Gabriele Boschetto

Aida Todri-Sanial

Assessing doping strategies for monolayer MoS 2 towards non-enzymatic detection of cortisol: a first-principles study

In this work, we investigate by means of atomistic density functional theory simulations the interaction between cortisol (the target molecule) and monolayer MoS 2 (the substrate). The aim is to assess viable strategies for the non-enzymatic chemical sensing of cortisol. Metal doping of the sensing material could offer a way to improve the device response upon analyte adsorption, and could also enable novel and alternative detection mechanisms. For such reasons, we explore metal doping of MoS 2 with Ni, Pd, and Pt, as these are metal elements commonly used in experiments. Then, we study the material response from the structural, electronic, and charge-transfer points of view. Based on our results, we propose two possible sensing mechanisms and device architectures: i) a field-effect transistor, and ii) an electrochemical sensor. In the former, Ni-doped MoS 2 would act as the FET channel, and the sensing mechanism involves the variation of the surface electrostatic charge upon the adsorption of cortisol. In the latter, MoS 2 decorated with Pt nanoparticles could act as the working electrode, and the sensing mechanism would involve the reduction of cortisol. In addition, our findings may suggest the suitability of both doped and metal-doped MoS 2 as sensing layers in an optical sensor.

Introduction

Cortisol, or hydrocortisone if supplied as a medication, is a steroid hormone which plays a fundamental role in many physiological processes in both humans and animals. It is part of the glucocorticoid class of hormones, which means it is directly involved in the metabolism of glucose. [START_REF] De Leon | Cortisol reduces hippocampal glucose metabolism in normal elderly, but not in alzheimer's disease[END_REF] In addition, prolonged high levels of such hormone in the body lead to its active role also in the protein and lipid metabolism. Notably, cortisol is also an important actor in the stress and immune response: a correlation has been observed between sustained stress and high levels of circulating cortisol, [START_REF] Mcewen | Protective and damaging effects of stress mediators[END_REF][START_REF] Burke | Depression and cortisol responses to psychological stress: A meta-analysis[END_REF] so that it is often regarded as "the stress hormone". Other aspects that have been observed to be affected by cortisol levels are, for instance, bone formation [START_REF] Chyun | Cortisol decreases bone formation by inhibiting periosteal cell proliferation[END_REF] and memory. [START_REF] Newcomer | Decreased memory performance in healthy humans induced by stress-level cortisol treatment[END_REF] Being able to detect and measure the change in cortisol levels in the human body can aid in the general monitoring of human health and well-being: [START_REF] Hellhammer | Salivary cortisol as a biomarker in stress research[END_REF][START_REF] Russell | Hair cortisol as a biological marker of chronic stress: Current status, future directions and unanswered questions[END_REF] for instance, this could be useful for the early detection of cardiovascular diseases, [START_REF] Iob | Cardiovascular disease and hair cortisol: a novel biomarker of chronic stress[END_REF] for the monitoring of a possible compromised immune state, and also for keeping track of the health condition of athletes during intense physical activities. [START_REF] Seshadri | Wearable sensors for monitoring the physiological and biochemical profile of the athlete[END_REF] Therefore, in the context of Internet of Medical Things (IoMT), [START_REF] Da Costa | Internet of health things: Toward intelligent vital signs monitoring in hospital wards[END_REF] there is currently a great interest in the development of innovative point-of-care biosensing devices that are able to detect and quantify cortisol in human biological samples.

Recently, atomically thin two-dimensional (2D) materials have been extensively studied to be used as biosensors, due to their unique mechanical, electrical, and optical properties. [START_REF] Akinwande | A review on mechanics and mechanical properties of 2d materials-graphene and beyond[END_REF][START_REF] Mas-Ballesté | 2d materials: to graphene and beyond[END_REF] Although graphene is perhaps the most notable example of a 2D material, research is also currently focusing on transition-metal dichalcogenides (TMDs) such as molybdenum disulphide (MoS 2 ). Within the chemical space of TMDs, single-layer MoS 2 is one of the most studied materials due to its stability, direct optical band gap of ∼1.8 eV, and good carrier mobility, making it suitable for many optoelectronic applications. [START_REF] Li | Electronic properties of MoS 2 nanoparticles[END_REF][START_REF] Baugher | Intrinsic electronic transport properties of high-quality monolayer and bilayer MoS 2[END_REF][START_REF] Schmidt | Transport properties of monolayer MoS 2 grown by chemical vapor deposition[END_REF][START_REF] Yim | Investigation of the optical properties of MoS 2 thin films using spectroscopic ellipsometry[END_REF][START_REF] Yu | Analyzing the carrier mobility in transition-metal dichalcogenide MoS 2 field-effect transistors[END_REF] Moreover, its properties can be fine-tuned, for instance, by both strain [START_REF] Conley | Bandgap engineering of strained monolayer and bilayer MoS 2[END_REF] and surface engineering (e.g., with the inclusion of defects, vacancies, and/or with doping). In the context of wearable electronics, single-layer MoS 2 could also be used for fabricating flexible devices, [START_REF] Zou | Flexible devices: from materials, architectures to applications[END_REF] thus paving the way for novel wearable point-of-care biosensors. [START_REF] Barua | Nanostructured MoS 2 -based advanced biosensors: A review[END_REF] In order to improve the sensitivity of the biosensor, a common technique is to modify (i.e., functionalize) the surface of the sensing material: this can be done either by binding an analyte-specific antibody/enzyme (enzymatic sensing) or by doping and/or by decorating the sensor's surface, typically with metallic nanoparticles or metal oxides (non-enzymatic sensing). The former strategy has the great advantage of providing devices with generally high selectivity towards the chosen analyte, however enzyme-based sensors are known to be rather unstable and prone to degradation to temperature and pH. On the other hand, non-enzymatic sensors can provide a higher stability and a prompt response, at the expense of a generally lower chemical selectivity.

A very popular biomarker for which many examples of both enzymatic and (to some extent) non-enzymatic biosen-sors exist in the literature is glucose, whereas less is available regarding cortisol; moreover, most of the studied devices are enzymatic sensors. For instance, Kinnamon et al. [START_REF] Kinnamon | Portable biosensor for monitoring cortisol in low-volume perspired human sweat[END_REF] developed a portable biosensing device able to detect cortisol in human sweat: the authors have used MoS 2 nanosheets functionalized with a specific antibody. The electrochemical response of the sensor is modulated by the interaction of cortisol with such antibody. Sekar et al. [START_REF] Sekar | Carbon fiber based electrochemical sensor for sweat cortisol measurement[END_REF] developed an enzymatic flexible electrochemical sensor based on conductive carbon fiber for the detection of cortisol in sweat samples. Gold nanoparticles have also been functionalized with cortisol-selective aptamers by Dalirirad et al., [START_REF] Dalirirad | Aptamer-based lateral flow assay for point of care cortisol detection in sweat[END_REF] once again for the detection of cortisol in human sweat. Another aptamer-based cortisol biosensor has been studied by Fernandez et al.: [START_REF] Fernandez | Disposable aptamersensor aided by magnetic nanoparticle enrichment for detection of salivary cortisol variations in obstructive sleep apnea patients[END_REF] the method of detection involved the reduction reaction of the analyte, catalyzed by a copper metalloporphyrin (Cu-PP) ink attached to multi-walled carbon nanotubes. Recently, a non-enzymatic cortisol sensor has been proposed by Mugo et al.: [START_REF] Mugo | Flexible molecularly imprinted electrochemical sensor for cortisol monitoring in sweat[END_REF] in their work the authors have used a polymer, poly(GMA-co-EGDMA), deposited on carbon nanotube-cellulose nanocrystals. The authors observed good performance and rapid analyte response.

The relatively smaller number of scientific publications on the topic, if compared to enzymatic sensing, clearly shows that non-enzymatic biosensing is a rather challenging task, from the point of view of both the sensing mechanism and the sensor development. Given the complexity of the topic, theoretical models can undoubtedly prove extremely useful in designing such devices, as models allow to shed light into the analyte/sensing material interaction and into the physical and chemical sensing mechanisms. To this end, atomistic modelling with density functional theory (DFT) has been widely used not only to study the interaction of small molecules (mainly gases) with the sensing materials, [START_REF] Mehmood | Density functional theory study of chemical sensing on surfaces of single-layer MoS 2 and graphene[END_REF][START_REF] Zhang | Effects of noble metal doping on hydrogen sensing performances of monolayer MoS 2[END_REF][START_REF] Cui | Rh-doped MoSe 2 as a toxic gas scavenger: a first-principles study[END_REF] but to some extent also to explore the sensing mechanism of somewhat "larger" biomolecules, like glucose and dopamine. [START_REF] Ortiz-Medina | Differential response of doped/defective graphene and dopamine to electric fields: A density functional theory study[END_REF][START_REF] Lei | Single-atom doping of MoS 2 with manganese enables ultrasensitive detection of dopamine: Experimental and computational approach[END_REF] However, to the best of our knowledge, the physico-chemical interaction between cortisol, which is a bigger and more complex molecule, and MoS 2 is still largely unexplored.

Therefore, the aim of this paper is to explore the interaction of cortisol with both doped and undoped MoS 2 , in order to elucidate possible non-enzymatic sensing mechanisms. To do so, we used atomistic modelling with DFT to thoroughly investigate the cortisol/MoS 2 interaction from the point of view of structural, electronic, and charge transfer properties. We computed different figures of merit, such as band gaps, net atomic charges, and adsorption energies, in order to understand and quantify the nature and the strength of the interaction. We then studied the effect on such quantitites of common metal dopants, such as Ni, Pd, Pt, that have already been used for sensding purposes, either as point defects or in the form of nanoparticles. [START_REF] Sarkar | Functionalization of transition metal dichalcogenides with metallic nanoparticles: Implications for doping and gas-sensing[END_REF][START_REF] Ma | Modulating electronic, magnetic and chemical properties of MoS 2 monolayer sheets by substitutional doping with transition metals[END_REF][START_REF] He | Enzyme-free glucose biosensors based on MoS 2 nanocomposites[END_REF] This paper is organized as follows: in Methods, the simulation details of the DFT calculations are described; in Results and Discussion, results on cortisol, metal-doped MoS 2 , and their interaction are shown, together with their impli- cations for the biosensing of cortisol. The Conclusions are then presented in the final section.

