Enrico Battiston
email: enrico.battiston@unifi.it

Livio Antonielli

Stefano Di Marco

Florence Fontaine

Laura Mugnai

Disease Control and Pest Management Innovative Delivery of Cu(II) Ions by a Nanostructured Hydroxyapatite: Potential Application in Planta to Enhance the Sustainable Control of Plasmopara viticola

Keywords: drug delivery, smart pesticides, sustainability

Downy mildew caused by Plasmopara viticola is probably the most serious disease affecting grapevine (Vitis vinifera), and it is capable of causing consistent yield losses. In organic viticulture, the only acceptable and effective means to control the disease is by applications of copperbased fungicides. However, the use of copper in agriculture is expected to be further restricted by European countries because of its critical ecotoxicological and phytotoxicological profile. Research on ways to reduce the effective amounts of copper by developing innovative formulations as well as optimization of the distribution and persistence of copper-based pesticides for downy mildew control seems to be a promising approach. This research investigated the delivery properties of biomimetic synthetic hydroxyapatite (HA) to enhance the biological activity of Cu(II) ions. To this aim, four Cu(II) compounds were formulated with the innovative HA component and applied in an in vitro antifungal assay against Botrytis cinerea, a common grapevine pathogen suitable for in vitro activity tests, and finally, in in planta efficacy assays against P. viticola under greenhouse conditions. The in vitro results highlighted a different inhibition activity for each Cu(II) compound and indicated a different interaction between the cupric compounds and HA, potentially related to different delivery mechanisms of Cu(II) from HA. Under greenhouse conditions, additional findings on the biological activity of the applied formulations were gained, especially on the efficacy of various concentrations of HA in the formulations, the influence of dose variation of the formulation and the treatment efficiency, and the persistence under rain-washing effect. This study revealed promising findings on the formulation based on the HA particles and the soluble Cu(II) compound, which resulted in reduced disease severity and incidence in all of the experimental conditions, including the lower Cu(II) dosage and the rain-washing effect. This suggests that coformulation of the three insoluble Cu(II) compounds with HA might significantly enhance the adsorption and release of Cu(II) ions by HA particles.

Grapevine (Vitis vinifera L.) is the most widely cultivated and economically important fruit crop [START_REF] Vivier | Genetic improvement of grapevine: Tailoring grape varieties for the third millennium[END_REF]. Grapevine, grown both for table grape and wine production, is also one of the crops that requires the highest fungicide input for disease control [START_REF] Pertot | A critical review of plant protection tools for reducing pesticide use on grapevine and new perspectives for the implementation of IPM in viticulture[END_REF]. The large amounts of fungicides used are especially linked to the susceptibility of most grapevine cultivars to downy and powdery mildews in climatic conditions favorable to these diseases [START_REF] Gomès | Molecular aspects of grapevinepathogenic fungi interactions[END_REF]. Downy mildew, caused by the oomycete pathogen Plasmopara viticola (Berk. & M.A. Curt.) Berl. & de Toni 1888, is probably the most serious grapevine disease, especially in grape-growing regions with relatively cool and wet spring seasons [START_REF] Kassemeyer | Downy mildew[END_REF]. In optimal weather conditions (relative humidity [RH]: 95 to 100%; temperature: 20 to 24°C) for the pathogen and with no protective treatment, downy mildew can cause huge losses [START_REF] Agrios | Downy mildew of grape[END_REF]. For this reason, in such climates, disease control becomes crucial to avoid yield losses.

Chemical control is the most effective option currently used to control downy mildew on grapes [START_REF] Selim | Elicitation of grapevine defense responses against Plasmopara viticola, the causal agent of downy mildew[END_REF]). In the last decades, fungicides based on different chemical families (strobilurins, dithiocarbamates, phenylamides, phthalimides, or cupric compounds) have been developed and are applied by vine growers according to a calendar schedule as protection against the disease [START_REF] Jermini | Quantification of the influence of Plasmopara viticola on growth, yield and plant response for the development of an integrated control strategy on Vitis vinifera (cv. merlot[END_REF]. However, other than the environmental impact, the emergence of resistant strains of P. viticola is one of the major critical aspects related to the chemical control of downy mildew as a direct consequence of the continual use of synthetic fungicides [START_REF] Chen | At least two origins of fungicide resistance in grapevine downy mildew populations[END_REF], especially single-site fungicides owing to their specific mode of action. Resistant strains were also detected in an experiment under controlled conditions after the application of a mixture based on multisite synthetic fungicides [START_REF] Samoucha | Use of two-and threeway mixtures to prevent buildup of resistance to phenylamide fungicides in Phytophthora and Plasmopara[END_REF].

Because copper was extensively used for the control of oomycete pathogens [START_REF] Heitefuss | Pflanzenschutz: Grundlagen der praktischen Phytomedizin[END_REF], no resistant strains to cupric fungicides were reported in P. viticola. This observation is related to the nonspecific mode of action of copper-containing fungicides. The wide activity spectrum of copper is based on the complexes that copper forms with membrane enzymes with sulphydryl, hydroxyl, amino, or carboxyl groups, which lead to enzyme inactivation [START_REF] Selim | Elicitation of grapevine defense responses against Plasmopara viticola, the causal agent of downy mildew[END_REF]. However, unlike some systemic fungicides, copper needs to be applied before zoospores germinate to ensure efficient disease control. Based on these properties, because copper was discovered to be effective against downy mildew by Millet in the 19th century [START_REF] Gessler | Plasmopara viticola: A review of knowledge on downy mildew of grapevine and effective disease management[END_REF], different cupric salts have been applied over the years in preventive control strategies according to the meteorological conditions favorable for downy mildew infection [START_REF] Gisi | Chemical control of downy mildews[END_REF].

Applications of copper-based fungicides are still the most reliable means to protect grapevines against downy mildew in organic viticulture [START_REF] Berkelmann-Löhnertz | Kupferreduzierung und Kupfersubstitution im Weinbau, zum Stand der Dinge aus Sicht der Forschung[END_REF]). However, concerns have been expressed about the use of copper for plant protection, mainly owing to the critical ecotoxicological profile of cupric fungicides, which is well described in the literature [START_REF] Flemming | Copper toxicity and chemistry in the environment: A review[END_REF]. Repeated applications of copper for downy mildew control may be responsible for several phytotoxic effects, such as burning of young shoots and leaves [START_REF] Claus | 90 Jahre Kupferanwendung im Weinbau und immer noch Erkenntnislücken[END_REF]. The main effect of high copper concentrations on plant cells is an oxidative stress caused by the increased concentration of reactive oxygen species, which can severely damage the cell membranes, causing them to rupture and resulting in leakage of the cell contents [START_REF] Apel | Reactive oxygen species: Metabolism, oxidative stress, and signal transduction[END_REF][START_REF] Yruela | Copper in plants[END_REF]). Among the side effects of copper, its accumulation in agricultural soils is considered the most controversial. Being a heavy metal, copper is not degraded in soil, and the long-term use of cupric fungicides in organic agriculture is responsible for extensive copper accumulation in soils [START_REF] Komárek | Contamination of Vineyard soils with fungicides: A review of environmental and toxicological aspects[END_REF][START_REF] Rusjan | Copper accumulation regarding the soil characteristics in Sub-Mediterranean vineyards of Slovenia[END_REF]). Increased copper concentrations negatively affect the concentration and diversity of the microbial communities in vineyard soils [START_REF] Lejon | Copper dynamics and impact on microbial communities in soils of variable organic status[END_REF], and consequently, the reduction of microbial activity and changes in microbial populations can lead to lower mineralization rates of organic pesticides [START_REF] Jacobson | Electron microprobe and synchrotron X-ray fluorescence mapping of the heterogeneous distribution of copper in high-copper vineyard soils[END_REF]). In addition, the excessive accumulation of copper in the soil profile may pollute the groundwater [START_REF] Robinson | Leaching of copper, chromium and arsenic from treated vineyard posts in Marlborough, New Zealand[END_REF].

In view of the side effects of copper, European regulations are limiting the amount of copper applied in vineyards (European Commission 2018). In Spain, Italy, and France, up to 6 kg ha _ 1 per year or 30 kg ha _ 1 per 5 years of copper is allowed for crop protection as established in Regulation (European Commission) 354/2014 (European Commission 2014). In some other European countries (e.g., The Netherlands and Denmark), the use of copper in agriculture is forbidden, whereas in other countries, there are additional restrictions (e.g., 3 kg ha _ 1 per year in Germany). In 2018, the European Food Safety Authority reviewed the maximum residue levels of copper currently established at the European level for food commodities, including wine grapes, because the exposure risk for consumers was found to be slightly higher than the tolerable threshold (European Food Safety Authority 2018).

Nevertheless, the use of copper is still tolerated, especially in organic viticulture, considering its exclusive property as a widespectrum fungicide and the lack of efficient alternative treatments for control of grapevine downy mildew. In view of the legislative restrictions, studies have been aimed at reducing the effective amount of copper used for the control of P. viticola in organic viticulture, revealing the potential for efficient control at 200 to 400 g of Cu ha _ 1 per application with 12 to 14 applications per year [START_REF] Cabús | Efficacy of reduced copper dosages against Plasmopara viticola in organic agriculture[END_REF]). This study confirmed previous results related to the control of downy mildew in vineyards applying a maximum of 3 kg of Cu ha _ 1 per year using concentrations of 50 to 400 g of Cu ha _ 1 according to the phenological phase [START_REF] Hoffman | Optimisation of downy mildew (Plasmopara viticola) control in organic viticulture with low copper doses, new copper formulations and plant strengtheners[END_REF].

Research oriented toward the development of innovative formulations of copper seems to be a promising approach to enhancing the control of downy mildew and minimizing the side effects of copper. In a comparative trial performed in a greenhouse and vineyard [START_REF] Dagostin | Are there alternatives to copper for controlling grapevine downy mildew in organic viticulture?[END_REF], two novel copper-based formulations showed positive results. The first, based on copper gluconate, was particularly effective in the vineyard, and the second one, based on copper peptidate, provided high levels of disease control in both conditions but caused phytotoxicity in treated plants. The possibility to optimize the distribution and persistence in planta of copper-based pesticides has also been considered by many studies in nanotechnology. In particular, the development of slowrelease systems for pesticides has opened new possibilities to reduce the amount of the active substance applied, leading to efficient plant protection and disease control [START_REF] Madhuri | Nanotechnology in agricultural diseases and food safety[END_REF][START_REF] Nair | Nanoparticulate material delivery to plants[END_REF]. Promising results were achieved by the engineered nanoparticles (NPs), some of which were formulated with copper (Cu NPs) [START_REF] Lee | Toxicity and bioavailability of copper nanoparticles to terrestrial plants Phaseolus radiatus (Mung bean) and Triticum aestivum (Wheat): Plant agar test for water-insoluble nanoparticles[END_REF]. Nonetheless, numerous authors have reported the need for further evaluations of such NPs on the cytotoxicity and genotoxicity within the plant tissues [START_REF] Jo | Antifungal activity of silver ions and nanoparticles on phytopathogenic fungi[END_REF][START_REF] Lin | Root uptake and phytotoxicity of ZnO nanoparticles[END_REF].

