H Benisty

A Ramdane

A Lupu

Y Liang

Q Gaimard

V Klimov

A Uskov

Coupling of nanoantennas in loss-gain environment for application in active tunable metasurfaces

Keywords: metasurface, Parity-Time symmetry, coupled-mode theory

HAL is

I. INTRODUCTION

The advent of metasurfaces, with their ability to manipulate reflection and refraction beyond the limits of classical optics [START_REF] Yu | Light propagation with phase discontinuities: generalized laws of reflection and refraction[END_REF][START_REF] Ni | Broadband light bending with plasmonic nanoantennas[END_REF], or to control the orbital angular momentum of light beams and their polarization state [START_REF] Yu | Flat optics with designer metasurfaces[END_REF], has led to the emergence of a plethora of applications of flat optics ranging from microwave and THz to near-infrared and optical spectral domains [START_REF] Lalanne | Metalenses at visible wavelengths: Past, present, perspectives[END_REF][START_REF] Chen | Dualpolarity plasmonic metalens for visible light[END_REF][START_REF] Aieta | Aberration-Free Ultrathin Flat Lenses and Axicons at Telecom Wavelengths Based on Plasmonic Metasurfaces[END_REF][START_REF] Ni | Metasurface holograms for visible light[END_REF][START_REF] Huang | Aluminum plasmonic multicolor meta-hologram[END_REF][START_REF] Huang | Helicity dependent directional surface plasmon polariton excitation using a metasurface with interfacial phase discontinuity[END_REF]. However, despite these spectacular advances, current metasurfaces are mostly limited to static applications. Once manufactured, it is generally not possible to modify their optical properties unless special strategies for the implementation of a tunability mechanism are deployed.

The most currently studied tunability mechanisms are aimed at modifying either the real part of the refractive index of the very resonator material or that of its surrounding environment. Typical means encompass electric gates, photoexcitation, use of phase change materials, magneto-optical control, optical non-linearity, beam shaping, mechanical actuators or a deformation system to affect the geometrical parameters of the resonators. Progress in each of the listed tunability mechanisms is presented in [START_REF] Shaltout | Spatiotemporal light control with active metasurfaces[END_REF]. The ultimate goal would be to independently address each pixel of the metasurface to control at a sub-wavelength scale the phase, intensity and polarization of transmitted or reflected waves. Such reconfigurable active metasurfaces would be highly desirable for a range of applications including beam steering modulators, varifocal lenses, dynamic holograms and other adaptive optics metadevices [START_REF] Shaltout | Spatiotemporal light control with active metasurfaces[END_REF].

In the meantime, despite massive efforts from numerous teams worldwide, there is currently no clear strategy on the optimal technological solution to bring this breakthrough. In this landscape, the dawn of Parity-Time symmetry optics has heralded the advent of a new challenger into the arena. Here, the paradigm shift comes from the idea of primarily manipulating the imaginary part of the refractive index of the resonator or its surrounding environment by introducing losses and/or gain into the system. Following this approach, experimental observation of the transition through exceptional point (EP) [START_REF] Lawrence | Manifestation of PT symmetry breaking in polarization space with terahertz metasurfaces[END_REF][START_REF] Park | Symmetry-breaking-induced plasmonic exceptional points and nanoscale sensing[END_REF][START_REF] Park | Observation of an exceptional point in a non-Hermitian metasurface[END_REF] has been reported, followed by theoretical and modeling results predicting the ability to design optical devices for the control of light at the nanometer scale [START_REF] Manjavacas | Anisotropic optical response of nanostructures with balanced gain and loss[END_REF][START_REF] Sanders | Nanoantennas with balanced gain and loss[END_REF][START_REF] Klimov | Entanglement of bright and dark modes in parity-time-symmetric plasmonic nanoantennas[END_REF] and to obtain spectral singularities in active hybrid metamaterials [START_REF] Feng | Loss-induced super scattering and gain-induced absorption[END_REF][START_REF] Zhang | Exceptional singular resonance in gain mediated metamaterials[END_REF][START_REF] Li | Exceptional points and spectral singularities in active epsilon-near-zero plasmonic waveguides[END_REF][START_REF] Chen | Manipulating the critical gain level of spectral singularity in active hybridized metamaterials[END_REF]. The exceptional point is not the whole story, however. When systems interact with more degrees of freedom (external for scattering and their own degrees of freedom), subtleties that are reminiscent of those of Fano resonances open avenues that do not rely on the EP, all the more if the gain value to operate at this EP is large. The interplay of other degrees of freedom then leads to other interesting working points, with the hope of requesting much less gain than would be needed in a restricted system, with only its own degrees of freedom, including gain and loss, but no scattering channel. Ref.20 can serve as a realistic implementation of the principle that we nevertheless want to discuss with some generality.

The objective of this paper is to further consolidate this research direction by addressing the problem of optimal metasurface design in terms of ensuring an affordable level of gain to achieve the required spectral singularity that corresponds to the laser emission threshold. As is well known, an abrupt variation in intensity and phase is obtained for a small stimulus close to the lasing threshold, representing a "sweet spot" much desired for active tunable metasurfaces.

