lines represent the mean values observed for "OFF" and "ON" trees, respectively. A one-way ANOVA was used to estimate the significance of the crop status effect. The level of significance of the effect of the crop status is represented in the first line of the sub-figures legend.

Figure 7 .Fig. 2 .FigFig. 5 .

 725 Figure7. Results of the path analysis performed on net carbon assimilation (A net ) and nonstructural carbohydrate concentrations in leaves on "ON" and "OFF" trees. On these graphs, only the significant relationships of the model are represented. Single-headed arrows represent causal relationships and double-headed arrows represent free correlations. Normalized path coefficients together with their significance level were represented above each arrow. *** significant at P<0.001, ** significant at 0.001<P<0.01, * significant at 0.05<P<0.01.

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Table

	TABLES

  ANOVA were performed for the PART values considering first each light condition separately for the four periods and the two crop status, and second each measurement period separately for the three light conditions and the two crop status cademic.oup.com/jxb/advance-article/doi/10.1093/jxb/eraa559/6010466 by INRAE Institut National de Recherche pour l'Agriculture, l'Alimentation et l'Environnement us

		-Ending dates	Crop status	Incoming PAR (PAR i , mol.m -2 .day -1 )	Transmitted PAR (PAR T , mol.m -2 .s -1 ) High Light (H) Medium Light (M) Low Light (L)	Light condition	Crop Status
	1	26 June -10 July 2016	"ON" "OFF"	53.7 +/-8.4	35.4 +/-6.2 (3) 35.8 +/-5.4 (7)	23.8 +/-5.0 (9) 20.7 +/-0.0 (1)	13.3 +/-3.9 (6) 15.9 +/-1.6 (4)	***	ns
		15 July -	"ON"		33.2 +/-2.9 (6)	21.8 +/-2.9 (7)	11.3 +/-3.8 (5)
	2	01 August 2016	"OFF"	46.5 +/-9.8	37.5 +/-3.4 (4)	25.5 +/-1.4 (3)	13.9 +/-1.9 (5)	***	*
		17 August -	"ON"		26.2 +/-1.9 (4)	16.0 +/-3.9 (5)	8.7 +/-3.1 (9)
	3	31 August 2016	"OFF"	43.3 +/-8.6	27.3 +/-5.0 (6)	17.6 +/-3.7 (5)	6.8 +/-0.0 (1)	***	ns
	4	11 July -25 July 2017	"ON" "OFF"	51.6 +/-8.9	16.0 +/-3.6 (6) 16.5 +/-4.4 (4)	11.0 +/-0.9 (7) 11.8 +/-0.8 (3)	6.3 +/-2.8 (5) 7.8 +/-1.9 (5)	***	ns
			Date		***	***	***
			Crop
			status		*	ns	ns
	Two-way

Table 2 .

 2 Correlation coefficient and associated level of significance between the non-structural carbohydrates forms and net carbon assimilation (A net ). The upper and lower panels correspond for "OFF" and "ON" trees, respectively.

		Glucose	Fructose	Sucrose	Sorbitol	Starch	A net
	Glucose		0.78***	ns	0.56***	0.36*	ns
	Fructose Sucrose Sorbitol	0.92*** -0.30** ns	-0.29* ns	-0.48** ns	ns 0.59***	0.35* ns ns	ns 0.35* ns	'OFF' trees
	Starch	ns	ns	ns	ns		ns
	A net	ns	-0.27*	0.75***	ns	0.61***
				'ON' trees
	*** significant at P<0.001, ** significant at 0.001<P<0.01, * significant at 0.01<P<0.05, ns non
	significant.

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ACKNOWLEDGMENTS

This study was funded by the ANR-DFG "Alternapp" project (ANR-14-CE35-0001-01). The authors acknowledge SILVATECH (ANR-11-LABX-0002-01) from UMR 1434 SILVA, 1136 IAM, 1138 BEF and 4370 EA LERMAB of the research center INRAE Nancy-Lorraine for the leaf nitrogen analyses. Dr Marc Saudreau and Dr André Lacointe (UMR 0547 PIAF) are thanked for insightful advice regarding light sensor positioning in the field and for useful comments on the manuscript, respectively. Xavier Le Roux (Fondation pour la Recherche sur la Biodiversité) is acknowledged for having initiated questioning the within-tree variability of leaf function at the PIAF unit. Dr Farés Belhassine is also thanked for providing additional data used to build allometric relationships.