This research arises from the need to improve the distribution and persistence of copper on grapevine leaves by modifying its structure through a specific and achievable formulation with a biocompatible material. In that respect, the aggregation and stability of synthetic nanostructured particles of hydroxyapatite (HA) and four Cu(II) compounds were previously investigated, revealing promising results [START_REF] Battiston | Functionalization of a nanostructured hydroxyapatite with Cu(II) compounds as a pesticide: In situ transmission electron microscopy and environmental scanning electron microscopy observations of treated Vitis vinifera L. leaves[END_REF]. Indeed, HA has been studied extensively and applied successfully in the medical field as a biocompatible and biomimetic material thanks to its unique drug delivery properties, which are active on metal ions as well as both organic and inorganic compounds [START_REF] Kim | Antimicrobial effects of metal ions (Ag + , Cu 2+ , Zn 2+ ) in hydroxyapatite[END_REF][START_REF] Roveri | Evolving application of biomimetic nanostructured hydroxyapatite[END_REF][START_REF] Suzuki | Cationexchange characteristics of sintered hydroxyapatite in the strongly acidic region[END_REF].

The aim of this study was to assay the activity, under controlled conditions, of formulations based on HA particles and four different Cu(II) compounds against P. viticola. More specifically, the work was focused on (i) the antifungal activity of each Cu(II) compound formulated with HA and tested on reference fungal pathogens in vitro and in vivo; (ii) the efficacy of various concentrations of HA in the formulations; (iii) the influence of dosage variation of the treatments [at lower Cu(II) concentrations than the dosages recommended for cupric fungicides]; and (iv) the evaluation of protective treatments based on the same formulations under rainwashing effects.

MATERIALS AND METHODS

Functionalization of HA with Cu(II). A water suspension containing 30% wt wt _ 1 of nanostructured HA (Ndg Natural Development Group Srl) was prepared according to a patented process of synthesis [START_REF] Roveri | Particule d'hydroxyapatite, compositions a base de cette particule, utilisations comme vecteur de molecules bioactives[END_REF]. The technical powder of four Cu(II) compounds (Cnr-Ibimet) was prepared to functionalize HA: copper sulfate pentahydrate (CuSPHy), tribasic copper sulfate (CuTBS), copper oxychloride (CuOxCl), and copper hydroxide (CuHyOx). Functionalization of the products was carried out by maintaining the HA slurry with the respective Cu(II) compound and water complex. The various Cu(II) compounds were presolubilized or suspended in water and then added to the HA slurry with slow agitation for 4 h. Formulations were prepared based on two approaches for two different efficacy assays (EAs): (i) varying both the HA and Cu(II) percentage (Table 1) and (ii) varying the HA percentage and maintaining a predefined Cu(II) concentration (Table 2). The formulations were analyzed by inductively coupled plasma optical emission spectrometry (Arcos-Spectro; Ametek) to verify the copper concentration. Copper doses. In the samples (Tables 1 and2), the Cu(II) concentration was established at 5.25 ± 0.04% wt wt _ 1 for the formulations up to 5.4% wt wt _ 1 of HA and 4.15 ± 0.30% wt wt _ 1 for the formulations with 6% wt wt _ 1 of HA owing to the Cu(II) compound stability in the formulation with HA.

The amount of product applied (or treatment dose) for each sample was varied so that the final amount of Cu(II) applied in planta in each replicate was standardized among all treatments. According to a previous study, which analyzed the effective amount of Cu(II) on treated leaves in downy mildew control assays [START_REF] Cabús | Efficacy of reduced copper dosages against Plasmopara viticola in organic agriculture[END_REF], samples were applied in planta by spraying solutions/ suspensions with the following empirically derived concentrations of Cu(II): 0.01, 0.025, 0.05, and 0.075% wt wt _ 1 (Table 3). Such concentrations were also adopted according to the aim of each assay. Otherwise, considering the irrelevant antimicrobial activity of the pure HA described in the literature [START_REF] Groza | Structural properties and antifungal activity against Candida albicans biofilm of different composite layers based on Ag/Zn doped hydroxyapatite-polydimethylsiloxanes[END_REF][START_REF] Kim | Antimicrobial effects of metal ions (Ag + , Cu 2+ , Zn 2+ ) in hydroxyapatite[END_REF], in the preliminary in vitro antifungal assay, the samples (Table 1) were applied at higher concentrations than in planta. More specifically, the solid growth media were dosed with Cu(II) at concentrations of 0.05, 0.1, and 0.2% wt wt _ 1 .

Preliminary in vitro antifungal assay. For a preliminarily understanding of the putative antifungal activity of HA formulated with each Cu(II) compound, the samples (Table 1) were applied in vitro for the mycelial growth inhibition test [START_REF] Aqueveque | Antifungal activities of extracts produced by liquid fermentations of Chilean Stereum species against Botrytis cinerea (grey mould agent)[END_REF]. A strain of Botrytis cinerea Pers. was chosen as the representative grapevine pathogen, which is often tested for in vitro antifungal assays alongside in vivo control assays on P. viticola [START_REF] Hao | Biocontrol of grapevine aerial and root pathogens by Paenibacillus sp. strain B2 and paenimyxin in vitro and in planta[END_REF]. Malt extract agar (MEA), composed of malt extract 20 g liter _ 1 (Liofilchem Srl), agar 15 g liter _ 1 (Liofilchem Srl), and distilled water, was amended with three different dosages (Table 1) of three Cu(II) concentrations (0.05, 0.1, and 0.2% wt wt _ 1 ) combined with the HA concentration related to the sample. Petri dishes (9-cm diameter), each containing 15 ml of medium, were inoculated by transferring 7-mm-diameter mycelial discs taken from the periphery of 5-to 7-day-old cultures of B. cinerea and placing them mycelium side down at the center of the plate. Two replicates of treated and untreated control plates were incubated at 25°C in darkness and repeated in three independent experimental runs. Control plates were plain MEA. Growth inhibition percentage (GI%) was calculated daily until the fifth day postinoculation as follows:

GI% = ðDC-DOÞ DC × 100
where DC is the diameter of mycelial growth in control plates and DO is the diameter of mycelial growth in treated plates.

In planta antifungal assay. Experiments in controlled conditions were performed in an experimental greenhouse at Fondazione Edmund Mach (San Michele all'Adige, Trento, Italy). Four consecutive EAs against P. viticola were carried out to evaluate (EA1) the performance of each Cu(II) compound formulated with HA, (EA2 and EA3) the efficacy of various concentrations of HA in the formulations based on the two most effective Cu(II) compounds and applied in planta at various dosages, and (EA4) the efficacy and stability of the most effective formulations under a rain-washing effect. The same protocol was applied for all of the EAs, applying a rain fastness test in EA4. Each EA was repeated in three independent experimental runs.

Plant material. One-year-old grapevine plants (V. vinifera 'Chardonnay' grafted on Kober 5BB rootstock) were grown in individual 2.5-liter pots of peat-rich, prefertilized (nitrogen, phosphorus, potassium: 14:16:18) standard soil (Topfsubstrat D450; Stender) under natural light (15 h each day) at temperatures ranging from 18 to 28°C. Six potted vines with at least one to two shoots and 8 to 10 developed leaves were prepared for each treatment: two potted vines were biological replicates for each treatment repeated in three independent experimental runs for each of the EAs.

Preventive treatments and inoculation. Distilled water was used as the control treatment alongside the standard treatments based on cupric or organic commercial fungicides (Table 4). In laboratory conditions (temperature 20 ± 1°C, RH 65 ± 5%, and artificial light), reference fungicides were diluted according to the recommended dosage, whereas each experimental sample was dissolved or suspended in a specific volume of distilled water according to the Cu(II) concentration investigated in planta in each EA. The pH of the diluted samples and distilled water (Table 1) was measured with a pH meter (pH 538; WTW GmbH). Each treatment was performed by spraying 30 ml of diluted formulation on the plants with a garden spray pump (Sprayer 0.6 L; Leroy Merlin), taking care to cover homogenously both the adaxial and abaxial leaf surfaces. Before inoculation, plants were left to dry at room temperature. Inoculum of P. viticola was prepared immediately before inoculation by washing grapevine leaves bearing freshly sporulating lesions with cold (4°C) distilled water. The concentration of the inoculum suspension was adjusted to 5 × 10 5 sporangia ml _ 1 based on sporangial counts estimated with a hemocytometer. Six hours posttreatment, the inoculum suspension was sprayed on potted vines, taking care to cover the abaxial surface of leaves. The control plants were not inoculated. Plants were transferred to a dark growth chamber for 16 h at 20 ± 1°C and RH of 80 to 99%, and then, they were kept in the greenhouse for 7 days (incubation period) at 25 ± 1°C with an RH of 60% and natural light. After the incubation period, plants were placed again in a dark growth chamber for 16 h at 20 ± 1°C with an RH of 80 to 99% to promote P. viticola sporulation.

Rain fastness test. In EA4, rain fastness was simulated 4 h after the treatments. Potted vines were subjected to 0 or 30 mm of simulated rain (30 mm h _ 1 ) applied by means of 14 sprinklers positioned 2.2 m above the soil (Fig. 1) that were protected from wind and regulated to produce drops similar in size to raindrops (0.3 to 2.5 mm). After the simulated rainfall, plants were left to dry for 4 h and then inoculated with the pathogen as previously described. Results recorded on commercial fungicides and the positive control were analyzed separately from results recorded on experimental treatments to avoid any misinterpretation of the data. Assessment of disease severity and incidence. The treatment activity was evaluated based on two parameters: disease incidence (percentage of leaves with oil spot symptoms and/or visible sporulation) and disease severity (percentage of leaf area covered by sporulating lesions). According to the European and Mediterranean Plant Protection Organisation (EPPO) standard scale (European and Mediterranean Plant Protection Organization 2004), both parameters were visually estimated using continuous values of percentage (from 1 to 100%).

Environmental scanning electron microscopy. In EA1, the distribution of the treatments on the plant foliage and the structural features of the particles suspended in the tested formulations (based on HA 3%) were assessed by direct analyses in planta with an environmental scanning electron microscope (ESEM; Fei Quanta 200 ESEM; FEI Corporation) operating in low-vacuum mode at 25 kV without pretreatment of the samples. X-ray (EDS) microanalysis by an energy-dispersive system coupled to the ESEM (EDAX; software EDAX Genesis; AMETEK) was used to investigate the composition of the particles and the distribution of the related elements on the leaf surface, which are (namely) Ca, P, Cu, S, and Cl. Observations were performed on the leaves of treated potted vines 8 days posttreatment. Foliar samples were collected from each replicate from all of the investigated conditions by counting from the basal part of the primary shoot and sampling the fourth leaf. Leaves were cut into small portions (10 × 10 mm) and transferred to a conductive adhesive carbon mounted on aluminum stubs.

