Simone Costa

Paolo Fulignati
email: paolo.fulignati@unipi.it

Anna Gioncada

Marco Pistolesi

Delphine Bosch

Olivier Bruguier

Tracking metal evolution in arc magmas: Insights from the active volcano of La Fossa, Italy

Keywords:

The mineralization potential of arc magmas depends, among other factors, on the timing of sulfide melt saturation relative to magma differentiation and to exsolution of a magmatic fluid phase. In fossil mineralized or barren systems, understanding the evolution of metals along the magma differentiation path is often hindered by late magmatic processes and hydrothermal alteration. To better understand the process of metal evolution "caught in the act" in crustal reservoirs, we analyzed magmatic sulfides and melt inclusions found within eruptive products from the active arc volcano, La Fossa (Vulcano Island, Italy), for the basalt to rhyolite compositional spectrum. We found that, in case of sulfide-undersaturated and volatile-rich arc basalts, metals are scarcely subtracted by degassing during ascent to shallow crustal reservoirs and reach the highest abundances in intermediate magmas (250 ppm Cu). At sulfide saturation the sulfide melt has 34-66 wt% Cu, leading to a dramatic decrease in chalcophile metals dissolved in the silicate melt. After fractionation of only 0.2-0.3 wt% of sulfide in the solid assemblage, the exsolved sulfide is a monosulfide solid solution (pyrrhotite) containing <3 wt% Cu. Metals that do not partition in sulfides (Pb, Zn) increase their concentrations during magmatic evolution until they are sequestered by a Cl-rich aqueous fluid phase exsolved at the rhyolitic stage. The absolute and Cu-normalized concentrations of metals in sulfide inclusions are similar to sulfide accessories in magmatic rocks associated with world-class porphyry Cu systems. Our results demonstrate that the mechanisms governing metal evolution inferred for the magmatic stage in porphyry Cu environments can be also tracked at an active arc volcano, using eruptive products as snapshots of the magmatic evolution. Arc volcanoes can thus be viewed as ideal active analogues when studying these crucial processes for the formation of porphyry Cu deposits.

Introduction

Metal evolution in arc magmas is difficult to constrain due to the loss of volatiles and the loss of metals during crystallization and because, in most cases, magmas become saturated in sulfides at some stage during their evolution [START_REF] Audétat | Magmatic controls on porphyry copper genesis[END_REF]. Indeed, due to the strong affinity of chalcophile and siderophile elements (e.g., Platinum-Group Elements, Cu, Au, and Ag) for the sulfide phase, sulfides exsolved from silicate magmas lead to severe metal depletion in the residual silicate melt [START_REF] Park | The role of late sulfide saturation in the formation of a Cu-and Au-rich Magma: Insights from the platinum group element geochemistry of Niuatahi-Motutahi Lavas, Tonga Rear Arc[END_REF].

A primary control on metal evolution in arc magmas is exerted by: 1) the timing of sulfide saturation relative to magmatic differentiation and volatile exsolution; 2) the amount of metal segregated into magmatic sulfides; 3) the amount of sulfide formed; 4) and whether sulfides are 'irretrievably lost' or may instead release metals again at later stages [START_REF] Bai | Early sulfide saturation in arc volcanic rocks of Southeast China: Implications for the formation of co-magmatic porphyryepithermal Cu-Au deposits[END_REF][START_REF] Chang | Petrogenesis and metal content of Horneblende-rich Xenoliths from two Laramide-age Magma systems in Southwestern USA: insights into the Metal Budget of Arc Magmas[END_REF][START_REF] Halter | Magma evolution and the formation of porphyry Cu-Au ore fluids: evidence from silicate and sulfide melt inclusions[END_REF][START_REF] Hao | Platinum-group element geochemistry of the Escondida Igneous suites, Northern Chile: Implications for ore formation[END_REF][START_REF] Mungall | Transport of metals and Sulphur in magmas by flotation of sulphide melt on vapour bubbles[END_REF][START_REF] Park | The role of late sulfide saturation in the formation of a Cu-and Au-rich Magma: Insights from the platinum group element geochemistry of Niuatahi-Motutahi Lavas, Tonga Rear Arc[END_REF][START_REF] Park | Chalcophile element fertility and the formation of porphyry Cu ± Au deposits[END_REF][START_REF] Wilkinson | Triggers for the formation of porphyry ore deposits in magmatic arcs[END_REF][START_REF] Zhang | What caused the formation of the giant bingham canyon porphyry Cu-Mo-Au deposit? Insights from melt inclusions and magmatic sulfides[END_REF]. The combined role of these factors has proven difficult to resolve, largely because of the complexity in measuring the metal content of the magmas during their evolution [START_REF] Park | Chalcophile element fertility and the formation of porphyry Cu ± Au deposits[END_REF]. Information mostly derives from the roots -sulfidebearing cumulates -of their plumbing system or from the mineralized bodies [START_REF] Chang | Petrogenesis and metal content of Horneblende-rich Xenoliths from two Laramide-age Magma systems in Southwestern USA: insights into the Metal Budget of Arc Magmas[END_REF][START_REF] Chen | Sulfide-bearing cumulates in deep continental arcs: the missing copper reservoir[END_REF]. As magmatichydrothermal ore deposits can be considered the extinct equivalent of active magmatic systems [START_REF] Hedenquist | The role of magmas in the formation of hydrothermal ore-deposits[END_REF], the investigation of these processes in the products of active arc volcanoes, particularly with the support of data from silicate melt inclusions, can provide pivotal information on metal budget and ore genetic models associated with arc-related magmas. A significant advantage in studying active volcanic systems is the lack of hydrothermal alteration or mineralization overprints, as shown by recent works for magmatic sulfide saturation studies [START_REF] Fulignati | Magmatic sulfide immiscibility at an active magmatic-hydrothermal system: the case of la Fossa (Vulcano, Italy)[END_REF][START_REF] Georgatou | Magmatic sulphides in Quaternary Ecuadorian arc magmas[END_REF][START_REF] Georgatou | Magmatic sulfides in high-potassium calc-alkaline to shoshonitic and alkaline rocks[END_REF][START_REF] Nadeau | Sulphide magma as a source of metals in arc-related magmatic hydrothermal ore fluids[END_REF][START_REF] Zelenski | Silicate-sulfide liquid immiscibility in modern arc basalt (Tolbachik volcano, Kamchatka): part I. Occurrence and compositions of sulfide melts[END_REF]. Despite that, very few works have tackled the investigation of metal evolution through the processes of magma differentiation, sulfide exsolution and fluid exsolution at active volcanoes or across the wide compositional spectra of magma types [START_REF] Cox | Chalcophile element processing beneath a continental arc stratovolcano[END_REF][START_REF] Park | Platinum-alloy and sulfur saturation in an arc-related basalt to rhyolite suite: evidence from the Pual Ridge lavas, the Eastern Manus Basin[END_REF][START_REF] Park | The role of late sulfide saturation in the formation of a Cu-and Au-rich Magma: Insights from the platinum group element geochemistry of Niuatahi-Motutahi Lavas, Tonga Rear Arc[END_REF][START_REF] Timm | Sources of chalcophile and siderophile elements in kermadec arc lavas[END_REF].

La Fossa volcano (Italy) is an ideal site to study mineralizing processes beneath arc volcanoes, being characterized by an active magmatic-hydrothermal system [START_REF] Boyce | Fluids in early stage hydrothermal alteration of high-sulfidation epithermal systems: a view from the Vulcano active hydrothermal system (Aeolian Island, Italy)[END_REF][START_REF] Fulignati | Geologic model of the magmatichydrothermal system of Vulcano (Aeolian Island, Italy)[END_REF] and providing evidence of sulfide melt-silicate melt immiscibility [START_REF] Fulignati | Magmatic sulfide immiscibility at an active magmatic-hydrothermal system: the case of la Fossa (Vulcano, Italy)[END_REF]. Here we use melt inclusions, magmatic sulfides and host minerals to track the evolution of metals for the entire basalt to rhyolite compositional spectrum. The suite belongs to a shoshonitic to potassic series in a subduction setting, similar to part of the magma types found in association with porphyry Cu deposits [START_REF] Audétat | Magmatic controls on porphyry copper genesis[END_REF][START_REF] Sillitoe | Porphyry copper systems[END_REF]. Moreover, we compare our results to metal contents in sulfides from magmatic systems associated with ore deposits, showing that strong analogies exist between metal evolution in active arc volcanoes and those reported for porphyry Cu environments.