DATA AVAILABILITY

The data that support the findings of this study are openly available in a Data INRAE repository (doi: XXXXXX to be completed).

AUTHOR CONTRIBUTIONS

JN and BP designed the experiment. AM and JN installed and monitored the functioning of the PAR sensors. SM, BP and SB performed the field measurements, and BSJ and SB performed the biochemical analyses. BP and JN performed the statistical analyses and wrote the manuscript. EC reviewed and improved the manuscript.


Aimé Labbé
email: aime.labbe@universite-paris-saclay.fr

Rose-Marie Dubuisson

Jean-Christophe Ginefri

Cornelis J Van Der Beek

Luc Darasse

Marie Poirier-Quinot

Static field homogeneity artefacts due to magnetic flux expulsion by HTS coils for highresolution magnetic resonance imaging

High-Temperature Superconducting (HTS) radiofrequency coils can greatly improve the sensitivity of Magnetic Resonance Imaging (MRI), with Signal to Noise Ratios (SNR) increased by up to 16 times. However, as homogeneity of the static field B 0 is a major condition for MR acquisitions, their propensity to warp the magnetic field in their vicinity (Rev2-Typos) as a result of magnetic flux expulsion could cause severe image degradation. In this letter, we report on the first observation of artefacts generated by magnetic flux expulsion from a HTS coil. To that end, we acquired MR images of a water sample in the vicinity of a non-resonant HTS coil for different cooling conditions. These are zero field cooling as well as field cooling of the coil inside a clinical MRI bore magnet of 1.5 T, for a range of working temperatures of the HTS coil. After zero-field cooling, we observed significant artefacts in the MR images, increasing with lower temperature; images acquired after field cooling did not display these alterations. We propose a phenomenological model for the magnetic field disturbance induced by the HTS coil. This model reproduces, in good agreement with the experiments, the phase distortion observed in the MR images and allows one to extract the critical current density of the HTS coil, an important technological parameter of superconductors. Finally, we discuss the necessity of field cooling as a way to avoid these B 0 inhomogeneity artefacts.

High-Temperature Superconductors (HTS) are promising candidates for the development of a new generation of highly sensitive cryogenic radiofrequency (RF) coils for applications in high resolution (< 100 m) Magnetic Resonance Imaging (MRI). Their low electric resistance combined with a low working temperature of about 70 K ensure electric noise levels unattainable with traditional materials such as copper [START_REF] Darrasse | Perspectives with cryogenic rf probes in biomedical MRI[END_REF] . In the context of MRI, when the RF coil electric noise dominates the other noise sources such as sample magnetism, i.e. when non-conductive samples are probed with small (~10 mm) surface antennas, images acquired with a HTS coil at about 80 K can display signal-to-noise ratios (SNR) of up to 16 times that of similar images acquired with room temperature copper coils [START_REF] Poirier-Quinot | Performance of a miniature high-temperature superconducting (hts) surface coil for in vivo microimaging of the mouse in a standard 1.5 T clinical whole-body scanner[END_REF] .

Since the first HTS surface coils for MRI devised by Black et al. in 1993 3 , this technology has never quite succeeded in getting through the infamous valley of death. This is because two major technical issues had to be resolved. First, the technology for reliable low-noise MRIcompatible cryostats had to be developed. This has been achieved by implementing recent commercial pulse-tube cryocoolers, as proposed by Saniour et al [START_REF] Saniour | A temperature-controlled cryogen free cryostat integrated with transceiver-mode superconducting coil for high-resolution magnetic resonance imaging[END_REF] . Second, decoupling strategies had to be devised to minimize RF field homogeneity (B1-) artefacts in MR images, such as large-scale signal amplitude modulations and localized -phase shifts. A promising strategy has been to exploit nonlinearities in the HTS coil response to achieve decoupling [START_REF] Saniour | Novel passive decoupling approach for high resolution HTS rf coils based on the nonlinear electrical properties of superconductors[END_REF] .