Statistical analysis. Statistical analysis was performed using R Statistical Software. In the in vitro assay, the measurements were performed on two replicates repeated in three independent experimental runs. Analysis of variance (ANOVA) was performed to determine the significance of differences (P £ 0.05) between treatment mean values of GI%. Experiments under greenhouse conditions were designed as randomized complete blocks with two replicates per treatment repeated in three independent experimental runs for each EA. Preliminary analyses of disease severity and incidence on leaves were conducted in separate experiments, and homogeneity of variance was checked before ANOVA. Data were then combined and considered in the same regression model for which homoscedasticity was again tested via a "residuals versus fitted values" plot, and distribution fitting was evaluated using the bootstrapping method implemented in the fitdistrplus::descdist R function. Data on disease severity and incidence on leaves were analyzed with ANOVA. When differences were found (P £ 0.05), Tukey's honestly significant difference (HSD) test based on least square means (lsmeans R package) was applied to detect differences between the various levels of the factor [START_REF] Lenth | Least-squares means: The R Package lsmeans[END_REF]. In order to not affect the data interpretation, contrasts between reference treatments (the positive control and the commercial fungicides) were performed separately from the contrasts between the experimental treatments, as the reference treatments do not express the factors and the factor levels expressed by the experimental treatments. Results on commercial fungicides were also plotted (ggplot2 R package) to evaluate the effects of these products on severity of downy mildew and determine the relationship between the amount of the active ingredient applied and the efficacy of the treatment.

RESULTS

Preliminary in vitro antifungal assay. The activities of three concentrations of formulations based on Cu(II) compounds and HA on mycelial growth of B. cinerea are shown in Figure 2. All of the Cu(II) compounds in different concentrations inhibited the growth of B. cinerea. CuSPHy was the most effective for inhibiting mycelial growth at all applied concentrations of Cu(II) (0.05, 0.1, and 0.2% wt wt _ 1 ). Mycelial growth of B. cinerea was inhibited by CuTBS at nearly 65% by the lower concentration and 87% by the higher concentration of Cu(II). CuHyOx showed the lowest activity against pathogen growth at 0.05 and 0.1% Cu(II), with no increase in inhibition at the highest concentration of Cu(II). The concentration of CuOxCl affected its activity, because the lowest concentration of Cu(II) showed the lowest inhibition of the pathogen (GI% = 10), which significantly increased (GI% = 70) at 0.2% Cu(II). HA had a variable effect on the Cu(II) compounds depending on its concentration. At 3% HA, CuSPHy was still the most effective inhibitor of B. cinerea growth, even when the concentration of Cu (II) was reduced. At the lowest concentration of Cu(II), the same level of HA had an opposite effect on CuHyOx and CuOxCl, reducing the inhibitory activity of the former and increasing the growth inhibition of the latter. CuTBS showed a similar inhibition of the corresponding pure Cu(II) compound, whereas the activity of CuHyOx was reduced by 3% HA, especially at the higher amount of Cu(II). Different results were reported by 6% HA. Such a level reduced the inhibitory activity of the lowest concentration of CuSPHy, whereas on the other Cu(II) compounds, it increased the GI%, especially for CuOxCl, and CuHyOx at 0.2% Cu(II). The GI% index differed significantly (P £ 0.05) between the different Cu(II) compounds, the applied Cu(II) amounts, and the percentage of HA.

In planta EA. Effect of Cu(II) compounds formulated with HA. The greenhouse trial EA1 investigated the efficacy of four Cu (II) compounds formulated with two percentages of HA in the control of the grapevine pathogen P. viticola. Results of disease severity are shown in Figure 3. Data of treatments based on (i) water as positive control, (ii) organic fungicide, (iii) cupric fungicide, and (iv) 3% HA are presented separately (Fig. 3A) and compared with the results of the experimental treatments (Fig. 3B). The positive control showed various degrees of disease severity, with a maximum value of nearly 75% and a mean of 35%. Mean disease severity in the plants treated with the organic fungicide and the cupric fungicide was significantly lower than the positive control, indicating good disease control (P = 0.0129 and P = 0.0163, respectively). No infected leaves were seen in the noninoculated control plants. The treatment based on 3% HA did not have any effect on P. viticola, resulting in a disease severity that was not significantly different from the positive control. The effects owing to Cu(II) compound and HA were both found to be significantly different from each other (P £ 0.05). In Table 5, the contrasts (Tukey's HSD test) within the factor Cu(II) compound and the factor HA percentage are reported for disease severity and incidence. Considering the pure Cu(II) compounds, the lowest disease severity of 5% was reported by CuSPHy, which was significantly different from CuHyOx (P = 0.0189), CuTBS (P = 0.0001), and CuOxCl (P < 0.0001). The applied Cu(II) concentration (0.025% wt wt _ 1 ) was not effective for the other pure compounds. Concerning the formulations based on 3% HA, CuTBS resulted in a significant reduction (P = 0.0040) in disease severity compared with CuOxCl, whereas at 6% HA, the effect was slighter reduced. CuOxCl responded positively to the formulation with HA, showing a significant difference in disease severity at 6% HA, but it did not correspond to an acceptable disease control. The apparent efficiency of the formulation based on CuHyOx with 3% HA was not significant and did not increase at 6% HA. Concerning the disease incidence, the most useful results were observed with CuSPHy and 3% HA, in which 52% of the leaves were symptomatic, followed by CuTBS and 3 and 6% HA with ;70% disease incidence. In all other treatments, disease incidences were >80%, and the positive control had 100% disease incidence (data not shown). A consistent phytotoxic effect was reported on all of the leaves treated with CuSPHy, but this was not observed with the same compound at 3 and 6% HA. No phytotoxic signs were visible on plants in the control, commercial fungicide treatments (Table 4), or any other treatments.

Effect of HA concentration and applied amount of Cu(II). The variability of the factor HA percentage in the formulation and the effect of the factor dosage percentage were studied in greenhouse trials EA2 and EA3 by applying treatments based on CuSPHy and CuTBS, which were the two most effective Cu(II) compounds in EA1. In Table 4, results of the control and the comparison treatments are shown. No symptoms were detected in the negative control. Symptoms were more severe and diffused in EA2 (61 and 100%, respectively) than in EA3 (39 and 86%, respectively), and in both experiments, the respective differences were significant. The treatment dimetomorf was highly efficient in reducing both disease severity and incidence. Figure 4 shows the disease severity (percentage) detected in EA2 (Fig. 4A) and EA3 (Fig. 4B). Considering the formulations based on CuSPHy (Fig. 4A) in comparison with the CuSPHy fungicide (Table 4), good disease control was reported at all of the levels of HA and at 0.05% Cu(II), Fig. 3. Results on disease severity (percentages) detected in potted grapevines (cultivar Chardonnay) treated with water (positive control), dimetomorf, cupric fungicide, or 3% hydroxyapatite (HA) and comparison with the experimental treatments. A, Commercial fungicides and the positive control are presented and analyzed separately from the experimental treatments to not affect the data interpretation. B, Experimental treatments. CuHyOx, copper hydroxide; CuOxCl, copper oxychloride; CuSPHy, copper sulfate pentahydrate; CuTBS, tribasic copper sulfate; HA, hydroxyapatite. TABLE 5. Contrasts in pairs (Tukey's honestly significant difference (HSD) test) within the factor copper compound and the factor hydroxyapatite (percentage) showing the significant differences on disease severity and incidence (efficacy assay 1) z but it had a wider distribution of disease severity values at 5.4% HA and the lowest mean severity between 2.4 and 3.6% HA. At lower levels of the factor dosage percentage, the same formulations also had a wider distribution of the results in disease severity, which is close to the commercial fungicide (4.6%) at 0.025% Cu(II), whereas at 0.01% Cu(II), it shows higher mean values. A high phytotoxic effect was detected on the grapevine leaves treated with the CuSPHy formulations at 0.6% HA and less at 1.2% HA, with major intensity at the higher Cu(II) dosage. Overall, the CuSPHy treatments resulting in lower disease severity, and the most stable results, even at lower Cu(II) percentage, were based on 2.4 and 3.6% HA. In the parallel experiment EA3, the CuTBS fungicide (Table 4) was effective in controlling P. viticola. For CuTBS formulations applied at 0.05% Cu(II), the factor HA percentage (from 0.6 to 5.4%) resulted in reduced distribution of disease severity values, showing good disease control compared with the 2.4% HA. The contrast was observed in the same treatments applied at 0.025% Cu(II), but the trend was not observed at the lowest dosage of Cu(II), where disease severities were nearly 20% for all HA percentages. No signs of phytotoxicity were detected on the leaves treated with CuTBS-based formulations at all Cu(II) percentages.

In both experiments EA2 and EA3, the factor dosage percentage was significant (P £ 0.05), whereas the factor HA percentage was also significant as seen in EA2. Comparisons of means by Tukey's HSD test within the factor HA percentage and the factor dosage percentage (a = 0.05% wt wt _ 1 , b = 0.025% wt wt _ 1 , and c = 0.01% wt wt _ 1 ) are presented in Table 6, highlighting the significant differences in disease severity in both trials. Unlike EA1, few contrasts in EA2 and EA3 were significant for both factors. However, based on the disease severity, the most effective formulations were found at 2.4 to 3.6% HA for CuSPHy and 3.6 to 5.4% HA for CuTBS applied at 0.5% Cu(II). The same results, in terms of tendency and significance, were observed based on disease incidence recorded in both trials (data not shown).

Treatments efficacy and stability under a rain-washing effect. Based on the previous results, which revealed the optimal HA level for CuSPHy and CuTBS, both Cu(II) compounds formulated with 3% HA were applied in a greenhouse rain fastness test (EA4) to study their efficacy and stability in comparison with the pure Cu(II) compounds and the reference treatments (Table 4). No significant differences were detected in both positive controls (potted vines washed by the simulated rain and unwashed), which had 100% disease incidence and nearly 55% disease severity. The rainwashing effect was not detected on leaves treated with organic fungicide, which was highly effective under both conditions. CuSPHy fungicide (Table 4) showed the best performance in reducing disease incidence and severity and provided good disease control, even after the simulated rain. CuTBS fungicide (Table 4) lost efficacy in the simulated rain condition, showing approximately the same degree of downy mildew infection as the positive control (Fig. 5A). The treatment based on CuSPHy revealed the highest control activity, reducing both severity and incidence, with low level of variability in the results under both conditions (Fig. 5B). However, the treatment resulted in severe phytotoxicity. CuSPHy formulated with HA did not show any phytotoxicity, and despite the nonsignificant difference from the results reported by the same pure compound, disease severity was <5% in both conditions (Fig. 5B). Treatment based on CuTBS was significantly less effective than CuSPHy. The differences in disease severity and incidence were much greater in the simulated rain test. Under such conditions, the formulation based on CuTBS and HA did not give a significant reduction in severity or incidence of P. viticola compared with the CuTBS-based treatment, revealing a similar protection to the CuTBS fungicide. Pairwise comparisons by Tukey's HSD test within the factor Cu(II) compound and the factor rain-washing effect were highly significant for both factors.