Methods

In this work, we explored the interaction of cortisol with both pristine and M-doped MoS 2 . We chose three metal dopants commonly used for sensing applications: Ni, Pd, and Pt. To simulate metal-decorated MoS 2 sheets, we placed these metal atoms on top of the monolayer as adsorbed adatoms (non-substitutional doping). We placed cortisol on top of MoS 2 horizontally, in order to maximize the orbital overlap between the analyte and the sensing material.

Cortisol, being a steroid, is composed of four fused hydrocarbon rings, and possesses many possible binding and reactive sites, as can be observed from its chemical structure in Fig. 1. However, given previous reports [START_REF] Fernandez | Disposable aptamersensor aided by magnetic nanoparticle enrichment for detection of salivary cortisol variations in obstructive sleep apnea patients[END_REF][START_REF] Suda | Oriented, molecularly imprinted cavities with dual binding sites for highly sensitive and selective recognition of cortisol[END_REF][START_REF] Manickam | Salivary cortisol analysis using metalloporphyrins and multi-walled carbon nanotubes nanocomposite functionalized electrodes[END_REF] of the good reactivity of the carbonyl group directly attached to the ring A (carbon C-3), we decided to focus mainly on such moiety. Furthermore, our DFT simulations on isolated cortisol, presented in the following section, showed that the ring A of such molecule is particularly electron-rich, corroborating the data in the literature. Therefore, as the initial guess before performing the geometry optimization, we placed cortisol on top of doped MoS 2 so that the oxygen atom of the carbonyl group would sit above the metal dopant. When placing the analyte on top of the undoped monolayer, we ensured that the oxygen atom would sit above the Mo atom (top Mo ) in order for it to interact with the surrounding three S atoms, before carrying out a full geometry relaxation. To avoid the spurious interaction of cortisol with its periodic images, we considered a large orthorombic 8 × 4 × 1 MoS 2 supercell with a total of 192 atoms, and with at least 15 Å of vacuum padding above and below the sheet. We also note that by choosing this large supercell we achieved a doping density of ∼ 1.8 × 10 13 cm -2 , within the range of typical doping values obtainable in experiments. [START_REF] Luo | Doping engineering and functionalization of two-dimensional metal chalcogenides[END_REF] Computer simulations were carried out at the DFT level by using QuantumATK R-2020.09 [START_REF] Smidstrup | Quantumatk: An integrated platform of electronic and atomic-scale modelling tools[END_REF][START_REF]QuantumATK version R-2020.09[END_REF] atomic-scale modelling software. All simulations were performed in vacuum using the Perdew-Burke-Ernzerhof (PBE) exchangecorrelation functional, [START_REF] Perdew | Generalized gradient approximation made simple[END_REF] and to model core electrons we used norm-conserving pseudopotentials from the Pseu-doDojo library. [START_REF] Van Setten | The pseudodojo: Training and grading a 85 element optimized norm-conserving pseudopotential table[END_REF] We employed the LCAO approach with a density-mesh cut-off of 250 Ry, and we used the QuantumATK-optimized Medium basis set for geometry optimizations. The High basis set was used for single-point and properties calculations. We included dispersion effects by employing the D2 correction by Grimme. [START_REF] Grimme | Semiempirical gga-type density functional constructed with a long-range dispersion correction[END_REF] Given the size of the simulation cell, we chose a k-point mesh defined by a 2×2×1 Monkhorst-Pack (MP) grid, [START_REF] Monkhorst | Special points for brillouin-zone integrations[END_REF] whereas for computing the density of states (DOS) we employed a 4 × 4 × 1 MP grid. All geometry optimizations were converged with residual atomic forces no larger than 0.03 eV/Å. We computed net atomic charges following the electron density partitioning scheme of the DDEC6 method, by using the chargemol program. [START_REF] Manz | Chargemol program for performing DDEC analysis[END_REF] Differently from the widely used Mulliken population analysis, DDEC6 charges are independent of the basis set type and size, and have been shown to be chemically meaningful. [START_REF] Manz | Introducing DDEC6 atomic population analysis: Part 1. charge partitioning theory and methodology[END_REF][START_REF] Manz | Introducing [DDEC6 atomic population analysis: Part 2. computed results for a wide range of periodic and nonperiodic materials[END_REF] We defined the adsorption energy as:

E ads = E A+B -(E A + E B ), (1)
where E A+B is the total energy of the substrate and the adsorbate, whereas E A and E B are the total energies of the isolated fragments. For instance, when taking into consideration the adsorption of cortisol on (doped and undoped) MoS 2 , E A+B would correspond to the total energy of the MoS 2 /cortisol system, whereas E A and E B would be the total energies of MoS 2 and cortisol fragments, respectively. Finally, we took into account the basis set superposition error (BSSE) by including the counterpoise correction [START_REF] Boys | The calculation of small molecular interactions by the differences of separate total energies. some procedures with reduced errors[END_REF] in our total energy calculations.

Results and Discussion

Chemical Reactivity of Cortisol

We initially focused our efforts on the isolated cortisol molecule, in order to better understand its reactivity. The core structure of cortisol (see Fig. 1), common to the class of steroid hormones, consists of four fused carbon rings: rings A, B, and C are all 6-carbon rings, whereas ring D is composed of 5 carbon atoms. In addition, C-4 and C-5 in ring A are double-bonded. Attached to the core there are different functional groups, more specifically: two hydroxyl groups attached to C-11 and C-17, and one carbonyl group attached to C-3; attached to C-17 is also a small side chain which itself has both one hydroxyl and one carbonyl group. Intuitively, based on basic assumptions on its chemical structure, possible reactive centers of cortisol could be ring A and the side chain attached to ring D.

We first looked at the bond length of some of the potential reactive sites of the molecule: we first observed that the bond length of the carbonyl group at C-3 is slightly longer -and therefore the bond strength slightly weaker-than that at the side chain (1.24 Å and 1.22 Å, respectively). We also found that the C4=C5 double bond, whose length is 1.36 Å, is slighlty longer than the typical C=C double bond length This suggests that cortisol is characterized by an electronrich donor part, the ring A, and an electron acceptor part, the side chain. To further confirm this finding, we artificially added and removed a small amount of charge (±0.1 e), and computed the electron density difference (EDD) for both positively-and negatively-charged cortisol; both plots are also shown in Fig. 2. Once again, it is possible to observe that the carbonyl group and the ring A overall act as an electron-donating group, whereas the carbonyl group attached on the side chain acts mainly as an electron-accepting group. However, for the negatively-charged molecule, we also note a slight increase of the electron density localized on the ring A. No variation of the electron density was observed on rings B and C. Given these findings, together with the previously mentioned work from the literature, from this point onward we will focus our attention on the electron-rich ring A of cortisol, more specifically on the carbonyl group attached to it.

Electronic

Properties of Metal-Decorated MoS 2 As one possible strategy to modulate the interaction between the analyte (cortisol) and the sensing material (MoS 2 ), we chose non-substitutional doping with three metal atoms, i.e., Ni, Pd, and Pt, adsorbed onto the MoS 2 surface. We chose these metal elements because of their increasing trend in the electronegativity (1.91, 2.20, 2.28 for Ni, Pd, and Pt, respectively), because they each belong to the 3d (Ni), 4d (Pd), and 5d (Pt) class of transitionmetal compounds, and because such metallic species have already been used in experiments with MoS 2 . We placed the adatoms at the top Mo adsorption site of MoS 2 , i.e., above the Mo atom and at the center of three S atoms. From Table 1: Summary of the structural, electronic, and charge-transfer properties of pristine and M-doped MoS 2 . E ads is the adsorption energy of the metal M on MoS 2 , d M-Mo and d M-S are the bond lengths between the metal M and Mo or S atoms, respectively, ∆Q is the net charge transferred upon metal adsorption, Φ is the work function, and E HOMO-LUMO is the effective HOMO-LUMO gap; we point out that the latter is equal to the material's band gap only in the case of pristine MoS 2 , whereas in the other three cases it simply represents the energy difference between the extra bands given by the metal dopants 3. We expect such different bond lengths to correlate with the adsorption energy (E ads ) of the metal adatoms on the MoS 2 substrate: indeed, Ni leads to the strongest bonding with MoS 2 , with a total adsorption energy of -4.10 eV, followed by Pt (-3.30 eV), and then Pd (-2.66 eV).

Substrate E ads (eV) dM-Mo (Å) dM-S (Å) ∆Q (|e|) Φ (eV) EHOMO-LUMO (eV) MoS 2 - - - - 5
In terms of charge-transfer properties, we note that each metal adatom acts as an electron-donating compound to the MoS 2 substrate. The computed DDEC net atomic charges of these metal species were all found to be positive: we observed a value of +0.645 e, +0.367 e, and +0.375 e for Ni, Pd, and Pt, respectively. Once again, we note the significantly stronger interaction of Ni with respect to both Pd and Pt, and this correlates with the structural parameters discussed above. We expect this metal-to-substrate charge transfer to also impact the work function (Φ) of the material, that is, the minimum amount of energy to remove an electron from the substrate to the vacuum outside the material's surface. We computed this quantity for both the pristine and the doped materials by taking the chemical potential at a point in the vacuum, and we obtained a value of Φ MoS 2 = 5.16 eV for MoS 2 , in extremely good agreement with the experimental data of 5.15 eV. [START_REF] Choi | Layer-numberdependent work function of MoS 2 nanoflakes[END_REF] All metal species were found to cause a slight decrease of this quantity, with Φ M-MoS 2 = 5.03 eV, 5.09 eV, 5.09 eV for Ni, Pd, and Pt, respectively. This is consistent with the strenght of the metal-MoS 2 interaction and the amount of transferred charge. Moreover, we point out that such small decrease is most likely due to our relatively lower doping concentration with respect to other computational studies in the literature: [START_REF] Costa-Amaral | Unveiling the adsorption properties of 3d, 4d, and 5d metal adatoms on the MoS 2 monolayer: A dft-d3 investigation[END_REF] effectively, Ni causes a transfer of just 0.01 |e| per MoS 2 formula, whereas for both Pd and Pt this value is only ∼0.006 |e|, thus confirming that the substrate is only weakly doped.