A possible complication of using superconductors for MRI coils is the static field (B0) inhomogeneity induced by dc magnetic flux expulsion. In the presence of a magnetic field, the superconductor generates screening currents on its surfaces/edges, of magnitude and distribution such that the flux density in its interior vanishes. These currents flow in a thin surface sheet of thickness  -the London penetration depth -or, if the superconductor is thinner than 2, through the entire thickness of the material. In type-II superconductorswhich include all HTS materials -magnetic flux is partially re-admitted in the form of quantized magnetic flux lines or "vortices" 6 when the applied field exceeds the first critical field Bc1. The vortex (flux) distribution in the material strongly depends on the temperature and the magnetic history of the superconductor, notably whether it was zero-field cooled ZFC (i.e. in Earth's field) or not. Hence, type-II superconductors have hysteretic magnetic properties, and may display perfect or imperfect diamagnetism depending on the circumstance.

The total or partial flux exclusion and the concomitant concentration of field lines around the HTS coil perimeter is expected to result in dc field inhomogeneity artefacts, or "B 0 artefacts", in MR images. These include image deformation, localized signal loss and continuous phase shifts. So far, HTS coils have been used in liquid nitrogen at temperatures close to T c with disregard to the cooling conditions, fortuitously avoiding such artefacts (Rev2-Q1). However, with better-controlled experimental parameters and new cryostats achieving lower temperatures, vortex penetration in HTS coils is incomplete at standard clinical imaging fields of 1.5 T and higher. Then, this becomes an issue.

In this letter, we report on the first observation of B0 artefacts generated by HTS coil diamagnetism in MR images. We study these effects as a function of temperature and for different cooling conditions. A practical way to observe the B0 inhomogeneities while avoiding B 1 artefacts is to use a non-resonant HTS coil. In this configuration, a standard copper volume coil, commonly named ''whole-body coil'', is used to generate and collect the MR signal while the HTS coil has no active role in the MRI experiment. In addition to the experimental observation of B0 artefacts, we also propose a simple phenomenological model reproducing the artefacts observed in the phase images. Finally, we define a set of experimental conditions under which they can be avoided or minimized.

The equipment used in this experiment is shown in Figure 1; the reference coordinate system is displayed in Figure 1d. The cryostat is a MRI compatible and cryogen-free vacuum chamber that uses a pulse-tube cryocooler (PT60, Cryomech, USA) and conductive heat transfer to attain a minimal temperature of ~ 60 K at the coil position. Temperature readings are performed with a sensor (Pt100) located on a sapphire slate that supports the HTS coil (Figure 1b). The whole system is fully described by Saniour et al. The MRI system is a clinical 1.5 T set-up (Philips, The Netherlands) with a 60 cm bore diameter (Rev2-Q3) and the static magnetic field B 0 oriented along z. A whole-body RF coil was used for both transmission and reception, and the MRI sequence was a standard 3D gradient-echo with the following parameters: Echo Time (TE) / Repetition Time = 5/20 ms, flip angle=50°, spatial resolution = 1.0  0.5  0.5 mm 3 , Field of View = 50  100  100 mm 3 , pixel receiver bandwidth = 439 Hz/pixel, readout gradient towards the y-axis, number of acquisitions = 2, total acquisition time = 6'35". The imaging sample is a cylindrical phantom of diameter 50 mm filled with a 20 ml solution of water with a gadolinium-based contrast agent (T1=20 ms). The phantom was sealed with a latex membrane and positioned upsidedown on top of the cryostat, centred on the position of the HTS coil (Figure 1a). The latter is located on a sapphire slate directly beneath the cryostat inner surface (Figure 1b), ~1.7 mm away from the bottom of the phantom.