ESEM. The in planta ESEM observations showed aggregation of the HA particles (Fig. 6). Distribution of the particles on the leaf surfaces of treated potted vines was studied 8 days posttreatment (EA1). Particles based on pure HA revealed the Ca/P ratio of HA (i.e., 1.67). These particles were aggregated in spotted areas and were not regularly distributed over the leaf surface (Fig. 6A). A similar observation was noted on the CuSPHy-HA-based particles, which were distributed on the leaf surface and tended to be concentrated in one point (Fig. 6B). The HA-CuTBS-based treatment showed a more homogeneous and dispersed distribution of particles on the leaf than the HA-CuSPHy treatment (Fig. 6C). The same observation was seen for HA-CuOxCl-and HA-CuHyOx-based treatments in Figure 6D andE, highlighting, in the first case, the joint presence of particles and round patchy TABLE 6. Contrasts in pairs (Tukey's honestly significant difference (HSD) test) within the factor hydroxyapatite (percentage) and the factor dosage percentage (a = 0.05%, b = 0.025% wt wt _ 1 , c = 0.01% wt wt _ 1 ) showing the significant differences on disease severity (efficacy assays 2 and 3) z clusters of the same and in the second one, the higher density of micrometric aggregates. In the leaf samples treated with distilled water (positive control), a particulate distributed on the leaf surface was detected. Elemental analysis of this particulate did not reveal any signal corresponding to copper, calcium, or phosphorous, indicating that the particulate was not attributable to the applied substances (Fig. 6F).

CuTBS

CuSPHy 0.6 1.2 2.4 3.6 5.4 a b c a b c a b c a b c a b c 0.6 a _ n.s. * n.s. _ _ n.s. _ _ n.s. _ _ n.s. _ _ b * _ n.s. _ n.s. _ _ n.s. _ _ n.s. _ _ n.s. _ c n.s. n.s. _ _ _ n.s. _ _ n.s. _ _ n.s. _ _ n.s. 1.2 a n.s. _ _ _ n.s. * n.s. _ _ n.s. _ _ n.s. _ _ b _ n.s. _ n.s. n.s. _ n.s. _ _ n.s. _ _ n.s. _ c _ _ n.s. n.s. n.s. _ _ _ * _ _ * _ _ n.s. 2.4 a * _ _ n.s. _ _ _ n.s. n.s. n.s. _ _ * _ _ b _ n.s. _ _ n.s. _ n.s. n.s. _ n.s. _ _ n.s. _ c _ _ n.s. _ _ n.s. * n.s. _ _ _ n.s. _ _ * 3.6 _ a * _ _ n.s. _ _ n.s. _ _ _ n.

DISCUSSION

The main aim of this research was to evaluate the application in planta of an innovative tool to enhance the biological activity of Cu (II) ions for the sustainable control of the grapevine pathogen P. viticola. The research highlighted the delivery properties of the biomimetic synthetic HA, which was shown to enhance the biological activity of Cu(II) ions. Clearly promising results were shown by applying HA in the final in planta EAs against P. viticola under greenhouse conditions, especially on the soluble Cu(II) salt (CuSPHy), reducing both disease severity and disease incidence in all of the experimental conditions. The treatment also showed a high efficacy and persistence under rain-washing effect.

Despite the higher practical significance and efficiency of the in planta assays in screening fungicides [START_REF] Varo | Screening water extracts and essential oils from Mediterranean plants against Verticillium dahliae in olive[END_REF], significant and remarkable findings on the antifungal activity of the investigated substances were revealed by the preliminary in vitro assay. Being susceptible to broad-spectrum treatments based on copper [START_REF] Jacometti | Review: Alternatives to synthetic fungicides for Botrytis cinerea management in vineyards[END_REF], B. cinerea was also studied in previous laboratory trials performed to evaluate mycelial growth inhibition by innovative antimicrobial particles [START_REF] Ouda | Antifungal activity of silver and copper nanoparticles on two plant pathogens, Alternaria alternata and Botrytis cinerea[END_REF]. In general, different grades of inhibition by each Cu(II) compound were highlighted according to their applied dosage. CuSPHy was highly efficient in inhibiting mycelial growth of B. cinerea at all of the applied concentrations, possibly because of the high solubility of this Cu(II) salt, which dissolves in solution the highest concentration of Cu(II). The lower antifungal activity reported by the other Cu(II) salts, such as CuTBS, CuOxCl, and CuHyOx, is a result of their lower solubility, because such compounds tend to remain in suspension, releasing slowly and in certain conditions, the Cu(II) ions [START_REF] Gessler | Plasmopara viticola: A review of knowledge on downy mildew of grapevine and effective disease management[END_REF]. The insignificant antimicrobial activity reported in the literature for particles based on HA [START_REF] Groza | Structural properties and antifungal activity against Candida albicans biofilm of different composite layers based on Ag/Zn doped hydroxyapatite-polydimethylsiloxanes[END_REF][START_REF] Kim | Antimicrobial effects of metal ions (Ag + , Cu 2+ , Zn 2+ ) in hydroxyapatite[END_REF]) could explain the contradictory role shown by the HA formulation on each Cu(II) compound. With CuSPHy, the most effective Cu(II) salt, the highest concentration of Fig. 5. Results of the rain fastness test on disease severity (percentages) and disease incidence (percentages) detected on leaves of potted grapevine (cultivar Chardonnay) under greenhouse conditions. Plants were treated and exposed to 0 or 50 mm of simulated rain before inoculation with Plasmopara viticola (5 × 10 5 sporangia ml _ 1 ). A, Commercial fungicides and the positive control are presented and analyzed separately from the experimental treatments to not affect the data interpretation. B, Experimental treatments. CuSPHy, copper sulfate pentahydrate; CuTBS, tribasic copper sulfate; HA, hydroxyapatite.

HA (6%) significantly reduced the inhibitory activity of CuSPHy when applied at the lowest concentration of Cu(II) (0.05%). This was thought to be related to the excess of HA, with no antimicrobial activity, compared with the Cu(II) ions in solution. In the same condition, the opposite effect was reported with CuHyOx. In general, this effect was shown on all of the Cu(II) compounds applied at 0.2% Cu(II), in which the 6% HA enhanced significantly the inhibition of B. cinerea. These observations have suggested to investigate the delivery role potentially played by HA in planta, in relation to each Cu(II) salt and to the concentration ratio between HA and Cu(II) ions into the formulation.

Under greenhouse conditions, promising findings on the biological activity of formulations based on Cu(II) and nanostructured particles of HA were gained from these experiments. The formulations previously applied in vitro were sprayed in the trial EA1 onto the foliage of potted vines at the same Cu(II) ions concentration (0.025%) of the cupric fungicide in comparison according to early greenhouse EAs, which defined such amount as the minimal quantity of copper ions able to acceptably prevent downy mildew [START_REF] Dagostin | Are there alternatives to copper for controlling grapevine downy mildew in organic viticulture?[END_REF]. In this condition, CuSPHy formulated with 3% HA reduced significantly both disease incidence and severity, whereas with a higher HA content (6%), the HA-CuSPHy formulation lost protective activity against P. viticola, confirming the tendency detected in the growth inhibition of B. cinerea by the same formulations. The nonsignificant biological activity shown by the same concentration of HA confirms that the high efficiency of the HA-CuSPHy formulation is not a consequence of any fungitoxic activity of the HA-based particles. However, very good disease control was also achieved by the treatment based on the pure CuSPHy, but this resulted in severe phytotoxicity on the treated leaves. As described by [START_REF] Gessler | Plasmopara viticola: A review of knowledge on downy mildew of grapevine and effective disease management[END_REF], CuSPHy is the main constituent of Bordeaux mixture, which is a cupric fungicide developed by neutralizing and fixing the highly soluble and phytotoxic Cu(II) ions of this copper salt. It is known in the literature for being the most ancient and efficient fungicide applied for the control of P. viticola [START_REF] Romanazzi | Impact of alternative fungicides on grape downy mildew control and vine growth and development[END_REF]). Among the nonsoluble Cu(II) compounds, in the EA1, there was no evidence of a significant effect on controlling the disease compared with the cupric fungicide (based on CuHyOx). However, in the experimental treatments, the formulation with HA revealed the same tendencies shown in vitro, such as the reduced variability of the results (CuOxCl) and the general increase in treatment efficiency (CuTBS), except for CuHyOx, which showed the lowest disease severity at 3% HA. Likewise, the low efficiency reported by the treatments based on the pure nonsoluble Cu(II) compounds is certainly related to the application of the pure technical compounds without any coformulate that is used in the commercial products.

Electron microscopy was useful for studying the distribution of particles and their aggregation in planta, because the application of HA arises from its property of generating nanostructured biologically active coatings [START_REF] Roveri | Evolving application of biomimetic nanostructured hydroxyapatite[END_REF]. Such aggregated particles were detected on the leaf samples treated with HA. A similar configuration was observed on leaves treated with HA-CuSPHy. However, treatments based on the insoluble Cu(II) compounds and HA seemed to be distributed in smaller particle aggregations, showing different aggregates compared with the HA clusters. The diverse particle conformation and distribution reflect the different results shown in the greenhouse trial EA1. This aspect highlights the importance of spreading and delivering of Cu(II) ions on the leaf surface with respect to the control of early fungal infection and their agents, the P. viticola zoospores [START_REF] Jürges | The mode of interaction between Vitis and Plasmopara viticola Berk. & Curt. ex de Bary depends on the host species[END_REF][START_REF] Kiefer | The host guides morphogenesis and stomatal targeting in the grapevine pathogen Plasmopara viticola[END_REF]. Furthermore, the variable response of treatments in EA1 may be explained by the effect of the irregular aggregation of particles and therefore, their irregular size, which have a direct impact on the droplet size generated during the spraying application of the protective substance, thus influencing significantly the treatment efficiency [START_REF] Ferguson | Pressure, droplet size classification, and nozzle arrangement effects on coverage and droplet number density using air-inclusion dual fan nozzles for pesticide applications[END_REF].

The formulation HA-CuSPHy was further investigated as a potential innovative cupric fungicide compared with the formulation HA-CuTBS based on the insoluble Cu(II) compound. In both formulations, the efficacy of various concentrations of HA was studied in relation to Cu(II) concentrations. In general, the results (EA2) confirmed that the most effective CuSPHy formulation [containing 5.2% Cu(II)] is based on HA varying between 2.4 and 3.6% as seen in the greenhouse trial EA1. This encouraging result was shown by the overdosage [0.05% Cu(II)] and unexpectedly, underdosage treatments [0.01% Cu(II)]. This latter result opens up interesting perspectives in comparison with early studies aimed at investigating the efficacy of reduced copper dosage against P. viticola [START_REF] Cabús | Efficacy of reduced copper dosages against Plasmopara viticola in organic agriculture[END_REF][START_REF] Dagostin | Are there alternatives to copper for controlling grapevine downy mildew in organic viticulture?[END_REF][START_REF] Heibertshausen | Using copper in organic viticulture: Doing it best with less? The 3rd QLIF Congress[END_REF][START_REF] Hoffman | Optimisation of downy mildew (Plasmopara viticola) control in organic viticulture with low copper doses, new copper formulations and plant strengtheners[END_REF] and considering probable future restrictions on the use of copper in agriculture. Otherwise, the findings collected on the formulations based on CuTBS (EA3) indicate a dissimilar activity of the factor HA percentage on the insoluble copper salt. In fact, despite a generally lower efficacy of CuTBS formulations than the ones based on CuSPHy, the less variable results in disease severity were reported at the highest percentage of HA and the over-and underdosage of Cu(II) ions. This observation suggests a deeper investigation into the methods and materials applicable to the optimal coformulation between the suspension of HA nanostructured particles and the suspensions of the insoluble Cu(II) compound, such as CuTBS.