Finally, we also computed the projected density of states (PDOS) of each system, with projections onto the relevant atomic orbitals of S, Mo, and M (M = Ni, Pd, Pt), all shown in Fig. 4. As expected, in the PDOS of the pristine material the bands that give the largest contribution to the total DOS are those of the 2p orbitals of S atoms and of the 4d orbitals of Mo. We also note that our computed band gap of 1.77 eV matches well with the corresponding experimental value of ∼1.8 eV. Regarding the doped materials, results further confirm the weak doping effect, as the extra bands due to the metal adatoms are very close to the valence bands of MoS 2 (shallow-level doping). The difference in energy between the original valence band of MoS 2 and the extra highest occupied band of the dopant (the "new" material's HOMO) is rather small in each case, and is 0.21 eV, 0.15 eV, 0.15 eV for Ni-MoS 2 , Pd-MoS 2 , and Pt-MoS 2 , respectively. Once again, this shows the stronger doping effect given by Ni. Interestingly, the effect of Pt also extends onto the conduction states of MoS 2 , as can be seen from the (very low) extra shoulder which appears at the conduction band edge of Pt-MoS 2 . For this band (the "new" material's LUMO), the energy difference with the original conduction band of the substrate is only 0.10 eV. However, as expected, doping does not cause any appreciable change in the band gap of the original material. From the PDOS, one can also observe that the 3d, 4d, and 5d orbitals of Ni, Pd, and Pt, respectively, overlap with both S-2p and Mo-4d, further indicating chemical bonding between the metal and the substrate. This is particularly evident for Ni, with clearly visible states further extending to lower energies.

To sum up, our simulation results on chemical bonds and charge transfer show that Ni has the strongest interaction with MoS 2 , among the metal species considered in this study. A summary of all the computed structural, electronic, and charge-transfer properties discussed so far is shown in Table 1.

Cortisol Adsorption

Adsorption Mechanism.

We placed cortisol above the MoS 2 substrate (pristine and with metal doping) as described in the Methods section, and we fully relaxed the atomic coordinates of the systems taking into account dispersion forces at the PBE-D2 level.

We first looked at the analyte/substrate interaction from the structural point of view. We analyzed the forma-tion/disruption of chemical bonds, and the variation of bond lengths and interatomic distances upon adsorption. The optimized geometries of each system are shown in Fig. 5. Results show the interaction between cortisol and pristine MoS 2 to be rather weak, as no significant atom displacement was observed neither in the substrate nor in the analyte. The average distance between the carbonyl O atom and the substrate was found to be ∼2.82 Å. In addition, we also notice that no bending and/or strain occur in MoS 2 upon the adsorption of cortisol. On the contrary, including metal adatoms as point defects led to stronger interactions with the analyte, as can be observed from the non-negligible atomic displacement mostly occurring in the ring A of cortisol and in the proximity of the metal species. The rather small interatomic distances between the metal M and the O atom of the carbonyl group (1.94 Å, 2.18 Å, 2.12 Å for Ni, Pd, and Pt, respectively) could hint to some type of chemical bonding. Interestingly, whereas Ni and Pd tend to bind mostly to the O atom, Pt shows a somewhat different reactivity, with a significant interaction also with the C-3 atom of the carbonyl group. From Fig. 5 one can observe that the Pt and O atoms are not positioned on the same vertical axis, as Pt moves closer to the C-3 atom (d Pt-C3 = 2.38 Å).

Further hints of chemical reactivity can be found by looking at the variation of the cortisol C=O bond length. This quantity increases from the initial 1.24 Å up to 1.28 Å, 1.27 Å, 1.31 Å with Ni, Pd, and Pt, respectively. We note that Pt-MoS 2 significantly weakens the C=O bond, which might suggest the partial activation of the carbonyl group, opening the path to its possible catalytic reduction. Finally, we also observed some variation in the metal M-Mo bond lengths of Ni-MoS 2 and Pt-MoS 2 , which were both found to increase (∆d Ni-Mo = 0.06 Å, ∆d Pt-Mo = 0.05 Å), whereas no change has been observed in Pd-MoS 2 .

To further elucidate the adsorption mechanism, and to confirm the nature of the bonds, we also computed the electron localization function (ELF) for each system, shown in Fig. 6. From the image it is clear that the interaction between cortisol and pristine MoS 2 is purely given by dispersion forces, as the ELF ≈ 0 in between the two fragments. On the other hand, it is also clear that all metal adatoms M are chemically bound to the O atom of the carbonyl group, as ELF = 0 in the M-O bond region. Moreover, the spatial localization of the ELF of Pt-MoS 2 /cortisol confirms the strong interaction between Pt and C-3.

Finally, we quantified the interaction strength by computing the adsorption energy of each system. To gain the maximum amount of information, we decomposed the total adsorption energy (E tot ads ) into its dispersion (E disp ads ) and electrostatic (E elec ads ) contributions. A summary of such quantities can be found in Table 3. As expected, when considering pristine MoS 2 we found E tot ads to be relatively low (-1.14 eV), and almost entirely depending on weak dispersion interactions (E disp ads = -1.27 eV). We also observed a repulsive electrostatic contribution (E elec ads = +0.13 eV) which weakens the overall adsorption energy. This confirms that, without any surface point defect, cortisol adsorbs on pristine MoS 2 via a We also found that such stronger adsorption energies are due to both dispersion forces and attractive electrostatic interactions, confirming the occurring of chemical bonding. This is particularly evident for Pt-MoS 2 , where E elec ads (-1.16 eV) accounts for more than half of the total adsorption energy. On the contrary, in the case of both Ni-MoS 2 and Pd-MoS 2 , the electrostatic contribution is smaller than that of the dispersion forces, although still significant. We assume that such attractive electrostatic contribution in the case of Pt-MoS 2 is due to its tendency to react with both the O and the C-3 atoms of the carbonyl group, whereas Pd and Ni only bind to O, with a negligible interaction with C-3. Clearly, these results all point towards a chemisorption mechanism.

Overall, we can conclude that cortisol interacts with bare MoS 2 mainly via weak dispersion forces. When the substrate is doped, such interaction is dramatically improved by the chemical bonding of the analyte's ring A with the metal adatoms, locking the molecule onto the MoS 2 surface.

Charge Transfer and Charge Redistribution.

We investigated the electrostatic charge transfer occurring between the substrates and cortisol upon its adsorption, and we did so by computing the net atomic charges with the DDEC6 method. Also, to spatially visualize the charge redistribution, we computed the electron density difference (EDD) map of each system. Our charge analysis showed that, overall, cortisol acts as a charge donating molecule, and we observed such behaviour with both undoped and doped MoS 2 . From a quantitative point of view, we found a net non-negligible charge transferred (∆Q) of 0.111 e with pristine MoS 2 . Interestingly, we observed that not all metal dopants brought a significant increase of such quantity: overall, Ni-MoS 2 led to ∆Q = 0.179 e, Pt-MoS 2 to ∆Q = 0.113 e, and Pd-MoS 2 to ∆Q = 0.132 e. These results show that Ni is the metal dopant which leads to a higher charge transferred from cortisol to the substrate, whereas with Pd the improvement is visible, although not significant. On the other hand, Pt does not seem to bring any improvement on ∆Q with respect to the pristine material. EDD maps can also aid to better visualize the charge redistribution upon the adsorption of cortisol. From Fig. 7 it is possible to observe that the charge redistribution with pristine MoS 2 is rather limited, and spatially localized mainly in the area in the proximity of the side chain of cortisol. Here, the tail seems to act as a charge donating unit. On the contrary, we note very little charge redistribution on the other side of the molecule, that is, ring A. The situation is dramatically different with M-doped MoS 2 : we observe a great charge redistribution in the region between the cortisol carbonyl group and the metal adatom, consistently with our previous results indicating the occurring of chemical bonding. EDD maps suggest that the metal adatoms generally act as charge donating units, whereas in the ring A of cortisol the charge appears to get mostly re-Table 2: Net atomic charges of the relevant atoms of Mdoped/cortisol systems, computed by means of the DDEC6 method. Q i and Q f are the atomic charges before and after the adsorption of cortisol, respectively. We note that to be consistent with the EDD maps, we performed the population analysis on single fragments in the geometry of the complex distributed. Interestingly, we note that with Pt-MoS 2 the charge recombination is somewhat more spatially delocalized, with some significant electron enrichment in the area between Pt and the C-3 atom of cortisol. Once again, this points to the increased reactivity of the metal adatom towards the carbon atom of the carbonyl group. We point out that a greater charge recombination does not necessary lead to an increased charge transfer between the substrate and the adsorbate, as ultimately what matters is only the net transferred amount. In particular, with large molecules like cortisol, it is highly probable for different parts of the analyte to act non-trivially as both charge donating and charge accepting units.

To further elucidate the flow of charge in the systems consisting of M-doped MoS 2 , we looked at the variation of the atomic charge in selected atoms upon cortisol adsorption; results are shown in Table 2. For instance, we observed that metal adatoms all lose some amount of charge: 0.007 e, 0.052 e, and 0.052 e for Ni, Pd, and Pt, respectively. Sulphur atoms bound to the metal adatoms also generally lose charge. On the other hand, the Mo atom to which the adatoms are bound show a gain in electrons: 0.016 e, 0.010 e, 0.021 e in Ni-MoS 2 , Pd-MoS 2 , and Pt-MoS 2 , respectively. Regarding the ring A of cortisol, we observed the atoms with the most significant charge variation being O, C-3, C-4, and C-5 (the reader is referred to Fig. 1 for the numbering scheme of C atoms). O and C-5 both lose charge, whereas C-3 and C-4 gain charge. Consistently with the increased reactivity of Pt towards the C-3 atom and the larger charge redistribution observed in the corresponding EDD map, we note a significant gain of charge in C-3 in the Pt-MoS 2 /cortisol system. Overall, results suggest that charge transfer and charge redistribution processes are non-trivial, given the complex interplay between charge donating and charge attracting units in the cortisol molecule. When cortisol is adsorbed on pristine MoS 2 , the charge gets transferred mainly through the molecule's tail, whereas with M-doped MoS 2 the charge transfer occurs in the proximity of the M-O bond. Nevertheless, cortisol as a whole always acts as the charge donating fragment.

