David González-Santana
email: david.gonzalezsantana@univ-brest.fr

Melchor González-Dávila

Maeve C Lohan

Lise Artigue

Hélène Planquette

Géraldine Sarthou

Alessandro Tagliabue

J Magdalena Santana-Casiano

J Magdalena Santana- Casiano

Variability in iron (II) oxidation kinetics across diverse hydrothermal sites on the northern Mid Atlantic Ridge

Keywords: Fe(II) oxidation kinetics, Fe(II) half-life time, Kinetic equation, Hydrothermal, Mid Atlantic Ridge

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

Introduction

It is now well-established that phytoplankton growth is limited by the concentration of dissolved iron (Fe) in up to 30% of the world oceans [START_REF] Moore | Processes and patterns of oceanic nutrient limitation[END_REF]. Iron in the ocean, can be found as both ferric (Fe(III)) and ferrous (Fe(II)) iron, where 99% of the dissolved Fe(III) is complexed by organic ligands [START_REF] Rue | Complexation of iron(III) by natural organic ligands in the Central North Pacific as determined by a new competitive ligand equilibration/adsorptive cathodic stripping voltammetric method[END_REF]. In oxic waters, Fe(II) tends to oxidize to the most thermodynamically stable form, Fe(III), in a period of minutes to hours [START_REF] Santana-Casiano | Oxidation of nanomolar level of Fe(II) with oxygen in natural waters[END_REF]. Oxidation of Fe causes the solubility to decrease (Millero et al., 1995), therefore, reducing its bioavailability [START_REF] Shaked | A general kinetic model for iron acquisition by eukaryotic phytoplankton[END_REF][START_REF] Morel | The role of unchelated Fe in the iron nutrition of phytoplankton[END_REF].

Recently, in the context of the international GEOTRACES program (www.geotraces.org), several studies showed that Fe supplied by hydrothermal activity from mid-ocean ridges can have a substantial impact on Fe distributions at basin scales [START_REF] Tagliabue | Hydrothermal contribution to the oceanic dissolved iron inventory[END_REF][START_REF] Conway | Quantification of dissolved iron sources to the North Atlantic Ocean[END_REF][START_REF] Resing | Basin-scale transport of hydrothermal dissolved metals across the South Pacific Ocean[END_REF][START_REF] Fitzsimmons | Iron persistence in a distal hydrothermal plume supported by dissolved-particulate exchange[END_REF][START_REF] Tagliabue | The integral role of iron in ocean biogeochemistry[END_REF].

Hydrothermal vent supply of dFe is required to reproduce deep ocean observations [START_REF] Tagliabue | Hydrothermal contribution to the oceanic dissolved iron inventory[END_REF] could represent up to 11-22 % of the dissolved iron (dFe, filtered by 0.2 µm) present in the deep ocean globally [START_REF] Bennett | The distribution and stabilisation of dissolved Fe in deep-sea hydrothermal plumes[END_REF], accounting for a similar dFe flux as continental riverine runoff [START_REF] Elderfield | Mid-ocean ridge hydrothermal fluxes and the chemical composition of the ocean[END_REF]. Therefore, hydrothermalism acts as an important Fe source in the deep ocean which may affect the global biological carbon pump [START_REF] Tagliabue | Hydrothermal contribution to the oceanic dissolved iron inventory[END_REF][START_REF] Resing | Basin-scale transport of hydrothermal dissolved metals across the South Pacific Ocean[END_REF].

The concentration of dissolved Fe(II) (dFe(II)) in the open ocean is very low, between 0.02 and 2 nmol L -1 , due to its fast oxidation under oxic conditions following the Fenton reaction mechanism [START_REF] González-Davila | Oxidation of iron (II) nanomolar with H2O2 in seawater[END_REF][START_REF] Santana-Casiano | Oxidation of nanomolar level of Fe(II) with oxygen in natural waters[END_REF]. However, specific oceanic regions present dFe(II) concentrations which are orders of magnitude higher. In marine sediment interstitial waters, concentrations can reach around 300 μmol L -1 (de Baar and De Jong, 2001), upwelling systems can increase Fe(II) concentrations up to 50 nmol L -1 [START_REF] Hong | Redox state of iron in the offshore waters of Peru 1[END_REF], while hydrothermal fluids can contain as much as 25 mmol L -1 of dFe(II) [START_REF] German | Hydrothermal processes[END_REF]. Water emanating from hydrothermal systems contains high concentrations of Fe(II) amongst other elements [START_REF] Mottl | Chemical exchange during hydrothermal alteration of basalt by seawater-II. Experimental results for Fe, Mn, and sulfur species[END_REF][START_REF] Mandernack | Manganese scavenging and oxidation at hydrothermal vents and in vent plumes[END_REF]. Studies conducted at hydrothermal vent sites in different ocean basins have revealed different Fe(II) oxidation rate constants, with Fe(II) half-life times varying from 0.5 to 220 min, which has important implications for the dispersion of produced Fe-oxide phases [START_REF] Massoth | Manganese and iron in hydrothermal plumes resulting from the 1996 Gorda Ridge Event[END_REF][START_REF] Field | Dissolved and particulate Fe in a hydrothermal plume at 9°45'N, East Pacific Rise: Slow Fe (II) oxidation kinetics in Pacific plumes[END_REF][START_REF] Statham | Iron (II) distribution and oxidation kinetics in hydrothermal plumes at the Kairei and Edmond vent sites, Indian Ocean[END_REF][START_REF] Wang | The geochemical characteristics and Fe (II) oxidation kinetics of hydrothermal plumes at the Southwest Indian Ridge[END_REF][START_REF] Santana-González | Emissions of Fe(II) and its kinetic of oxidation at Tagoro submarine volcano, El Hierro[END_REF][START_REF] Rouxel | Geochemical and iron isotopic insights into hydrothermal iron oxyhydroxide deposit formation at Loihi Seamount[END_REF]. Recently, [START_REF] Gartman | Impacts of hydrothermal plume processes on oceanic metal cycles and transport[END_REF] compiled all the available data for Fe(II) half-life from four hydrothermal systems. One site was the TAG vent site in the Atlantic Ocean, while the others were located in the Indian and Pacific Oceans, with Fe(II) half-life estimated using large Fe(II) spikes (500 nmol L -1 ) that may affect the role played by different reactive oxygen species [START_REF] González-Dávila | Competition between O2 and H2O2 in the oxidation of Fe (II) in natural waters[END_REF]. Temperature (T), pH, and oxygen concentration (O2) are the primary variables known to directly affect the Fe(II) oxidation [START_REF] Stumm | Oxygenation of ferrous iron[END_REF][START_REF] Millero | The oxidation kinetics of Fe(II) in seawater[END_REF][START_REF] Millero | The oxidation of Fe (II) with H2O2 in seawater[END_REF][START_REF] Santana-Casiano | Oxidation of nanomolar level of Fe(II) with oxygen in natural waters[END_REF]. Salinity also affects the Fe(II) oxidation, as reported in previous laboratory experiments [START_REF] Millero | The oxidation kinetics of Fe(II) in seawater[END_REF][START_REF] Santana-Casiano | Oxidation of nanomolar level of Fe(II) with oxygen in natural waters[END_REF]. However, other factors such as changes in the inorganic complexation of Fe(II) due to the specific ionic composition of the vent fluid, or organic complexation can influence these oxidation rate constants [START_REF] Rose | Effect of dissolved natural organic matter on the kinetics of ferrous iron oxygenation in seawater[END_REF][START_REF] Statham | Iron (II) distribution and oxidation kinetics in hydrothermal plumes at the Kairei and Edmond vent sites, Indian Ocean[END_REF]. Therefore, the oxidation rate constants must be termed "apparent" due to the effect of organic complexation [START_REF] Voelker | Effects of fulvic acid on Fe (II) oxidation by hydrogen peroxide[END_REF], as the nature and concentrations of organic ligands vary between samples. Moreover, pyrite nanoparticles formed in hydrothermal vent sites, have been estimated to oxidize more slowly than dissolved Fe(II) [START_REF] Yücel | Hydrothermal vents as a kinetically stable source of iron-sulphide-bearing nanoparticles to the ocean[END_REF], showing that particle composition also influences the oxidation rate constants. The first empirical equation describing the Fe(II) oxidation rate constants in seawater was reported by [START_REF] Millero | The oxidation kinetics of Fe(II) in seawater[END_REF], and later updated by [START_REF] Santana-Casiano | Oxidation of nanomolar level of Fe(II) with oxygen in natural waters[END_REF] for nanomolar concentrations. This equation has been included in coupled physical-biogeochemical models in the ocean (OGCBMs) to explore the impact of future climate change on the oxidation of Fe(II) [START_REF] Tagliabue | Towards accounting for dissolved iron speciation in global ocean models[END_REF]. However, this equation was established for water temperatures ranging from 10 to 25 ºC, which leads to discrepancies for the Fe(II) oxidation rate constants for cold, deep ocean water masses.

The aims of this study were to measure the oxidation kinetic constants (k') of Fe(II) from different hydrothermal vents and to investigate whether the variations of pH, T and S can explain the observed variability, or if other factors such as the presence of particles, colloids or dissolved organic matter (DOM) are significant contributors. This updated version of the equation incorporates a wider range of temperatures, which lowers the error associated with the theoretical Fe(II) oxidation rate constants. Thus, it becomes applicable to the calculation of theoretical Fe(II) oxidation for the deep waters in which hydrothermal systems are typically found.