In greenhouse experiments carried out with rain-washing simulation, it was possible to evaluate the stability and persistence on grapevine leaves of the formulations based on HA-CuSPHy and HA-CuTBS. In contrast to the study by [START_REF] Dagostin | Salvia officinalis extract can protect grapevine against Plasmopara viticola[END_REF], the cupric treatments were applied at higher dosage of Cu(II) ions (0.075%) and had a higher amount of simulated rain (50 mm) received by the potted vines to highlight in this condition the potential performance of the less-efficient formulation based on CuTBS. However, despite the high solubility in water of CuSPHy, the formulations based on this salt strongly reduced the disease severity and incidence in both conditions (0 and 50 mm). Excluding the positive control represented by the pure CuSPHy treatment, because of the severe and diffused phytotoxicity on the treated leaves, the remarkable control achieved by the HA-CuSPHy without any side effect on the plants was confirmed, thus indicating a significant interaction between the Cu(II) ions and the HA nanostructured particles. This result may become even more promising considering the strong impact of climate change on the downy mildew management. In fact, [START_REF] Salinari | Downy mildew (Plasmopara viticola) epidemics on grapevine under climate change[END_REF] predicted the need for at least two more fungicide sprays to control P. viticola epidemics under the most negative climate change scenario. In this perspective, the possibility to enhance the persistence of copper under a rain-washing effect may significantly contribute to disease control in future.

The significant reduction in control activity under rain-washing effect by the HA-CuTBS treatment was further correlated to a nonoptimal coformulation method considering the similar tendency reported by the pure CuTBS treatment and in comparison with the lower disease severity shown by the CuTBS fungicide. In this respect, the relevance of the formulation process on cupric fungicide efficacy has already been commented on in the literature, especially under environmental conditions, such as weather conditions and plant growth, that can influence strongly the product efficiency [START_REF] Dagostin | Are there alternatives to copper for controlling grapevine downy mildew in organic viticulture?[END_REF].

In conclusion, this study indicates the possibility of enhanced biological activity in vitro and in planta of Cu(II) ions by modifying their distribution, persistence, and delivery on the leaf surface through a formulation with nanostructured particles of HA. This forms a biocompatible material able to generate biologically active coatings on the treated surface. In this context, a deeper study of functional models might encourage research on other interesting applications of agricultural tools also based on organic and inorganic compounds that are applicable for sustainable plant protection purposes.

Fig. 1 .

 1 Fig. 1. Rain fastness simulator (FEM, San Michele all'Adige, Italy) equipped with 14 sprinklers positioned 2.2 m above the soil and regulated to produce drops similar in size to raindrops (0.3 to 2.5 mm).

Fig. 2 .

 2 Fig. 2. Effects on mycelial growth of Botrytis cinerea of different Cu(II) concentrations from four Cu(II) compounds formulated with different hydroxyapatite (HA) concentrations. Petri dishes were incubated at the temperature of 25°C for 5 days in darkness. HA (%) indicates the HA concentration in the applied formulation, and Cu(II) (%) indicates the Cu(II) concentration in the applied formulation. CuHyOx, copper hydroxide; CuOxCl, copper oxychloride; CuSPHy, copper sulfate pentahydrate; CuTBS, tribasic copper sulfate; DPI, days postinoculation; GI (%), growth inhibition percentage of B. cinerea.

Fig. 4 .

 4 Fig. 4. Results on disease severity (percentages) detected in potted grapevines (cultivar Chardonnay). A, Results of copper sulfate pentahydrate-based treatments. B, Results of tribasic copper sulfate-based treatments. Both Cu(II) compounds were formulated with five different percentages of hydroxyapatite (HA) and applied in planta in three different dosages corresponding to decreasing amounts of Cu(II).

Fig. 6 .

 6 Fig. 6. Environmental scanning electron microscope images paired to the related X-ray spectra of elements and related to the formulations applied on the leaf surface of Vitis vinifera. A, Pure suspension of hydroxyapatite (HA; scale bar = 1 mm). B, Formulation of copper sulfate pentahydrate (scale bar = 1 mm). C, Formulation of HA-tribasic copper sulfate (scale bar = 1 mm). D, Formulation of copper oxychloride (scale bar = 1 mm). E, Formulation of HA-copper hydroxide (scale bar = 0.3 mm). F, Distilled water in control leaf sample (scale bar = 0.5 mm).

TABLE 1

 1

	. Samples based on hydroxyapatite (HA) and Cu(II) compounds and
	related formulations prepared according to the variation of both the HA and Cu(II) % wt wt _ 1z
	Samples	HA % wt wt _ 1	Cu(II) compound % wt wt _ 1	Cu(II) % wt wt _ 1	pH
	HA-3	3	0.0	0.0	7.88
	HA-6	6	0.0	0.0	10.35
	CuSPHy-0	0	21.0	5.2	5.57
	CuSPHy-3	3	21.0	5.2	5.70
	CuSPHy-6	6	16.0	4.0	6.05
	CuTBS-0	0	9.6	5.2	7.52
	CuTBS-3	3	9.6	5.2	7.79
	CuTBS-6	6	7.4	4.0	7.35
	CuOxCl-0	0	9.5	5.2	7.61
	CuOxCl-3	3	9.5	5.2	7.80
	CuOxCl-6	6	7.0	3.8	7.31
	CuHyOx-0	0	8.5	5.2	7.65
	CuHyOx-3	3	8.5	5.2	7.80
	CuHyOx-6	6	6.5	4.4	7.19

TABLE 2

 2

	. Samples based on hydroxyapatite (HA) and two Cu(II) compounds
	(copper sulfate pentahydrate [CuSPHy] and tribasic copper sulfate [CuTBS]) and related formulations prepared varying the HA (% wt wt _ 1 ) and main-taining a predefined Cu(II) concentration (5.2% wt wt _ 1 ) z
	Samples	HA % wt wt _ 1	Cu(II) compound % wt wt _ 1	Cu(II) % wt wt _ 1
	EA2
	CuSPHy-0.6	0.6	21.0	5.2
	CuSPHy-1.2	1.2	21.0	5.2
	CuSPHy-2.4	2.4	21.0	5.2
	CuSPHy-3.6	3.6	21.0	5.2
	CuSPHy-5.4	5.4	21.0	5.2
	EA3
	CuTBS-0.6	0.6	9.6	5.2
	CuTBS-1.2	1.2	9.6	5.2
	CuTBS-2.4	2.4	9.6	5.2
	CuTBS-3.6	3.6	9.6	5.2
	CuTBS-5.4	5.4	9.6	5.2
	Efficacy assay			Cu(II) % wt wt _ 1
	EA1			0.025
	EA2			0.050, 0.025, 0.010
	EA3			0.050, 0.025, 0.010
	EA4			0.075

z EA, efficacy assay. TABLE 3. Cu(II) concentrations applied in planta by the experimental treatments per each efficacy assay (EA)

TABLE 4 .

 4 Reference treatment results on the mean disease severity (percentages) and mean disease incidence (percentages) detected in potted grapevines (cultivar Chardonnay) in each efficacy assay (EA) z

	Active ingredient % wt wt _ 1	Treatment	Dosage % wt wt
	EA1 Water	Positive control	_	35.4 ± 10.6	96.4 ± 3.6
	Dimetomorf 50	Quantum (Adama)	0.05	5.5 ± 1.0	72.6 ± 6.6
	CuHyOx 42.37	Coprantol WG (Syngenta)	0.20	6.6 ± 1.3	66.6 ± 7.2
	EA2 Water	Positive control	_	60.9 ± 7.4	100.0 ± 0.0
	Dimetomorf 50	Quantum (Adama)	0.05	2.4 ± 0.5	20.0 ± 8.4
	CuSPHy 49.6	Bordo Flow (Manica)	0.40	4.6 ± 0.6	63.1 ± 10.4
	EA3 Water	Positive control	_	38.7 ± 11.7	86.2 ± 8.5
	Dimetomorf 50	Quantum (Adama)	0.05	1.7 ± 0.4	28.0 ± 5.5
	CuTBS 28	Tri Base (Nufarm)	0.33	6.5 ± 2.0	61.3 ± 10.8
	EA4
	0-mm rain Water	Positive control	_	55.7 ± 7.9	100.0 ± 0.0
	Dimetomorf 50	Quantum (Adama)	0.05	2.8 ± 0.8	44.4 ± 10.3
	CuSPHy 49.6	Bordo Flow (Manica)	0.60	1.2 ± 0.5	20.0 ± 7.0
	CuTBS 28	Tri Base (Nufarm)	0.49	2.4 ± 0.3	40.8 ± 3.4
	50-mm rain Water	Positive control	_	54.9 ± 2.9	100.0 ± 0.0
	Dimetomorf 50	Quantum (Adama)	0.05	5.6 ± 0.7	63.5 ± 9.6
	CuSPHy 49.6	Bordo Flow (Manica)	0.60

_ 1 Disease severity (%) ± SE Disease incidence (%) ± SE 5.3 ± 1.9 65.9 ± 11.7 CuTBS 28

Tri Base (Nufarm) 0.49 12.6 ± 0.6 97.8 ± 1.3

z CuHyOx, copper hydroxide; CuSPHy, copper sulfate pentahydrate; CuTBS, tribasic copper sulfate; SE, standard error.

Vol. 109, No. 5, 2019 757

Vol. 109, No. 5, 2019 759

ACKNOWLEDGMENTS

We thank I. Pertot, D. Angeli, and O. Giovannini from the Department of Sustainable Agro-Ecosystems and Bioresources of the Fondazione Edmund Mach (San Michele all'Adige, Italy) for technical and logistical support in performing the greenhouse trials; C. Comparini and M. Santoro from the Department of Agrifood Production and Environmental Sciences of the University of Firenze for managing the in vitro assay and A. Simoni from the Department of Agricultural Sciences of the University of Bologna for giving the technical support in performing the samples preparation and characterization; and A. Phillips for providing a careful review of this paper.


Pierre Peterlongo
email: pierre.peterlongo@irisa.fr

Laurent Noé
email: laurent.noe@lifl.fr

Dominique Lavenier
email: dominique.lavenier@irisa.fr

Hoa Van

Gregory Nguyen

Mathieu Kucherov

Giraud

Van Hoa Nguyen
email: vhnguyen@irisa.fr

Gre- Gory Kucherov
email: gregory.kucherov@lifl.fr

Mathieu Giraud
email: mathieu.giraud@lifl.fr

Background: Similarity inference, one of the main bioinformatics tasks, has to face an exponential growth of the biological data. A classical approach used to cope with this data flow involves heuristics with large seed indexes. In order to speed up this technique, the index can be enhanced by storing additional information to limit the number of random memory accesses.