Special attention is given to explicitly taking into account the open nature of a system due not only to the presence of losses and/or gain but also to the antenna radiation properties, typical of plasmonic resonators. To better grasp this specific context, a first section is devoted to the relevance of the various concepts: parity-time symmetry, spectral singularity, and to their phenomenological modeling. In particular, it is stressed that radiative loss engineering is an important factor in diminishing the gain level required to reach the laser emission threshold condition. On the basis of the analysis performed, an optimized design of coupled resonators is proposed.

II. CONCEPTS AND MODELS

In the last decades, the ability to carve wavelength of sub-wavelength scale resonators supporting few modes or a single mode has prompted a large application of coupled mode theory. The flavor most used in this endeavor is a frequency domain version [START_REF]temporal domain[END_REF][START_REF] Haus | Waves and Fields in Optoelectronics[END_REF][START_REF] Fan | Temporal coupled-mode theory for the Fano resonance in optical resonators[END_REF][START_REF] Suh | Temporal Coupled-Mode Theory and the Presence of Non-Orthogonal Modes in Lossless Multimode Cavities[END_REF][START_REF] Suh | Displacement sensing using evanescent tunneling between guided resonances in photonic crystal slabs[END_REF][START_REF] Lepetit | Resonance continuum coupling in high-permittivity dielectric metamaterials[END_REF], at variance with the spatial coupled mode theory of holograms, distributed feedback (DFB) lasers and waveguide-type structures with dielectric or metallic periodicity (e.g. photonic crystals and plasmonic systems). The focus on small or mesoscale systems has ben more prone to bring the consideration of openness as a characteristic. In a classical laser, openness is treated primarily through the threshold condition and as an edge boundary condition. For the typical elements of metasurfaces, conversely, radiation to open space or to the outside must be a built-in feature to describe the local energy flow. Periodic higher-order DFB lasers indeed also feature radiation and feedback altogether, and their initial in-depth depiction, over 30 years ago, [START_REF] Kazarinov | Second-order distributed feedback lasers with mode selection provided by first-order radiation losses[END_REF] has regained popularity in recent times, e.g. to discuss bound-states-incontinuum and similar remarkable resonances [START_REF] Blanchard | Fano resonances in photonic crystal slabs near optical bound states in the continuum[END_REF].

The focus on parity-time symmetry has further strengthened the popularity of a frequency(time) approach, even though guided optics was a cornerstone of the PTS studies [START_REF] Rüter | Observation of parity-time symmetry in optics[END_REF][START_REF] Benisty | Implementation of PT symmetric devices using plasmonics: principle and applications[END_REF][START_REF] Lupu | Switching using PT symmetry in plasmonic systems: positive role of the losses[END_REF]. Thus, starting from a closed conservative system and adding gain/loss on the one hand and openness (radiation losses) on the other hand, we must expect an interplay of two kinds of singularities: (i) The gain-loss parameter and the coupling parameter are expected to produce the exceptional point (EP), whereby the eigenvalues of the evolution equation merge and change nature (from real to imaginary, with adequate conventions). (ii) the spectral singularity, which can be assimilated to the lasing threshold at first order, although the examination of the coherence of the system under the various noises (pump, spontaneous emission) should be investigated in detail to provide an exact picture.

Due to this complexity, and to the many systems described in the literature, we choose to focus on the generic coupled mode (frequency/temporal) description, without specifying a material basis. The reader can refer to the various works on nanoresonator-based metasurfaces and related devices [START_REF] Lalanne | Metalenses at visible wavelengths: Past, present, perspectives[END_REF][START_REF] Yan | Rigorous modal analysis of plasmonic nanoresonators[END_REF][START_REF] Koshelev | Asymmetric Metasurfaces with High-Q Resonances Governed by Bound States in the Continuum[END_REF] to assess how the correspondence is done based on the response of subsystems, not yet routinely nowadays, but in a reasonably established manner.

The overall framework is linear scattering, with two degrees of freedom in the local system, each able to radiate in the far-field.

Thus the equation ( 1) applies

  -1 † eff S=C+ V ωI-H V i ( 1
)
where C is the background scattering which does not interact with the resonator and V is the radiation-resonator coupling, relating impinging wave to eigenmode weights. For a closed system, the effective Hamiltonian [START_REF] Lepetit | Resonance continuum coupling in high-permittivity dielectric metamaterials[END_REF] H eff would comprise only

1 1 eff * 2 2 ω κ χ 0 H = + κ ω 0 χ i             (2)
with frequencies ω 1,2 , coupling κ, and where  1 and  2 define either absorption losses ( i >0) or gain ( i <0) experienced by the isolated resonator mode. Thus the exceptional point of PTS would arise when  1  2 =, as is well-known. For strongly coupled systems such as a close pair of antenna, the values of gain and loss involved are substantial (more exactly their difference