Electronic Structure Properties.

Finally, we looked at the change in the electronic structure of MoS 2 substrates upon cortisol adsorption. Fig. 8 shows the DOS of each system, projected onto both MoS 2 (doped and undoped) and cortisol fragments. DOS plots offer yet another mean to investigate the analyte/substrate interaction. The PDOS in Fig. 8 further confirm the different reactivity of cortisol with pristine and M-doped MoS 2 : when the material is undoped no chemical interaction can be observed, as the DOS of MoS 2 does not change upon cortisol adsorption (the reader is referred to Fig. 4 for the DOS of the pristine materials without the adsorbed analyte). Moreover, the states found in the MoS 2 band gap region are due exclusively to the cortisol molecule, and therefore no variation in the band gap of MoS 2 occurs. This is corroborated by the bandstructure and the HOMO orbital plot of this system, which is localized exclusively on cortisol (see Fig. S1 in Supplementary Information).

On the other hand, from previous results showing chemical reactivity between cortisol and M-doped MoS 2 , we expect to observe some changes in the DOS of the substrate: indeed, when comparing the DOS of metal-decorated MoS 2 before (Fig. 4) and after the adsorption of cortisol (Fig. 8), we note the appearance of extra bands in the band gap region of the substrate. These broaden the original bands due to the metal elements. As expected, in such extra bands hybridization between the states of cortisol and those of the M-doped materials can be observed. Once again, this is corroborated by the bandstructures and the HOMO orbital plots of the M-doped systems (see Figs. S2-S4 in Supplementary Information). Interestingly, when cortisol chemically adsorbs to Pt-MoS 2 we also observe the removal of the band near the conduction states of the substrate, which was due to Pt doping.

Although overall no appreciable change in the band gap of the MoS 2 substrates can be observed, we note that the extra bands due to the adsorption of cortisol lead to a smaller effective HOMO-LUMO gap (E HOMO-LUMO ): we observe a variation of E HOMO-LUMO of 0.40 eV, 0.33 eV, 0.26 eV, and 0.14 eV for pristine, Ni-decorated, Pd-decorated, and Pt-decorated MoS 2 , respectively. Among the M-doped substrates, Ni-MoS 2 shows the largest change, whereas Pt-MoS 2 the smallest. This is due to a compensating effect between the removal of the near-conduction doping band and the broadening of the near-valence bands.

Sensing Mechanisms.

Here, we discuss the possible sensing mechanisms of cortisol, taking into account the results presented so far, summarized in Table 3. The design of the sensor would vary depending on the type of signal (see Fig. 9), which could be measured either by physical, chemical, or optical means.

One obvious sensing strategy would be the detection of the electrostatic charge transferred upon the adsorption of cortisol on the monolayer MoS 2 substrate. This can be achieved, for instance, with a field-effect transistor (FET): [START_REF] Sarkar | MoS 2 field-effect transistor for next-generation label-free biosensors[END_REF] the working mechanism first involves the adsorption of the analyte onto the sensing material (i.e., the channel in a FET); this causes the transfer of a certain amount of charge to the latter. In turn, this will lead to a variation of the surface electrostatic potential of MoS 2 , and to a change in the measured device current. Essentially, cortisol would modulate the threshold gate voltage (V th ) of the device, thus enabling the detection of an electrical signal. For this type of device, results suggest Ni to be the best metal dopant (among those tested in the present work) as it significantly enhances the cortisol-to-MoS 2 charge transfer, and in turn the sensitivity of the device.

Another possible sensing mechanism which involves the transfer of charge could be enabled by the catalytic reduction of the carbonyl group of cortisol in C-3. In this situation, the redox reaction would cause a variation of the electric current passing through the device, which can be detected and measured. A similar sensing mechanism has been proposed for the non-enzymatic detection of glucose, achieved via its catalytic oxidation using NiO-decorated MoS 2 . [START_REF] Jeevanandham | Nickel oxide decorated MoS 2 nanosheet-based non-enzymatic sensor for the selective detection of glucose[END_REF] In our study, for such purpose Pt might be a suitable doping material, given its strong reactivity towards the carbonyl group of cortisol: as previously discussed, we found this metal element to donate a significant amount of charge to C-3, which leads to the strongest weakening of the C=O double bond. In addition to single-atom doping, decorating MoS 2 surface with Pt nanoparticles may be a viable alternative that could be explored. Finally, our results also suggest that optical methods could offer yet another alternative route for cortisol biosensing. Results showed that the adsorption of cortisol on MoS 2 substrate causes a number of near-valence extra states inside the MoS 2 band gap. These are purely due to cortisol for the pristine substrate, whereas for the M-doped substrates such states have hybrid character. The appearance of these states causes a decrease of the effective HOMO-LUMO gap of the MoS 2 /cortisol systems, which could be detected via optical means. On the one hand, with pristine MoS 2 we expect to observe a series of charge-transfer excitations from cortisol to the substrate, as suggested by the PDOS plot in Fig. 8. Such excitations would lead to a small add-on shoulder to the MoS 2 optical spectrum, which can be detected, for instance, with photoluminescence. On the other hand, the optical spectra of M-doped MoS 2 would already present small extra shoulders due to doping, and therefore in this case the sensing can be achieved by measuring the shift of these shoulders upon the adsorption of the analyte. Ni, Pd, and Pt all causes a decrease in the effective HOMO-LUMO gap of the sytems, which would reflect in the red shift of the shoulders. Once again, Ni seems to perform better than the other metal dopants here considered, as it leads to the highest decrease of the effective gap, ∆E HOMO-LUMO = 0.33 eV, thus leading to the strongest red shift.

As a final note, we observed that all the metal dopants cause an increase in the adsorption energy of cortisol, which in principle would be detrimental for the reusability of the biosensor. Nevertheless, we point out that a stronger interaction would also probably correlate with a higher device sensitivity, and therefore this is a trade-off that has to be carefully taken into consideration. In order to restore the device, a possible strategy could be to remove the analyte, for instance, thermally.

Conclusions

In summary, we used density functional theory simulations to explore the interaction between cortisol and MoS 2 , both in its pristine state and metal-decorated with Ni, Pd, and Pt. Our aim was to assess the possibility of using commonly experimentally employed metal adatoms as a mean to modulate such interaction towards the non-enzymatic detection of cortisol.

Chemical Reactivity of Cortisol and Electronic Properties of MoS 2

We first focused on the substrate (MoS 2 ) and the analyte (cortisol) separately. Based on the electron density difference maps, we found that cortisol has two main reactive centers, its ring A and the tail attached to the ring D (see Figure 1). Moreover, we also found that the bond length of the carbonyl group in C-3 is slightly longer than that found in the side chain, suggesting that to be a possible reactive site. We note that also previous reports of cortisol sensing studies in the literature focused on the C=O group in C-3, and therefore, given our results and those found in the literature, we chose this carbonyl group as the reactive site of interest. We then explored the structural and electronic properties of M-doped MoS

Adsorption of Cortisol on MoS 2

We placed cortisol above both pristine and M-doped MoS 2 substrate, and we thoroughly studied the material response upon the analyte adsorption. Our results showed a weaker physisorption mechanism with pristine MoS 2 , whereas a stronger chemisorption mechanism was found with the Mdoped materials. We observed a significant increase of the adsorption energy with all metal adatoms, with nonnegligible attractive electrostatic and dispersion forces. Furthermore, ELF, DOS, and EDD plots all suggested the formation of chemical bonds between the O atom of cortisol carbonyl group and the metal adatom. Interestingly, Pt showed enhanced reactivity also towards the C-3 atom of the carbonyl group, which led to a significant weakening of the C=O double bond, thus possibly activating such functional group for its catalytic reduction. In terms of charge transfer properties, we found that cortisol always acts as the electron donating unit towards the substrate, both pristine and M-doped, at least with the metal elements tested in this study. Ni-MoS 2 was the substrate which showed the largest amount of charge transferred, whereas with Pt-MoS 2 the charge transferred was comparable to that of undoped MoS 2 , despite a large electron density redistribution in proximity of the Pt-O bond. These results suggest that the mechanism of charge transfer between cortisol and the substrate is not trivial, as the molecule is rather complex and relatively large, and therefore different parts of cortisol were found to react differently towards MoS 2 . Furthermore, here we note that theoretical modelling is crucial, as it would be rather challenging to know a priori whether a metal element would enhance or not the cortisol-to-MoS 2 charge transfer, and if so, the magnitude of such quantity. Finally, we looked at the change in the electronic properties of MoS 2 by computing the DOS plots, and we observed the appearance of extra states within the band gap region of the substrates: these are due only to cortisol with the pristine substrate, whereas the extra states showed hybrid character with the M-doped materials.

Chemical Sensing of Cortisol

Overall, our results suggested two main possible sensing mechanisms and device architectures that could be used for the non-enzymatic detection of cortisol: i) a field-effect transistor (FET) and ii) an electrochemical sensor. In the first proposed device, the change in the electrostatic surface charge of the MoS 2 channel can be detected and correlated to the adsorption of cortisol. For such device we propose Ni as the doping material, as it significantly enhances the charge transfer with respect to pristine MoS 2 . In the second proposed device, the signal would derive from the catalytic reduction of cortisol upon its adsorption. In this case, MoS 2 decorated with Pt nanoparticles could be used as the working electrode, as our results might suggest. In addition, we found evidence suggesting that an optical sensor might also work, and the optical spectra could be measured, for instance, with photoluminescence. The adsorption of cortisol would produce either an extra low-intensity peak or a red shift of the peaks, depending on theabsence or presence of dopants in MoS 2 .