However, this improvement leads to a larger index that may become a bottleneck. In the case of protein similarity search, we propose to decrease the index size by reducing the amino acid alphabet.

Results: The paper presents two main contributions. First, we show that an optimal neighborhood indexing combining an alphabet reduction and a longer neighborhood leads to a reduction of 35% of memory involved into the process, without sacrificing the quality of results nor the computational time. Second, our approach led us to develop a new kind of substitution score matrices and their associated e-value parameters. In contrast to usual matrices, these matrices are rectangular since they compare amino acid groups from different alphabets. We 1 describe the method used for computing those matrices and we provide some typical examples that can be used in such comparisons. Supplementary data can be found on the website http://bioinfo.lifl.fr/reblosum.

Conclusions: We propose a practical index size reduction of the neighborhood data, that does not negatively affect the performance of large-scale search in protein sequences. Such an index can be used in any study involving large protein data. Moreover, rectangular substitution score matrices and their associated statistical parameters can have applications in any study involving an alphabet reduction.

Optimal neighborhood indexing for protein similarity search Background One fundamental task in bioinformatics concerns large scale comparisons between proteins or families of proteins. It often constitutes the first step before further investigations. A typical comparison, for example, is to query a database with a newly discovered sequence.

Observed similarities witness a putative common biological function and direct further studies.

In this paper, we focus on massive protein sequence comparisons: a large database is iteratively compared with relatively short queries (such as newly sequenced data). A possible approach is to use the exact dynamic programming method [START_REF] Smith | Identification of common molecular subsequences[END_REF]. For a given similarity model, this method provides optimal alignments within a quadratic computation time. Some optimizations achieve a sub-quadratic complexity [START_REF] Crochemore | A Sub-quadratic Sequence Alignment Algorithm for Unrestricted Cost Matrices[END_REF], but the computation time remains prohibitive for large scale comparisons. Thus, in practice, the full dynamic programming approach is applied to comparison of short sequences.

A successful family of similarity search methods is provided by seed-based heuristics, starting with Fasta [START_REF] Lipman | Improved tools for biological sequence comparison[END_REF] and Blast [START_REF] Altschul | Basic local alignment search tool[END_REF] and including specific methods for protein similarities such as Blastp [START_REF] Altschul | Gapped BLAST and PSI-BLAST: a new generation of protein database search programs[END_REF]. Seed-based heuristics were recently enhanced by advanced seeding tools like the spaced seeds used in PatternHunter [START_REF] Li | PatternHunter II: Highly Sensitive and Fast Homology Search[END_REF] or Yass [START_REF] Noé | YASS: enhancing the sensitivity of DNA similarity search[END_REF] (see [START_REF] Brown | Bioinformatics Algorithms: Techniques and Applications[END_REF] for a recent survey).

Authors of this paper also worked on the alliance between advanced seeds techniques and reconfigurable architectures [START_REF] Peterlongo | Protein similarity search with subset seeds on a dedicated reconfigurable hardware[END_REF].

The main idea of seed-based heuristics is to anchor the detection of similarities using matching short words or short subsequences occurring in both compared sequences. The form of these words or subsequences is provided by a pattern called a seed. A word that respects the seed is called a key. For instance, MVK is one of 20 3 possible keys for the seed of three consecutive characters on the protein alphabet. Detection of similarities between two strings is done in three stages, as presented in Figure 1: • Stage 1: search for keys that occur in both strings,

• Stage 2: extension of these matching keys with an ungapped alignment, keeping only the alignments with a score greater than a given threshold T ,

• Stage 3: full dynamic programming algorithm, applied only to successfully extended matching keys.

In this work, we consider comparisons between a set of protein queries against a large protein database of N amino acids. A common usage of Blast is to index the queries, and then to scan the full database at the runtime. If the size of the query and the database allow it, a full indexation of both leads to advantageous results [START_REF] Nguyen | Speeding up Subset Seed Algorithm for Intensive Protein Sequence Comparison[END_REF]. In our work, we applied approach used e.g. in Blat [START_REF] Kent | BLAT-the BLAST-like alignment tool[END_REF] where the database is indexed once and each query is successively processed.

To be efficient, the database positions are indexed by seed keys. The usual indexing scheme is shown Figure 2: for each key, a list of all its occurrences is stored. At Stage 1, each query position corresponds to a seed key (or, for the Blastp approach, a set of seed keys that are similar to the query seed key). An index access provides the list of key occurrences in the database, enabling Stage 2. We call such an approach the offset indexing approach. In this case, for each seed position, an offset of ⌈log 2 N ⌉ bits is stored. The index size is thus equal to S offset = N × ⌈log 2 N ⌉ bits.

For each query position, each execution of Stage 2 needs to access all the occurrences of the corresponding key. This leads to numerous random memory accesses that are time consuming: memory accesses at random positions are not efficiently cached and require high latencies [START_REF] Hennessy | Computer Architecture, A Quantitative Approach[END_REF]. A way to reduce the computation time is thus to avoid as far as possible such random memory accesses. For that purpose, it is possible to additionally store, for each key occurrence, its left and right neighborhoods in the sequence, as illustrated in Figure 3. Thus, given a position in the query and its corresponding key, all neighborhoods of this key occurrences in the database are obtained through a single random memory access. For each database position, two neighborhoods are additionally stored. We call this indexing approach the neighborhood indexing approach. The overall index size is then equal to S neighborhood = N × (⌈log 2 N ⌉ + 2αL) bits, where

• α is the number of bits for coding a character (amino acid), and

• L is the length of each neighborhood.
As seen in Figure 4, the main advantage of the neighborhood indexing is that it speeds up the execution time by a factor ranging between 1.5 and 2 over the offset indexing. The actual speed gain depends on the database length and on many implementation and architecture parameters (such as memory and cache sizes, cache strategies and access times) that will not be discussed here. An obvious drawback of the neighborhood indexing is the additional memory it requires to store neighborhoods. Comparing the two indexing schemes, the ratio r between the overall index sizes of the neighborhood indexing and the offset indexing is

r = S neighborhood S offset = 1 + 2αL ⌈log 2 N ⌉ .
In common experiments, ⌈log 2 N ⌉ is between 20 and 40, αL is between 20 and 200, hence r is between 2 and 21. It is worth mentioning that the ⌈log 2 N ⌉ value is often raised to a more practical 32 or 64 bits, reducing the ratio r even more. Storing neighborhoods becomes then relevant with the reduction of memory prices. For instance, the modern technology brings the possibility to get gigabytes of Flash memory in a personal computer for some hundred dollars. It is thus interesting to exploit this storage space as much as possible. It can be used for treating larger databases, but also, as in this work, for speeding up widely used applications.

However, the index size still remains the main limitation. In this paper, we study how the size of a large neighborhood index can be reduced while preserving the result quality. For this purpose, we worked on reducing as much as possible the ratio r. A way for doing this is to reduce the factor αL. We propose to simultaneously increase the neighborhood length (L) and reduce the alphabet size (2 α ). We limit the alphabet size by partitioning amino acids into groups. This reduces α by encoding neighborhood characters in less than 5 bits required for coding 20 amino acids. Partitioning the amino acids into 16 groups enables to encode each group using 4 bits, and partitioning into 8, 4 or 2 groups enables to encode each group by 3, 2, and 1 bits respectively. All these reduced alphabets are tested in this paper.

Grouping amino acids was studied in several papers [START_REF] Murphy | Simplified amino acid alphabets for protein fold recognition and implications for folding[END_REF][START_REF] Cannata | Simplifying amino acid alphabets by means of a branch and algorithm and substitution matrices[END_REF][START_REF] Li | Reduction of protein sequence complexity by residue grouping[END_REF][START_REF] Edgar | Local homology recognition and distance measures in linear time using compressed amino acid alphabets[END_REF]. Groups can rely on amino acid physical-chemical properties or on a statistical analysis of alignments. For example, the authors of [START_REF] Murphy | Simplified amino acid alphabets for protein fold recognition and implications for folding[END_REF] computed correlation coefficients between pairs of amino acids based on the BLOSUM50 matrix and used a greedy algorithm to merge them. A branch-and-bound algorithm for partitioning the amino acids was proposed in [START_REF] Cannata | Simplifying amino acid alphabets by means of a branch and algorithm and substitution matrices[END_REF]. Those papers mainly deal with the construction of reduced alphabets, but none of them studies how the alphabet reduction affects the sensitivity of similarity search, or undertakes a quantitative analysis of the trade-off between search sensitivity and index size for those alphabets. This raises the following problem that is solved in this paper: Can reduced alphabets allow one to decrease the factor αL while preserving the quality of similarity search results?

Results and Discussion

The main result of our work is an effective reduction of the index size without deteriorating the quality of the results of similarity search. Moreover, we provide substitution score matrices and e-value parameters to be used with reduced alphabets. Our results are based on the alphabets defined by the amino acids groups proposed by Li and al. (Table 3 of [START_REF] Li | Reduction of protein sequence complexity by residue grouping[END_REF]), but our method can be applied to any other amino acids partitions. The website http://bioinfo.lifl.fr/reblosum provides data for all the alphabets reported in [START_REF] Edgar | Local homology recognition and distance measures in linear time using compressed amino acid alphabets[END_REF].

In the rest of the paper, the original alphabet of 20 amino acids is denoted by Σ 20 , where each character is encoded by 5 bits. Reduced alphabets Σ 16 , Σ 8 , Σ 4 and Σ 2 , respectively of size 16, 8, 4 and 2, have each character encoded by 4, 3, 2 and 1 bits respectively. We used the following alphabets, defined in [START_REF] Li | Reduction of protein sequence complexity by residue grouping[END_REF]:

Σ 16 = {[C], [F Y ], [W ], [M L], [IV ], [G], [P ], [A], [T ], [S], [N ], [H], [QE], [D], [R], [K]}, Σ 8 = {[CF Y W ], [M LIV ], [G], [P ], [AT S], [N H], [QED], [RK]}, Σ 4 = {[CF Y W ], [M LIV ], [GP AT S], [N HQEDRK]}, and
Σ 2 = {[CF Y W M LIV ], [GP AT SN HQEDRK]}.
The main idea is to represent the neighborhoods of keys stored in the index (see Figure 3) over a reduced alphabet. Consequently, at Stage 2 of the similarity search, amino acid sequences are compared with sequences over the reduced alphabet. By an alignment over Σ × Σ ′ , we understand an alignment between a sequence over Σ and a sequence over Σ ′ .

Thus, in this paper we will consider alignments over

Σ 20 × Σ 20 , Σ 20 × Σ 16 , Σ 20 × Σ 8 , Σ 20 × Σ 4 and Σ 20 × Σ 2 .
In the next sections, we describe how to evaluate the quality of Stage 2 and how a substantial index size reduction can be obtained by using longer neighborhoods on reduced alphabets. As presented in Figure 5, using a reduced alphabet involves several parameters that we study in the following sections. In section Rectangular substitution score matrices, we present substitution score matrices used for alignments over Σ 20 × Σ 8 and Σ 20 × Σ 16 .