 1  2 ).
For an open system, there is an extra coupling that comes from the interaction of the radiated field with the resonators. Under the essential assumptions of an identical symmetry of both resonator mores [START_REF] Fan | Temporal coupled-mode theory for the Fano resonance in optical resonators[END_REF][START_REF] Suh | Temporal Coupled-Mode Theory and the Presence of Non-Orthogonal Modes in Lossless Multimode Cavities[END_REF], the result is that the extra coupling and the decay rates must be strongly related so that one must add the middle matrix of eq. ( 3) below

12 1 1 1 1 eff * 2 2 2 2 γγ γγ γ ω κ χ 0 H = + + κ ω 0 χ γ i i                     (2)
i.e. the nondiagonal terms are not free. The off-diagonal elements 12 γγ describe the indirect coupling, or in other terms the radiative coupling, between the resonances induced by the interaction between each resonator and the free space. We stick to this established description rather than modifying κ by a complex addition i 12 γγ .

We also note that many numerical and practical examples were given in [START_REF] Lepetit | Resonance continuum coupling in high-permittivity dielectric metamaterials[END_REF], based on cylindrical inclusion in waveguides, in the microwave domain. The high dielectric constant achievable in this domain makes the separation of individual resonator modes better defined than for lower dielectric constants (and low Q) resonators. We thus wish to focus on the main finding without such explicit examples. We will only add hints to what it means it terms of relevant examples of references [START_REF] Suh | Temporal Coupled-Mode Theory and the Presence of Non-Orthogonal Modes in Lossless Multimode Cavities[END_REF][START_REF] Lepetit | Resonance continuum coupling in high-permittivity dielectric metamaterials[END_REF].

We finally distinguish between features of the resonator and features of the scattering: on the one hand, parity-time symmetry (PTS) as defined here involves only the first and third matrix, it is defined as independent of coupling and scattering. On the other hand, characteristic configurations of scattering are (i) the spectral singularity, akin to the laser threshold, which is a pole in the response and (ii) the darkmode feature, which is based on the sole absence of radiative decay even in the absence of resonator's own gain and loss. We intend here to discuss findings that point to the possibility of obtainment of the latter features at much lower gain and losses than the PTS feature.

III. MODELING AND DISCUSSION

Temporal Coupled Mode Theory model

The first point of our analysis concerns examination of the requirements for attaining the superscattering regime with its characteristic spectral singularity. To this end we consider a system of two coupled antenna-type resonators. Let us note for convenience

=( 2 - 1 )/2, =( 1 + 2 + 1 + 2 )/2, =( 2 - 1 )/2, =( 2 - 1 )/2 and 0 1 2 γ = γ γ .
The eigenmodes of H eff are complex-frequency poles of the transmission matrix and correspond to sharp features in the spectral response. They can be classified as even  + or odd  -(symmetric or antisymmetric, while the individual modes have the same symmetry, as stressed above, the symmetry or antisymmetry relates here to the field's similar or opposite phases in both resonator). As follows directly from Eqs. (1,3)[8-10] and using above notations we get:

      2 2 1 2 ± 0 ω +ω ω = + σ± δ+ η+ξ + κ+ γ 2 i i i (4)
The lasing threshold condition occurs when the imaginary part of the antisymmetric mode eigenfrequency in Eq. ( 3) vanishes. Note that condition   -Im ω =0 can be also satisfied in the case of a totally passive system without the presence of losses and gain, i.e. when  i =0. In this case it corresponds to the operation in the dark-mode (DM) regime [START_REF] Benisty | Healing near-PT-symmetric structures to restore their characteristic singularities : analysis and examples[END_REF]. By direct calculation this simpler DM condition is then as follows:

21 0 12 γγ δ = γ 2 γγ     (5a)
It corresponds to the blue diagonal wedge in Fig. 1a forming an angle =atan( 0 ) with the ordinate axis. It says how coupling and detuning must be re-balanced for the DM condition to cope with the difference in radiative coefficient of the individual resonator, essentially to produce the proper resonator amplitude algebraic ratio. Note that it has only a distant relation to PTS, as argued above. Moreover, exceptional points arise here in a detuned system, due to the complex coupling [START_REF] Benisty | Healing near-PT-symmetric structures to restore their characteristic singularities : analysis and examples[END_REF][START_REF] Nguyen | Recovering parity-time symmetry in highly dispersive coupled optical waveguides[END_REF]. From this consideration, for a given particular choice of  1 and  2 determining the angle , either the detuning  or coupling coefficient  could be adjusted to satisfy condition given by Eq. (5a). An obvious exception is the point of origin (=0, =0) where DM operation is fulfilled independently of the values  1 and  2 .