Methods

Sampling sites and characteristics

Seawater samples were collected during the GA13 section cruise (JC156) along the Mid Atlantic Ridge (MAR) onboard the RRS James Cook. This cruise departed Southampton, UK on December 20 th , 2017 and arrived into Guadeloupe, France on February 1 st , 2018.

Alongside the large scale ocean section survey, sampling focused on six hydrothermal vent sites along the MAR: Menez Gwen (37° 50'N 31° 31'W; [START_REF] Charlou | Compared geochemical signatures and the evolution of Menez Gwen (35°50N) and Lucky Strike (37°17N) hydrothermal fluids, south of the Azores Triple Junction on the Mid-Atlantic Ridge[END_REF], Lucky Strike (37° 17'N 32° 16'W; [START_REF] Charlou | Compared geochemical signatures and the evolution of Menez Gwen (35°50N) and Lucky Strike (37°17N) hydrothermal fluids, south of the Azores Triple Junction on the Mid-Atlantic Ridge[END_REF], Rainbow (36° 14'N 33° 54'W; [START_REF] Douville | The rainbow vent fluids (36°14′N, MAR): The influence of ultramafic rocks and phase separation on trace metal content in Mid-Atlantic Ridge hydrothermal fluids[END_REF] , Lost City (30° 7'N 42° 7'W; Kelley et al., 2001), Broken Spur (29 °N;James et al., 1995), and TAG (26°N;[START_REF] Gamo | Chemical characteristics of hydrothermal fluids from the TAG Mound of the Mid-Atlantic Ridge in August 1994: Implications for spatial and temporal variability of hydrothermal activity[END_REF] (Fig. 1). These six hydrothermal vent sites represent a wide range of possible hydrothermal conditions due to different underlying geological conditions. Lost City and Menez Gwen are the shallowest sites, with the vent site depths located at 700-720 m and 840-850 m, respectively. The Lucky Strike hydrothermal field is situated between 1560 and 1730 m depth. The Rainbow vent site is found at 2270-2280 m, within the average range (2000-3000 m) of oceanic ridge depth [START_REF] Searle | Mid-ocean ridges[END_REF], while Broken Spur and TAG are deeper hydrothermal systems located at 3100-3300 m and 3670-3700 m, respectively. Chemically, Lost City is an alkaline hydrothermal vent, with pH ranging from 9.0 to 9.8. The vent fluid is at a lower temperature of 40-75 °C, compared to 185-365 °C at the other vent sites and has extremely low concentrations of most trace elements (e.g. Fe below the detection limit compared to 2-24000 µmol L -1 at the other vent sites) [START_REF] Ludwig | Formation and evolution of carbonate chimneys at the Lost City Hydrothermal Field[END_REF][START_REF] Fouquet | Geodiversity of hydrothermal processes along the mid-atlantic ridge and ultramafic-hosted mineralization: A new type of oceanic Cu-Zn-Co-Au volcanogenic massive sulfide deposit[END_REF]. All other hydrothermal vent sites are acidic with pH lower than 4, and act as important sources of trace metals [START_REF] Charlou | Compared geochemical signatures and the evolution of Menez Gwen (35°50N) and Lucky Strike (37°17N) hydrothermal fluids, south of the Azores Triple Junction on the Mid-Atlantic Ridge[END_REF][START_REF] Douville | The rainbow vent fluids (36°14′N, MAR): The influence of ultramafic rocks and phase separation on trace metal content in Mid-Atlantic Ridge hydrothermal fluids[END_REF][START_REF] Andreani | Tectonic structure, lithology, and hydrothermal signature of the Rainbow massif (Mid-Atlantic Ridge 36°14′N)[END_REF]. Geologically, Menez Gwen and Lucky Strike are similar, their basement rocks are mafic, enriched-Mid-Ocean Ridge Basalt (E-MORB, enriched with light rare earth elements, LREE), and present sulfide mounds. Rainbow also presents sulfide mounds, but its basement rock is ultramafic. Further south, the alkaline Lost City is also situated above an ultramafic base with carbonate chimneys. Finally, Broken Spur and TAG have sulfide mounds and basement rocks formed by normal-MORB (N-MORB, LREE depletion) (references within Fouquet et al., 2010).

Seawater samples were collected according to the GEOTRACES guidelines (http://www.geotraces.org/images/Cookbook.pdf). Briefly, a titanium rosette fitted with 24 x 10 L trace metal-clean Teflon-coated OTE (Ocean Test Equipment) bottles, a CTD profiler (Sea-bird Scientific), light scattering sensor (PMEL MAPR), and a redox potential sensor (PMEL MAPR), were deployed on a conducting Kevlar wire to collect samples from the water column. Sampling depths were actively chosen from the continuous T, salinity (S), light scattering sensor (https://datasearch.nerc.ac.uk:443/geonetwork/srv/api/records/8ba648f2759d57fbb2246671f8065939) and redox potential readings.

Upon recovery, the OTE bottles were transported into an ISO class 6 clean air van. Unfiltered samples (UF) for Fe(II) oxidation kinetics were immediately transferred into thoroughly rinsed acid-cleaned 250 mL or 1 L low-density polyethylene bottles (LDPE; Nalgene) following the GEOTRACES Cookbook (http://www.geotraces.org/images/Cookbook.pdf) and frozen at -20 °C. Samples remained frozen in a -20 °C freezer for one year before their analysis. pH samples were collected in 125 mL borosilicate bottles and kept in the dark until the time of analysis.

pH determination

pH was measured onboard and during laboratory-based kinetic experiments in the free scale using a Tris buffer solution [START_REF] Millero | The pH of estuarine waters[END_REF]. Onboard pH samples were kept in the dark, inserted into a 25 °C water bath, and measured at 25 °C, within less than 1 hour after collection. Laboratory-based kinetic experiments used a Titrino 719 (Metrohm TM ) which automatically added 0.01M hydrochloric acid (HCl, PANREAC Hiperpur-plus) in order to keep the pH constant. The pH at in situ conditions were computed considering the total alkalinity for an average profile of the area [START_REF] Key | Global ocean data analysis project[END_REF][START_REF] Olsen | The Global Ocean Data Analysis Project version 2 (GLODAPv2)-an internally consistent data product for the world ocean[END_REF]. The average profile was obtained from plotting all the available alkalinity data from the studied region (20-30 °N and 40-50 °W). The associated error of the estimate was ±6 µmol kg -1 . [START_REF] Gray | Applications of in situ pH measurements for inorganic carbon calculations[END_REF] showed that computed pH values are relatively insensitive to errors in alkalinity, and that pH measurements can be used to compute the magnitude and variability of inorganic carbon variables. A fluctuation of 400 µmol kg -1 in total alkalinity values (e.g. from 2325 to 2725 µmol kg -1 ) will change the pH in +0.005, which lies within the error of determination for potentiometric pH. The set of constants from [START_REF] Lueker | Ocean pCO2 calculated from dissolved inorganic carbon, alkalinity, and equations for K1 and K2: validation based on laboratory measurements of CO2 in gas and seawater at equilibrium[END_REF] were used.

All the pH data in the text and in the figures, including kinetics and profile data are expressed in the free scale.

Fe(II) measurements

In order to measure the Fe(II) oxidation rate constants, continuous Fe(II) concentrations were determined using the FeLume System (Waterville Analytical), with a data point acquisition every 1 s. This direct Flow Injection Analysis system uses luminol (5-amino-2,3-dihydro-1,4phthalazinedione, Sigma-Aldrich) as the reagent [START_REF] King | Rates and Mechanism of Fe(II) Oxidation at Nanomolar Total Iron Concentrations[END_REF] which reacts with Fe(II).

The sample was continuously aerated with pure air (Carburos Metalicos S.A.). A 0.8 nmol L -1 addition of Fe(II) (ammonium iron(II) sulfate hexahydrate, Sigma-Aldrich) was introduced into each sample and the Fe(II) concentration was continuously monitored until the signal had reduced by 70 %. This method produces apparent rate constants (kapp) because the oxidation rate constant is measured on a Fe(II) spike rather than on the ambient Fe(II).

Although, the oxidation rate constant is not affected by the initial Fe(II) in solution [START_REF] Millero | The oxidation kinetics of Fe(II) in seawater[END_REF][START_REF] Roy | Persistence of iron (II) in surface waters of the western subarctic Pacific[END_REF][START_REF] Roy | Evidence for regulation of Fe (II) oxidation by organic complexing ligands in the Eastern Subarctic Pacific[END_REF][START_REF] Santana-González | Fe (II) oxidation kinetics in the North Atlantic along the 59.5° N during[END_REF], the equilibrium with the organic ligands and particle surfaces could be affected. Moreover, due to the effects of organic complexation and that the concentrations of the organic ligands in each sample are not constant, the apparent oxidation rate constants are consequently not true constants. Some previous oxidation kinetic studies have found a second-order dependency of the Fe(II) concentration against time (e.g. [START_REF] Statham | Iron (II) distribution and oxidation kinetics in hydrothermal plumes at the Kairei and Edmond vent sites, Indian Ocean[END_REF]. However, in oxygen saturated samples a pseudo-first order rate dependency was obtained, where the slope (ln([Fe(II)] against time) represents the pseudo-first order rate constant k' (Eq. 1). The linearity remained longer than the half-life time and was thus considered acceptable in all the analyses (R 2 = 0.983 ± 0.017, n samples = 298). The observed linearity confirms that the equilibrium between the added Fe(II) with organic ligands and particles is achieved before 30 s (our first Fe(II) determination time limit). The k' error associated with these high R 2 values was 2% for in situ condition experiments, and 1% for experiments carried out at 25 °C. The half-life (t1/2) of Fe(II) in seawater can be calculated from k' (Eq. 1 and 2).