Outlook

Clearly, we point out that in real devices external effects may also play a role, thus further complicating the analyte/substrate interaction: few examples could be the increase/decrease of temperature, the variation of the pH, and the presence of other analytes in the sample. Nevertheless, this study provides important insights into the mechanism of cortisol adsorption on monolayer MoS 2 , both pristine and metal-doped, together with possible design strategies of the sensing device. Future work could involve the investigation of more complex sensing platforms, such as functionalized MoS 2 and supported metal nanoparticles. Thus, we expect our results to be the starting point for further investigations on the non-enzymatic detection of cortisol with 2D nanomaterial-based devices.

Figure 1 :

 1 Figure 1: Chemical structure of cortisol (left), together with the carbon numbering and ring labels (right) that will be used throughout this work.

Figure 2 :

 2 Figure 2: (a) Frontier orbitals of cortisol, isovalue 0.02 eV/Å 3 . (b) EDD plots of cortisol, where magenta corresponds to electron depletion, whereas green to electron enrichment; isovalue 0.001 eV/Å 3 . The numbers shown in the figure represent the total charge of the molecule: for instance, +0.1 e means that 0.1 electrons have been removed from the molecule.

Figure 3 :

 3 Figure 3: Chemical structures of metal-decorated MoS 2 , zoomed in the proximity of the metal adsorption site. The figures represent, from top to bottom, Ni-MoS 2 , Pd-MoS 2 , and Pt-MoS 2 . Relevant structural parameters, such as M-Mo and M-S distances, are shown.

Figure 4 :

 4 Figure 4: Projected density of states (PDOS) of pristine and M-doped MoS 2 , centered around the Fermi level of each system. The projections are onto the relevant atomic orbitals of S, Mo, and M (M = Ni, Pd, Pt). Insets were added for clarity, and they show the zoomed area around the Fermi level, where the effect of metal doping becomes evident. The gaussian smearing is 0.05 eV.

Figure 5 :

 5 Figure 5: Optimized geometries (PBE-D2) of the MoS 2 /cortisol systems considered in this paper, zoomed in the vicinity of the adsorption site (top and side views).

Figure 6 :

 6 Figure 6: Electron localization function (ELF) of cortisol adsorbed on pristine and M-doped MoS 2 , projected on a cut plane intersecting the carbonyl group of cortisol and the metal adatoms (Mo atom in the case of pristine MoS 2 ). Colour blue corresponds to ELF = 0, whereas colour red to ELF = 1.

Figure 7 :

 7 Figure7: EDD maps of MoS 2 substrates upon adsorption of cortisol, zoomed in the proximity of the adsorption site. Magenta colour corresponds to electron depletion, whereas green colour to electron enrichment; isovalue 0.002 eV/Å 3 . The amount of net charge transferred from cortisol to the substrate, computed with the DDEC6 method, is also shown.

Figure 8 :

 8 Figure 8: Projected density of states (PDOS) of cortisol adsorbed on pristine and M-doped MoS 2 , centered around the Fermi level of each system. The projections are onto the MoS 2 and cortisol fragments. Insets were added for clarity, and they show the zoomed area around the Fermi level, where the effect of cortisol bound to the metal adatoms becomes evident. The gaussian smearing is 0.05 eV.

Table 3 :

 3 Summary of the electronic and charge transfer properties of cortisol adsorbed on pristine and M-doped MoS 2 . E tot ads is the total adsorption energy, decomposed into its dispersion (E disp ads ) and electrostatic (E elec ads ) contributions. ∆Q is the net charge transferred upon cortisol adsorption, and E HOMO-LUMO is the effective HOMO-LUMO gap, which simply represents the energy difference of the extra bands given by doping and/or the adsorption of cortisol

	Substrate/analyte	E tot ads (eV)	E disp ads (eV)	E elec ads (eV)	∆Q (|e|)	EHOMO-LUMO (eV)
	MoS 2 /cortisol	-1.14	-1.27	+0.13	0.111	1.37
	Ni-MoS 2 /cortisol	-2.21	-1.33	-0.88	0.179	1.24
	Pd-MoS 2 /cortisol	-1.72	-0.99	-0.73	0.132	1.39
	Pt-MoS 2 /cortisol	-2.15	-0.99	-1.16	0.113	1.40

  Schematics of FET, electrochemical, and optical sensors based on monolayer MoS 2 . In the FET sensor, MoS 2 acts as the channel, whereas in the electrochemical sensor as the working electrode (WE). CE represents the counter electrode, and RE the reference electrode.

		FET sensor			Electrochemical sensor
	Gate 1	Source	MoS2	Drain	Gate 2	CE	MoS2	RE
			SiO2				SiO2
			Si				Si
					hν	Optical sensor
						MoS2
					Substrate
	Figure 9:

Table 1 .

 1 [START_REF] Mcewen | Protective and damaging effects of stress mediators[END_REF] , and we found that all metal adatoms act as electron donating units to the substrate. Ni is the metal element with the strongest reactivity towards MoS 2 , followed by Pt, and then Pd. This finding is based on the amount of charge transferred (+0.645 e of Ni with respect to +0.367 e and +0.375 of Pd and Pt, respectively), and the adsorption energies (-4.10 eV with Ni against -2.66 eV and -3.30 eV with Pd and Pt, respectively). Moreover, from the structural point of view, Ni was found to have the shortest bond lengths with both S and Mo atoms. All the relevant structural, electronic, and charge transfer parameters of pristine and M-doped MoS 2 are summarized in

Acknowledgements

The authors would like to thank Stefania Carapezzi for providing feedback and for many helpful discussions. The authors ackowledge funding from the European Union's Horizon 2020 research and innovation programme, EU H2020 SmartVista project (www.smartvista.eu), grant agreement No. 825114. All the simulations were carried out on the Occigen Supercomputer hosted at C.I.N.E.S. (Centre Informatique National de l'Enseignement Supérieur), based in Montpellier (France).

Conflicts of interest

There are no conflicts to declare.


D Calvo

R Real

A Amaro

V Van Beveren

T Chiarusi

S Mastroianni

P Musico

G Pellegini

P Jansweijer

S Colonges

C Bozza

C Nicolau

A Díaz

A Ilioni

R Le Breton

C Champion

P Keller

C Boutonnet

The gateware Calibration Unit for the KM3NeT Telescope

Keywords: Neutrino telescope, Calibration, Instrumentation

A

: The KM3NeT Collaboration is currently deploying the first Detection Units of a neutrino observatory in the Mediterranean Sea, which, once completed, will be equipped with thousands of so-called Digital Optical Modules. In addition to the Detection Units KM3NeT has designed an independent Calibration Unit, housing a set of calibration instruments, including e.g. an acoustic beacon and a laser beacon. The Calibration Unit and the embedded software developed to operate it are presented here.

The KM3NeT collaboration [START_REF] S Adrián-Martínez | Letter of intent for KM3NeT 2.0[END_REF] is constructing a neutrino telescope distributed throughout the Mediterranean Sea with two main objectives: the detection of cosmic neutrinos and the determination of the neutrino mass hierarchy. This detector will consist of blocks, called Building Blocks (BBs), of 115 lines called Detection Units (DUs). Each DU will be made up of 18 optical modules, called Digital optical Modules (DOMs) [START_REF] Cirella | Kooijman for the KM3NeT Collaboration The Digital Optical Module (DOM) for the KM3NeT detector[END_REF]. The DOMs of the DUs are kept vertical and aligned by a system of buoys. The functionalities of the DOMs are controlled by specific hardware, the so-called Central Logic Board (CLB) [START_REF] Real | Beveren for the KM3NeT Collaboration, KM3NeT front-end and readout electronics system: hardware, firmware, and software[END_REF]. The KM3NeT telescope will be installed in two sites: the Italian site, located about 100 km from Capo Passero, called Astroparticle Research with Cosmics Abyss (ARCA) which will be mainly dedicated to the detection of cosmic neutrinos, and the French site, located about 40 km from Toulon, called Oscillation Research with Cosmics Abyss (ORCA), which main objective is to study the neutrino oscillations and to determine the neutrino mass hierarchy.

The performance of KM3NeT relies on making precise measurements of the energy and time arrival of the events, for which it is necessary to achieve good temporal accuracy. In this regard, it is important to take into account the effect produced by the optical properties of water, as well as the sea currents. These parameters can be monitored by devices installed within the DOMs and in the Bases of special DUs, the so-called Calibration Units (CUs) which will be distributed throughout the telescope. The CU is powered by the DU through an interlink cable of 50 m and is composed of the so-called Calibration Base (CB) and the so-called Instrumentation Unit (IU). Figure 1 shows an overview of some DUs of the ORCA telescope with the CU and the interconnections between CU and the Base of the DU.

Calibration Base

The CB is a DU Base module equipped with the following devices: • A Laser Beacon used for time calibration and to measure optical properties of the sea water.

The Laser emits at 532 nm and is able to emit trains of pulses of high power with a maximum frequency of 4 kHz.

• An acoustic emitter to determine the DOMs positions in the sea water.

• A hydrophone which provides the position of the CB in the seafloor Moreover the CB also contains the same electronic and optical devices included in a DU Base: two Erbium Doped Fiber Amplifiers (EDFAs) and a CLB to control all the devices.

Instrumentation Unit

The IU is composed of two subsystems: the Instrumentation Base (IB) and the Instrumentation Line (IL). The IB is a Titanium container with an Inductive Modem inside. The power is provided by the CB but IU also includes a power system based on internal batteries. The IL is composed of several instrumentation devices placed at different depths depending whether it is ORCA or ARCA.

The IL is composed of:

• A CDT (Conductivity, Temperature, Depth ) probe intended to measure water properties such as salinity and temperature which influence the sound velocity in the sea water.