Geological background

La Fossa is the active volcanic center of Vulcano Island, in the Aeolian archipelago, a continental volcanic arc located in southern Tyrrhenian Sea (Fig. 1a,b). The volcanic activity of the island started at 130 ka with high-K calcalkaline (HKCA), shoshonitic (SHO) and, recently, potassic (KS) magmas [START_REF] De Astis | Transition from calc-alkaline to potassium-rich magmatism in subduction environments: geochemical and Sr, Nd, Pbisotopic constraints from the island of Vulcano (Aeolian arc)[END_REF], showing the entire range in composition from basalt to rhyolite (Fig. 1c,d). The plumbing system of La Fossa is polybaric, dominated by fractional crystallization, crustal assimilation and magma mixing processes [START_REF] Costa | Magma evolution at La Fossa volcano (Vulcano Island, Italy) in the last 1000 years: evidence from eruptive products and temperature gradient experiments[END_REF][START_REF] De Astis | Geology volcanic history and petrology of Vulcano (central Aeolian archipelago)[END_REF][START_REF] Peccerillo | Modeling the magma plumbing system of Vulcano (Aeolian Islands, Italy) by integrated fluid-inclusion geobarometry, petrology, and geophysics[END_REF]. These occur in a shoshonitic to latitic magma chamber at about 15 km deep, fed by shoshonitic basaltic magmas, and in shallower and smaller trachytic to rhyolitic reservoirs at 5-2 km deep [START_REF] Costa | Magma evolution at La Fossa volcano (Vulcano Island, Italy) in the last 1000 years: evidence from eruptive products and temperature gradient experiments[END_REF][START_REF] De Astis | Geology volcanic history and petrology of Vulcano (central Aeolian archipelago)[END_REF][START_REF] Fulignati | Magmatic sulfide immiscibility at an active magmatic-hydrothermal system: the case of la Fossa (Vulcano, Italy)[END_REF]. Basaltic magmas have been only erupted at about 50 ka. They are H 2 O-rich (water up to 5 wt%; Le [START_REF] Voyer | Zonation of H 2 O and F concentrations around melt inclusions in olivines[END_REF] and oxidized. La Fossa has been quiescent since 1890 CE, with a high temperature fumarolic field fed by magmatic and hydrothermal fluids [START_REF] Paonita | The episodic and abrupt geochemical changes at La Fossa fumaroles (Vulcano Island, Italy) and related constraints on the dynamics, structure, and compositions of the magmatic system[END_REF]. A similar hydrothermal system was active in the past, as testified by hydrothermally altered lithics found in the eruptive products of recent (post-1000 CE) eruptions (e.g. Breccia di Commenda eruption; [START_REF] Fulignati | Geologic model of the magmatichydrothermal system of Vulcano (Aeolian Island, Italy)[END_REF][START_REF] Gurioli | The historic magmatic-hydrothermal eruption of the Breccia di Commenda, Vulcano, Italy[END_REF][START_REF] Rosi | Dynamics of shallow hydrothermal eruptions: new insights from Vulcano's Breccia di Commenda eruption[END_REF].

Materials and analytical methods

Samples were selected to ensure that the entire range of magma types, from basalt to rhyolite, was included in this study. They were analyzed for the composition of their sulfide (SIs) and melt (MIs) inclusions hosted within phenocrysts. Samples were preferentially selected from explosive eruptions, targeted to ensure quenching of melt inclusions to a glass with the eruption. This minimizes the potential for post-entrapment crystallization of microlites in the trapped melt or crystallization of the host mineral on the inclusion walls. They include scoriaceous lapilli of La Sommata and Vulcanello, of basaltic and shoshonitic composition, respectively. The latitic, trachytic and rhyolitic samples are represented by the Palizzi eruptive period of La Fossa and consist of dark grey coarse ash of Pal A (latite) and Pal C (latite, trachyte), pumiceous lapilli of Pal D (trachyte) and Pal B (rhyolite), and the Palizzi lava flow (trachyte) (see De [START_REF] De Astis | Geology volcanic history and petrology of Vulcano (central Aeolian archipelago)[END_REF][START_REF] Di Traglia | Growth and erosion: The volcanic geology and morphological evolution of La Fossa (Island of Vulcano, Southern Italy) in the last 1000 years[END_REF] for further information on volcanic stratigraphy). Lapilli were crushed and crystals were hand-picked under a stereomicroscope, embedded in epoxy resin mounts and polished. Slices of the Palizzi lava flow sample were also prepared in epoxy resin mounts for petrographic investigations and microanalyses. The polished resin mounts were first studied under reflected light with a petrographic microscope at the Dipartimento di Scienze della Terra at the Università di Pisa. Melt and sulfide inclusions were identified for the analytical follow-up. To avoid post-entrapment modifications of the melt composition due to melt crystallization or leakage, the selected melt inclusions are entirely glassy (no microlites) and lack large vapor bubbles or other evidence of only partial enclosing by the host crystal. Shrinkage bubbles are absent or small in Vulcanello MIs while they are common in La Sommata basalt and in Palizzi trachyte; bubbles may host traces of volatile elements escaped from melt, but the observation that they are apparently empty means that we can consider their metal content negligible. Based on the inspection of MIs under back-scattered electron (BSE) microscopy and on their major element composition, post-entrapment crystallization of the host on the inclusion walls can also be considered negligible with respect to chalcophile metals. This is in agreement with previous estimates (<2 wt%) of olivine host crystallization for Vulcanello MIs [START_REF] Fusillo | Deciphering post-caldera volcanism: insight into the Vulcanello (Island of Vulcano, Southern Italy) eruptive activity based on geological and petrological constraints[END_REF], corresponding to a variation of the Cu content within analytical uncertainty.

After carbon-coating, backscattered electron images and the major element chemical composition of sulfide and melt inclusions were obtained with a Quanta 450 Field Emission-Scanning Electron Microscope (FE-SEM) (15 kV accelerating voltage, 10 mm working distance and 0.1 nA) equipped with Bruker microanalytical EDS system QUANTAX installed at the Centro Interdipartimentale di Scienza e Ingegneria dei Materiali (CISIM) at the Università di Pisa. Major and minor element compositions for each melt inclusion were also characterized using an electron probe microanalyzer (EPMA) JEOL JXA-8200, operating in wavelength dispersive mode with a defocused beam of 5 μm (15 kV accelerating voltage and 5 nA beam current) at the Dipartimento di Scienze della Terra at the Università di Milano.

The bulk major element compositions of the texturally nonhomogeneous sulfide inclusions were reconstructed using spot analyses on the various sulfide phases present within each exposed sulfide inclusion. The reconstructed bulk composition was calculated dependent on the relative area percent of each sulfide phase, in the BSE images. Area percentages were determined using the image processing software package ImageJ (Image Processing and Analysis in Java, http://rsb.info. nih.gov/ij/) and the 2D images were segmented by manual thresholding. The uncertainty on the reconstructed bulk composition, involving both instrumental analytical error and manual image thresholding error, was evaluated to be <10%.

Trace element analyses of melt and sulfide inclusions and of host minerals were performed in situ by laser ablation inductively coupled plasma mass spectrometry (LA-ICPMS) at Géosciences Montpellier (Université de Montpellier, AETE-ISO regional facility of the OSU OREME), with a pulsed 193 nm ArF excimer laser (Analyte G2 from Teledyne) coupled to a Thermofinnigan Element XR mass spectrometer. For the analyses of host minerals, the laser was operated at a repetition rate of 8 Hz using spot sizes of 85 and 110 μm and a 6 J/cm 2 energy density. Total analysis time was 120 s with the first 80 s used for the background measurement and the last 40 s for sample ablation. Synthetic glass NIST 612 was used for external calibration. For melt inclusions, the laser was operated at a repetition rate of 6 Hz using spot sizes of 10 to 20 μm and a 6 J/cm 2 energy density. Total analysis time was 120 s with the first 80 s used for background measurement and the last 40 s for sample ablation. Synthetic glass NIST 610 was used for external calibration. For minerals and glass inclusions the accuracy of the analyses was monitored using the standard glass BIR-1 and SiO 2 of each mineral/glass, used as internal standard. For sulfide inclusions, only those where their exposed diameter was >15 μm were analyzed. The beam spot sizes were 5 to 10 μm. Only two non-homogeneous (polymineralic) sulfide inclusions were sufficiently large to be analyzed; the laser spot was tuned to approximate the "bulk" composition of the sulfide inclusion, without distinguishing among the single sulfide phases. The laser was operated at a repetition rate of 6 Hz using and a 6 J/cm 2 energy density with a total analysis time of 240 s (200 s for background measurement and 40 s of sample analysis). The Synthetic standard MASS-1 was used for external calibration. FeO (measured FeO, in the case of homogeneous sulfide inclusions, and FeO reconstructed with the above described procedure, in the case of non-homogeneous polymineralic sulfide inclusions) was used as an internal standard. Data reduction for the mineral, melt and sulfide inclusion was performed with the software package Glitter (http://www.glitter-gemoc.com). Detection limits, results of reference materials and control standard analysis are provided in the Supplementary Material S1.