A similar situation still holds in the presence of losses and gain. The Im( -)=0 condition for superscattering is then given by the expression:

2 2 1 1 0 12 γ +χ -γ -χ δ η+χ == κγ 2 γγ (5b)
In the presence of losses and gain the Im( -)=0 line is now forming an angle '=atan(( 0 ) with the ordinate axis, larger in absolute terms if > 0 and  > 0. Thus, as shown in Fig. 1, the given point A in the - plane, which was not originally on the DM line (the present example was chosen to lie in the greenish area, the middle of the logarithmic range), can be made to satisfy the exact DM condition when losses and gain are introduced into the system to tilt the DM line to the appropriate angle. We will see below that this evolution is accompanied by a radical change in the spectral response. 11); c) Sketch of the coupled system with radiative channels. The coupling κ is direct, not radiative. The radiative coupling 12 γγ results from the radiative channels.

Single-layer metasurface

To assert this point, we calculate the transmission and reflection coefficients of a single-layer metasurface using the temporal coupled mode theory approach [START_REF] Haus | Waves and Fields in Optoelectronics[END_REF][START_REF] Fan | Temporal coupled-mode theory for the Fano resonance in optical resonators[END_REF][START_REF] Suh | Temporal Coupled-Mode Theory and the Presence of Non-Orthogonal Modes in Lossless Multimode Cavities[END_REF][START_REF] Suh | Displacement sensing using evanescent tunneling between guided resonances in photonic crystal slabs[END_REF][START_REF] Lepetit | Resonance continuum coupling in high-permittivity dielectric metamaterials[END_REF]. Since there is no general theory for lossy and gainy systems yet, we use formulas from lossless theory [START_REF] Suh | Temporal Coupled-Mode Theory and the Presence of Non-Orthogonal Modes in Lossless Multimode Cavities[END_REF] with transition to the complex plane in terms of the dielectric permeability and frequencies i.e., we use the analytical extension of the results [START_REF] Suh | Temporal Coupled-Mode Theory and the Presence of Non-Orthogonal Modes in Lossless Multimode Cavities[END_REF] (a very favorable element is that the algebra does not raise any Riemann sheet or similar issue). The scattering matrix is then:

                             1 1 1 2 2 2 2 1 0 0 1 1 1 2 2 2 0 0 ω-ω γ + γ + ω-ω γ +χ γ -2γ γ -κ -r t -r t rt =+ -r t -r t tr ω-ω γ + ω-ω γ +χ -γ -κ γ -κ i i i ii i ii i i i i i                          S ( 6
)
where r and t describe non-resonant, real reflection and transmission coefficients (

2 2 r t 1   ).
For what follows, we consider that the reflection of the substrate is negligible and we set r = 0 and t = 1.

Figures 2a and2b show the spectral response in intensity and phase variation, respectively, of an ideal lossless passive plasmonic metasurface operated near the DM condition given by Eq. (5a). The intensity variation shows, beside the main broad line, a sharp characteristic asymmetrical resonance of the Fano type, in a very narrow range (around 8.46 n.u.) due to operation near the DM (asymmetry can only be seen in magnified plots but brings no novel data per se). A Fano type characteristic is also observed for the phase response which shows a variation of 2 for the transmitted wave and a back-and-forth jump of - to + for the reflected wave (see inset of Fig. 2b). The introduction of losses into the system leads to a radical change in the complex spectral response. As can be seen in Figs. 2c and2d, the Fano resonance features in intensity and phase have almost completely disappeared, while for the rest of the spectral response the changes are barely noticeable. Based on a similar approach, an active control of electromagnetically induced transparency (EIT) analogue in terahertz metamaterials was demonstrated in [START_REF] Gu | Active control of electromagnetically induced transparency analogue in terahertz metamaterials[END_REF]. As expected in these resonant phenomena, the bandwidth is reduced when the tuning sensitivity increases.

Further avenues are opened with the introduction of the gain into the system. Firstly, such an introduction can obviously restore the DM singularity, albeit in a modified form. Whereas for the initial "Off" state in the absence of absorption, the normalized sum of the reflected and transmitted intensities is equal to unity, it becomes unbounded (Fig. 3a, semilog scale) in the "On" superscattering state occurring in the presence of losses and gain. The resonant frequency can be determined by explicitly solving equation   -Im ω =0. Using a straightforward calculation, the following expression can be obtained:

    0 2 2 1 1 1 2 1 2 1 2 2 1 κγ γ +χ -γ -χ δ= Δ 2 γ γ +χ χ +γ χ +γ χ  (7)
where the discriminant  is:

        2 2 2 2 2 2 2 0 Δ=64σ κ +σ -η+ξ γ + η+ξ -σ (8)
The gain level required to reach the superscattering threshold corresponds to the condition =0, which is fulfilled when one of the three elements of the product given by Eq. ( 8) vanishes. The first term =0 means operation at the EP represented in the - plane by black dots in Fig. 1. As evidently appears and as the large distance between EP and DM line in Fig. 1 suggests, operation at the EP is a poor option in terms of the large gain it requires:

  2 1 2 1 χ =-γ +γ +χ (9)
The physical meaning is clear: the level of gain in the second resonator should fully compensate for the radiative losses in both resonators as well as possible absorption losses in the first resonator. Note that despite the fact that loss and gain are not balanced, the system still has PT-symmetric and PT-symmetry-broken phases, but PTsymmetric phase no longer exhibit real spectra.