• A sound velocimeter to measure the time of flight of the acoustic signals.

• An Acoustic Doppler Current Profiler (ADCP) hydro-acoustic instrument used to measure the speed and current flow of water over a specified depth range.

The CLB is the main electronic element of KM3NeT. It is a multi-layer electronic board which controls the operation of the DOM, including the acquisition, synchronization, instrumentation, communication interfaces and devices of the CU. The CLB is also used in the Bases of both the DU and CU. The control of all the components of the electronic board has been implemented on a Field-Programmable Gate Array (FPGA) Kintex-7 from Xilinx Inc company. The FPGA is in charge of carrying out the acquisition and digitization of the optical and acoustic events, which are digitized with a timestamp provided by the White Rabbit (WR) [START_REF] Lipiński | White Rabbit: a PTP application for robust sub-nanosecond synchronization[END_REF] synchronization protocol, a protocol that allows all KM3NeT nodes to be synchronized with a precision of 1 ns. The FPGA has two embedded microprocessors developed by the Lattice Semiconductor Corporation company, to control the synchronization protocol and to manage the rest of the functions: acquisition, instrumentation, connections, communication and the control of the CU and DU devices.

Firmware

The CLB firmware is based on Lattice Mico LM32 embedded microprocessors, an open source firmware microprocessor from Lattice. One of them is entirely dedicated to the WR protocol, while the other one runs the embedded software to control the acquisition, instrumentation, and Bases devices [START_REF] Calvo | Real for the KM3NeT Collaboration, Architecture and performance of the KM3NeT front-end firmware[END_REF]. All the sensors and instrumentation devices placed on the CLB are controlled by the FPGA through four Inter-Integrated Circuit (I2C) communication buses. For the instruments of the DU and CU the serial Recommended Standard 232 (RS-232) protocol is used. Seven serial interfaces are needed to control the CU. All the CU devices are connected to an expansion FPGA Mezzanine Card (FMC) board plugged on the CLB.

Software

The control of the DOM is achieved through robust embedded software running in the Lattice Mico LM32 microprocessor. No operating system is used in order to reduce power consumption.

The software has been structured in three layers, named Common, Platform and Application. The Common layer contains the common functions, macros and standard libraries used throughout the software. The Platform layer includes the start-up code and drivers to control the connected hardware, the network protocol and the system services. Finally the Application layer includes the high level functionalities to monitor and configure the hardware. It contains the specific code for detectors, peripherals and slow control. The implementation for all the drivers within both CB and IU, as well as its slow control are coded in the Application layer. Figure 2 shows the layers and structure of the embedded software for the CU. The embedded software is able to execute and manage remote communication and commands from the on-shore station. A Java Graphical User Interface has been developed for this purpose.

Conclusions

Several CUs will be placed in the KM3NeT neutrino telescope. The purpose of these special units is to measure the physical properties of the surroundings of the detector. All the CU functionalities are controlled by a CLB inside the CB. The drivers for CU, CB and IU, have been implemented in the embedded software running in the LM32. A Java Graphical User Interface has also been developed to manage the CU functionalities remotely from the on-shore station.

Figure 1 .

 1 Figure 1. Overview of some DUs and a CU. CU is powered by an interlink cable connected to the DU.The CB and IU subsystems are shown.

Figure 2 .

 2 Figure 2. Representation of the layers and structure of the CU embedded software implemented in the LM32 microprocessor.

Acknowledgments

Plan Estatal de Investigación (refs. FPA2015-65150-C3-1-P, -2-P and -3-P, (MINECO/FEDER)), Severo Ochoa Centre of Excellence program (MINECO), Red Consolider MultiDark, (ref. FPA2017-90566-REDC, MINECO) and Prometeo and Grisolía programs (Generalitat Valenciana), "la Caixa" Foundation (ID 100010434) through the fellowship LCF/BQ/IN17/11620019, and the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement no. 713673, Spain.


Emilien Delmont
email: emilien.delmont@ap-hm.fr

Shahram Attarian

Jean-Christophe Antoine

Stephane Paul

Jean Philippe Camdessanché

Aude-Marie Grapperon

Alexandre Brodovich

Jose Boucraut

Delmont Emilien

Relevance of Anti-HNK1 antibodies in the management of anti-MAG neuropathies

Keywords: anti-MAG antibodies, anti-HNK1 antibodies, peripheral neuropathy, biomarker

Intoduction: In peripheral neuropathies with antibodies against Myelin Associated Glycoprotein (MAG), an IgM monoclonal gammopathy recognizes a specific epitope called Human Natural Killer 1 (HNK1) shared by NK lymphocytes and several components of the peripheral nerve myelin. Recently an ELISA test has been developed to detect antibodies against HNK1 epitope. Objectives were to determine the usefulness of this assay in the management of anti-MAG neuropathy.

Methods: Anti-HNK1 antibodies were assessed with the GanglioCombi™ MAG ELISA test (Buhlmann) in 41 anti-MAG neuropathies and in 118 controls: 34 chronic inflammatory demyelinating polyradiculoneuropathies, 3 Miller Fisher syndromes, 12 sensory neuronopathies, 63 length-dependant axonal sensory polyneuropathies, 6 healthy controls. Anti-HNK1 antibody were tested before and 1 year after rituximab therapy in 7 patients with anti-MAG neuropathy.

Results: Anti-HNK1 antibodies were positive in 40/41 anti-MAG neuropathies, and in 1/118 controls (sensitivity 98%, specificity 99%). Only considering controls with IgM paraprotein, specificity was 96% (23/24). In anti-MAG neuropathies, anti-HNK1 titre was correlated with sensory deficiency evaluated with the INCAT sensory sum score (r=0.4, p=0.01) and with disability evaluated with the Rasch-built Overall Disability Scale (r= -0.4, p=0.01) and Overall Neuropathy Limitation Scale (r=0.4, p=0.02). Anti-HNK1 titres were not related to age, disease duration, atypical clinical features and anti-MAG antibodies titres. Anti-MAG titres were not associated with disease severity.

Anti-HNK1 titres were decreased by 18% 1 year after rituximab treatment.

Conclusions: Anti-HNK1 antibodies have good sensitivity and specificity for the diagnosis of anti-MAG neuropathy. Interestingly, anti-HNK1titres are related to the disease severity and decrease after rituximab infusions.

Introduction:

Peripheral neuropathies with antibodies against Myelin Associated Glycoprotein (anti-MAG neuropathies) are chronic sensory neuropathies characterized by the presence of an IgM monoclonal gammopathy and high titres of anti-MAG antibodies [START_REF]Joint Task Force of the EFNS and the PNS (2010) European Federation of Neurological Societies/Peripheral Nerve Society Guideline on management of paraproteinemic demyelinating neuropathies[END_REF]. Typical clinical features are foot paraesthesia, sensory gait ataxia and postural tremor.

Muscle weakness is rare and when existent, it involves mainly the distal part of the legs [START_REF] Svahn | Anti-MAG antibodies in 202 patients: clinicopathological and therapeutic features[END_REF]. Up to 24% of the patients may have atypical clinical features as proximal weakness, upper limbs involvement and subacute progression [START_REF] Svahn | Anti-MAG antibodies in 202 patients: clinicopathological and therapeutic features[END_REF][START_REF] Gazzola | Predictive factors of efficacy of rituximab in patients with anti-MAG neuropathy[END_REF][START_REF] Magy | Heterogeneity of Polyneuropathy Associated with Anti-MAG Antibodies[END_REF].

The range of disability is wide, but most of the patients can walk independently [START_REF] Nobile-Orazio | Long-term prognosis of neuropathy associated with anti-MAG IgM M-proteins and its relationship to immune therapies[END_REF][START_REF] Delmont | Determinants of health-related quality of life in anti-MAG neuropathy: a cross-sectional multicentre European study[END_REF]. Nerve conduction studies usually show distal demyelination [START_REF] Attarian | terminal latency index and modified F ratio in distinction of chronic demyelinating neuropathies[END_REF]. Nerve biopsy, when performed, reveals IgM deposits and widening of the peripheral myelin sheathes. There is no definitely recognized treatment but Rituximab (RTX) is often used for disabled patients [START_REF] Lunn | Immunotherapy for IgM anti-myelin-associated glycoprotein paraproteinassociated peripheral neuropathies[END_REF][START_REF] Gazzola | Predictive factors of efficacy of rituximab in patients with anti-MAG neuropathy[END_REF].

The diagnosis of anti-MAG neuropathy relies on the detection of anti-MAG antibodies in the patients 'serum.

Western blot technique using bovine or human MAG preparation was historically first used for antibody detection but it was less convenient and less sensitive than ELISA (enzyme-linked immunosorbent assay) kits [START_REF] Kuijf | Detection of anti-MAG antibodies in polyneuropathy associated with IgM monoclonal gammopathy[END_REF]. The main issue with the ELISA technique is a loss of specificity with low titres of anti-MAG antibodies and the absence of correlation between anti-MAG titres and disease severity [START_REF] Svahn | Anti-MAG antibodies in 202 patients: clinicopathological and therapeutic features[END_REF][START_REF] Caudie | Diagnostic value of autoantibodies to MAG by ELISA Bühlmann in 117 immune-mediated peripheral neuropathies associated with monoclonal IgM to SGPG/SGLPG[END_REF].

The antigenic region of MAG is a specific carbohydrate epitope called Human Natural Killer 1 (HNK1), which comprises three sugar residues with sulphated modifications (sulfate-3-glucuronyl paragloboside) [START_REF] Hamada | Binding specificity of anti-HNK-1 IgM M-protein in anti-MAG neuropathy: Possible clinical relevance[END_REF][START_REF] Mcgarry | Recognition of myelin-associated glycoprotein by the monoclonal antibody HNK-1[END_REF]. This epitope is borne by natural killer (NK) lymphocytes and shared with several glycoproteins and glycolipids of the peripheral nerve myelin sheath (MAG, P0, PMP22, SGPG, SGLPG, phosphocan) [START_REF] Van Den Berg | Characterization of HNK1 bearing glycoproteins in human peripheral nerve myelin[END_REF][START_REF] Morise | The role of human natural killer-1 (HNK-1) carbohydrate in neuronal plasticity and disease[END_REF]. The injection of a glycopolymer mimicking the natural HNK1 epitope led to the removal of the pathological antibodies in a mouse model of anti-MAG neuropathy [START_REF] Herrendorff | Selective in vivo removal of pathogenic anti-MAG autoantibodies, an antigen-specific treatment option for anti-MAG neuropathy[END_REF].