We then present the computation of e-value to estimate the significance of alignments over reduced alphabets. The last section, Experimental validation, describes a practical application of reduced alphabets to real biological data.

Stage 2 algorithm and quality

A detailed description of Stage 2 is given in Algorithm 1. Query and database neighborhoods of a matching key (detected during Stage 1) are compared character by character over L positions. During this comparison that uses substitution score matrices (lines 5 and 9), the highest scores for the left and right neighborhoods are kept (lines 6 and 10). If the sum of the highest scores exceeds a threshold T , the alignment is kept for Stage 3 (line 12), otherwise it is rejected (line 13). Note that in the offset indexing case, a random memory access is performed in order to retrieve neighborhoods left db and right db (line 1). This is not the case for the neighborhood indexing, as the neighborhoods are stored directly in the index.

result left ← result left + subst score(left db [i], left query [i]) 6:
if result left > highest left then highest left ← result left endif 7: end for 8: for i from 1 to L do The performance of Stage 2 gets better for higher sensitivity and lower selectivity.

Increasing the threshold T or decreasing the neighborhood length L makes Stage 2 more selective but less sensitive (faster execution at the price of worse quality results) while decreasing T or increasing L increases the sensitivity and decreases the selectivity (better quality results at the price of a slower execution).

Reducing the index size by 35% without loss of quality

As shown in Figure 6, the sensitivity/selectivity trade-off follows a convex curve. We propose here to achieve an equivalent trade-off with a reduction of the index size.

Clearly, for a fixed neighborhood length L (in Figure 6, 16 amino acids), the sensitivity/selectivity trade-off is always better when using the full amino acid alphabets than a reduced alphabet. This is easily explained by the fact that reducing the alphabet size decreases the alignment accuracy. In order to keep up with the sensitivity/selectivity ratio, the neighborhood length L should be increased. In Figure 7, all reduced alphabets, used with increased neighborhood lengths, now perform equivalently (or slightly better) than the full alphabet.

Figure 8 shows the dependency, for different reduced alphabets, between the number of bits needed to store both neighborhoods (X axis) and the selectivity (Y axis), for an equivalent quality (fixed sensitivity). Those results are obtained with the use of special substitution score matrices, adapted to reduced alphabets, that are presented in the next section. Our main result is that for any given selectivity, using any of the reduced alphabets for storing neighborhoods leads to a smaller αL factor than for the Σ 20 alphabet.

Therefore, for a fixed memory usage, the sensitivity/selectivity trade-off is always better with a reduced alphabet than with the full Σ 20 alphabet.

In practice, this result enables a reduction of the index size without any sacrifice in running time or in result quality. Table 1 shows the memory requirements for different alphabets.

We obtain a practical reduction of 42% of the factor αL using the reduced alphabet Σ 2 instead of Σ 20 . The ratio r on the overall index size is then reduced by 35%.

Rectangular substitution score matrices

We designed a method for computing substitution score matrices for any pair of possibly reduced amino acid alphabets. As this method is based on the original programs of [START_REF] Henikoff | Amino Acid Substitution Matrices form Protein Blocks[END_REF], we call such matrices ReBlosum for Rectangular Blosum matrices. The ReBlosum matrices for alphabets Σ 20 × Σ 20 are the original Blosum matrices. Tables 2 and3 present ReBlosum matrices for alignments over alphabets Σ 20 × Σ 16 and Σ 20 × Σ 8 respectively. Such matrices can be applied in any method reducing the amino acid alphabets by residue grouping. As one may be interested in using any other pair of alphabets, we additionally propose a web interface available at http://bioinfo.lifl.fr/reblosum. The web interface computes ReBlosum matrices for other amino acids alphabets, in particular for Σ 20 × Σ 4 and Σ 20 × Σ 2 that are not presented in Tables 2 and3, as well as for other alphabets listed in [START_REF] Edgar | Local homology recognition and distance measures in linear time using compressed amino acid alphabets[END_REF] and for custom alphabets provided by the user.

Parameters for e-value computation

The e-value, or expected value, provides the expected number of alignments with a given score, when comparing a text T and a query Q of length |T | and |Q| respectively. Local alignment methods like Blast sort results by increasing e-value, thus reflecting their decreasing significance. In the Blast algorithm, the e-value of an alignment is obtained by

e-value = K • |Q| • |T | • e -λs ,
where s is the score of the alignment obtained with substitution matrices. Parameters λ and K are two constants that fit the Gumbel law, computed using methods described in [START_REF] Karlin | Methods for assessing the statistical significance of molecular sequence features by using general scoring schemes[END_REF]. Table 4 provides those parameters for several ReBlosum substitution matrices.

Experimental validation

In a model where the Stage 2 alignments are ungapped, using reduced alphabets and alignments on longer neighborhoods can affect the result quality. Indeed, the longer the neighborhoods are, the bigger the chance to meet a gap in the sequences. More generally, the probabilities distributions used in theoretical sensitivity and specificity computations do not truly reflect the nature of the biological sequences. We thus validated our approach with large-scale tests on biological sequences. We set a database to be the hard-masked human chromosome 21 (UCSC Release hg18) translated according to the six possible reading frames. The query set was a set of seven archea and bacteria proteomes derived from a study of mitochondrial diseases. This set was selected for is interest toward the detection of potential insertions of mitochondrial genes in the human genome. Moreover, testing out our approach comparing such distant species represents one of the hardest application case. Indeed more typical homology searches on closer sequences is easier.

Tests on such homology searches could have hidden potential issue on our approach.

The database contained 12 700 507 amino acids whereas the query was composed by 5 321 439 amino acids. Using the ssearch method [START_REF] Lipman | Rapid and Sensitive Protein Similarity Searches[END_REF], 650 alignments were obtained between the database and the query (maximal e-value: 10 -3 ). This set of exhaustive optimum alignments was sufficient to validate our method in comparison with results obtained using different alphabets. The seed used in Stage 1 was a subset seed (see [START_REF] Roytberg | Efficient seeding techniques for protein similarity search[END_REF]), as in [START_REF] Peterlongo | Protein similarity search with subset seeds on a dedicated reconfigurable hardware[END_REF]. For the neighborhood indexing, we indexed the database using each of the alphabets Σ 20 , Σ 16 , Σ 8 , Σ 4 and Σ 2 . We selected the neighborhood length to have a theoretical sensitivity close to 0.95 and a theoretical selectivity close to 0.01. Theoretical sensitivity and selectivity are defined according distributions presented on page 11. This leads to indexing 2 × 11 characters for Σ 20 , 2 × 12 characters for Σ 16 , 2 × 14 characters on Σ 8 , 2 × 19 characters for Σ 4 , and 2 × 32 characters for Σ 2 (Figure 7). The database index sizes are reported in Table 6. Using alphabet Σ 2 instead of Σ 20 reduces the overall index size: the ratio r goes from r 20 = 5.58 to only r 2 = 3.67, that is a 35% reduction. The initial assumption of ungapped alignments in the Stage 2 can be wrong with a neighborhood length of 2 × 32. Thus one could prefer to use the alphabet Σ 4 with 2 × 19 characters, giving a 25% reduction of the overall index size (r 4 = 4.17).

As shown in Table 5, each of the reduced alphabets yields a practical full sensitivity, as all the 650 alignments are found in each test. Moreover, the practical selectivity, close to 10 -3 , is here better than the theoretical one (0.01).

Conclusions

We proposed a method for reducing the index size when storing neighborhoods of seed keys in protein databases. This approach is based on reducing the alphabet of indexed data while using a longer neighborhood. We save 35% of the index size without any modification on the result quality assuming an ungapped alignment model. We provided optimal lengths for selected alphabets. Furthermore, the proposed method requires unusual substitutions score matrices that are called ReBlosum, for rectangular Blosum matrices. These matrices provide substitution scores between letters from different alphabets. We extended the computation of traditional Blosum matrices in order to compute ReBlosum matrices, and adapted the computation of λ and K parameters for e-value estimation to reduced alphabets. We provided ReBlosum matrices and their corresponding λ and K values for selected alphabets. Other matrices and parameters can be obtained from the website http://bioinfo.lifl.fr/reblosum.

Methods

In this section, we describe the methods we used to compute the sensitivity and selectivity of similarity search on reduced alphabets as well as the neighborhood length. We further describe the computation of ReBlosum substitution score matrices and of the e-value parameter. Moreover, we explain how the threshold T is computed at Stage 2 depending on the e-value specified by the user. Finally, we describe how we estimated the time gain of the the neighborhood indexing over the offset indexing.

Selectivity and sensitivity computation

The sensitivity of Stage 2 is defined by the ratio of retained "true alignments" (a "true alignment" is an alignment known to be relevant, according to a model or to a reference set like the Blocks database) : sensitivity = # successfully extended true alignments # true alignments ,

The selectivity is defined as the ratio of retained "random alignments" (a "random alignment" means an alignment of randomly chosen amino acid pairs drawn according to an appropriate probability distribution) : selectivity = # successfully extended random alignments # random alignments .

Note that here we focus on the behavior of Stage 2 and do not take into consideration the sensitivity/selectivity of Stage 1. In particular, in the above fractions we consider only alignments that extend a hit presumably reported at Stage 1.

The sensitivity and the selectivity of Stage 2 rely on three parameters: the alphabet choice, the neighborhood length, and the score threshold T . Given these three parameters, we applied a dynamic programming algorithm to compute the probability for the filter to retain an alignment drawn according to a given amino acid pair distribution. Applied to distributions of "true" and "random" alignments (foreground and background distributions, respectively), the algorithm gives a theoretical estimation of the sensitivity and the selectivity of the filter. The two distributions were the Bernoulli models (namely the expected and the observed probabilities, see below), obtained with the Blosum programs on the Blocks protein database when processing the Blosum-62 matrix.

In our Algorithm 1, two neighborhoods (left and right) are processed. We thus consider the sum of two maximal scores, reached in the left and right neighborhoods. The probability that this sum reaches a given threshold T at least once is computed as follows. First, we compute the probability for each neighborhood independently to reach any given maximal score s (s ≥ 0) within the neighborhood length. Then, these two independent discrete distributions are combined to compute the T threshold requirement.

For our experiments, we calibrated the neighborhoods lengths to have a sensibility close to 0.95 and a selectivity close to 0.01, and computed related thresholds values (available of the ReBlosum website).

Computing ReBlosum matrices

There are several substitution score matrices for the regular Σ 20 × Σ 20 alphabet, and the most common of them are matrices from the Blosum family [START_REF] Henikoff | Amino acid substitution matrices from protein blocks[END_REF] (BLOcks SUbstitution Matrix). They are built from the Blocks database of ungapped multiple alignments [START_REF] Henikoff | Automated assembly of protein blocks for database searching[END_REF].