𝑑[𝐹𝑒(𝐼𝐼)] 𝑑𝑡 ⁄ = -𝑘 [O2][𝐹𝑒(𝐼𝐼)] (1)
In oxygen saturated concentrations, the corresponding pseudo-first order rate constant k′ = kapp[O2].

𝑡 ⁄ = ln(2) 𝑘′ ⁄ (2)
The minimum energy required to start the oxidation reaction (activation energy, Ea, J mol -1 ) and the corresponding preexponential or frequency factor (A) were computed from the calculated k' using the empirical Arrhenius equation, where R is the universal gas constant (8.314 J mol -1 K -1 ):

log(𝑘′) = log(𝐴) - • ( )• (3)
Iron (II) blanks were obtained from a 2 h aerated, magnetically stirred sample which was kept in the dark to achieve the oxidation of Fe(II) [START_REF] Santana-Casiano | Oxidation of nanomolar level of Fe(II) with oxygen in natural waters[END_REF]. Iron (II) in theses blanks always below the detection limit. Calibration curves (0 to 1 nmol L -1 ) were produced daily and confirmed linearity in the Fe(II) signal. The detection limit, defined as three times the standard deviation of the blank after being aerated for 10 minutes, was lower than 50 pmol L -1 . Reproducibility was checked by running the same sample three times throughout the day after an addition of 1nmol L -1 of Fe(II) with an agreement in concentrations that was better than ± 0.1 nmol L -1 . Accuracy could not be determined since reference materials currently do not exist. Results are systematically given as t1/2 (in min), followed by the measured k' (in min -1 ).

Experimental setup

Using natural seawater samples, kinetic experiments were carried out under different conditions, with pH and T set to in situ conditions (data shown in the supplementary Table S1), and with pH and T normalized to constant values, in unfiltered, filtered and filtered and UV-irradiated samples. These later experiments required a high sample volume, limiting the number of experiments.

The steps required for the Fe(II) oxidation kinetics determination are as follows. The day before the experiments, three to four frozen samples were taken out of the freezer and placed in a fridge set to 4 ˚C. The next morning, a temperature-controlled water bath was set to the coldest in situ potential temperature (supplementary Table S1). While the water bath was cooling down, each sample was subsampled into three 60 mL acid cleaned LDPE bottles and placed back into the fridge. One of the subsamples was inserted into the temperaturecontrolled water bath, which was set to the original in situ potential temperature of the sample. The sample was left in the water bath for acclimatization during 15 min and then transferred into the reaction vessel. In the reaction vessel, the sample was aerated prior to and during the study. After 10 minutes of aeration, the Fe(II) addition was made and the Fe(II) concentration and time were continuously monitored. After finishing with the coldest subsample, the temperature of the water bath was increased to the following coldest temperature, and the next sample was left to acclimate. The samples remained frozen at -20 °C during one year until analysis. Two days prior to the analysis, samples were thawed in a 4 °C fridge. This allowed a slow melting of the samples in the dark, thus limiting any photoproduction of Fe(II) and also removal of any superoxide and hydroxyl radicals in the sample [START_REF] Voelker | Iron reduction by photoproduced superoxide in seawater[END_REF].

The samples were then transfered into 60 mL LDPE bottles (one for each condition).

Temperature effect experiments were performed at constant pH, and those for pH effect at constant temperature. The temperature effect experiments were carried out at in situ temperature, 10, 20 and 25 °C at a fixed pH of 8. The pH effect experiments were carried out at in situ pH, and pH 7, 7.5 and 8 at a fixed temperature of 25 °C.

Oxidation rate constants through the water column at the six hydrothermal vent sites

To assess the expected Fe(II) oxidation rate constants at in situ conditions, the experiments were carried out at in situ potential temperature and pH (TispHis). The temperature was then increased to 25 °C (T25pHis) to obtain the temperature effect on the oxidation rate constants.

A third set of experiments were performed at 25 °C and pH 8 (T25pH8). The T and pH normalization of all the samples allowed for the interpretation of the effect of other variables, such as organic matter and particles, in the oxidation rate constants. This allows to investigate where seawater composition is influencing the oxidation rate, a process that cannot be isolated when comparing two samples with different temperatures and/or pH.

Experimental setup to assess the effect of colloidal and organic matter

The unused unfiltered (UF) sample volumes remaining from the quantification of the temperature and pH effect experiments were used to assess the impact of particles, colloids and organic matter. Unfiltered samples underwent sequential filtration. Three aliquots were filtered through 0.2 µm (F0.2; Whatman® Anodisc), and one of them was then filtered through 0.02 µm (F0.02; Whatman® Anotop®), while the last aliquot was filtered through 0.02 µm followed by UV-irradiation (F0.02+UV). All samples were left in the dark for 6 days to limit the effect of any photochemically generated reactive oxygen species (ROS) produced during the UV-irradiation [START_REF] Yuan | The distribution of hydrogen peroxide in the southern and central Atlantic ocean[END_REF][START_REF] Roy | Persistence of iron (II) in surface waters of the western subarctic Pacific[END_REF]. All samples were analyzed following the same procedure as for the assessment of the pH effect (see section 2.4.2 above). In order to assess whether the generated ROS species could affect the Fe(II) oxidation rate constants determined after 0.02 µm filtration and UV-irradiation, the effect of the amount of hydrogen peroxide (H2O2) generated during this process was considered [START_REF] Yuan | The distribution of hydrogen peroxide in the southern and central Atlantic ocean[END_REF][START_REF] O'sullivan | Photochemical production of hydrogen peroxide and methylhydroperoxide in coastal waters[END_REF]. Other short-lived ROS species such as hydroxyl radicals were not accounted for, since their nanosecond half-life times do not allow for their determination using our analytical method.

Results

Temperature and pH effects on the oxidation rate constants

Experiments for the temperature effect study were carried out at a pH of 8. When plotting log k' vs. 1/T (K -1 ) (Fig. 2, Eq. 3), results showed an average slope (-Ea/R/ln(10)) of -4992 ± 232. Notably, the data obtained from samples collected west of TAG at 2700 m depth (Station 30) showed a slope of -3732 ± 216, which is more than three standard deviations away from the average value. This lower slope corresponds to a much lower activation energy for this sample, with a value of 71 ± 4 KJ mol -1 . This effect was probably caused by the interaction of organic compounds or particles with the Fe(II) species which affected the When experiments were carried out at a constant T of 25 ºC and at 5 different pH values in the range from 7 to 8, log k' and pH were linearly related, with slopes of 1.00 ± 0.06 (Fig. 3) and with no data points outside of 3standard deviations. As with the temperature relationship, the sample from the station West of TAG at 2700 m presented a slope (1.19 ± 0.08) out of the 1:1 dependence. A second sample, (TAG at 1999 m depth, over 1600 m above the vent site)

showed a lower slope (0.81 ± 0.12).

The unique use of lower temperature samples in this study, allowed a better estimation of data, was used to compare the equation performance (Armstrong et al., 2001 and references therein). The log(L) was calculated as in [START_REF] Moriceau | Si-C interactions during degradation of the diatom Skeletonema marinoi[END_REF], where a difference in log(L) of at least two points is considered as a criterion of a better fit to the observations. The three most recent equations present better RSS, RMSE and log(L), with the new equation presented here providing consistently better statistical results (Table 1). values presented a wider range than those determined using the physico-chemical parameters in the improved theoretical equation. The Lost City vent site, was the only station where all the measured t1/2 at TispHis conditions presented measured oxidation rate constants higher (shorter t1/2) than the theoretically calculated rate constants. At T25pH8 conditions, all the measured oxidation rate constants were higher than the theoretical ones for all stations except at TAG.

The theoretical t1/2 values presented in Figure 5a, show the expected high variability in the Fe(II) half-life times associated with T, pH and S. These discrepancies were further highlighted in the measured samples, where only Menez Gwen and Lucky Strike theoretical values are within the measured results (a paired t-test did not show a statistical difference between the theoretical and the measured t1/2, with P > 0.35 for both).

At Menez Gwen (Fig. 4a), measured in situ t1/2 varied between 8.3 and 32.0 min (k' between 0.084 and 0.022 min -1 ), with short measured t1/2 observed in the samples collected at 743, 821, and 827 m. When the temperature was increased and fixed to 25 ºC, while the pH was kept at in situ conditions (Supplementary Table S1), a significant T effect was observed in k', with the measured t1/2 decreasing to less than 4 min. When the pH was fixed to a constant value of 8 along the water column, the measured t1/2 was slightly affected indicating a small effect, as the change in pH was always lower than 0.22. Overall, at T25, samples presented measured t1/2 in the same order of magnitude as the theoretical T25 pH8. Samples collected within the lower part of the plume, at less than 30 m above the seafloor (hereafter asf) presented higher oxidation rate constants than theoretical ones (t1/2 decreased).