Neither is the condition given by the second term in product decomposition given by Eq. ( 8) is a good option: κ +γ γ +γ χ χ =γ +χ [START_REF] Shaltout | Spatiotemporal light control with active metasurfaces[END_REF] In the limit   0 and  1  0 the lowest "threshold" gain for reaching DM is  2 =  2 . It corresponds to the compensation by gain of the radiative losses in the second resonator. Note also that the same lowest gain  2 =  2 can be achieved when  1 >>  1 while   0. Though this operation regime in terms of gain requirement is less demanding compared to the operation at the EP, it is still much less favorable than the demand when the last factor in the product decomposition given by Eq. ( 8) vanishes:

21 2 11
γχ χ =γ +χ [START_REF] Lawrence | Manifestation of PT symmetry breaking in polarization space with terahertz metasurfaces[END_REF] In the limit of  1 <<  1 ,  2 → - 1 ( 2 / 1 ). This means that in theory the required gain level  2 can be arbitrary small, and notably much lower than the loss  1 , provided that  2 << 1 .

This can lower the gain requirement to only 1% for instance of the loss compensation, essentially at the expenses of a narrower bandwidth. In other words, the resonant character of the system is optimally utilized, accumulating amplitude and phase changes for degrees of freedom that most easily compensate the losses. Another remarkable feature is that the gain condition given by Eq.( 11) is independent of the coupling strength . Also note that when the lasing threshold condition given by Eq. ( 11) is satisfied, Eq. ( 7) becomes identical to Eq. (5b). A practical implementation of such dark mode metasurface design may be akin that shown in Fig. 4. It consists of a dolmen type structure with a bright dipole element and a dark quadripole element embedded in gain medium. Full-wave simulations of such type of structure was reported in [START_REF] Chen | Manipulating the critical gain level of spectral singularity in active hybridized metamaterials[END_REF]. For the operation wavelength around 1µm it was found that the gain level to required to achieve the superscattering condition is about 1760cm -1 . Such a gain level is attainable by using either organic dyes [START_REF] Han | Inducing lasing in organic materials with low optical gain by three-dimensional plasmonic nanocavity arrays[END_REF] or semiconductor materials [START_REF] Novitsky | Transmission enhancement in lossgain multilayers by resonant suppression of reflection[END_REF].

Double-layer metasurface

Though detuning  between expressed by Eq. ( 7) is sensitive , its deviation from nominal value can be adjusted through either variation of the gain level  2 or loss level  1 . It is clear that the ability to independently adjust the losses level  1 as well as the gain level  2 in controlling the phase and intensity of the transmitted and reflected waves and fine-tuning the superscattering frequency. The technological implementation of such an independent control of  1 and  2 with a single metasurface is, however, not trivial. The solution to this problem is to use a doublelayer metasurface. In this case, one metasurface can support only gain elements consisting, for example, of III-V semiconductor resonators and another metasurface supports resonators either based on III-V heterostructures where absorption is controlled by the quantum-confined Stark effect (QCSE), or consisting of metal-type resonators.

The intensity and phase spectral response of a double layer metasurface calculated using the same approach as in [START_REF] Suh | Displacement sensing using evanescent tunneling between guided resonances in photonic crystal slabs[END_REF] is shown in Figs. 3c and3d, respectively. As can be seen, it is very similar to that of single-layer metasurface (the broad peak is only slightly sharper) and, importantly, presents the same divergence of intensity when approaching the superscattering threshold condition.

IV. SUMMARY AND CONCLUSIONS

Tunability mechanisms based on gain or loss variation in a system of two coupled antenna-type resonators were considered. The primary interest of the study is to focus on operation condition other than those implying the EP of the bare resonators. In a spirit similar to Fano resonances, we found that when the scattering channel are included, new operation conditions for switching effects with much smaller gain excursion can be realized. In some sense, focusing on the "traditional" EP could obscure more advantageous working points. According to our study of two coupled nanoantenna-type systems with proper phenomenological addition of scattering channels, there is room for such working points, in relation with the dark mode condition. It also gives rise to the superscattering regime with strong response for small parameter modulation. There is logically a price to pay in terms of limited bandwidth. However, in the telecom context for instance, the plasmonic nanoantenna-related bandwidths are way too broad compared to telecom optical switching requirements for narrow channels, thus it does make sense to put such features to good use.