Results

Sulfide inclusions

Based on their textures (polymineralic and homogeneous), two types of sulfide inclusions (Type 1 SIs, polymineralic and Type 2 SIs, homogeneous) were identified in the Vulcano products. Both types are spherical when found in glass, and spherical or ovoid to elongated in shape when enclosed in host phenocrysts, with shape partially defined by surrounding crystal growth (Fig. 2a).

Type 1 SIs (17 inclusions) are between 1 and 20 μm in diameter (mostly <10 μm) and consist of two or three Cu-rich sulfide phases each (Fig. 2a). These SIs are hosted in clinopyroxene, magnetite and feldspars (Fig. 2b). The composition of Type 1 sulfides (Table 1), when plotted in a Cu-Fe-S diagram at 1000 °C (Fig. 2c), spans from bornite solid solution (bnss) to the sulfide liquid field (SL). The reconstructed bulk composition of these unmixed SIs ranges from 66 wt% to 34 wt% Cu in the Cu-Fe-S diagram (Fig. 2c). Trace elements were measured up to 493 ppm Ni, 131 ppm Co, 1145 ppm Zn, 397 ppm As, 208 ppm Se, 354 ppm Ag and 2020 ppm Pb (Table 2) within the two Type 1 SIs analyzed (which contained 65 and 46 wt% Cu).

Type 2 SIs (59 inclusions) are 5-60 μm in diameter with a mean size of 20 μm and homogeneous textures (Fig. 2a); they occur in clinopyroxene, olivine, Ti-magnetite, plagioclase, sanidine, biotite and glass and prevail in mafic phases and glass. Type 2 SIs plot, at 1000 °C, in the pyrrhotite field (mss, monosulfide solid solution), with Cu content up to 2.6 wt% (Fig. 2c; Table 1). If compared to Type 1 SIs, they show markedly higher Ni and Co contents, up to 3495 ppm and 4248 ppm, respectively, similar Zn and lower Pb (up to 385 ppm), with Ag and Se, in the tens of ppm range. The only SI found in a rhyolite is pyrrhotite with 0.4 wt% Cu, characterized by very low Zn, Pb and Ag and higher Mo contents (Tables 1 and2).

Type 1 and Type 2 SIs are common accessories in trachytes, whereas they are extremely rare in latites (only Type 1 SIs) and in rhyolites (only Type 2 SIs), where just a couple of SIs were found after the inspection of several dozens of crystals. They are absent in basalt-shoshonite rocks. The two types of SIs never coexist in the samples of the same eruption. The entire dataset of analyses of the sulfides and hosts are reported in Tables 1 and2 and Supplementary Material S1. Some differences can be found when comparing the host mineral compositions for Type 1 and Type 2 SIs. Clinopyroxene (the most frequent host for both types of SIs; Fig. 2b) shows higher Cu, Cr, V and Ni contents for Type 1 sulfides compared to Type 2, for a similar Mg# range (see Supplementary Material S1). This is confirmed also when comparing the entire clinopyroxene analytical dataset (Supplementary Material S1) for the Vulcano products hosting Type 1 and Type 2 SIs.

Melt inclusions

The composition of glassy MIs in olivine, clinopyroxene, plagioclase, sanidine and biotite found in the products of explosive eruptions of basaltic, shoshonitic, latitic, trachytic and rhyolitic magmas is assumed to be representative of the magmas spanning the whole La Fossa magmatic differentiation path (Fig. 1c, Table 3 and Supplementary Material S1). The differentiation trend involves the fractionation of olivine, clinopyroxene, Ti-magnetite, labradorite to andesine plagioclase and, in evolved magmas, sanidine, minor oligoclase and biotite [START_REF] Gioncada | A study of melt inclusions at Vulcano (Aeolian Islands, Italy): insights on the primitive magmas and on the volcanic feeding system[END_REF]. Ti-magnetite joins the fractionating assemblage early, as shown by the decrease of Fe with Mg (Fig. 1d), while apatite joins later in intermediate terms.

The Cu content of MIs reaches the highest values at intermediate compositions (Zr around 160-200 ppm, at the latite-trachyte transition) and, when the highest Cu contents are considered, defines a trend that increases with magmatic differentiation from basalt (~50 ppm) to latite and trachyte (~250 ppm), and then abruptly drops to <60 ppm (Fig. 3a). Low Cu values have also been measured in 2018) are reported in Table 1 and in the supplementary material S1. L, liquid; bnss, bornite solid solution; mss, monosulfide solid solution. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) some intermediate composition MIs. Conversely, Pb concentration in MIs increases from basalt (5 ppm) to trachyte (35 ppm) and remains constant in rhyolites (Fig. 3b).

The average metal concentrations measured in Type 2 SIs (Table 2) and in coexistent MIs (Table 4) allow the sulfide phase/ silicate melt partition coefficients for Cu (1184), Ni (352), Zn (1.25), V (3.17), Pb (1.77) to be calculated. The sulfide phase/silicate melt partition coefficients for the same metals in Type 1 sulfides, mostly lacking coexistent melt inclusions, are determined assuming the average Cu content of latitic-trachytic melt inclusions (Table 4) and are 1538 for Cu, 154 for Ni, 1.32 for Zn, 1.8 for V and 76 for Pb. Major element composition (wt%) of Type 1 and Type 2 SIs; Ol: olivine; Cpx: clinopyroxene; Bt: biotite; Pl: plagioclase; Sa: sanidine; Ti-Mt: Ti-magnetite. Reconstructed: calculated bulk t1:3 composition of the sulfide inclusions (see methods section for details and supplementary materials for phase proportions); bdl: below detection limit; source a: [START_REF] Fulignati | Magmatic sulfide immiscibility at an active magmatic-hydrothermal system: the case of la Fossa (Vulcano, Italy)[END_REF]

Discussion

Evolution of metals in the magmas

The petrographic features and the chemical compositions of MIs and SIs found in Vulcano eruptive products allow the evolution of metals in the magmatic system of an active arc volcano to be tracked from basalt to rhyolite. This system is fed by sulfide-undersaturated, H 2 O-rich and oxidized basaltic magmas. The first appearance of SIs indicates that sulfide saturation occurs late, during magma evolution, at the latitetrachyte transition. Accordingly, the fO 2 value decreases from basalts (NNO-NNO + 1) to intermediate magmas (trachyte magma ∆NNO -1 to -2; [START_REF] Fulignati | Magmatic sulfide immiscibility at an active magmatic-hydrothermal system: the case of la Fossa (Vulcano, Italy)[END_REF]. This is potentially due to the combined effects of lower temperatures, the fractionation of Fe-bearing minerals and the volatile loss during differentiation [START_REF] Richards | The oxidation state, and sulfur and Cu contents of arc magmas: implications for metallogeny[END_REF][START_REF] Scaillet | Experimental and thermodynamic constraints on the Sulphur yield of peralkaline and metaluminous silicic flood eruptions[END_REF][START_REF] Scaillet | A model of Sulphur solubility for hydrous mafic melts: application to the determination of magmatic fluid compositions of Italian volcanoes[END_REF]. At Vulcano island, sulfide saturation is unrelated to the sudden onset of magnetite crystallization ("magnetite crisis", [START_REF] Jenner | The magnetite crisis in the evolution of arc-related magmas and the initial concentration of Au[END_REF], because magnetite fractionation starts early, while sulfide saturation is late.

Magmatic sulfide inclusions could be trapped either as a liquid (SL) or as a solid, which can be either a monosulfide solid solution (mss) or an intermediate solid solution (iss), having a composition close to pyrrhotite and chalcopyrite, respectively [START_REF] Parat | Sulfur-bearing magmatic accessory minerals[END_REF]. For most metals, the partition coefficient between sulfide and silicate melt strongly depends on the nature of the sulfide phase (mss, iss, or SL; [START_REF] Li | Effects of temperature, silicate melt composition, and oxygen fugacity on the partitioning of V[END_REF]. Thus, determining the nature of the sulfide phases at the time of trapping is important to constrain the metal budget of the magmatic system (Rottier et al., 2019 and references therein). By plotting both Type 1 and Type 2 SIs analyses on the ternary diagram of the Cu-Fe-S system (at 1000 °C), the reconstructed Type 1 SIs compositions fall in the liquid field, whereas Type 2 SIs fall in the pyrrothite (mss) field, suggesting that the latter were trapped as a solid phase. This evidence is supported by comparing their sulfide phase-silicate melt partition coefficients (for Cu, Ni, Pb, Zn), calculated from measured concentrationsandpredictedaccordingtotheequationsforD X SL/SM , D X mss/SM of [START_REF] Li | Effects of temperature, silicate melt composition, and oxygen fugacity on the partitioning of V[END_REF] for a trachyte melt with 950 °C, ΔFMQ -0.77 and FeO 4.4 wt%. The comparison shown in Fig. 4 demonstrates a good match for both the Type 1 and the Type 2 SIs (these elements were selected because they could be reliably quantified in both magmatic sulfide and silicate melt inclusions, and because their partition coefficient is markedly different for mss versus SL). The different partition coefficients SL/SM and mss/SM are also in agreement with the measured Ag and Pb contents, which are considerably higher in Type 1 SIs than in Type 2 SIs.