Lucky Strike (Fig. 5a) presented lower oxidation rate constants than Menez Gwen related to lower temperatures in deeper waters (from about 8.5 ºC to 4.5 ºC). From 1600 m to 1680 m, measured t1/2 averaged 46.5 ± 2.5 min (k' of 0.015 ± 0.001 min -1 , n = 4) (Fig. 4b). This t1/2 average is higher than the theoretical value of 39.7 min, while at 1703 m, the Fe(II) half-life decreased to 26.3 min (k' to 0.026 min -1 ). Overall, at T25, samples presented measured t1/2 in the same order of magnitude as the theoretical T25 pH8. In situ pH averaged 7.89, where the increase in acidity produced a lower oxidation rate constant than the measured t1/2 at T25 pH8.

At Rainbow, station 16, the t1/2 measured at in situ conditions presented a wide range of variation, from 17.3 to 65.3 min (k' varied from 0.040 min -1 to 0.011 min -1 ). The theoretically expected values were within that range, with an average value of 39 ± 3 min (n=8, Fig. 4c).

The shortest t1/2 were observed between 1986 m and 2108 m (175 to 295 m asf) averaging 22.2 ± 3.6 min (k' = 0.032 ± 0.006 min -1 ) while the shorter t1/2 were found below the plume and above 300 m asf (Fig. 4c). The light scattering data shows that the Rainbow plume reached heights over 400 m asf (although samples were only collected within the first 330 m).

Temperature was an important factor controlling the oxidation rate constant. At T25 conditions t1/2 were similar to the theoretical value. When the pH was fixed to 8, small changes were observed, and most of the values were close to the theoretical value except for those around 1986 m and 2108 m which had shorter t1/2.

Lost City (Fig. 4d), the only alkaline hydrothermal vent, was drastically different from the other hydrothermal sites (Fig. 4d), with temperatures around 10 ºC and pHis of 8.07 (Supplementary Table S1). The theoretical t1/2 associated with these temperatures and pH ranged between 16 and 20 min. However, most of the measured t1/2 were shorter than 3 min, reaching 0.5 min (k' of 1.299 min -1 ) at 725 m with the longest t1/2 of 7.8 min (k' of 0.088 min - 1 ) at 750 m. At 750 m depth with T25pHis conditions, the t1/2 decreased to 1.9 min (k' of 0.357 min -1 ) and further decreased to 1.5 min (k' of 0.468 min -1 ) at T25pH8 conditions. All the measured t1/2 were significantly shorter than the theoretical t1/2 of 3.2 min (k' of 0.218 min -1 ) at normalized conditions.

Broken Spur presented a wide range in measured t1/2, with values under in situ conditions ranging from 1.0 to 65.1 min (k' ranging from 0.714 min -1 at 2929 m to 0.011 min -1 at 2858 m; Fig. 4e). Two different behaviors can be observed. The two shallowest samples (2820 and 2830 m) were collected in local light scattering minima, with t1/2 averaging 63.2 ± 2.7 min (k' of 0.011 ± 0.001 min -1 ) and values slightly higher than the theoretical ones. Deeper than 2830 m, the samples were collected in local light scattering maxima, where half-life times were shorter with an average t1/2 of 1.9 ± 1.2 min (averaged k' of 0.464 ± 0.220 min -1 ).

Experiments at T25pH8 also showed that samples below 2830 m presented shorter t1/2 (high k'

values) than what was theoretically expected.

Half-life times measured at in situ conditions from the TAG vent site samples presented the widest range in t1/2 (Figs. 4 and 5a), varying from 35.1 to 131.2 min (k' between 0.019 min -1 and 0.005 min -1 ). These samples were characterized by little variability of Tis (2.67 ± 0.01 ºC)

and pHis (8.17 ± 0.01), producing a stable theoretical t1/2 of 43 ± 2 min. Furthermore, the measured t1/2 were the longest obtained in these experiments. When the experiments were repeated at both fixed T25 and pH8 the measured values encompassed the theoretical value of 3.3 min, with values slightly higher at around 3325 m (4.3-4.4 min). Therefore, even when temperature and pH affected the observed oxidation rate constants, the high range of values at in situ conditions could not be explained by only these two physico-chemical variables.

Investigating the spatial variability of Fe(II) oxidation rate constants around Rainbow and TAG sites

To investigate the spatial variability in t1/2 for Fe(II), samples were collected from four stations around the Rainbow site at 0.3º (30 km) S (St 15), E (St 12) and W (St 13) and 1º

(120 km) E (St 10) (Fig. 1) and from five stations around TAG at 0.3º N (St 26), S (St 27), W (St 30), and E (St 31) and 1º W (St 29) (Fig. 1). At both vent sites, turbidity and light scattering anomalies matched and described the shape of the plume (gray shading in Fig. 4).

The Rainbow plume anomaly was observed between 1930-1995 m, 2060-2090 m, and most strongly between 2100 and 2210 m. At the TAG site, the signal was three times lower than that observed at Rainbow, indicating the presence of a lower amount of particles, which could also be due to a displacement of the sampling with respect to the vent site. The largest anomalies were measured between 3160-3390 m, with several minor anomalies above (e.g.

2980-3030 m) and below (e.g. 3430-3520 m and 3600-3625 m; Fig. 4).

Turbidity and light scattering were useful for tracking the plume displacement even at 30 km from the vent site. The Rainbow plume was observed to the south and west (Stn. 13 and 15) at depths between 2000 and 2040 m, and 2270 and 2300 m. For TAG, only stations 27 (south of TAG, but inside the MAR valley) and 31 (east) showed deeper and thinner turbidity anomalies between 3400 and 3690 m and a smaller signal between 2920 and 3060 m.

For the Rainbow field, samples collected at the vent site in the 1980-2150 m range had shorter t1/2 at in situ conditions (high k' values) than the theoretical t1/2 (Fig. 6a). All the other samples (except for Stn 10 at 2430 m) had higher t1/2 values than those calculated theoretically, and greater t1/2 than observed at Rainbow at depths shallower than 1980 m, indicating very low oxidation rate constants. This allowed Fe(II) to stay in solution three times longer than under inorganic seawater conditions. However, when T and pH were fixed (Fig. 6b), the oxidation rate constants between stations were much closer to the theoretical value, indicating the T and pH control over the Fe(II) oxidation rate constant. Nevertheless, plume samples at the 2100-2210 m range and around 2400 m indicated t1/2 values that were still at least double the theoretical value.

At the TAG hydrothermal field, stations situated towards the N and W of TAG presented shorter t1/2 (high k' values) than those at the vent site and towards the S and E (Fig. 7a).

Station 30, situated 30 km W of TAG, exhibited both patterns, with long t1/2 (low k' values) at depths shallower than 2600 m and short t1/2 (high k' values) at depths below 2700 m. When all the TAG hydrothermal field station samples were normalized (i.e. T25pH8; Fig. 7b), most of the variability was removed, and t1/2 averaged 3 ± 1.5 min. The same pattern as for in situ conditions was maintained, with stations situated towards the N and W having shorter t1/2 than the theoretical values. These three stations were characterized by their lower turbidity in the deep waters. and F0.02 treatments (Fig. 8). For the other three samples (Figs. 8b-d), oxidation rate constants for UF and F0.2 did not present significant differences, with values that were reproducible within ±0.02 for the studied pH range. However, F0.02 samples had higher oxidation rate constants, while also maintaining the pH dependence (0.95 ± 0.07). Therefore, the presence of colloidal size particles delayed the oxidation process while not affecting the pH dependence, as shown in Fig. 8, where the intercept changes but the slope is unchanged.

All of the UV irradiated samples in Figs. 8a-d indicate that the absence of dissolved organic matter increased the oxidation rate constants. For TAG (3350 m) and Rainbow (2051 m), the k' values were so high that it was impossible to determine them at pH = 8 under our experimental conditions.

Discussion

Derived oxidation rate constants as a function of pH and temperature

In the 1990s, Fe(II) oxidation kinetics variability was reported at the TAG hydrothermal field

(2-3 min) [START_REF] Rudnicki | A chemical model of the buoyant and neutrally buoyant plume above the TAG vent field, 26 degrees N, Mid-Atlantic Ridge[END_REF] and near the Juan de Fuca Ridge hydrothermal systems (32 h) [START_REF] Chin | In situ observations of dissolved iron and manganese in hydrothermal vent plumes, Juan de Fuca Ridge[END_REF][START_REF] Massoth | Temporal and spatial variability of hydrothermal manganese and iron at Cleft segment, Juan de Fuca Ridge[END_REF] using the [START_REF] Millero | The oxidation kinetics of Fe(II) in seawater[END_REF] equation. Nevertheless, the variability between those two sites was difficult to explain and reflected fluctuations caused by differences in O2, T, and pH among the different sites.

When combining the six hydrothermal vent sites on the MAR (Fig. 9), the relationship between the measured oxidation rate constants under in situ conditions against the theoretically derived oxidation rate constants as a function of pH and temperature (in aerated water) can be obtained. Overall, equation 4 can explain 76 out of 104 data points. When color-coding the data points by stations, we observed that all the outliers corresponded to samples that were collected inside hydrothermal plumes (defined by turbidity, light scatter, and redox potential). Consequently, the results obtained from the theoretical equation (Eq. 4)

and figure 9, agree well with previous results that O2, S, T, and pH can be used to characterize the Fe(II) oxidation rate constant in open ocean waters but not from within hydrothermal plumes.