The coil design is a multi-turn Transmission Line Resonator 7 (MTLR). The dielectric is a 330 m-thick Al2O3 substrate initially covered on both sides by a 300 nm-thick YBa2Cu3O7- film made by Ceraco GmbH (Ismaning, Germany), with a critical temperature Tc = 87 K, a critical current density jc = 3.0 MA/cm 2 (as measured at T = 77 K and zero applied field) and a low temperature in-plane London penetration depth 8 ab = 200 nm. On each side, a 200 μm-wide six-turn spiral 200 μm-wide transmission line was fashioned by etching. The spacing between each turn is 150 μm (Rev2-Q3), and the coil inner and outer diameters are, respectively, 10.9 mm and 14.4 mm. This design leads to HTS coils resonating close to 63.898 MHz, the proton frequency at 1.5 T. For this experiment, we used a non-resonant antenna, the transmission line being interrupted by a fracture line as in Figure 1c. Thus, B1 artefacts are avoided since there is no RF coupling between the non-resonant HTS coil and the RF volume body-coil. In addition, this particular geometry does not alter the diamagnetic response of the HTS material.

(Rev2-Q2) 3D MR images were acquired for various experimental conditions. For zero-field cooling, starting from T > Tc, the cryostat was cooled down to 60 K outside the MRI scanner and then inserted into the magnet. During this procedure, the surface normal to the HTS coil was kept perpendicular to B0 (along y). For field cooling, starting from T > Tc, the cryostat was kept inside the MRI scanner during cooling procedure. Finally, diamagnetic effects were evaluated as function of temperature varying from 60 K to 90 K, turning off the cold head compressor.

Temperature monitoring was performed between acquisitions, and the temperature variation over the course of an acquisition (6'35") was ~ 4.2 K.

In Figure 2, we present three sets of reference images for magnitude (top row) and phase (bottom row). The phase data are displayed using a cyclic colour map to avoid discontinuities caused by phase wrapping (transition from 2 to 0). Each image is displayed in three standard The phantom images in Figure 2(a-b) were acquired at 90 K, with the HTS material in its resistive state. Although no artefact can be seen in the magnitude image (a), a slow variation of the background phase is observed. The B0 inhomogeneities at the origin of this variation are induced by experimental conditions unrelated to the HTS diamagnetism and can be removed by subtracting this initial phase map from all subsequent phase images.

The images in Figures 2(c-d) were acquired after zero-field cooling at 58 K. We observe signal loss in the magnitude image and important perturbations in the phase image. These anisotropic artefacts have the same characteristic dimensions as the antenna (~ 17 mm) and they increase in magnitude as the antenna is approached. They are minimal in the transverse plane ( B0) and maximal in the sagittal plane (|| B0).

The images in Figures 2(e-f) were acquired after field cooling to 58 K. They were obtained with only one average instead of two, explaining the lower SNR. Nevertheless, the SNR remains adequate to analyse the data over the volume of the sample.

In Figure 3, we present the results of the temperature study after zero-field cooling. The phase data were unwrapped using the algorithm developed by Abdul-Rahman et al 9 , resolving the 2 phase jumps in the images. As can be observed, the B0 artefacts show a strong dependence on temperature. The shape and size of the perturbation do not change, but its scale is continuously reduced as the temperature increases, up to the point where it becomes almost unnoticeable at 74 K (Figure 3e) and nonexistent at T > 80 K (Figure 3f). The B0 artefacts observed in the phase images can be reproduced with a simple phenomenological model of the diamagnetism of the HTS coil. The latter is a six-turn spiral without closed loops, with the normal to the surface oriented along y  B0. All six turns are interrupted as illustrated in Figure 1c. There are two scenarios for the looping of the screening currents in the superconductor. (1) In the case of perfect alignment, parallel magnetic flux would penetrate the coil sections initially from the lateral edge, tangent to B0. This would entail screening currents wrapping around the coil upper and lower surfaces, closed by perpendicular edge currents; the magnitude of the latter is determined by the (low) c-axis critical current density of the YBCO material [START_REF] Gutierrez | Vortex dynamics in thin films of YBa2Cu3O7-x with three-dimensional nanoscale patterns[END_REF] . At the B 0 value at stake (1.5 T), the entire film would be permeated by parallel flux, and no effect would be observable. Moreover, the (epitaxial) HTS film would have to be thicker than 2nm) for the screening current to fully develop in the coil. We are therefore led to assume a small but inevitable misalignment θ of the HTS coil, so that ΔB z TL is the variation of the local induction generated as a result of the (partial) expulsion of the static field component B 0 sin θ perpendicular to the transmission line (Rev1-Q2; Rev2-Q6). Then, perpendicular magnetic flux seeks to pass through the superconducting track composing the coil, a process opposed by in-plane screening currents circulating around the coil perimeter. We surmise that these are at the origin of the B0 inhomogeneities.