In our study, conditions corresponding to the operation in the adequate superscattering regime were identified. It was found that the optimal configuration in terms of lowest gain to be supplied corresponds to a system composed of gain and loss resonators with highly asymmetric radiative rates ( 2 / 1 ) and detuned resonance frequencies. We emphasize here that this is obtained in a regime of very limited gain i.e. with  2 <<  1 , i.e. a very small gain level, according to the rationale exposed above. The proposed approach can be exploited for the implementation of tunable metasurfaces with high-contrast. It can be used to further improve the enhancement of quantum emission phenomena, such as superradiance [START_REF] Fleury | Enhanced superradiance in epsilon-near-zero plasmonic channels[END_REF][START_REF] Li | Controlling collective spontaneous emission with plasmonic waveguides[END_REF], the enhancement of optical nonlinearities [START_REF] Li | Exceptional points and spectral singularities in active epsilon-near-zero plasmonic waveguides[END_REF][START_REF] Argyropoulos | Boosting optical nonlinearities in ε-near-zero plasmonic channels[END_REF], and could be extended to the study of strong coupling between resonant cavity and localized emitters modes. The obtained results are fully consistent with previously numerical modeling results with realistic gain parameters reported in [START_REF] Feng | Loss-induced super scattering and gain-induced absorption[END_REF][START_REF] Zhang | Exceptional singular resonance in gain mediated metamaterials[END_REF][START_REF] Chen | Manipulating the critical gain level of spectral singularity in active hybridized metamaterials[END_REF].

Fig. 1 :

 1 Fig. 1: Behavior of two coupled systems also coupled with scattering channels. The main panels a),b) are colormaps of the behavior while a sketch of the system is given in c). a),b) Logarithmic scale colormap representations of the imaginary part of the antisymmetric mode eigenfrequency m( -). The dotted line corresponds to the PT-symmetric path. Bold black dots indicate exceptional points. Void magenta dot indicates superscattering operation point in the - plane. Parameters of the coupled resonators system used in numerical modeling:  1 =10,  1 = 0.8,  2 = 0.2,  0 = 0.4,  = -0.3. All values are given in normalized frequency units. The two plotted cases are a) Lossless case ( 1 =  2 = 0); b) System with losses and gain ( 1 = 0.08,  2 = -0.0182. The values of  1 and  2 are bounded by the Eq. (11); c) Sketch of the coupled system with radiative channels. The coupling κ is direct, not radiative. The radiative coupling

Fig. 2 :

 2 Fig. 2: Scattering matrix Intensity (a) & (c) and phase (b) & (d) spectral responses, respectively. a) & b) Operation in the near vicinity of DM regime. Parameters of the lossless ( 1 = 2 =0) coupled resonators system used in numerical modeling:  1 =10,  2 =8.63,  1 =0.9,  2 =0.1. All values are given in normalized radial frequency units. Inset in (b) shows transmitted and reflected waves phase variation at the Fano resonance frequency; c) & d) Same resonators parameters as in (a) & (b) except  1 = 2 =0.01.

Fig. 3 :

 3 Fig. 3: Scattering matrix Intensity (a) & (c) and phase (b) & (d) spectral response, respectively. a) & b) Single-layer metasurface operation in the vicinity of superscattering regime. Parameters of the coupled resonators system used in numerical modeling:  1 =10,  2 =8.63,  1 =0.9,  2 =0.1,  1 =0.01,  2 =-0.0011. All values are given in normalized radial frequency units. Inset in (b) shows transmitted and reflected waves phase variation at the Fano resonance frequency; c) & d) Double-layer metasurface with dielectric spacer thickness 1 d=1.18×2πc/ω Same resonators

Fig. 4 :

 4 Fig. 4: Schematic diagram of the hybridized metamaterials consisting of a bright resonator (BR) dipole nanoantenna and a dark resonator (DR) quadrupole antenna embedded in a gain medium.

ACKNOWLEDGEMENTS

Funding by the French Agence Nationale pour la Recherche (project "PARTISYMO", contract number N° ANR-18-CE24-0024-01) is acknowledged by A.L., A.R. and H.B. Funding by the Russian Foundation for the Basic Research (grant №18-02-00315) is acknowledged by V.K. Funding by the China Scholarship Council is acknowledged by Y. L..


Castrec Justine
email: justine.castrec@gmail.com

Fabioux Caroline

Le Goïc

Boulais Myrina

Soudant Philippe

Hégaret Helene

Justine Castrec

The toxic dinoflagellate Alexandrium minutum affects oyster gamete health and fertilization potential

Keywords: Algal blooms, Algal toxins, Fertilization, Paralytic Shellfish Toxins (PST), Bioactive Extracellular Compounds (BEC), Spermatozoa, Oocyte, Flow cytometry, Crassostrea (=Magallana) gigas, Bivalves