Our study clearly indicates (Figs. 8 and9) that the presence of both colloidal particles and dissolved organic matter increases the half-life of Fe(II) (decreased k'). This agrees with previous work showing a decrease in the Fe(II) oxidation rate constants in seawater in the presence of some natural organic compounds [START_REF] Santana-González | Organic matter effect on Fe (II) oxidation kinetics in the Labrador Sea[END_REF]. However, organic matter can have a positive or negative effect on the oxidation rate constants of Fe(II) depending on the type of organic matter and its degree of remineralization [START_REF] Rose | Effect of dissolved natural organic matter on the kinetics of ferrous iron oxygenation in seawater[END_REF]. The variability in the effect of total organic carbon on Fe(II) oxidation proves that total organic carbon cannot be used as a variable in an equation describing k´ [START_REF] Santana-Casiano | The effect of organic compounds in the oxidation kinetics of Fe(II)[END_REF][START_REF] Santana-González | Fe (II) oxidation kinetics in the North Atlantic along the 59.5° N during[END_REF][START_REF] Santana-González | Organic matter effect on Fe (II) oxidation kinetics in the Labrador Sea[END_REF]. In this sense, a more detailed characterization of organic matter would be necessary, especially in a hydrothermal environment.

Influence of organic species on Fe(II) oxidation rate constants

The Fe(II) oxidation rate constant (Eq. 5) can be expressed as a function of each Fe(II) species (Fe 2+ , FeOH + , Fe(OH)2, FeHCO3 + , Fe(CO3), Fe(CO3)2 2-, Fe(CO3)OH -, FeCl + , FeSO4, FeH3SiO4 and any organically complexed Fe species). Species such as Fe(CO3)2 2-and Fe(OH)2 could become important at pH higher than 8 [START_REF] Ussher | Marine biogeochemistry of iron[END_REF][START_REF] González-Davila | Oxidation of iron (II) nanomolar with H2O2 in seawater[END_REF][START_REF] Santana-Casiano | Oxidation of nanomolar level of Fe(II) with oxygen in natural waters[END_REF] in solution. Considering the side reaction coefficient for each inorganic (𝛼 ) and organic (𝛼 ) Fe(II) species in seawater and the associated second-order oxidation rate constant for the kinetically reactive Fe(II) species (ki and kj) (Eq. 6) [START_REF] Millero | The oxidation of Fe (II) with H2O2 in seawater[END_REF][START_REF] King | Role of carbonate speciation on the oxidation rate of Fe (II) in aquatic systems[END_REF][START_REF] Santana-Casiano | Oxidation of nanomolar level of Fe(II) with oxygen in natural waters[END_REF]

𝑘 = ∑ 𝛼 𝑘 + ∑ 𝛼 𝑘 (6) α = 1 1 + ∑ 𝐾 [𝐿 ] + ∑ 𝐾 𝐿 (7)
Where α is the fraction of free Fe(II) including inorganic and organic speciation, [Li] is the concentration of each inorganic ligand with a conditional stability constant 𝐾 and [𝐿 ] is the concentration of each organic ligand with a conditional stability constant 𝐾 . The inorganic site reaction coefficient at pH 8 and 25 ºC was previously determined as 0.38 [START_REF] Santana-Casiano | The role of Fe(II) species on the oxidation of Fe(II) in natural waters in the presence of O2 and H2O2[END_REF]. For any inorganic or organic FeL complexes:

α = 𝐾 [𝐿]α (8)
According to our results, the presence of DOM in solution generated Fe(II)-organic complexes that were overall less reactive to oxidation and therefore, when removed by UV irradiation the resulting oxidation rate constants were higher (Fig. 8).

The amount of dissolved organic carbon (DOC) in the samples ranged between 50 and 79 µmol kg -1 (data not shown) and according to O' Sullivan et al. (2005) the maximum amount of H2O2 produced during irradiation could be 125 to 147 nmol kg -1 , respectively. Following [START_REF] González-Davila | Oxidation of iron (II) nanomolar with H2O2 in seawater[END_REF] and assuming the extreme case of no H2O2 decay after 6 days, the UV generated H2O2 could theoretically increase the Fe(II) oxidation rate constants in oxygen saturated conditions. The theoretical t1/2 associated with the H2O2 oxidation was between 48 % and 53 % of the t1/2 measured for 0.02 µm filtered samples. Nevertheless, the measured t1/2 for UV-irradiated samples (Supplementary Table S1 and Fig. 8) were shorter (higher k'), indicating that any H2O2 remaining in solution after 6 days was not the main factor that increased the oxidation rate constants and that the presence of dissolved organic matter was stabilizing Fe(II) in solution. Furthermore, laboratory experiments have shown that the t1/2 of H2O2 in oceanic waters is shorter than 5.5 days [START_REF] Yuan | The distribution of hydrogen peroxide in the southern and central Atlantic ocean[END_REF], therefore the impact of H2O2 in the experiments would be further reduced.

The role of organically complexed Fe(II) could be calculated from the following assumptions. Firstly, the Fe(II)-L complex was assumed to not oxidize in the pH range of 7.5 to 8. Secondly, the observed reduction in Fe(II) oxidation rate constants (Fig. 8 and

The UV-irradiation treatment (Fig. 8) removes the organic matter effect on the Fecomplexation, which for the studied samples resulted in an increase in the oxidation rate constants. Consequently, in these analyzed natural samples, organic matter ultimately lowered the oxidation rate constants (black data points below the straight line in Fig. 9).

The DOM is prone to natural and thermal degradation in hydrothermal systems [START_REF] Hawkes | Molecular alteration of marine dissolved organic matter under experimental hydrothermal conditions[END_REF]. Accordingly, the variety of organic-complexing ligands and their effect on oxidation could change with plume transport and distance to the vent site as observed in figures 6 and 7. In the proximities to the vent sites, samples presented greater than theoretical oxidation rate constants (above the straight line in Fig. 9). This could be due to the presence of organic matter with ligands complexing Fe that oxidizes faster than the inorganic Fe(II) species. At these locations, the organic ligand effect would dominate over processes that lower oxidation rate constants such as nanoparticle concentrations. Similar experiments considering organic matter degradation just above the vent site should be carried out to confirm this hypothesis. Nevertheless, the complexity of the organic matter pool and the extent and nature of Fe-DOM interactions make the resulting effect on the oxidation rate constants difficult to predict.

Effects of physical speciation

Lough et al. ( 2019) have shown that there is an Fe exchange between the different particle size fractions within the hydrothermal plume. This exchange could affect Fe(II) oxidation as found in this study for particles smaller than 0.2 µm and colloidal sized particles (0.2-0.02 µm) at different locations in TAG and in Rainbow (Fig. 8). The results shown in Figure 8 seem to indicate that the size-fractionation can significantly affect Fe(II) oxidation and thus, is a factor that should be considered in future studies. In this sense, previous work has shown that particulate Fe(II), such as pyrite nanoparticles are more resistant to oxidation, with Fe(II) half-life between 4 and 48 months at 2 °C [START_REF] Yücel | Hydrothermal vents as a kinetically stable source of iron-sulphide-bearing nanoparticles to the ocean[END_REF]. The presence of colloidal particles also enhances the decay of ROS allowing for longer t1/2 [START_REF] Yuan | The distribution of hydrogen peroxide in the southern and central Atlantic ocean[END_REF].

Therefore, nanoparticles could account for a substantial fraction of the decrease in the oxidation rate constants (Fig. 8). Another consequence of filtration is the reduction in larger size organic matter, which could also affect the stabilization of Fe(II) [START_REF] Buck | The organic complexation of dissolved iron along the U.S. GEOTRACES (GA03) North Atlantic Section[END_REF].

The variability observed in the oxidation rate constants inside the plume for the six studied hydrothermal vents indicates that changes in the composition of both the DOM and colloidal particles, both between sites and at different distances from the vent, can strongly affect the oxidation rate constants, thus, their role requires further study.

Conclusions

This study highlights the complexity of Fe(II) chemistry in the ocean, with a focus on hydrothermal vent settings. Fe(II) oxidation rate constants, and therefore persistence of Fe(II) in the environment, is shown to not only depend on the physico-chemical conditions (T, S, pH, O2 content) but also the physical state (soluble, colloidal and particulate) of the inorganic and organic species that are present. Our results indicate that organic ligands can stabilize Fe(II) and that nanoparticles present in hydrothermal plumes could increase the resistance to oxidation. Both processes contribute to the observed variability in the oxidation rate constants in the proximities of vents. We were able to revise the theoretical equation for the estimation of k´, and to further increase the existing temperature range to include seawater temperatures as low as 2 ºC. Future studies on iron oxidation kinetics in the marine environment should be accompanied by a characterization of the organic matter present in the medium, a sizefractionation of the samples, and a detailed description of the conventional physico-chemical factors (pH, T, and S). S1) and b) normalized to constant T of 25 ºC and a pH of 8.

Figure 7. The Fe(II) half-life (t1/2, min) at the TAG field a) under in situ conditions (see also Supplementary Table S1) and b) normalized to constant T of 25 ºC and a pH of 8.

2

  .4.1 Quantification of the temperature and pH effect on the iron (II) oxidation rate constant In order to improve the temperature range of the existing Fe(II) oxidation kinetic equation, 1 L samples of deep ocean water were collected during the JC156 cruise, at stations 13 (2339 m), 16 (2051 m), 24 (2829 m), 30 (2700 m), 31 (2796 m), and 35 (1999, 3350 and 3601 m).

limiting

  Fe(II) oxidation step, and therefore a result of a different oxidation reaction mechanism. If this sample is removed, the average slope increases to -5434 ± 183, and the activation energy of all the samples considered was 104 ± 3 KJ mol -1 . These values are within the experimental error of previous determinations from Gulf Stream water(-5362 ± 162, and an activation energy of 103 ± 3 KJ mol -1 ;[START_REF] Santana-Casiano | Oxidation of nanomolar level of Fe(II) with oxygen in natural waters[END_REF].