For a given identity level X and two amino acids i and j, the BlosumX score B i,j are log-likelihoods of amino acid pair frequencies:

B i,j = log q i,j p i • p j ,
where p i • p j is the expected probability of aligning i against j, and q i,j is the observed probability of the same event in a subset of alignments of the Blocks database that have at least X percent of identity. (Note that the computation of q i,j takes into account different contributions provided by alignments with different identity levels.)

In our case, sequences over different alphabets are compared and we then have to adapt the matrix computation to compute appropriate rectangular matrices. For this purpose, the original data file (Blocks database version 5) was downloaded and the original programs of [START_REF] Henikoff | Amino Acid Substitution Matrices form Protein Blocks[END_REF] 1 were modified in order to take into account the reduced alphabet on "one side" of the matrix and compute new log-likelihood scores. Given two alphabets Σ and Σ ′ , we compute such matrices for several identity levels X, using the log-likelihood of groups of amino acid pair frequencies:

B I,J = log q I,J p I • p J ,
where p I • p J is the expected frequency of aligning any amino acids from group I ⊆ Σ against any other amino acid from group J ⊆ Σ ′ , and q I,J is the observed frequency of the same event in a subset of alignments of the Blocks database that have at least X percent of identity. The recent paper [START_REF] Styczynski | BLOSUM62 miscalculations improve search performance[END_REF] discovered flaws in the original Blosum implementation, but shows that a corrected program does not improve (and even in some cases decreases) the results quality. Therefore, we did not take the proposed modifications into account.

The website http://bioinfo.lifl.fr/reblosum proposes a selection of ReBlosum matrices for several alphabets, as well as an interface to compute ReBlosum matrices for any alphabet and identity level specified by the user.

Prototype for estimating the time gain of offset indexing over neighborhood indexing

For comparing the execution time between offset indexing and neighborhood indexing, a C prototype was created. In the case of the offset indexing, the index stores positions of all seeds in an unique integer array. For each seed key, a pointer provides the first occurrence in this array. In the case of the neighborhood indexing, the index uses a (unique) structure array instead of an integer array. For each key occurrence, the structure contains the key position together with two neighborhoods.

Tests reported in Figure 4 were run on a 2 GHz PC with an AMD Opteron processor. The database size was selected so that the index fits into the main memory (4 GB) but not into the L1/L2 cache (1 MB). In those tests, the neighborhood indexing performs almost twice as fast as the offset indexing. 1, the other two columns refer to the experience described in section "Practical results". The index size is equal to N × (⌈log 2 N ⌉ + 2αL), as explained in the beginning of the paper. Here N = 12 700 507 and ⌈log 2 N ⌉ = 24. The ratio r is against the size of the index for offset indexing, which is here

C F Y W M L I V G P A T S N H Q E D R K [C] 9 -2 -2 -2 -1 -1 -1 -1 -3 -3 0 -1 -1 -3 -3 -3 -4 -3 -3 -3 [F Y ] -2 5 5 1 0 0 -1 -1 -3 -3 -2 -2 -2 -3 0 -2 -3 -3 -2 -3 [W ] -2 1 2 11 -1 -2 -3 -3 -2 -4 -3 -2 -3 -4 -2 -2 -3 -4 -3 -3 [M L] -1 0 -1 -2 3 4 1 1 -3 -3 -1 -1 -2 -3 -2 -2 -3 -3 -2 -2 [IV ] -1 0 -1 -3 1 1 3 3 -3 -3 -1 0 -2 -3 -3 -2 -3 -3 -3 -2 [G] -3 -3 -3 -2 -3 -4 -4 -3 6 -2 0 -2 0 0 -2 -2 -2 -1 -2 -2 [P ] -3 -4 -3 -4 -2 -3 -3 -2 -2 7 -1 -1 -1 -2 -2 -1 -1 -1 -2 -1 [A] 0 -2 -2 -3 -1 -1 -1 0 0 -1 4 0 1 -2 -2 -1 -1 -2 -1 -1 [T ] -1 -2 -2 -2 -1 -1 -1 0 -2 -1 0 5 1 0 -2 -1 -1 -1 -1 -1 [S] -1 -2 -2 -3 -1 -2 -2 -2 0 -1 1 1 4 1 -1 0 0 0 -1 0 [N ] -3 -3 -2 -4 -2 -3 -3 -3 0 -2 -2 0 1 6 1 0 0 1 0 0 [H] -3 -1 2 -2 -2 -3 -3 -3 -2 -2 -2 -2 -1 1 8 0 0 -1 0 -1 [QE] -3 -3 -2 -2 -1 -3 -3 -2 -2 -1 -1 -1 0 0 0 4 4 1 0 1 [D] -3 -3 -3 -4 -3 -4 -3 -3 -1 -1 -2 -1 0 1 -1 0 2 6 -2 -1 [R] -3 -3 -2 -3 -1 -2 -3 -3 -2 -2 -1 -1 -1 0 0 1 0 -2 5 2 [K] -3 -3 -2 -3 -1 -2 -3 -2 -2 -1 -1 -1 0 0 -1 1 1 -1 2 5
S offset = N × ⌈log 2 N ⌉ = 0.

9 :

 9 result right ← result right + subst score(right db [i], right query [i]) 10: if result right > highest right then highest right ← result right endif 11: end for 12: if highest left + highest right ≥ threshold T then return true endif 13: return false The quality of Stage 2 is measured by a trade-off between its sensitivity (ability to extend true alignments) and selectivity (ability to filter out spurious seed hits). Computation of those values is described page 11.

FiguresFigure 1 -

 1 FiguresFigure 1 -Schematic view of a Blast-like 3-stage algorithm

Figure 2 -

 2 Figure 2 -Offset indexing

Figure 3 -

 3 Figure 3 -Neighborhood indexing

Figure 4 -

 4 Figure 4 -Time saved by neighborhood indexing compared to offset indexing

Figure 5 -

 5 Figure 5 -Parameters involved in alphabet reduction

Figure

  Figure 6 -Sensitivity/selectivity trade-off using different alphabets with a constant neighborhood length

Table 3 - 8 Matrix

 38 ReBlosum matrix for alphabet Σ 20 × Σ ReBlosum62 for alphabet Σ 20 × Σ 16 . Scores located on the "diagonal" are shownin bold. C F Y W M L I V G P A T S N H Q E D R K [CF Y W ] 4 4 4 5 -1 0 -1 -1 -3 -3 -2 -2 -2 -3 0 -2 -3 -3 -3 -3 [M LIV ] -1 0 -1 -2 2 3 3 2 -3 -3 -1 -1 -2 -3 -3 -2 -3 -3 -2

Table 1 .

 1 6 -Sensitivity/selectivity trade-off using different alphabets with a constant neighborhood length When the length is fixed, reduced alphabets provide worse results than the Σ 20 × Σ 20 alphabet. The curves for alphabets Σ 20 × Σ 4 and Σ 20 × Σ 2 , not shown, are even worse. Now all reduced alphabets are equivalent (or slightly better, due to integer rounding of the neighborhood lengths) than the original alphabet Σ 20 × Σ 20 . smaller index sizes than the regular Σ 20 × Σ 20 alphabet.

		1
		0.99
		0.98	better
		0.97
		0.96
	sensibility	0.95
		0.94				Alph. size (neighb. length)
						20x20 (11)
						16x20 (11)
		0.93				8x20 (11) 4x20 (11)
						2x20 (11)
		0.92
		0.91
		0.9
		0	0.01	0.02	0.03	0.04	0.05
				specificity
	Sensitivity/selectivity trade-off for two neighborhoods of length 11 (other lengths give
	similar results).

Table 1 -

 1 Memory for neighborhood storage for different alphabets with adapted neighborhood lengths

	Memory needed for storing neighborhoods for sensitivity/selectivity trade-offs shown on
	Figure 7.
	indexed	bits per	neighborhoods	total	relative gain
	neighborhood	character	length	per index line	compared to Σ 20
	alphabet	(α)	(L)	(2αL)	(1 -2αL/110)
	Σ 20	5	11	110	0%
	Σ 16	4	12	96	13%
	Σ 8	3	14	84	24%
	Σ 4	2	19	76	31%
	Σ 2	1	32	64	42%

Table 2 -

 2 ReBlosum matrix for alphabet Σ 20 × Σ 16 Matrix ReBlosum62 for alphabet Σ 20 × Σ 16 . Scores located on the "diagonal" are shown in bold.

Table 4 -

 4 Parameters λ and K for different alphabets Parameters λ and K of the Gumbel law for different alphabets, obtained with the corresponding ReBlosum score matrices. Σ 20 0.320 0.139 Σ 20 × Σ 16 0.333 0.143 Σ 20 × Σ 8 0.223 0.142 Σ 20 × Σ 4 0.212 0.128 Σ 20 × Σ 2 0.161 0.101

	22

Table 5 -

 5 Practical results for different alphabets -Quality estimations Similarity search results obtained on reduced alphabets. The number of positions tested (validating Stage 1 only and independent from the chosen alphabet) is 1.59 * 10 9 . The practical selectivity is computed dividing the number of positions validating both Stage 1 and Stage 2 by the number of positions tested.

	alphabets	number of positions validating Stage 1 and Stage 2	practical selectivity	number of detected alignments	practical sensitivity
	Σ 20 × Σ 20	2.14 * 10 6	1.35 * 10 -3	650 (all)	1
	Σ 20 × Σ 16	1.39 * 10 6	0.88 * 10 -3	650 (all)	1
	Σ 20 × Σ 16	0.98 * 10 6	0.62 * 10 -3	650 (all)	1
	Σ 20 × Σ 8	0.62 * 10 6	0.39 * 10 -3	650 (all)	1
	Σ 20 × Σ 4	3.14 * 10 6	1.98 * 10 -3	650 (all)	1
	Σ 20 × Σ 2	2.93 * 10 6	1.85 * 10 -3	650 (all)	1

Table 6 -

 6 Practical results for different alphabets -Memory requirementsDatabase index size for neighborhood indexing on different alphabets. The first three columns are the same as in Table

  30 * 10 9 bits = 38 MBytes. alphabet α L S neighborhood r Σ 20 5 11 1.70 * 10 9 bits = 212 MBytes 5.58 Σ 16 4 12 1.52 * 10 9 bits = 190 MBytes 5.00 Σ 8 3 14 1.37 * 10 9 bits = 171 MBytes 4.50 Σ 4 2 19 1.27 * 10 9 bits = 159 MBytes 4.17 Σ 2 1 32 1.12 * 10 9 bits = 140 MBytes 3.67

downloaded from http://sci.cnb.uam.es/Services/ftp/databases/blocks/unix/blosum/

Acknowledgments

This work was supported by the INRIA ARC grant "Flash" (Seed Optimization and Indexing of Genomic Databases).

Authors contributions

All authors conceived the study. VHN created and tested the prototype estimating the time gain using a neighborhood index. LN and MG computed ReBlosum matrices and optimal neighborhood lengths using different alphabets and created the web interface. PP performed tests on biological sequences and drafted the manuscript. DL and GK proposed the setup of the work and participated in its coordination. All authors read and approved the final manuscript.