To calculate the magnetic fieldΔB generated by the screening current loop circulating in each section, we neglect the closure current at the section end points. Thus, the six spiral sections are approximated as six concentric loops with the screening currents modelled as two countercirculating current filaments on the loop outer-and inner perimeters. The two filaments carry the same current I0, but in opposite directions. The total magnetic field generated by unit current Δb = ΔB/I0 is the sum of the fields generated by the individual filaments in both spirals (Rev2.Q7). Magnetic field computations were carried out with Magpylib 11 .

In absence of B1 artefacts, the phase of the voxel at position r can be directly linked to the B0 inhomogeneities 11 :

(r,T) = TEI0(T)Δbz(r,r0) + 0(T) + r(T)r (1)
where Δb z is the z-component of Δb, r0 is the position of the antenna relative to the sample that can be numerically optimized using a gradient descent algorithm,  is the gyromagnetic ratio of the proton, TE is the echo time, and 0, r = [x,yz] and I0 are fitting parameters determined by linear regression for each temperature (Rev1-Q3). The first term on the RHS of Equation ( 1) is derived from the expression of the Larmor frequency and represents the phase shift induced by ΔB, and the last two terms correspond to a first order correction of the phase data. This correction is justified since (1) the origin of the phase is arbitrarily defined, and (2) large-scale B 0 inhomogeneities caused by the MRI environment need to be accounted for.

The results of this model are shown in Figure 4. We present the field map Δbz in the 3 standard planes in Figure 4a. The field displays the same geometry as the artefacts observed in Figure 3. Notably, Δbz is null in the transverse plane and reaches its maximum in the sagittal plane, which results in the same two-crescent shape in the coronal plane.

In Figure 4b, we present the experimental and modelled phase images for three different temperatures. Simulation and experimental data are in good agreement. At 58 K, the field inhomogeneities caused by the HTS coil attain 6.6 ppm at the bottom of the phantom. This is to be compared with the inhomogeneity < 0.5 ppm over a 35-cm diameter spherical volume [START_REF] Levitt | Spin dynamics: basics of nuclear magnetic resonance[END_REF] of clinical MRI scanners. In our case, this generates a strong and localized field gradient of ~ 8 mT/m, inducing a phase drift of ~1.4 π over a single voxel, enough to locally extinguish the MR signal (Figure 2c). Concurrently, the coil misalignment is estimated as θ≳ 5•10 -4 π rad. Finally, we extract the current I0 as a function of T, which allows us to estimate the screening current density j in the YBa2Cu3O7- strip (Figure 4c). We find that j ~ 2.6 MA/cm 2 at 58 K decreasing to j ~ 0.4 MA/cm 2 at 77 K. This is very close to the in-plane critical current density of pristine YBa2Cu3O7- films when the magnetic field nearly aligned with the film plane [START_REF] Sierra | Superconducting Films of YBa 2 Cu 3 O 7-d Nanocomposites with Embedded BaZrO 3 , BaHfO 3 , BaTiO 3 and SrZrO 3 Nanocrystals[END_REF] . By consequence, we infer that Figure 4c tracks the temperature dependence of the HTS coil critical current density jc.

In our experimental results, we highlight the impact of the cooling conditions of the HTS coil on the image quality of MR images. The artefacts were significant at lower temperature, and did not appear for T > 80 K. Hence, the reason why these effects had not been reported before is that in previous experiments the temperature was not low enough; most experiments described in the literature have used liquid nitrogen cryostats with working temperatures between 77 K and 80 K, close to the Tc of superconducting material.