The Cu behavior in the silicate melt confirms late sulfide saturation (Fig. 3a). In fact, Cu concentration in MIs increases from basalt to latite melts, which are sulfide-undersaturated, and then rapidly decreases within a narrow compositional interval (Zr 180-200 ppm; SiO 2 58-60 wt%) once sulfide saturation is reached, due to the stripping of Cu by Cu-rich sulfide melt. The scattered Cu concentrations, including very low values in the intermediate composition MIs range, might suggest that: (i) incipient sulfide saturation was achieved in some parts of the reservoir (at the contact with wall rock thanks to temperature decrease, fractional crystallization or silica assimilation?) although not revealed by sulfide trapping; (ii) Cu was episodically lost to a S-rich vapor phase from mafic magmas. Events of refilling by Cu-poor, S-rich and sulfide undersaturated magma could furthermore enhance the heterogeneity in the Cu content of an intermediate composition reservoir. This is particularly crucial because, in order to represent the entire basalt to rhyolite differentiation range, we analyzed samples that do not necessarily represent the evolution in a single reservoir but rather come from multiple, possibly independent magma batches with variable age.

The evolution of Cu and Pb in the silicate melt has been modeled with fractional crystallization, starting from a mean value of the La Sommata basaltic MIs and including a sulfide phase in the fractionating assemblage at the latite-trachyte stage (Fig. 3a,b). For this study, we t2:1 The models provide a robust explanation of the Cu behavior in the silicate melt. The fractional crystallization models predict that 0.2-0.3 wt% of sulfide melt fractionated along with clinopyroxene + plagioclase + Ti-magnetite + olivine + biotite + sanidine. This is sufficient to cause a sharp drop in the Cu content of silicate melt at the latite to trachyte transition. Because Type 1 and Type 2 SIs were never found to coexist, we suggest that the first sulfides formed at the highest Cu content are correspondingly Cu-rich (Type 1 SIs), whereas those exsolved from the Cu-depleted trachytic magma are the Cu-poor Type 2 SIs (Cu-bearing mss) found in trachyte and rhyolite (Fig. 3a). This reconstruction is in agreement with the composition of clinopyroxene crystals in the latites and trachytes. Clinopyroxene composition testifies that, in the latite-to-trachyte transition, the Cu-depleted trachytic magma is slightly more evolved (that is, having a lower Cr, V and Ni content in clinopyroxenes) than the Cu-rich trachyte and latite (Fig. 5). The trachyte-rhyolite step requires a high percentage (60 vol%) of fractionated solid [START_REF] Costa | Magma evolution at La Fossa volcano (Vulcano Island, Italy) in the last 1000 years: evidence from eruptive products and temperature gradient experiments[END_REF], strongly increasing the final concentration of incompatible elements and possibly explaining the large spread in Zr values measured in rhyolites.

The evolution of Pb shows an increase with differentiation up to rhyolite (Fig. 3b). This agrees well with the low sulfide melt/silicate melt partition coefficient for this element, which is orders of magnitude lower than that of Cu (this work and [START_REF] Li | Effects of temperature, silicate melt composition, and oxygen fugacity on the partitioning of V[END_REF]. The modeled Pb trend in rhyolites (Zr > 200 ppm), despite the higher D Pb , slightly deviates from the measured data. This may be ascribed to the partitioning of Pb in an exsolved Cl-bearing aqueous fluid.

The effect of fluid saturation

Tracking metal evolution in magmas cannot overlook the effect of fluid-saturation along differentiation. While Vulcano basalts are H 2 O-, S-, Cl-rich, the shoshonitic magmas have lower volatile contents [START_REF] Gioncada | A study of melt inclusions at Vulcano (Aeolian Islands, Italy): insights on the primitive magmas and on the volcanic feeding system[END_REF], suggesting that H 2 O, S and Cl may be lost to an exsolved aqueous fluid phase at the basalt-shoshonite transition. Our results show that, despite mafic magmas degassing during ascent, Cu and Pb increase with differentiation (Fig. 3a,b). This suggests that the evolution of these metals is not significantly affected by decompression degassing of mafic magmas as they refill crustal reservoirs. Indeed, Cu scarcely partitions into a hydrosaline fluid phase exsolved from mafic magmas according to the experimental results of [START_REF] Zajacz | Gold and copper in volatile saturated mafic to intermediate magmas: solubilities, partitioning and implications or ore deposit formation[END_REF].

In trachytes and rhyolites, the Cu-normalized abundances of S, Mo, Zn, Ag, Pt, Au, Pb in Type 1 (trachyte) and Type 2 (trachyte and rhyolite) SIs show different patterns (Fig. 6). While Mo/Cu ratio in the rhyolite Type 2 SIs is higher than that of Type 2 SIs in trachyte, Zn/Cu and Pb/ Cu are distinctly lower (Fig. 6a). This is in agreement with the exsolution of a Cl-rich magmatic fluid phase from the rhyolitic magma at La Fossa [START_REF] Fulignati | Magmatic sulfide immiscibility at an active magmatic-hydrothermal system: the case of la Fossa (Vulcano, Italy)[END_REF], causing Pb and Zn to preferentially partition with respect to Mo [START_REF] Zajacz | Determination of fluid/melt partition coefficients by LA-ICPMS analysis of co-existing fluid and silicate melt inclusions: controls on element partitioning[END_REF]. Mo, which is not efficiently partitioned in a Cl-rich magmatic fluid phase [START_REF] Candela | The partitioning of copper and molybdenum between silicate melts and aqueous fluids[END_REF][START_REF] Zajacz | Determination of fluid/melt partition coefficients by LA-ICPMS analysis of co-existing fluid and silicate melt inclusions: controls on element partitioning[END_REF], tends to also increase in the rhyolite SIs.

At Vulcano, previous data suggest that metal-bearing fluids can be involved in phreatic-phreatomagmatic eruptions [START_REF] Gurioli | The historic magmatic-hydrothermal eruption of the Breccia di Commenda, Vulcano, Italy[END_REF]). An example is the Breccia di Commenda eruption, a violent explosive Mean composition and standard deviation (SD) for major elements (wt%) of MIs in the Vulcano products. Literature EPMA data: [START_REF] Gioncada | A study of melt inclusions at Vulcano (Aeolian Islands, Italy): insights on the primitive magmas and on the volcanic feeding system[END_REF], [START_REF] Voyer | Zonation of H 2 O and F concentrations around melt inclusions in olivines[END_REF] for La t3:3 Sommata basalt; [START_REF] Fusillo | Deciphering post-caldera volcanism: insight into the Vulcanello (Island of Vulcano, Southern Italy) eruptive activity based on geological and petrological constraints[END_REF] for Vulcanello 1 shoshonite; [START_REF] Fulignati | Magmatic sulfide immiscibility at an active magmatic-hydrothermal system: the case of la Fossa (Vulcano, Italy)[END_REF] Basalt Host event occurred at La Fossa volcano during XIII Cent. AD. This eruption produced a high amount of lithics which showed acid-sulfate alteration [START_REF] Gurioli | The historic magmatic-hydrothermal eruption of the Breccia di Commenda, Vulcano, Italy[END_REF]. Interestingly, S/Cu, Zn/Cu, Pb/Cu ratios measured on the fine ash of the Breccia di Commenda deposits are higher than the same ratios measured in the trachytic and rhyolitic SIs (Fig. 6a). This suggests that Cl-rich fluids carrying Pb and Zn from the magmatic-hydrothermal system were involved in the Breccia di Commenda eruption.