Dinoflagellates from the globally distributed genus Alexandrium are known to produce both paralytic shellfish toxins (PST) and uncharacterized bioactive extracellular compounds (BEC) with allelopathic, ichthyotoxic, hemolytic and cytotoxic activities. In France, blooms of Alexandrium minutum appear generally during the spawning period of most bivalves. These blooms could therefore alter gametes and/or larval development of bivalves, causing severe issues for ecologically and economically important species, such as the Pacific oyster Crassostrea (=Magallana) gigas. The aim of this work was to test the effects of three strains of A. minutum producing either only PST, only BEC, or both PST and BEC upon oyster gametes, and potential consequences on fertilization success. Oocytes and spermatozoa were exposed in vitro for 2 hours to a range of environmentally realistic A. minutum concentrations (10 to 2.5 × 104 cells mL-1). Following exposure, gamete viability and reactive oxygen species (ROS) production were assessed by flow cytometry, spermatozoa motility and fertilization capacities of both spermatozoa and oocytes were analysed by microscopy. Viability and fertilization capacity of spermatozoa and oocytes were drastically reduced following exposure to 2.5 × 104 cells mL-1 of A. minutum. The BEC-producing strain was the most potent strain decreasing spermatozoa motility, increasing ROS production of oocytes, and decreasing fertilization, from the concentration of 2.5 × 103 cells mL-1. This study highlights the significant cellular toxicity of the BEC produced by A. minutum on oyster gametes. Physical contact between gametes and motile thecate A. minutum cells may also contribute to alter oyster gamete integrity. These results suggest that oyster gametes exposure to A. minutum blooms could affect oyster fertility and reproduction success.

Highlights

► Oyster spermatozoa and oocytes were exposed in vitro to Alexandrium minutum strains. ► Viability and fertilization capacity of gametes were drastically reduced. ► The toxicity of Alexandrium minutum upon oyster gametes is strain-specific. ► A non-PST-producing strain increased reactive oxygen species production in oocytes. ► This strain also decreased spermatozoa motility and gamete fertilization.

Introduction

Fertilization is essential for reproduction and population sustainability [START_REF] Marshall | Sperm environment affects offspring quality in broadcast spawning marine invertebrates[END_REF]. Most marine bivalve molluscs are broadcast spawners depending on external fertilization. Seawater quality is a main factor affecting fertilization and larval development successes in these organisms [START_REF] Havenhand | Near-future levels of ocean acidification reduce fertilization success in a sea urchin[END_REF]. In particular, contaminants could negatively affect their reproduction as demonstrated in oysters exposed to anthropogenic pollutants [START_REF] Akcha | Genotoxicity of diuron and glyphosate in oyster spermatozoa and embryos[END_REF][START_REF] Fitzpatrick | The relative sensitivity of sperm, eggs and embryos to copper in the blue mussel (Mytilus trossulus)[END_REF][START_REF] Mai | Environmental concentrations of irgarol, diuron and S-metolachlor induce deleterious effects on gametes and embryos of the Pacific oyster, Crassostrea gigas[END_REF][START_REF] Vignier | Sensitivity of eastern oyster (Crassostrea virginica) spermatozoa and oocytes to dispersed oil: Cellular responses and impacts on fertilization and embryogenesis[END_REF][START_REF] Rolton | Susceptibility of gametes and embryos of the eastern oyster, Crassostrea virginica, to Karenia brevis and its toxins[END_REF]. Experimental studies suggest that harmful algal blooms (HAB), often caused by dinoflagellates, can affect marine bivalve reproduction by altering gamete quality and larval development, growth, and survival [START_REF] Banno | Deleterious effects of harmful dinoflagellates and raphidophytes on egg viability and spermatozoa swimming velocity in the Japanese pearl oyster Pinctada fucata martensii[END_REF][START_REF] Basti | Sensitivity of gametes, fertilization, and embryo development of the Japanese pearl oyster, Pinctada fucata martensii, to the harmful dinoflagellate, Heterocapsa circularisquama[END_REF][START_REF] Basti | Effects of the toxic dinoflagellate Heterocapsa circularisquama on larvae of the pearl oyster Pinctada fucata martensii (Dunker, 1873)[END_REF][START_REF] Binzer | Effects of bioactive extracellular compounds and paralytic shellfish toxins produced by Alexandrium minutum on growth and behaviour of juvenile great scallops Pecten maximus[END_REF][START_REF] Bricelj | Effects of brown tide (Aureococcus anophagefferens) on hard clam Mercenaria mercenaria larvae and implications for benthic recruitment[END_REF][START_REF] Castrec | The toxic dinoflagellate Alexandrium minutum impairs the performance of oyster embryos and larvae[END_REF][START_REF] Castrec | The dinoflagellate Alexandrium minutum affects development of the oyster Crassostrea gigas, through parental or direct exposure[END_REF][START_REF] De Rijcke | Common European harmful algal blooms affect the viability and innate immune responses of Mytilus edulis larvae[END_REF][START_REF] Gaillard | Cultures of Dinophysis sacculus, D. acuminata and pectenotoxin 2 affect gametes and fertilization success of the Pacific oyster, Crassostrea gigas[END_REF][START_REF] Rolton | Impacts of exposure to the toxic dinoflagellate Karenia brevis on reproduction of the northern quahog, Mercenaria mercenaria[END_REF][START_REF] Rolton | Susceptibility of gametes and embryos of the eastern oyster, Crassostrea virginica, to Karenia brevis and its toxins[END_REF][START_REF] Rolton | Effects of the red tide dinoflagellate, Karenia brevis, on early development of the eastern oyster Crassostrea virginica and northern quahog Mercenaria mercenaria[END_REF][START_REF] Tang | Lethal effects of Northwest Atlantic Ocean isolates of the dinoflagellate, Scrippsiella trochoidea, on Eastern oyster (Crassostrea virginica) and Northern quahog (Mercenaria mercenaria) larvae[END_REF]. In coastal areas, HAB are a recurring phenomenon that can co-occur with the reproduction of free spawning marine organisms [START_REF] Gaillard | Cultures of Dinophysis sacculus, D. acuminata and pectenotoxin 2 affect gametes and fertilization success of the Pacific oyster, Crassostrea gigas[END_REF].