In the classic ELISA assay the entire MAG protein is coated in the wells of the plates. A new assay has been developed using a synthetic HNK1 carbohydrate moiety. This test detects antibodies only directed against the HNK1 epitope of the MAG protein. The diagnostic accuracy of this test has not been evaluated in a large cohort yet. Our objective is, thus, to determine sensitivity and specificity of anti-HNK1 antibodies in the diagnosis of anti-MAG neuropathy and to know if their titres are correlated with disease severity. Patients with anti-MAG neuropathy fulfilled the EFNS/PNS diagnostic criteria [START_REF]Joint Task Force of the EFNS and the PNS (2010) European Federation of Neurological Societies/Peripheral Nerve Society Guideline on management of paraproteinemic demyelinating neuropathies[END_REF]. They all have IgM monoclonal gammopathy and positive anti-MAG antibodies. The following data were collected: age, gender, duration of the disease, presence of IgM MGUS (monoclonal gammopathy of undetermined significance) or lymphoproliferative disease, 80-point Medical Research Council (MRC) sum score [START_REF] Delmont | Determinants of health-related quality of life in anti-MAG neuropathy: a cross-sectional multicentre European study[END_REF], Jamar grip dynamometry, 9 holes peg test, 10-meter timed walk, Inflammatory Neuropathy Cause and Treatment (INCAT) Sensory Sum Score (ISS) [START_REF] Merkies | Clinimetric evaluation of a new overall disability scale in immune mediated polyneuropathies[END_REF],

Methods

Overall Neuropathy Limitation Score (ONLS) [START_REF] Graham | A modified peripheral neuropathy scale: the Overall Neuropathy Limitations Scale[END_REF], Rasch-built Overall Disability Score (RODS) [START_REF] Van Nes | Rasch-built Overall Disability Scale (R-ODS) for immune-mediated peripheral neuropathies[END_REF], ataxia score [START_REF] Léger | Placebo-controlled trial of rituximab in IgM anti-myelinassociated glycoprotein neuropathy[END_REF], anti-MAG titres, dosage of the IgM monoclonal peak. Nerve conduction studies were performed on the median, ulnar, tibial, peroneal and sural nerves. Distal demyelination was considered as predominant if more than 2 nerves had a terminal latency index (TLI) above 0.25 [START_REF] Attarian | terminal latency index and modified F ratio in distinction of chronic demyelinating neuropathies[END_REF].

Seven patients with anti-MAG neuropathy received 2 infusions of 1 g of rituximab (RTX) with a 15 days interval. Improvement was defined by a decrease of at least one point of the ONLS disability scale [START_REF] Gazzola | Predictive factors of efficacy of rituximab in patients with anti-MAG neuropathy[END_REF]. Anti-MAG and anti-HNK1 antibody titres were determined before treatment, and 6 months (M6) and 12 months (M12) after RTX therapy.

One hundred and eighteen controls were included in this study: 34 chronic inflammatory demyelinating polyradiculoneuropathies (CIDP), 3 Miller Fisher syndromes, 12 sensory neuronopathies, 63 length-dependant axonal sensory polyneuropathies and 6 healthy controls. Among CIDP patients, 1 patients had antibodies against nodal isoform of neurofascin [START_REF] Delmont | Autoantibodies to nodal isoforms of neurofascin in chronic inflammatory demyelinating polyneuropathy[END_REF], 5 patients had IgM isotype antibodies against GD1b ganglioside, 1 patient against GM1 ganglioside, 1 patient against GD1a ganglioside and 3 patients had an IgM monoclonal gammopathy and antibodies against disialylated gangliosides responding to the diagnosis of CANOMAD (chronic ataxic neuropathy, ophthalmoplegia, IgM paraprotein, cold agglutinins and disialosyl antibodies) [START_REF] Willison | The clinical and laboratory features of chronic sensory ataxic neuropathy with anti-disialosyl IgM antibodies[END_REF]. The patients with Miller Fisher syndrome had IgG isotype antibodies against GQ1b antibodies. Aetiologies of sensory neuronopathies were Sjogren syndrome (3), paraneoplatic (3), metabolic (1) and idiopathic [START_REF] Nobile-Orazio | Long-term prognosis of neuropathy associated with anti-MAG IgM M-proteins and its relationship to immune therapies[END_REF]. Healthy controls were blood donors. Among the controls, 24 patients had an IgM monoclonal gammopathy (4 lymphoma and 20 MGUS) without anti-MAG antibodies: 12 CIDP, 3 CANOMAD, 8 length-dependant axonal sensory polyneuropathies and 1 sensory neuronopathy.

Anti-HNK1 antibodies were measured with the GanglioCombi™ MAG ELISA test (Buhlmann) according to the manufacturer instructions. In brief, 100 microlitres of patient's serum diluted at 1/50 were incubated at 4°C during 2 hours in wells coated with synthetic HNK1 carbohydrate. After washing, peroxidase labelled anti-human IgM antibody was applied for 2 hours at 4°C. Detection was performed using tetramethylbenzidine. Optical density was measured at 450nm with a plate reader (Infinite F200, Tecan). The antibody titres were expressed as the percentage ratio of the absorbance of samples and the absorbance of the calibrator.

Anti-MAG antibodies were assessed with the Buhlmann ELISA test (Buhlmann Company). Anti-MAG antibodies were considered positive if the titre was above 4000 Buhlmann titre units (BTU). When the result of anti-MAG test was >70,000 BTU, end point dilution was performed to obtain the final antibody titre.

Quantitative data were expressed as mean with standard deviation and were compared using a Student's T-test.

Linear regression, Spearman correlation coefficient, and Receiver Operator Characteristic (ROC) analysis were performed using GraphPad Prism 5 (GraphpadInc, California, USA) and IBM SPSS statistics (version 20). A twosided p value <0.05 was considered as significant.

Results

Forty-one patients with anti-MAG neuropathies were included (14 females and 27 males). Data are summarized in the table. Thirty-five patients had a typical clinical phenotype and 6 patients had an atypical clinical phenotype: 2 patients with proximal muscle weakness in the lower limbs (MRC 4/5), 3 patients with distal muscle weakness of both upper and lower limbs, 1 patient with subacute onset. Nerve conduction studies results were available for 36 patients. One patients had an axonal neuropathy and 35 had a demyelinating neuropathy. Demyelination was predominant in the distal parts of the nerves in 25 patients. Seventeen patients received a chemotherapy prior to anti-HNK1 dosage (rituximab alone for 13 patients). All the patients had an IgM monoclonal gammopathy, 8 with lambda light chain and 33 with kappa light chain. Twenty-nine patients had an MGUS and 12 a non-Hodgkin lymphoma or a Waldenstrom's macroglobulinemia. Mean anti-MAG titre was 132,000 BTU (184,000) and median 66,000 BTU, ranging from 4,000 to 900,000 BTU.

Mean anti-HNK1 antibody titre was 105 % (34) in anti-MAG neuropathies and 13 % (13) in controls (p<0.0001).

According to the ROC analysis, a threshold of 50 % gave the best balance of sensitivity and specificity (figure 1) for the diagnosis of anti-MAG neuropathy. Using a threshold of 50 %, anti-HNK1 antibodies assay had a 98% sensitivity (40/41) and a 99% specificity (117/118), with only one false negative and one false positive results. Only considering the controls with an IgM monoclonal gammopathy and a neuropathy, the specificity was 96% (23/24) The inappropriate negative result with the anti-HNK1 antibody test concerned an 82 years-old man with a 14 years history of sensory ataxia and mild distal motor weakness of the 4 limbs. Initial explorations revealed an IgM kappa MGUS, a positive Western blot against human MAG and a distal demyelinating sensory and motor neuropathy on nerve conduction studies. The patient never received any chemotherapy nor intravenous immunoglobulins. Nowadays, the patient has a severe sensory and motor neuropathy with distal muscle atrophy of the 4 limbs. Nerve conduction study shows a sensory and motor axonal loss. Current analysis display positive anti-MAG antibodies (titre 119,000BTU). Anti-HNK1 antibodies are negative (titre 37%) on the first analysed sample and slightly positive (titre 54%) on a control sample (positive if > 50%). The monoclonal IgM dosage is 1.7g/l without evidence of haematological malignancy. This patient has an uncommon anti-MAG neuropathy because of the early motor involvement and the severity of the axonal loss.

The inappropriate positive result with the anti-HNK1 antibody test corresponded to a 74 years-old woman suffering from CANO34MAD [START_REF] Willison | The clinical and laboratory features of chronic sensory ataxic neuropathy with anti-disialosyl IgM antibodies[END_REF]. Clinical examination showed sensory gait ataxia, Achilles tendon areflexia and foot hypoesthesia. Nerve conduction study displayed conduction blocks and reduced sensory and motor action potential amplitudes. Biological analysis revealed an IgM kappa MGUS and positive anti-ganglioside antibodies against both GD1b and GQ1b. Anti-HNK1 antibodies titre was 80% and anti-MAG antibodies were equivocal with a titre of 1,420 BTU [START_REF] Kuijf | Detection of anti-MAG antibodies in polyneuropathy associated with IgM monoclonal gammopathy[END_REF].

There was no correlation between the titres of anti-MAG and anti-HNK1 antibodies (table and figure 2). Anti-MAG antibody titre was only related to mean ulnar motor conduction velocity at the forehand (r=0.41, p=0.02).

There was no correlation between the anti-MAG titre and any of the clinical scores or other biological data (table).