To avoid the artefacts linked to a lower working temperature, our results indicate the HTS coil should be field cooled, preferably at its working position and orientation, as a change B 0 will lead to irreversible magnetic flux expulsion or further flux penetration in the HTS material, and therefore to inhomogeneity artefacts. In the context of MRI, this implies frequent temperature cycling of the HTS coil to reset its magnetic history and avoid any B0 artefacts.

This should be done between patients or after a change in the geometry of the experiment.

Hence, this temperature cycling procedure must be reasonably fast, on the order of a few minutes at most. This requires a practical implementation involving quick, localized and uniform heating of the HTS coil. Such a heating system could work by radiative, resistive, or conductive heating but without any interference with the MRI experiment.

Simultaneously, the observed artefacts provide valuable information about the HTS coil. The measured phase maps represent the magnetic image of the coil, more commonly obtained by low-field (B < 0,2 T) techniques such as magneto-optic imaging (MOI) [START_REF] Minoru Uehara | Advances in magneto-optical imaging applied to rock magnetism and paleomagnetism", G 3[END_REF] . Here, we were able to image to coil in fields exceeding 1 T. The combination of the phase data with our phenomenological model allowed us to extract the superconductor's critical current density.

To conclude, we have studied how the magnetic flux expulsion of a superconducting coil affects the image quality in MRI. We observe that static field inhomogeneity B0 artefacts arise predominantly when working at low temperature and after zero-field cooling, causing important signal loss and phase perturbation in MR images. Through a simple phenomenological model of the HTS coil diamagnetism, we accurately reproduce the phase maps experimentally measured by MRI. We were also able to extract the temperature dependence of the critical current density of YBa2Cu3O7- , in good agreement with the constructor's values. Finally, we discussed different avenues of minimizing or avoiding these artefacts by either choosing to work at temperatures close to Tc, or by implementing a quick and efficient temperature cycling procedure of the HTS coil into the cryostat. This work studies and solves an important issue in the implementation of HTS coil, and provides better understanding of the experimental conditions required to obtain better images with this technology.

France Life Imaging network and partially funded by the network (grant ANR-11-INBS-0006).

4

 4

FIG. 1 .

 1 FIG. 1. Experimental setup. (a) The phantom is on top of the cryostat and will be inserted in the bore of a 1.5 T MRI magnet. (b) View of the interior of the cryostat. (c) Schematic view of the non-resonant HTS coil with a fracture line. (d) Coordinate system of the experiment. The cryostat surface is in the xz-plane with B0 ‖ z. The three orthogonal xz, yz and xy planes represent, respectively, the coronal, sagittal and transverse planes.

  FIG. 2. Reference images obtained in presence of the HTS coil at (a,b) T = 90 K, and at T = 58 K after (c,d) zerofield cooling and (e,f) field cooling. Top row: magnitude images. Bottom row: phase images. In (d) and (f), the phase was corrected by subtracting the phase data of (b). The coronal slice (xz) is located ~ 4.2 mm above the HTS coil. The transverse (xy) and sagittal (yz) pass through the centre of the phantom.

FIG. 3 .

 3 FIG. 3. Unwrapped phase images in the coronal plane, 4.2 mm above the HTS coil, at different temperatures.

(

  Rev2-Q4) FIG. 4. Modelling of the HTS coil diamagnetism. (a) z-component of the static magnetic field map by unit of current B z =I 0 generated by the coil towards the three standard planes. For this representation, the coil is centered at (x, y, z) = (26, 26, 26) [mm] with its normal oriented towards the y-axis. (b) Comparison between the experimental and modelled phase images for three temperatures. (c) Estimated screening current I 0 normalized by half the 200 m  300 nm cross section of the YBa 2 Cu 3 O 7- strip as a function of temperature. Vertical error bars show a 95% confidence interval and horizontal error bars account for the 4.2 K temperature drift during acquisition.

ACKNOWLEDGMENTS

Experiments were performed on the 1.5 T MRI platform of CEA/SHFJ, affiliated to the

DATA AVAILABILITY

The data that support the findings of this study are available from the corresponding author upon reasonable request.