Comparison with mineralized systems

With the aim to compare the SIs composition in the products of an active arc volcano with that of SIs from magmas associated with porphyry mineralization, absolute and Cu-normalized metal concentrations from La Fossa are compared with those found in well-preserved SIs of ore-related igneous rocks. The metal ratios and absolute concentrations in Vulcano SIs (either in Type 1 and Type 2 SIs) match well with those of mineralized systems (Fig. 6b,c). This suggests that, at Vulcano, the late attainment of sulfide saturation during fractionation in mid-upper crustal reservoirs prevents the early depletion in S and chalcophile metals and produces magmatic sulfide melts with compositions comparable to those found in several porphyry systems. Once formed, the sulfides may be stored in crystal mushes of intermediate to evolved crustal reservoirs, re-melted by mafic sulfide-undersaturated recharges or eventually cannibalized by aqueous fluids exsolving at the rhyolite stage, thereby producing highly mineralizing solutions [START_REF] Audétat | Magmatic controls on porphyry copper genesis[END_REF][START_REF] Halter | The origin of Cu/au ratios in porphyry-type ore deposits[END_REF][START_REF] Keith | The role of magmatic sulfides and mafic alkaline magmas in the Bingham and Tintic mining districts[END_REF][START_REF] Nadeau | Sulphide magma as a source of metals in arc-related magmatic hydrothermal ore fluids[END_REF][START_REF] Wilkinson | Triggers for the formation of porphyry ore deposits in magmatic arcs[END_REF].

Our results indicate that the processes governing metal evolution through silicate melt differentiation in active arc magmatic systems share similarities to those inferred for magmas associated to porphyry Cu systems. Bearing in mind that the magmatic stage is arguably pivotal in the evolution of porphyry Cu systems [START_REF] Audétat | Magmatic controls on porphyry copper genesis[END_REF], arc volcanoes such as La Fossa can thus be viewed as active analogues and ideal sites for studying the critical early stages of porphyry Cu genesis. Their possibility to evolve toward mineralized systems will, of course, depend also on other factors (magma chamber size and depth, duration of magmatic and hydrothermal activity, and the efficiency of magmatic fluid focusing; [START_REF] Richards | Magmatic to hydrothermal metal fluxes in convergent and collided margins[END_REF][START_REF] Wilkinson | Triggers for the formation of porphyry ore deposits in magmatic arcs[END_REF] that can either promote or inhibit porphyry Cu formation.

Conclusive remarks

In this work, we used combined compositional data (major, minor and trace element) on melt inclusions, magmatic sulfides and host minerals from the eruptive products of the arc volcano of La Fossa (Vulcano Island, Italy), to track the evolution of metals along the magma differentiation path of an active magmatic system. We found that, in case of sulfide-undersaturated, volatile-rich arc basalts, metals are scarcely subtracted by degassing during ascent to shallow crustal reservoirs and thus reach their highest abundances in intermediate magmas. Further evolution results in sulfide saturation where Cu and chalcophile metals strongly partition into the sulfide melt, causing a dramatic decrease in abundance from the silicate melt. The evolution of Cu in the silicate melts was modeled with quantitative fractional crystallization, and the results are in close agreement with experimental data. The model shows that fractionation of only 0.2-0.3 wt% of sulfide is sufficient to deplete the silicate melt in Cu down to the values recorded by MIs in trachytic and rhyolitic products. Metals that do not partition in sulfides (Pb, Zn) increase their concentrations with magmatic evolution until they are scavenged by a Cl-rich aqueous fluid phase, possibly exsolved at the rhyolitic stage.

The comparison of metal ratios and absolute concentrations of the Vulcano magmatic sulfides with those of sulfides found in magmatic rocks, associated with world-class porphyry Cu systems, shows strong similarities. This suggests that the processes governing metal evolution through silicate melt differentiation in active arc magmatic systems are similar to those processes inferred for magmatic stage of porphyry Cu environments. Our results thus suggest that the investigation of metal evolution in active arc volcanoes such as La Fossa can provide information for interpreting the genetic mechanisms of porphyry Cu deposit formation.

Fig. 1 .

 1 Fig. 1. (a) Location of La Fossa volcano and Vulcano island in the Aeolian Arc; (b) Panoramic view toward N of La Fossa crater and its fumarolic field; (c) TAS (total alkali vs SiO 2 ) diagram of Vulcano rocks. Stars are the samples selected to represent the basalt to rhyolite suite; insert in (c) shows the composition of MIs of the selected samples; (d) Fe 2 O 3 tot. vs MgO diagram of Vulcano products. Whole rock data in (c) and (d) are re-calculated to 100 on anhydrous basis; literature data are from De Astis et al. (2013), Fusillo et al. (2015) and Costa et al. (2020). Melt inclusions major elements data are from Gioncada et al. (1998), Le Voyer et al. (2014), Fusillo et al. (2015), Fulignati et al. (2018) and this work. The complete data set of MIs is reported in the supplementary material S1.

Fig. 2 .

 2 Fig. 2. (a) BSE images of Type 1 SIs consisting of unmixed chalcopyrite (Cp)-bornite (Bn) and Type 2 SIs represented by homogeneous pyrrhotite (Po); (b) abundance of SIs in the various mineral phases and groundmass glass of eruptive products (Ol: olivine; Cpx: clinopyroxene; Bt: biotite; Pl: plagioclase; Sa: sanidine; Mt.: magnetite; Gl: groundmass glass); (c) Composition of SIs in the Cu-Fe-S system at 1000 °C (Craig and Kullerud, 1969), for Type 1 SIs analyses of unmixed phases and the correspondent reconstructed composition are shown and joined by red lines, error bars fall within the symbols; data from this work and Fulignati et al. (2018) are reported in Table1and in the supplementary material S1. L, liquid; bnss, bornite solid solution; mss, monosulfide solid solution. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 3 .

 3 Fig. 3. Copper (a) and Pb (b) versus Zr as differentiation index for the glassy MIs representative of the basalt to rhyolite suite at Vulcano, with quantitative fractional crystallization model for the evolution of Cu and Pb in the silicate melt. Bulk partition coefficients (D) for Cu, Pb and Zr have been calculated using minerals/silicate melt partition coefficients from literature and sulfide/silicate melt partition coefficients calculated with the model of[START_REF] Li | Effects of temperature, silicate melt composition, and oxygen fugacity on the partitioning of V[END_REF]. See supplementary material S1 for additional details. 1 sigma error for each analysis is shown as error bars, which if not visible, is smaller than the symbol. Symbols and numbers along the fractionation paths indicate melt fraction.

Fig. 4 .

 4 Fig. 4. Comparison of measured sulfide -silicate melt partition coefficients with values predicted by the model of Li and Audétat (2015); (a) sulfide liquid (Type 1 SIs)-silicate melt (b) monosulfide solid solution (Type 2 SIs)-silicate melt. T of 950 °C, ΔFMQ = -0.77 and FeO in the melt = 4.4 wt% estimated for La Fossa trachyte by Fulignati et al. (2018) have been used in the model.

Fig. 5 .

 5 Fig. 5. Cu versus Cr, V and Ni content for clinopyroxene crystals in the latitic and trachytic products of La Fossa hosting the type 1 (yellow and green symbols) and type 2 (red symbols) SIs. See the supplementary material S1 for the complete data set of analyses of clinopyroxene. 1 sigma error for each analysis is shown as error bars, which if not visible, is smaller than the symbol. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 6 .

 6 Fig. 6. (a) Cu-normalized composition of La Fossa SIs and Breccia di Commenda fine ash; (b) Cu-normalized composition (average and range) of Type 2 SIs compared to SIs of ore-related latitic magma at Bingham and at Santa Rita and Cerrillos; (c) Absolute metal concentrations in Type 1 and Type 2 La Fossa SIs compared with those found in mineralized systems (Bingham Canyon, Santa Rita, Cerrillos and Bajo de la Alumbrera).

Table 1

 1

	t1:2

  , EPMA analyses; source b: this work, FE-SEM-EDS analyses.