The anti-MAG antibody titre was similar in patients with typical and atypical clinical features (152,000 vs 151,000 BTU, p = 1).

In patients with anti-MAG neuropathies (table and figure 2), the anti-HNK1 antibody titre was correlated with the sensory deficit evaluated with the ISS score (r = 0.43, p = 0.01) and with disability measured with the ONLS score (r = 0.36, p = 0.02) and the RODS score (r = -0.43, p=0.01). The anti-HNK1 antibody titre was not related to age, disease duration, presence of a MGUS or a lymphoma, prior administration or not of a chemotherapy, 9 holes peg test, 10-metres walk test, grip test, ataxia score, MRC testing, level of the IgM monoclonal peak and electrophysiological analysis. The anti-HNK1 antibody titre was similar in patients with typical and atypical clinical features (94% vs 100%, p = 0.69).

Seven patients with anti-MAG neuropathy received RTX (figure 3). Four patients improved at one year of follow-up. The Mean ONLS score was decreased 34 %, the mean anti-HNK1 titres decreased by 18% and anti-MAG titre remained relatively stable (increase of 3%) one year after RTX therapy.

Discussion

The objective of this study was to evaluate the sensitivity and specificity of anti-HNK1 antibodies in the diagnosis of anti-MAG neuropathy and to search if the anti-HNK1 titres were related to the severity of the neuropathy.

In the anti-MAG ELISA assay, the entire MAG protein is coated in the well of the ELISA plates, meanwhile only a synthetic HNK1 component is coated in the well of the anti-HNK1 ELISA plates. As the HNK1 epitope is shared by several structures of the peripheral nerves [START_REF] Morise | The role of human natural killer-1 (HNK-1) carbohydrate in neuronal plasticity and disease[END_REF], the major issue of anti-HNK1 antibody detection could have been a loss of specificity with sera containing antibodies against other myelin components as P0, PMP22 or SGPG [START_REF] Lim | Peripheral nerve proteins as potential autoantigens in acute and chronic inflammatory demyelinating polyneuropathies[END_REF][START_REF] Roggenbuck | Diagnostic insights into chronic-inflammatory demyelinating polyneuropathies[END_REF]. To evaluate the accuracy of this test, we included a large cohort of controls who can be misdiagnosed with anti-MAG neuropathy: sensory neuropathies or neuropathies associated with IgM monoclonal gammopathy or with antiganglioside antibodies. Controls without paraproteins were included because a recent study demonstrated that the prevalence of the anti-MAG antibody in chronic demyelinating neuropathy without any detectable M-protein was 5.6%, and concluded that anti-MAG antibody might be detectable earlier than the M-protein [START_REF] Sakamoto | Chronic demyelinating neuropathy with anti-myelinassociated glycoprotein antibody without any detectable M-protein[END_REF].

All but one control were negative for anti-HNK1 antibodies, which lead to an excellent specificity of 99% (117/118) considering all the controls and 96% (23/24) only considering the controls with a neuropathy and an IgM paraprotein. The inappropriate positive anti-HNK1 result was in a patient suffering from CANOMAD syndrome with an IgM monoclonal gammopathy, anti GD1b and GQ1b antibodies. The anti-MAG ELISA assay was also equivocal with this sample in this patient. It has been demonstrated that for titre below 10,000 BTU, the anti-MAG ELISA assay can similarly give false positive results, mainly due to a cross reaction with antibodies against GM1 and disialylated gangliosides [START_REF] Caudie | Diagnostic value of autoantibodies to MAG by ELISA Bühlmann in 117 immune-mediated peripheral neuropathies associated with monoclonal IgM to SGPG/SGLPG[END_REF]. The most specific test to detect anti-MAG antibody is a Western blot using human MAG, but this assay was less sensitive and less convenient as a routine test in a study which compared Western blot and ELISA techniques [START_REF] Kuijf | Detection of anti-MAG antibodies in polyneuropathy associated with IgM monoclonal gammopathy[END_REF]. Nowadays, the anti-MAG ELISA assay is more often used to detect anti-MAG antibodies. For example the diagnosis of anti-MAG neuropathy was based on this technique in the recent report of 202 anti-MAG neuropathies [START_REF] Svahn | Anti-MAG antibodies in 202 patients: clinicopathological and therapeutic features[END_REF] and in the last therapeutic trials with rituximab [START_REF] Léger | Placebo-controlled trial of rituximab in IgM anti-myelinassociated glycoprotein neuropathy[END_REF].

Anti-HNK1 ELISA assay had a good sensitivity of 98% (40/41). Only one patient with anti-MAG neuropathy was not positive with this technique. The assay was negative on a frozen sample and was slightly positive on a fresh sample, suggesting that conservation of the sera may be an issue in the detection of these antibodies. Another hypothesize is that this patient's anti-MAG antibody is directed against a peptide epitope of the MAG and not the HNK1 carbohydrate moiety. Actually, immunisation of animals with human MAG leads to generation of different anti-MAG antibodies which react either with the protein or the carbohydrate epitope of the MAG [START_REF] Dobersen | Generation and characterization of mouse monoclonal antibodies to the myelin-associated glycoprotein (MAG)[END_REF].

The structure of the HNK1 epitope depends on the carrier glycoprotein. It can be a N-glycan structure as on GluA2 (subunit of AMPA receptor), a O-mannose-linked glycan structure as on phosphacan or a specific structure as in aggrecan [START_REF] Morise | The role of human natural killer-1 (HNK-1) carbohydrate in neuronal plasticity and disease[END_REF]. Antibodies of anti-MAG neuropathy patients exhibit differential affinity against the different HNK1 epitopes as illustrated in one study which compare the affinity against phosphocan and MAG [START_REF] Hamada | Binding specificity of anti-HNK-1 IgM M-protein in anti-MAG neuropathy: Possible clinical relevance[END_REF]. This difference of immunogenicity may explain why the titres of anti-MAG and anti-HNK1 antibodies are not correlated in our study.

Anti-HNK1 titres are correlated with sensory deficiency and disability whereas anti-MAG antibody titres have never been associated with the severity of the disease neither in previous studies nor in this one [START_REF] Svahn | Anti-MAG antibodies in 202 patients: clinicopathological and therapeutic features[END_REF][START_REF] Delmont | Determinants of health-related quality of life in anti-MAG neuropathy: a cross-sectional multicentre European study[END_REF]. Only one study [START_REF] Hamada | Binding specificity of anti-HNK-1 IgM M-protein in anti-MAG neuropathy: Possible clinical relevance[END_REF] showed that the patients with anti-MAG antibodies more reactive to phosphocan than to MAG had a more severe disease. Titres of anti-HNK1 and anti-MAG antibodies were similar in patients with typical and atypical clinical features.

Anti-MAG neuropathies are usually treated with rituximab [START_REF] Lunn | Immunotherapy for IgM anti-myelin-associated glycoprotein paraproteinassociated peripheral neuropathies[END_REF], which decreases the titres of anti-MAG antibodies [START_REF] Gazzola | Predictive factors of efficacy of rituximab in patients with anti-MAG neuropathy[END_REF][START_REF] Léger | Placebo-controlled trial of rituximab in IgM anti-myelinassociated glycoprotein neuropathy[END_REF][START_REF] Dalakas | Placebo-controlled trial of rituximab in IgM antimyelin-associated glycoprotein antibody demyelinating neuropathy[END_REF][START_REF] Renaud | Rituximab in the treatment of polyneuropathy associated with anti-MAG antibodies[END_REF]. In this study, rituximab induced also a decrease of anti-HNK1 antibodies titres in 7 treated patients.

Relation between the rituximab therapy and the initial titre of anti-MAG antibodies is not obvious: efficacy had been associated with a high titre of anti-MAG antibodies in two studies [START_REF] Svahn | Anti-MAG antibodies in 202 patients: clinicopathological and therapeutic features[END_REF][START_REF] Dalakas | Placebo-controlled trial of rituximab in IgM antimyelin-associated glycoprotein antibody demyelinating neuropathy[END_REF], with low titres of anti-MAG antibodies in another study [START_REF] Benedetti | Predictors of response to rituximab in patients with neuropathy and anti-myelin associated glycoprotein immunoglobulin M[END_REF] and we did not find any correlation in a retrospective analysis performed in our department [START_REF] Gazzola | Predictive factors of efficacy of rituximab in patients with anti-MAG neuropathy[END_REF]. The present study was not designed to assess if the anti-HNK1 antibody titre was correlated with the efficacy of the rituximab therapy.

This study provides evidence that anti-HNK1 antibodies have high sensitivity and specificity in the diagnosis of anti-MAG neuropathy. We suggest that anti-HNK1 assays may be used to diagnose anti-MAG neuropathy instead of ELISA or Western blot using human MAG substrate. As anti-HNK1 antibody titres are correlated with disease severity, we hypothesize that they may be tested for the monitoring of patients in routine or as secondary outcomes measures in clinical trials. However, these results need to be confirmed in a larger prospective cohort.

  Patients were followed in the Referral Centres for Neuromuscular diseases of Marseille or Saint Etienne in France. All patients gave informed consent. Clinical assessment and blood samples were part of their routine evaluation. Biological samples were provided by the Marseille Conception hospital immunology Bio-bank (authorisation number DC-2012-1704).

Figure 1 :

 1 Figure 1:

Figure 2 :Figure 3

 23 Figure 2:

Table :

 : Characteristics of the 42 patients with anti-MAG neuropathy and correlation with anti-

	MAG and anti-HNK1 antibodies titres.
	NS, non-significant; ONLS, overall neuropathy limitations scale; RODS, rasch-built overall
	disability scale; ISS, INCAT sensory scale; r, Spearman's correlation coefficient; p, p-value,
	HNK1, human natural killer 1; MAG, myelin associated glycoprotein; TLI terminal latency
	index; CMAP sum score, addition of distal motor amplitude of the median, ulnar, tibial and
	fibular nerves; SNAP sum score, addition of distal sensory amplitude of the median, ulnar and
	sural nerves; ms, milliseconds.