  Fe(II) oxidation kinetic rate constants at temperatures lower than 10 ºC, increasing the range of applicability of the Fe(II) oxidation kinetic equation of[START_REF] Santana-Casiano | Oxidation of nanomolar level of Fe(II) with oxygen in natural waters[END_REF].Using the equation and dataset from[START_REF] Santana-Casiano | Oxidation of nanomolar level of Fe(II) with oxygen in natural waters[END_REF], which had a wider range in pH and salinity, together with the additional pH data and a wider range of temperature from the present study, a revised equation was obtained. The pH and salinity dependence did not change, while the T relationship was modified (Eq. 4). Thus, an updated equation for the theoretical Fe(II) oxidation appropriate for deep waters is presented: log 𝑘 (𝑠 ) = 35.627 -6.7109 * 𝑝𝐻 + 0.5342 * 𝑝𝐻 -5434.02/𝑇 -0.04406 * 𝑆 / -0.002847 * 𝑆 (4)The T factor has been modified from -5362.6/T to -5434.02/T obtained from the average slope of Figure2. To assess the performance of the updated Fe(II) oxidation kinetic equation (Eq. 4), it was compared to three existing equations. The chosen equations were the first derived equation[START_REF] Millero | The oxidation kinetics of Fe(II) in seawater[END_REF], the equation by[START_REF] Santana-Casiano | Oxidation of nanomolar level of Fe(II) with oxygen in natural waters[END_REF], and a recent equation using Labrador Seawater[START_REF] Santana-González | Organic matter effect on Fe (II) oxidation kinetics in the Labrador Sea[END_REF]. The four equations were compared to the measured oxidation rate constants at in situ pH and T conditions. The residual sum of squares (RSS) and root mean square error (RMSE) between predicted and observed values were calculated. Smallest values of RSS and RMSE indicate the best equation fit to observations. Additionally, the difference in logarithms of the likelihood (Δlog(L)), based on a Gaussian error distribution with a constant variance of log-transformed

3. 2

 2 Figures 4 and 5 present the half-life times of Fe(II) samples collected above each

3. 4

 4 The effect of particles, colloids, and organic matter on oxidation rate constants Experiments with samples from Rainbow (Stn 16, 2051 m), West of Rainbow (Stn 13, 2339 m), Broken Spur (Stn 24, 2829 m) and TAG (Stn 35, 3350 m) were performed to improve our understanding of the impact of particulate and organic matter on the oxidation kinetics of hydrothermal vent fluids. The Rainbow sample at 2051 m, located outside the plume, did not show any difference in the log(k') due to the presence of particulates, with values at each pH unit varying by ± 0.03 and an average slope of log(k') against pH of 0.96 ± 0.07 for UF, F0.2

FiguresFigure 1 .

 1 Figures

Figure 2 .

 2 Figure 2. Arrhenius relationship between the oxidation rate constant (log k' (min -1 )) and

Figure 3 .

 3 Figure 3. pH effect (from 7.0 to 8.0) on the Fe(II) oxidation rate constants (log k' (min -1 )) for

Figure 4 .

 4 Figure 4. The measured Fe(II) half-life (t1/2, min) at TispHis (orange), T25pHis (green), and

Figure 5 .

 5 Figure 5. Boxplots of the Fe(II) half-life (t1/2, min) within the six hydrothermal plumes. a)

Figure 6 .

 6 Figure 6. The Fe(II) half-life (t1/2, min) at the Rainbow field a) under in situ conditions (see

Figure 8 .

 8 Figure 8. Oxidation rate constants at different pH (7.5, 7.7 and 8), for selected unfiltered (UF,

Figure 9 .

 9 Figure 9. Fe(II) oxidation rate constants (log(k')) determined under in situ conditions against

Table 1 .

 1 Statistical comparison of the available Fe(II) oxidation kinetic equations with the measured oxidation rate constants for deep ocean waters without including the hydrothermal neutrally buoyant plumes. Low residual sum of squares (RSS) and root mean square error (RMSE) indicate the best equation fit to observations. Greater than two points of difference in the difference in logarithms of the likelihood (Δlog(L)) presents a better fit.

		Millero et al.	Santana-Casiano	Santana-	González-
		(1987)	et al. (2005)	González et al.	Santana et al.
				(2019)	(Eq. 4 of this
					manuscript)
	RSS	0.019	0.003	0.006	0.002
	RMSE	0.019	0.008	0.011	0.007
	log(L)	24.2	33.6	32.5	36.7

Acknowledgements

The authors would like to thank the captain and crew of the R.R.S. James Cook as well as the scientific team during the GA13 cruise. The field work was supported by NERC (NE/N010396/1 and NE/N009525/1) awards to AT and MCL. This work was supported by ISblue project, Interdisciplinary graduate school for the blue planet (ANR-17-EURE-0015) and co-funded by a grant from the French government under the program "Investissements d'Avenir". Lab work was supported by the ATOPFe CTM2017-83476-P project (Spanish Ministry of Economy and Competitiveness) awarded to MSC and MGD.

Supplementary Table S1) at 25 ºC between the 0.02 µm filtered and the filtered and UV irradiated samples was due to organic complexation. The computed role of organic complexation produced a 78 ± 6% decrease in the concentration of reactive inorganic Fe(II) species. The effect of organic Fe(II) species was highest at Broken Spur and TAG sites (81 ± 5 %) and lowest at Rainbow (74.1 ± 4 %). [START_REF] Roy | Persistence of iron (II) in surface waters of the western subarctic Pacific[END_REF] found a value that was slightly lower for the western subarctic Pacific water, with a 61 ± 8% decrease. As both the organic ligand concentrations and the conditional constants are unknown, only the product 𝐾 • 𝐿 (Eq. 7) can be inferred. Knowing the inorganic distribution coefficient of Fe(II), which is pH dependent but can be calculated from [START_REF] Santana-Casiano | Oxidation of nanomolar level of Fe(II) with oxygen in natural waters[END_REF], and considering a unique class of ligand (L), the product 𝐾 • 𝐿 should be 9±2 (higher values at Broken Spur and TAG, while lower values at Rainbow) while 1 + ∑ 𝐾 [𝐿 ] in Eq. 7 is 2.6 (2.6 = 1/0.38, [START_REF] Santana-Casiano | The role of Fe(II) species on the oxidation of Fe(II) in natural waters in the presence of O2 and H2O2[END_REF]).

If the concentration of Fe(II) organic ligands in seawater is on the same order as Fe(III) ligands (1 to 10 nmol L -1 ), as assumed by [START_REF] Roy | Persistence of iron (II) in surface waters of the western subarctic Pacific[END_REF], the corresponding conditional constant should range between 10 9 to 10 10 , (respectively for 10 and 1 nmol L -1 of ligands).

The strength of these Fe(II) complexing ligands compared to those for Fe(III) is in the low affinity range [START_REF] Gledhill | The Organic Complexation of Iron in the Marine Environment: A Review[END_REF][START_REF] Bundy | Distinct pools of dissolved iron-binding ligands in the surface and benthic boundary layer of the California Current[END_REF]. However, the formation of these complexes would decrease the Fe(II) oxidation rate constant through both the effects on the side reaction coefficients (Eqs. 7-8) and because the complexes can be non-reactive to oxidation or may oxidize slower than other inorganic species. Moreover, it should be considered that organic matter might even increase the Fe(II) t1/2 due to the reduction of organically complexed Fe(III), which would increase the Fe(II) in solution, and therefore the t1/2 [START_REF] Santana-Casiano | Fe (III) reduction in the presence of catechol in seawater[END_REF].

Competing interests

The authors declare no competing interests.


Jessica Morel
email: jmorel2@chu-grenoble.fr

Augustin Pirvu

Amandine Elie

Nicolas Gallet

Jean Luc Magne

Rafaëlle Spear

Functional Results of Cervical Rib Resection for Thoracic Outlet Syndrome: Impact on Professional Activity

Keywords: thoracic outlet syndrome -cervical rib * EAST: Elevated Arm Stressed Test Arterial Thoracic Outlet Syndrome, ‡ NTOS Neurogenic Thoracic Outlet Syndrome Neurogenic Thoracic Outlet Syndrome, VTOS: Venous Thoracic Outlet Syndrome

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

Introduction

Cervical rib (CR) is an abnormal bone originating from the seventh vertebra [START_REF] Mcnally | The ossification of the costal element of the seventh cervical vertebra with particular reference to cervical ribs[END_REF]. CR is observed in 0.2 to 1% of the general population [START_REF] Guttentag | Keep your eyes on the ribs: the spectrum of normal variants and diseases that involve the ribs[END_REF][START_REF] Henry | Cervical rib prevalence and its association with Thoracic Outlet Syndrome: a meta-analysis of 141 studies with surgical considerations[END_REF]. Only 10 % of CR are responsible of thoracic outlet syndrome (TOS). TOS is secondary to the compression of the neurovascular bundle. CR is associated with an increased rate of arterial compression in TOS [START_REF] Orlando | A Decade of Excellent Outcomes after Surgical Intervention in 538 Patients with Thoracic Outlet Syndrome[END_REF][START_REF] Marine | Arterial Thoracic Outlet Syndrome: A 32-year Experience[END_REF]. Arterial injuries are frequently associated to stage 3 or 4 of Grüber's classification [START_REF] Chang | The significance of cervical ribs in thoracic outlet syndrome[END_REF].