	t1:4
	t1:5	Host rock	Unit	Host mineral	Sulfide ID	Sulfide type	Source	Fe	S	Co	Mn	Ni	Zn	Cu	Total
	t1:6	Trachyte	Pal D	sa	PAL-90 sulf1	2	a	58.48	37.19	0.09	0.08	0.06	bdl	1.44	97.33
	t1:7	Trachyte	Pal D	cpx	PAL-90 sulf2	2	a	59.12	38.05	0.03	0.09	0.03	0.10	1.19	98.60
	t1:8	Trachyte	Pal D	cpx	PAL-90 sulf2	2	a	59.89	38.08	0.07	0.12	0.05	0.03	0.42	98.65
	t1:9	Trachyte	Pal D	ol	pal90solf3	2	a	57.19	37.24	0.14	0.18	0.07	0.07	1.62	96.52
	t1:10	Trachyte	Pal D	gl	pal90solf4	2	a	58.01	37.24	0.16	0.11	0.09	bdl	2.32	97.93
	t1:11	Trachyte	Pal D	ol	pal90solf5	2	a	58.94	37.60	0.10	0.12	0.10	bdl	1.67	98.53
	t1:12	Trachyte	Pal D	ol	pal90solf5	2	a	59.19	38.08	0.09	0.18	0.04	bdl	1.29	98.88
	t1:13	Trachyte	Pal D	gl	pal90sulf8	2	a	57.09	38.05	0.07	0.10	0.04	0.11	1.34	96.80
	t1:14	Trachyte	Pal D	Ti-mt	pal90sulf10	2	a	58.72	38.24	0.05	0.16	0.05	0.05	0.97	98.23
	t1:15	Trachyte	Pal D	cpx	pal90sulf13	2	a	58.38	37.99	0.13	0.12	0.00	0.03	1.54	98.18
	t1:16	Trachyte	Pal D	cpx	pal90sulf13	2	a	58.25	37.70	0.07	0.04	0.01	0.06	1.46	97.58
	t1:17	Trachyte	Pal D	cpx	pal90sulf14a	2	a	53.30	39.64	0.14	0.09	0.06	bdl	2.16	95.39
	t1:18	Trachyte	Pal D	Ti-mt	PAL90 u293sulf17	2	a	58.15	37.73	0.09	0.08	0.01	bdl	1.31	97.37
	t1:19	Trachyte	Pal D	Ti-mt	PAL90 u293sulf17	2	a	58.60	38.26	0.07	0.12	0.09	0.02	1.39	98.54
	t1:20	Trachyte	Pal D	pl	PAL90U297 sulf18	2	a	56.63	37.48	0.03	0.10	0.08	0.10	1.55	95.95
	t1:21	Trachyte	Pal D	cpx	PAL-15D sulf1	2	a	56.33	37.35	0.11	0.11	0.04	bdl	1.34	95.28
	t1:22	Trachyte	Pal D	cpx	PAL-15D sulf2	2	a	57.60	37.53	0.12	0.13	0.05	bdl	1.32	96.75
	t1:23	Trachyte	Pal D	Ti-mt	PAL-15D sulf3	2	a	56.48	37.45	0.13	0.12	0.05	0.04	1.34	95.60
	t1:24	Trachyte	Pal D	gl	PAL-15D sulf4	2	a	56.85	37.61	0.09	0.11	0.05	0.11	1.30	96.12
	t1:25	Trachyte	Pal D	cpx	sulf5	2	a	56.06	37.68	0.06	0.14	0.06	bdl	1.84	95.84
	t1:26	Trachyte	Pal D	cpx	pal15sulf8.spc	2	a	57.15	37.63	0.04	0.13	bdl	0.04	1.02	96.00
	t1:27	Trachyte	Pal D	cpx	Pal 15 D sulf 6	2	a	56.28	37.64	0.08	0.10	0.05	0.06	2.51	96.71
	t1:28	Trachyte	Pal D	cpx	Pal 15 D sulf 6	2	a	56.35	37.64	0.14	0.12	0.11	0.11	2.54	97.01
	t1:29	Trachyte	Pal D	cpx	Pal 15 D sulf 6	2	a	56.40	37.67	0.15	0.01	0.07	0.07	2.72	97.09
	t1:30	Trachyte	Pal D	Ti-mt	Pal 15 D sulf 7	2	a	57.99	37.64	0.03	0.10	0.05	0.04	1.21	97.06
	t1:31	Trachyte	Pal D	Ti-mt	Pal 15 D sulf 8	2	a	57.96	37.57	0.12	0.11	0.08	0.04	1.58	97.46
	t1:32	Trachyte	Palizzi lava	pl	SC15-1_1	1	b	24.05	32.12	bdl	bdl	bdl	bdl	43.83	100.00
	t1:33	Trachyte	Palizzi lava	pl	SC15-1_1	1	b	38.65	33.84	bdl	bdl	bdl	bdl	27.51	100.00
	t1:34	Trachyte	Palizzi lava	pl	reconstructed *SC15-1_1	1	b	33.54	33.24	bdl	bdl	bdl	bdl	33.22	100.00
	t1:35	Trachyte	Palizzi lava	pl	SC15-1_2	1	b	21.84	31.58	bdl	bdl	bdl	bdl	46.58	100.00
	t1:36	Trachyte	Palizzi lava	pl	SC15-1_2	1	b	33.72	34.57	bdl	bdl	bdl	bdl	31.70	100.00
	t1:37	Trachyte	Palizzi lava	pl	reconstructed *SC15-1_2	1	b	28.50	33.25	bdl	bdl	bdl	bdl	38.25	100.00
	t1:38	Trachyte	Palizzi lava	cpx	SC15-1_3	1	b	20.92	28.88	bdl	bdl	bdl	bdl	50.20	100.00
	t1:39	Trachyte	Palizzi lava	cpx	SC15-1_3	1	b	5.09	22.51	bdl	bdl	bdl	bdl	72.40	100.00
	t1:40	Trachyte	Palizzi lava	cpx	SC15-1_3	1	b	20.74	30.62	bdl	bdl	bdl	bdl	48.64	100.00
	t1:41	Trachyte	Palizzi lava	cpx	reconstructed *SC15-1_3	1	b	15.57	27.94	bdl	bdl	bdl	bdl	56.48	100.00
	t1:42	Trachyte	Palizzi lava	cpx	SC15-1_3b	1	b	21.60	23.91	bdl	bdl	bdl	bdl	54.49	100.00
	t1:43	Trachyte	Palizzi lava	cpx	SC15-1_3b	1	b	12.40	21.58	bdl	bdl	bdl	bdl	66.02	100.00
	t1:44	Trachyte	Palizzi lava	cpx	SC15-1_4	1	b	37.20	29.81	bdl	bdl	bdl	bdl	32.99	100.00
	t1:45	Trachyte	Palizzi lava	cpx	SC15-1_4	1	b	30.91	31.85	bdl	bdl	bdl	bdl	37.24	100.00
	t1:46	Trachyte	Palizzi lava	pl	SC15-1_5	1	b	10.02	25.69	bdl	bdl	bdl	bdl	64.29	100.00
	t1:47	Trachyte	Palizzi lava	pl	SC15-1_5	1	b	22.46	29.18	bdl	bdl	bdl	bdl	48.36	100.00
	t1:48	Trachyte	Palizzi lava	pl	reconstructed *SC15-1_5	1	b	20.64	28.67	bdl	bdl	bdl	bdl	50.69	100.00
	t1:49	Trachyte	Palizzi lava	pl	SC15-1_6	1	b	18.07	30.59	bdl	bdl	bdl	bdl	51.35	100.00
	t1:50	Trachyte	Palizzi lava	pl	SC15-1_6	1	b	9.64	24.69	bdl	bdl	bdl	bdl	65.66	100.00
	t1:51	Trachyte	Palizzi lava	pl	reconstructed *SC15-1_6	1	b	15.62	28.88	bdl	bdl	bdl	bdl	55.50	100.00
	t1:52	Trachyte	Pal D	sa	SC_18_20c1	2	b	62.38	37.48	bdl	bdl	bdl	bdl	0.14	100.00
	t1:53	Trachyte	Pal D	sa	SC_18_20c2	2	b	62.83	36.85	bdl	bdl	bdl	bdl	0.32	100.00
	t1:54	Trachyte	Pal D	sa	SC_18_20c3	2	b	62.18	37.21	bdl	bdl	bdl	bdl	0.60	100.00
	t1:55	Trachyte	Pal D	sa	SC_18_20c4	2	b	63.61	36.11	bdl	bdl	bdl	bdl	0.28	100.00
	t1:56	Trachyte	Pal D	pl	SC_18_20c5	2	b	63.70	36.20	bdl	bdl	bdl	bdl	0.10	100.00
	t1:57	Trachyte	Palizzi lava	Ti-mt	sc1824 11-12	1	b	24.18	28.79	bdl	bdl	bdl	bdl	47.04	100.00
	t1:58	Trachyte	Palizzi lava	Ti-mt	sc1824 11-12	1	b	31.37	29.73	bdl	bdl	bdl	bdl	38.91	100.00
	t1:59	Trachyte	Palizzi lava	cpx	sc1824 4-5-6	1	b	20.42	28.20	bdl	bdl	bdl	bdl	51.38	100.00
	t1:60	Trachyte	Palizzi lava	cpx	sc1824 4-5-6	1	b	2.27	18.68	bdl	bdl	bdl	bdl	79.05	100.00
	t1:61	Trachyte	Palizzi lava	cpx	reconstructed *sc1824 4-5-6	1	b	10.89	23.21	bdl	bdl	bdl	bdl	65.90	100.00
	t1:62	Trachyte	Palizzi lava	cpx	sc1824 7-8	1	b	29.89	29.63	bdl	bdl	bdl	bdl	40.48	100.00
	t1:63	Trachyte	Palizzi lava	cpx	sc1824 7-8	1	b	22.97	28.30	bdl	bdl	bdl	bdl	48.73	100.00
	t1:64	Trachyte	Palizzi lava	cpx	reconstructed *sc1824 7-8	1	b	25.18	28.73	bdl	bdl	bdl	bdl	46.09	100.00
	t1:65	Latite	Pal C	Ti-mt	sulf n4	1	b	28.65	32.34	bdl	bdl	bdl	bdl	39.01	100.00
	t1:66	Latite	Pal C	Ti-mt	solf n4	1	b	11.75	25.37	bdl	bdl	bdl	bdl	62.88	100.00
	t1:67	Latite	Pal C	Ti-mt	reconstructed *solfn4	1	b	18.51	28.15	bdl	bdl	bdl	bdl	53.34	100.00
	t1:68	Rhyolite	Pal B	sa	pallentiasulf1	2	a	59.58	36.72	0.03	0.03	0.04	0.09	0.33	96.81
	t1:69	Rhyolite	Pal B	sa	pallentiasulf1	2	a	58.57	36.56	0.04	0.07	0.01	bdl	0.42	95.67

Table 2 t2 : 2

 2: Major and trace elements (ppm) bulk composition of Type 1 and Type 2 SIs analyzed by LA-ICP-MS; Ol: olivine; Cpx: clinopyroxene; Sa: sanidine; Ti-Mt: Ti-magnetite.