Different subtypes of TOS are described according to the compressed anatomical structure: vascular TOS (arterial or venous) or neurogenic TOS [START_REF] Illig | Reporting standards of the Society for Vascular Surgery for thoracic outlet syndrome[END_REF]. Surgical decompression in TOS without anatomical abnormality is indicated when physiotherapy fails. While physiotherapy is associated with favorable results in NTOS, conservative treatment is rare in vascular TOS.

Where CR is associated with TOS, it must be surgically corrected. No conservative treatment was performed in case of symptomatic CR. CR resection was first described by Coote in 1861 [START_REF] Coote | Exostosis of the left transverse process of the seventh cervical vertebra, surrounded by blood vessels and nerves; successful removal[END_REF]. Many studies report short and long-term results of surgical decompression for TOS [START_REF] Peek | Outcome of Surgical Treatment for Thoracic Outlet Syndrome: Systematic Review and Meta-Analysis[END_REF].

First rib resection and scalenectomy (FFRS) associated with CR resection when present is the surgical treatment of TOS. The association of FRRS and CR resection is controversial. Most studies report results of combined FRRS and CR resection. CR resection without FRRS for TOS is rarely studied in the literature. Nevertheless, the presence of CR can be responsible for specific vascular complications like subclavian aneurysms that require appropriate treatment.

In this study, we reported the monocentric experience of CR resection in TOS over 12 years.

We evaluated long term functional results following cervical rib resection for TOS and the occupational impact of the surgery.

Material and Methods

Study population:

From 2004 to 2016, all patients who underwent CR resection were selected from the hospital electronic database. Research was made with keywords "rib resection" and "thoracic outlet syndrome" and all operative reports were reviewed. In this analysis, we included all patients with FRRS who required complementary CR resection. We excluded from this study cases of FFRS without CR resection.

Demographic and clinical data such as gender, age at the time of surgery, medical history, active smoking, pre-operative symptoms, and the orthopedic history of the upper limb, medical therapy, professional activity and occupational disability were collected. The Roos or elevated arm stress test (EAST) was performed as part of the clinical examination before the procedure and 1 month after the procedure [START_REF] Roos | Congenital anomalies associated with thoracic outlet syndrome. Anatomy, symptoms, diagnosis, and treatment[END_REF].

Patients were classified according to reporting standards [START_REF] Illig | Reporting standards of the Society for Vascular Surgery for thoracic outlet syndrome[END_REF]. Preoperative symptoms could be arterial (ATOS) (arm claudication, the absence of radial pulse, finger ulcer or necrosis, upper limb ischemia with or without neurologic impairment), neurogenic (NTOS) (paresthesia, weakness, muscle atrophy of the upper limb), both arterial and neurogenic (ANTOS) or venous (VTOS) (edema, deep vein thrombosis). Clinical exam classified subtype of TOS (ATOS, NTOS, ANTOS and VTOS).

All patients were explored by Chest X Ray, dynamic ultrasound and CTA. A chest X Ray depicted a cervical rib. Patients were retrospectively categorized using Grüber's classification.

Grüber's classification of cervical rib was described in 1968 and differentiated 4 anatomical presentations [START_REF] Gruber | Über die Halsrippen des Menschen mit vergleichend anatomischen Bemerkungen[END_REF] : 1: a rudimentary rib that does not penetrate into the transverse process; 2: a small cervical rib that extends beyond the transverse process of the seventh cervical vertebra with a free distal end; 3: a cervical rib continued by a fibrous or fibromuscular band ending at the first thoracic rib and 4: a cervical rib connected to the first thoracic rib by true cartilage. Dynamic Doppler ultrasound was systematically performed to explore vascular TOS and diagnose potential associated arterial injuries. Doppler ultrasound was performed by a trained physician. Both venous and arterial vessels are explored. Blood flow cessation during dynamic maneuver (45° abduction above the shoulder) while normal at rest confirmed the diagnosis. Computed tomography angiography (CTA) both at rest and during dynamic maneuver was systematically performed. Anatomical abnormality, vessel compression location and the arterial run off was analyzed and helped surgical planning. An angiogram was performed pre-operatively if distal emboli were depicted on CTA or in cases of distal ulcers, lack of radial or ulnar pulses. Electromyogram (EMG) with nerve conduction was performed in patients with symptoms suggesting NTOS. The decrease of distal nerve conduction and low velocity (50 m/s) suggested a brachial plexus impairment.

Surgical technique:

All surgeries were performed under general anesthesia as described by Shein in 1971 [START_REF] Schein | A technic for cervical rib resection[END_REF].

The phrenic nerve was systematically assessed by external monitoring at the beginning and at the end of the procedure. Access was supraclavicular. CR was systematically performed. FRR and/or C7 transverse process resection were performed if dynamic maneuvers depicted a stress compression of vessels or of neurologic bundles after CR resection. Bone resection was performed with a Kerisson clamp. Adjunctive cervical sympathectomy (CS) was performed prior to 2015 in patients presenting with aneurysms and distal emboli. Data on intra-operative complications and on additional arterial subclavian repair (aneurysmorraphy, aneurysm resection, bypass, embolectomy) were collected. At the end of the procedure, dynamic maneuvers were systematically performed to confirm the release of the neurovascular bundle during upper limb abduction. When confirmed, the procedure was considered as a technical success. All patients except those with isolated NTOS received antiplatelet therapy following surgery. A postoperative Doppler ultrasound was systematically performed in ATOS and ANTOS at one month.

For the purpose of this study, we updated the follow-up of each patient either using the report of their last medical visit in the year (general practitioner, neurologist or Doppler ultrasound) or by phone.

We evaluated each patient's quality of work life pre-and post-operatively. Preoperative EAST and professional activity was systematically evaluated preoperatively and collected retrospectively. We also evaluated the EAST during the post-operative period. Post-operative EAST was collected retrospectively from the report of surgical visit at one month. The postoperative ability of work was evaluated on November 2017 using standardized telephone questionnaire to evaluate professional occupation and compare it to preoperative status.

Early outcomes were those within the first 30 days of follow up. Short term outcomes are the outcomes after the 30 first postoperative days up to the first year and long-term outcomes were those after the 1 st postoperative year.

Statistical analysis:

Categorical variables were presented as percentages and continuous variables were expressed as median with interquartile ranges (Q1-Q3).

Results:

Demographic data

From January 2004 to December 2016, 36 cervical ribs were resected in 33 patients at our institution. Three patients (9%) required bilateral CR resection.

The population consisted in 27 women and 6 men with a median age of 38.5 year old (30-46) at the time of surgery. The youngest patient was 13 years old and the oldest 58 years old. One patient had a history of ipsilateral collarbone fracture, and 7 were followed for upper limb orthopedic disease. Details of demographic data are summarized in Table I. Among the 36 cervical resections, 22 were on the right side. The most common Grüber's category for the resected cervical rib side treated was the fourth (22/36, 61%). Contralateral CR was present in 27 patients (27/33, 82%) mostly of category 3 in Grüber's classification.

Most frequently, patients were treated for NTOS (14/36, 39%). VTOS was only depicted in one patient (3%) (Table II). There were 2 asymptomatic patients (6%). The youngest patient of this study was a 13-year-old girl who presented with a severe scoliosis treated with a back brace. A unilateral CR was discovered on the X Ray of the spine. The CR was removed after multidisciplinary discussion including orthopedic and vascular surgeons. The second one was a 28-year-old female who presented with a left cervical rib complicated of a voluminous subclavian aneurysm. It was decided to remove the contralateral CR preventively.

EAST was positive for 64% (23 limbs) as detailed in Table Iva.

On preoperative exams, 9 subclavian aneurysms, 6 subclavian stenosis and 6 subclavian poststenotic dilations (3 aneurysms and 3 ectasia) were depicted. EMG was performed in 23 limbs and reported suffering of the brachial plexus in 49% limbs (11/23). III).

Procedure results (Table

Among patients with upper limb ischemia (19%, 7/36), two (6%, 2/36) required CR resection associated with urgent revascularization. The last required anticoagulation therapy before CR resection.

The resection of CR was complete in 94% (34/36) of procedures. CR resection was left incomplete when the release of the neurovascular bundle was obtained and the whole CR could not be accessed without risking neurologic or vascular damage.

Additional arterial procedures were required during 9 procedures (25%) with arterial aneurysms: 1 aneurysmorraphy, 5 aneurysm resections with direct reconstruction and 3 prosthetic bypasses. Three subclavian ectasias were left untreated.

The technical success rate was 100%. Intraoperative complications were observed in 11% of procedures: 4 pleural breach treated by adjunctive chest tube. All pleural breach resolved favorably at 48h. No brachial plexus or phrenic nerve injury was described.

Early outcomes

The median length of hospitalization was 3.5 days [START_REF] Henry | Cervical rib prevalence and its association with Thoracic Outlet Syndrome: a meta-analysis of 141 studies with surgical considerations[END_REF][START_REF] Orlando | A Decade of Excellent Outcomes after Surgical Intervention in 538 Patients with Thoracic Outlet Syndrome[END_REF].

Postoperative complications were detected in 11% of the cases studied: 3 (8%) Claude Bernard Horner's (CBH) syndrome, spontaneously resolved and an asymptomatic subclavian dissection (3%) was depicted on a systematic postoperative Doppler ultrasound. This dissection was treated only by antiplatelet therapy with favorable outcomes. No access complication were diagnosed.

On clinical exam at 1 month, 7 limbs (19%) were EAST positive: 4 NTOS (29%) and 3 ATOS (25%) (Table IVa). All patients treated with adjunctive CS had a radial pulse postoperatively.

Short and long-term outcomes:

The median follow-up was 91 months (39-123). The last procedure performed had a followup of eleven months and the earliest 165 months. Two patients were lost to follow up because they could not be reached by phone. They were both considered as unable to have a normal professional activity. One of them had no clinical evaluation during the postoperative period and was considered worsened (EAST positive on follow-up).

Late complications were two bypass thromboses (6%) at 6 weeks and 16 months. One required a secondary procedure. The embolectomy performed in emergency was not successful and a thoracic sympathectomy by videothoracoscopy was required at one year to treat upper limb claudication with a good clinical outcome. The last bypass occlusion was asymptomatic and detected at 16 months on standard follow up Doppler ultrasound.

During follow-up, patients with ATOS, ANTOS or VTOS were followed up with Doppler ultrasound or CTA. The patency rate was 75 % at 1 year, 67% at two years, 67% at 5 years.

Three patients presented with a reoccurrence of symptoms at 6 weeks, at 4 years and at 10 years after the surgery. The first patient was the patient who presented a bypass thrombosis.

The two others were NTOS.

Professional activity:

During the pre-operative period, 9 patients (27%) had a normal work life and 24 (73%) were unable to work. On latest follow up, 64% (21/33) had a normal work life: 14 (42%) were improved and seven (21%) patients showed no improvement. Patients were unable to work after the surgery in 36% of cases (12/33). Ten patients (30%) showed no modification and two patients (6%) worsened: one patient suffering from fibromyalgia who required a reorganization of activity and one lost to follow-up considered as worsened. There were no missing data for pre and post-operative EAST and professional activity evaluation. Details according to symptoms are summarized in Table IVb.

Discussion

We described outcomes of our surgical approach of CR resection for TOS with a supraclavicular access associated with FRR only when neurovascular entrapment was persistent during intraoperative dynamic maneuvers testing. CR resection was most often studied when performed with FRRS. Our postoperative outcomes are acceptable considering both clinical and functional evaluation. Functional results and quality of life after surgery of TOS in the literature were previously analyzed [START_REF] Peek | Outcome of Surgical Treatment for Thoracic Outlet Syndrome: Systematic Review and Meta-Analysis[END_REF]. We focused on the occupational ability in our evaluation of postoperative functional outcome in this young population [START_REF] Henry | Cervical rib prevalence and its association with Thoracic Outlet Syndrome: a meta-analysis of 141 studies with surgical considerations[END_REF]. Divi et al in 2005 reported similarly results on ability to work in patients presenting with venous and neurogenic TOS [START_REF] Divi | Thoracic outlet decompression for subclavian vein thrombosis: experience in 71 patients[END_REF].

TOS was difficult to diagnose. Many symptoms may be related to TOS while not specific [START_REF] Davies | Surgical management of the thoracic outlet compression syndrome[END_REF]. We reported eleven cases (31%) associated with rheumatologic disease (shoulder of neck). Diagnostic tools were limited. In our study, all patients benefitted of clinical exam, Doppler ultrasound and CTA. We performed systematically both imaging in order to confirm TOS, plan surgery and explore vascular complications. TOS may associate vascular and neurogenic subtypes. In our population, 19.4% presented with ANTOS. Diagnostic tools of NTOS appeared less reliable. While EAST was majorly positive in NTOS and ANTOS (86% and 87% respectively), only 49% were confirmed by nerve conduction velocities decrease.

The reliability of EMG in NTOS diagnosis may be questioned. EAST evaluation could be more effective for NTOS diagnosis as previously advocated [START_REF] Roos | Congenital anomalies associated with thoracic outlet syndrome. Anatomy, symptoms, diagnosis, and treatment[END_REF][START_REF] Sanders | Thoracic outlet syndrome: a common sequela of neck injury[END_REF].

Our technique was to prioritize CR resection. FRR was only removed when the neurovascular bundle was found intraoperatively compressed after CR resection. This technique was previously described by Davies et al, Desai and Robbs and Ambrad-Chalela et al [START_REF] Davies | Surgical management of the thoracic outlet compression syndrome[END_REF][START_REF] Desai | Arterial complications of the thoracic outlet syndrome[END_REF][START_REF] Ambrad-Chalela | Recurrent neurogenic thoracic outlet syndrome[END_REF].

Little evidence is available when considering CR resection alone [START_REF] Chang | The significance of cervical ribs in thoracic outlet syndrome[END_REF][START_REF] Sanders | Management of cervical ribs and anomalous first ribs causing neurogenic thoracic outlet syndrome[END_REF][START_REF] Degeorges | Thoracic Outlet Syndrome Surgery: Long-Term Functional Results[END_REF][START_REF] Brown | Results of excision of a cervical rib in patients with the thoracic outlet syndrome[END_REF]. Whether CR resection must be associated with FRRS remains controversial. Where applicable, CR resection for TOS is mandatory [START_REF] Toso | Thoracic outlet syndrome: influence of personal history and surgical technique on long-term results[END_REF]. Many studies described removing CR along with the first rib to prevent a late recurrence [START_REF] Chang | The significance of cervical ribs in thoracic outlet syndrome[END_REF][START_REF] Sanders | Management of cervical ribs and anomalous first ribs causing neurogenic thoracic outlet syndrome[END_REF][START_REF] Toso | Thoracic outlet syndrome: influence of personal history and surgical technique on long-term results[END_REF]. However, the FRR may increase postoperative morbidity because of a deeper dissection [START_REF] Sanders | Management of cervical ribs and anomalous first ribs causing neurogenic thoracic outlet syndrome[END_REF]. Interestingly, FRR resection was only required in our population in NTOS patients and is preformed partially in half of them. One did not improve after surgery. C7 transverse process resection was also performed in 42% of procedures when a large apophysis was depicted. Cormier et al [START_REF] Cormier | Arterial complications of the thoracic outlet syndrome: fifty-five operative cases[END_REF] also described a C7 process resection in their study in 1989. No result considering the association with C7 process resection was available to our knowledge. Two CR resections were not complete. Both procedures were technical success One was the only VTOS of this series. The second one was an ANTOS with a negative EAST. He was able to return at work post-operatively.

Our results suggested a safety and efficiency of CR resection alone. On follow-up, a low rate of recurrence of TOS was depicted (9%, 3/36). All were treated by CR resection only. This rate was similar to the 11.5% recurrence of TOS described after exclusive FRRS [START_REF] Urschel | Thoracic outlet syndrome: a 50-year experience at Baylor University Medical Center[END_REF]. No recurrence of symptoms was observed on follow-up after CR was partially removed.

Recently, Gelabert et al [START_REF] Gelabert | Regrown First Rib in Patients with Recurrent Thoracic Outlet Syndrome[END_REF] advocated the necessity to withdraw completely the CR bone or the first rib bone to avoid the recurrence of symptoms. Recurrent TOS after CR resection exclusively was not studied to our knowledge.

Where additional arterial procedures were required, long term functional results were favorable. Aneurysm resection and direct anastomosis of subclavian artery seemed to provide good results as described previously [START_REF] Cormier | Arterial complications of the thoracic outlet syndrome: fifty-five operative cases[END_REF]. As opposed to direct anastomosis, use of Dacron graft was associated to a risk of postoperative occlusion during the first year. Prosthetic use should be avoided for arterial repair during TOS surgery, as previously described [START_REF] Marine | Arterial Thoracic Outlet Syndrome: A 32-year Experience[END_REF][START_REF] Vemuri | Clinical presentation and management of arterial thoracic outlet syndrome[END_REF] .

Subclavian ectasia left untreated did not evolve into aneurysm when CR resection was performed as reported elsewhere [START_REF] Vemuri | Clinical presentation and management of arterial thoracic outlet syndrome[END_REF][START_REF] Short | The subclavian artery in 16 patients with complete cervical ribs[END_REF]. Association between CR and ATOS [START_REF] Marine | Arterial Thoracic Outlet Syndrome: A 32-year Experience[END_REF] and severity of ATOS could justify the preventive resection of a complete CR in case of contralateral arterial injury [START_REF] Chang | The significance of cervical ribs in thoracic outlet syndrome[END_REF][START_REF] Rochlin | Bilateral first rib resection and scalenectomy is effective for treatment of thoracic outlet syndrome[END_REF]. In this study, one patient was treated preventively after ATOS as described above.

Our study was one of the largest on CR resection in TOS to our knowledge. However, limits may be discussed. The study was a retrospective and monocentric study of a small population.

Different subtypes of TOS were analyzed as the surgical strategy did not differ. Nevertheless, results may be biased by the heterogeneity of the TOS symptoms. Furthermore, we did not use validated questionnaires of quality of life because of numerous symptoms presented by our population. We favored the evaluation of the professional activity to evaluate functional results as this pathology concerned young active patients.

Conclusion

CR resection itself seems to be a safe and efficient treatment of TOS. FRRS may be required depending on intraoperative dynamic maneuvers. Favorable long term outcomes in terms of occupation are associated to this technique. A larger population is required to confirm these results.

* NTOS Neurogenic Thoracic Outlet Syndrome. † ATOS: Arterial Thoracic Outlet Syndrome ‡ ANTOS: Arterial and Neurogenic Thoracic Outlet Syndrome.

§ VTOS: Venous Thoracic Outlet Syndrome.