	S. Costa, P. Fulignati, A. Gioncada et al.															Lithos xxx (2020) xxx
	S V Mn Fe Co Ni Cu Zn As Se Mo Ag Cd Sn Sb Te Pt Au Tl Pb Bi		371,919 bdl 671 676,629 823 269 17,048 241 bdl 25.84 0.47 3.98 1.16 2.05 0.18 bdl 0.08 0.01 0.07 3.90 bdl	380,658 8.80 275 249,572 362 111 6626 378 bdl 2.21 bdl 3.46 bdl 3.47 bdl bdl 0.48 bdl 0.01 4.38 0.08	378,390 1.39 493 454,061 1406 690 35,369 150 bdl 183.55 1.67 3.43 3.85 bdl 0.06 bdl 0.02 0.14 60.27 4.50 0.13	382,459 170 762 690,365 593 85 17,666 314 34.08 bdl 26.79 2.21 1.16 bdl 0.12 1.67 0.51 bdl 4.06 194 78.4	378,456 24.98 1202 533,044 1701 380 20,826 157 3.19 bdl 2.78 4.13 0.46 1.41 1.00 1.23 bdl 0.26 1.35 3.27 0.14	396,402 6.23 795 695,233 1334 354 29,342 230 bdl bdl 3.81 3.22 0.50 1.07 bdl bdl 0.08 0.10 0.07 3.08 0.17	379,924 85.56 797 445,303 1107 153 11,738 294 3.32 78.58 2.31 2.28 0.16 2.77 bdl bdl bdl 0.04 1.09 35.01 0.71		379,924 32.83 746 459,804 869 185 10,467 243 8.76 bdl 7.57 2.19 3.60 0.94 bdl 0.37 bdl bdl 0.49 19.60 10.8		149,585 1068 39,728 582,983 1438 1145 6334 1664 bdl 84.77 0.20 17.52 bdl 16.35 bdl 2.31 bdl bdl bdl 12.81 0.85	341,034 119 6800 582,983 2627 2917 13,900 603 2.11 4.71 2.09 3.68 4.18 0.48 bdl 2.00 0.13 0.18 0.03 4.15 0.30	346,344 206 12,951 582,983 2412 375 10,979 1445 bdl 107 2.36 9.86 10.95 4.96 0.99 bdl 0.29 0.04 0.20 6.64 0.38	370,083 1.66 3026 582,983 4248 3495 24,755 433 bdl 48.50 1.68 1.87 1.31 0.93 bdl 0.48 0.18 0.18 0.35 14.51 7.60	232,691 132 2413 582,983 1550 2145 12,373 644 50.61 15.36 22.58 13.36 6.27 bdl 1.82 1.52 0.34 0.46 7.18 384.56 166	422,053 712 3501 582,983 3248 2661 15,932 1006 bdl bdl 2.12 6.36 1.07 1.29 bdl bdl 0.10 0.11 0.45 4.66 0.23	349,260 314 2605 582,983 3377 3397 16,455 830 bdl 11.01 1.72 3.74 1.60 3.16 bdl bdl 0.12 0.07 0.32 3.72 0.12	595,243 117 1505 173,263 59 47 1,193,582 1145 397.31 208 6.46 354.05 0.64 14.27 4.93 0.50 0.07 bdl 0.03 34.41 3.31		148,141 0.05 682 108,824 131 493 248,441 607 0.47 15.66 0.02 9.07 16.64 3.95 0.11 1.14 bdl 0.04 0.03 2020 32.6	362,456 bdl 1616 582,983 1216 1979 8003 44 bdl 45.77 76.36 1.85 2.14 1.83 bdl 3.41 bdl 0.03 0.12 0.80 0.23
	Sulfide	type	2	2	2	2	2	2	2		2		2	2	2	2	2	2	2	1		1	2
	Sulfide ID		PAL-90 sulf1	PAL-90 sulf2	pal90solf5	pal90sulf10	pal90sulf13	pal90sulf14a	PAL90	u293sulf17	PAL90	u293sulf17	PAL-15D sulf1	PAL-15D sulf2	sulf5	Pal 15 D sulf 6	Pal 15 D sulf 6	Pal 15 D sulf 7	Pal 15 D sulf 8	sc1824 4-5-6		sc1824 7-8	pallentiasulf1
	Host	mineral	sa	cpx	ol	Ti-mt	cpx	cpx	Ti-mt		Ti-mt		cpx	cpx	cpx	cpx	cpx	Ti-mt	Ti-mt	cpx		cpx	sa
	Host Unit	rock	Trachyte Pal D	Trachyte Pal D	Trachyte Pal D	Trachyte Pal D	Trachyte Pal D	Trachyte Pal D	Trachyte Pal D		Trachyte Pal D		Trachyte Pal D	Trachyte Pal D	Trachyte Pal D	Trachyte Pal D	Trachyte Pal D	Trachyte Pal D	Trachyte Pal D	Trachyte Palizzi	lava	Trachyte Palizzi	lava	Rhyolite Pal B
	t2:3	t2:4	t2:5	t2:6	t2:7	t2:8	t2:9	t2:10	t2:11		t2:12		t2:13	t2:14	t2:15	t2:16	t2:17	t2:18	t2:19	t2:20		t2:21	t2:22

neglected crustal assimilation processes. The model employs bulk distribution coefficient for Zr, Cu and Pb, calculated for each step of the differentiation process using partition coefficients derived from the literature and the relative proportions of crystallizing phases for Vulcano

[START_REF] Costa | Magma evolution at La Fossa volcano (Vulcano Island, Italy) in the last 1000 years: evidence from eruptive products and temperature gradient experiments[END_REF]

; see Supplementary Material S1 for details of the model). The sulfide phase/silicate melt partition coefficients for Pb and Cu were calculated according to

[START_REF] Li | Effects of temperature, silicate melt composition, and oxygen fugacity on the partitioning of V[END_REF]

(Supplementary Material S1).

Table 3

 3

	t3:2

  for Pal D trachyte. Pal C latite and Pal B rhyolite are FE-SEM-EDS analyses from this work.

	t3:4	Host rock composition	Unit		SiO 2	TiO 2	Al 2 O 3	FeO t	MnO	MgO	CaO	Na 2 O	K 2 O	P 2 O 5	Cl
	t3:5	Basalt	La Sommata	mean (15)	45.91	0.62	10.99	8.93	0.17	8.76	14.34	1.99	1.85	0.31	0.29
	t3:6			SD	0.80	0.06	0.40	0.49	0.02	1.36	0.49	0.17	0.28	0.20	0.05
	t3:7	Shoshonite	Vulcanello 1	mean (33)	54.34	0.63	17.31	7.05	0.15	2.16	4.51	4.57	6.83	0.66	0.30
	t3:8			SD	1.44	0.09	0.63	0.90	0.04	0.59	0.89	0.34	0.66	0.12	0.03
	t3:9	Latite	Pal C	mean (5)	56.55	0.86	18.08	6.18	0.14	1.10	3.39	4.94	7.93	0.40	0.42
	t3:10			SD	1.09	0.15	0.80	1.59	0.13	0.24	0.77	0.39	1.01	0.15	0.09
	t3:11	Trachyte	Pal D	mean (22)	60.00	0.58	17.38	4.41	0.14	1.01	2.49	4.59	6.82	0.20	0.38
	t3:12			SD	0.86	0.12	0.56	0.57	0.06	0.32	0.54	0.54	1.04	0.08	0.06
	t3:13	Rhyolite	Pal B	mean (18)	70.44	0.13	14.87	2.02	0.11	0.13	0.95	4.53	6.64	0.06	0.51
	t3:14			SD	0.79	0.05	0.62	0.29	0.05	0.11	0.16	0.48	0.51	0.00	0.08

Acknowledgements

We warmly thank Prof. Jung-Woo Park for the review of an early version of the manuscript. We would also like to thank Greg Shellnutt for editorial handling. The present manuscript benefited from the constructive review of two anonymous referees whose comments and suggestions helped to improve the quality and clarity of the manuscript. The authors thank R. Ishak (Università di Pisa), A. Risplendente (Università di Milano), for assistance during analytical work, F. Colarieti and M. Gemelli (Università di Pisa) for sample preparation and M. D. Suttle for helping us with English editing. This research was funded by projects PRA_2018_41 to PF and MP and FFABR2017 to AG. This research is part of SC PhD program funded by a Tuscany Regional "Pegaso" doctoral grant.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi. org/10.1016/j.lithos.2020.105851.


Pierre Laville

Juliette Martin

Guillaume Launay

Leslie Regad

Anne-Claude Camproux

Sjoerd De Vries

Michel Petitjean
email: petitjean.chiral@gmail.com

A non-parametric method to compute protein-protein and protein-ligands interfaces. Application to HIV-2 protease-inhibitors complexes

Motivation:

The accurate description of interfaces is needed to identify which residues interact with another molecule or macromolecule. In addition, a data structure is required to compare interfaces within or between families of protein-protein or protein-ligands complexes. In order to avoid many unwanted comparisons, we looked for a parameter free computation of interfaces. This need appeared at the occasion of bioinformatics studies by our research team focusing on HIV-2 protease (PR2) resistance to its inhibitors. Results: We designed the PPIC software (Protein Protein Interface Computation). It offers three methods of computation of interfaces: (1) our original parameter free method, (2) the Voronoi tessellation approach, and (3) the cutoff distance method. For the latter, we suggest on the basis of 1050 dimers protein-protein interfaces that the optimal cutoff distance is 3.7 Å, or 3.6 Å for a set of 18 PR2-ligand interfaces. We found at most 17 contact residues with PR2 ligands.

Introduction

As noticed by [START_REF] Vangone | Contacts-based prediction of binding affinity in protein-protein complexes[END_REF], the number of connections between each pair of proteins is a strong predictor of how tightly the proteins connect to each other. According to [START_REF] Janin | Protein-protein interaction and quaternary structure[END_REF], de [START_REF] De Vries | How proteins get in touch: Interface prediction in the study of bio-molecular complexes[END_REF] and [START_REF] Dequeker | INTerface Builder: A fast protein-protein interface reconstruction tool[END_REF], there are three main methods to compute interfaces between protein chains:

1. The cutoff method (implemented in PPIC).

2. The loss of ASA (accessible surface area) upon binding.

The Voronoi tessellation method (implemented in PPIC).

The cutoff method assumes that two residues are in contact when they have a pair of heavy atoms separated by a distance smaller than the cutoff distance. This cutoff distance may be set to 4.5 Å between non H atoms [START_REF] Gao | iAlign: a method for the structural comparison of proteinprotein interfaces[END_REF][START_REF] Esque | Comparative analysis of threshold and tessellation methods for determining protein contacts[END_REF]Triki et al., 2018), to 5 Å from side-chain centers of mass [START_REF] Viloria | An optimal distance cutoff for contact-based protein structure networks using side-chain centers of mass[END_REF], or to 8 Å between C α atoms [START_REF] Esque | Comparative analysis of threshold and tessellation methods for determining protein contacts[END_REF]. The choice of the cutoff can significantly influence the result (de [START_REF] De Vries | How proteins get in touch: Interface prediction in the study of bio-molecular complexes[END_REF]. This method critically relies on the choice of atomic radii, which strongly depend on how they are defined [START_REF] Bondi | Van der Waals volumes and radii[END_REF][START_REF] Allinger | Molecular mechanics parameters[END_REF]. The values recommended in the literature [START_REF] Gavezzotti | The calculation of molecular volumes and the use of volume analysis in the investigation of structured media and of solid-state organic reactivity[END_REF] induce the existence of intersections of 6 spheres or more. These intersections above 3 or 4 spheres are ignored by a number of published methods, inducing in turn large errors in surface calculations [START_REF] Petitjean | On the Analytical Calculation of van der Waals Surfaces and Volumes: Some Numerical Aspects[END_REF][START_REF] Petitjean | Spheres unions and intersections and some of their applications in molecular modeling[END_REF].

In its original variant, the Voronoi tessellation method is parameter-free [START_REF] Cazals | Revisiting the Voronoi description of protein-protein interfaces[END_REF][START_REF] Bouvier | Shelling the Voronoi interface of protein-protein complexes reveals patterns of residue conservation, dynamics, and composition[END_REF]. It was implemented in PROVAT [START_REF] Gore | PROVAT: a tool for Voronoi tessellation analysis of protein structures and complexes[END_REF]. The full mathematical presentation of Voronoi diagrams and their calculation algorithms are out of the scope of this paper (see [START_REF] Edelsbrunner | Voronoi Diagrams[END_REF]. We may just say that each atom lies inside a convex polyhedral cell having its polygonal faces located at mid distance from its neighbouring atoms. Thus, two atoms are neighbours if their Voronoi cells share a common face. Extensions taking in account atomic spheres were proposed [START_REF] Esque | Comparative analysis of threshold and tessellation methods for determining protein contacts[END_REF][START_REF] Mahdavi | Computational analysis of RNA-protein interaction interfaces via the Voronoi diagram[END_REF], but these latter are no more parameter-free.

Methods

Our original method, which is implemented in PPIC, is a variant of the one of [START_REF] Cerisier | Cavity versus ligand shape descriptors: Application to urokinase binding pockets[END_REF]. The input is a complex with two partners (molecule or macromolecule), A and B. The algorithm has no parameter. It has two steps:

1. Generate the interface in A as the non-redundant set of all nearest neighbours in A of the atoms of B.

2. Generate the interface in B as the non-redundant set of all nearest neighbours in B of the atoms of A.

The interface has two parts, one in A and one in B. Each one is a subset of the interface that would be output by the Voronoi tessellation method (proof: see Eppstein et al., 1997). However our method is much simpler that the latter, and it does not generate neighbours at long distances in the interface, while large Voronoi cells can induce such long distances. Furthermore, looking at interacting atom pairs among the nearest neighbours makes more sense that looking at interacting atom pairs at farther distances that the nearest neighbours.

Results and discussion

We considered the dimers set of [START_REF] Martin | Taking advantage of local structure descriptors to analyze interresidue contacts in protein structures and protein complexes[END_REF], containing 1050 protein homoand heterodimers. We compared the 1050 couples of interfaces with the ones obtained with the cutoff distance method, for a cutoff ranging from 2 to 6 Å. For the full database, computing these interfaces took about 288 min on a workstation Ubuntu 18.04 (16 Intel R Xeon R CPUs, 3 GHz). This computing time was roughly the same for the three methods implemented in PPIC. The subsets of atoms defining the interfaces were compared with the symmetric difference metric [START_REF] Deza | Encyclopedia of Distances[END_REF]. Similarly, we compared the 36 couples of interfaces for the set of 18 PR2ligand interfaces from Triki et al. (2018). Figure 1 shows that the closest results for the two methods were observed at a cutoff of 3.7 Å for the dimers set, and at 3.6 Å for the PR2 complexes set. This is a remarkable agreement since these two data sets are of different nature. It suggests an optimal cutoff value of 3.6-3.7 Å between heavy atoms. This optimal value is in agreement with the statistical analysis of M c Donald and Thornton (1994): the distance donor-acceptor should be less than 3.9 Å and the distance hydrogen-acceptor should be less than 2.5 Å. So, assuming a covalent H bond length of 1.1 Å, the distance donor-acceptor should be in fact at most 2.5 + 1.1 = 3.6 Å, which is our suggested value. For the Voronoi tessellation method, the closest results were observed at the respective cutoffs of 5.1 Å and 4.6 Å. In the case of distances between heavy atoms, these cutoff values are too large, as predicted in section 2.

For the PR2 complexes, we found that at most 17 residues are in contact with the ligands: Arg

  8, Leu 23, Asp 25, Gly 27, Ala 28, Asp 29, Asp 30, Ile 32, Ile 46, Val 47, Gly 48, Gly 49, Ile 50, Phe 53, Pro 81, Ile 82 and Ile 84. All were found in the binding pocket computed by the consensus method of Triki et al. (2018) based on a 4.5 Å cutoff distance. This confirms the pertinence of our parameter-free method.

Figure 1 :

 1 Figure 1: Mean symmetric difference distances in function of the cutoff value, for the 1050 dimers data set (on the left) and for the 18 PR2 complexes (on the right).

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