In France, blooms of Alexandrium minutum usually occur from April to November [START_REF] Pouvreau | Velyger database: the oyster larvae monitoring French project[END_REF] overlapping with Pacific oyster breeding and spawning periods (Fig. S1). An understanding of the effects of A. minutum cells and its toxic compounds on gametes and early life stages of Crassostrea (=Magallana) gigas [START_REF] Bayne | The proposed dropping of the genus Crassostrea for all Pacific cupped oysters and its replacement by a new genus Magallana: A dissenting view[END_REF] is therefore critically important, considering the economic and ecological importance of this bivalve species. The known consequences of Alexandrium blooms are both ecological (e.g., alteration of marine trophic structure, large-scale mortality of fish and shellfish) and economic (e.g., impairment of tourism and recreational activities, fishery closure and sell prohibition of shellfish) (Anderson et al., 2012b).

HAB species from the genus Alexandrium are known to produce paralytic shellfish toxins (PST) that can cause human poisoning through shellfish-mediated intoxications (Bricelj and J o u r n a l P r e -p r o o f [START_REF] Bricelj | Paralytic shellfish toxins in bivalve molluscs: Occurrence, transfer kinetics, and biotransformation[END_REF] and/or poorly uncharacterized bioactive compounds exerting allelopathic, hemolytic, ichthyotoxic or cytotoxic activities [START_REF] Arzul | Comparison of allelopathic properties in three toxic Alexandrium species[END_REF][START_REF] Bianchi | Separate and combined effects of neurotoxic and lytic compounds of Alexandrium strains on Mytilus edulis feeding activity and hemocyte function[END_REF][START_REF] Castrec | The toxic dinoflagellate Alexandrium minutum impairs the performance of oyster embryos and larvae[END_REF][START_REF] Castrec | Bioactive extracellular compounds produced by the dinoflagellate Alexandrium minutum are highly detrimental for oysters[END_REF][START_REF] Ford | Deleterious effects of a nonPST bioactive compound(s) from Alexandrium tamarense on bivalve hemocytes[END_REF][START_REF] Lelong | A new insight into allelopathic effects of Alexandrium minutum on photosynthesis and respiration of the diatom Chaetoceros neogracile revealed by photosynthetic-performance analysis and flow cytometry[END_REF]Long et al., 2018aLong et al., , 2018b;;[START_REF] Mardones | Fish gill damage by the dinoflagellate Alexandrium catenella from Chilean fjords: Synergistic action of ROS and PUFA[END_REF]. These bioactive compounds were proposed to be implicated in the toxicity of Alexandrium upon early embryo development of several marine bivalves, such as Mytilus edulis [START_REF] De Rijcke | Toxic dinoflagellates and Vibrio spp. act independently in bivalve larvae[END_REF], C. gigas [START_REF] Castrec | The toxic dinoflagellate Alexandrium minutum impairs the performance of oyster embryos and larvae[END_REF][START_REF] Mu | Effects of the dinoflagellate Alexandrium catenella on the early development of the Pacific oyster Crassostrea gigas[END_REF], and Pinctada fucata martensii [START_REF] Basti | Differential inimical effects of Alexandrium spp. and Karenia spp. on cleavage, hatching, and two larval stages of Japanese pearl oyster Pinctada fucata martensii[END_REF], independently of the well-known toxins PST, gonyautoxins, and spirolids. However, no clear demonstration of the respective effects of the different toxic compounds has been provided. In addition to the well-known and characterized PST, recent studies demonstrated the toxicity of unidentified bioactive extracellular compounds (BEC) produced by A. minutum on other microalgae species [START_REF] Lelong | A new insight into allelopathic effects of Alexandrium minutum on photosynthesis and respiration of the diatom Chaetoceros neogracile revealed by photosynthetic-performance analysis and flow cytometry[END_REF]Long et al., 2018aLong et al., , 2018b) ) and their deleterious effects upon the behavior of the scallop Pecten maximus (Borcier et al., 2017) and physiology of the oyster C. gigas [START_REF] Castrec | Bioactive extracellular compounds produced by the dinoflagellate Alexandrium minutum are highly detrimental for oysters[END_REF]. These BEC were supposed to affect oyster oocytes exposed in vitro (Le [START_REF] Goïc | Flow cytometric assessment of morphology, viability, and production of reactive oxygen species of Crassostrea gigas oocytes: Application to toxic dinoflagellate (Alexandrium minutum) exposure. Cytom[END_REF] as well as spermatozoa derived from exposed oysters [START_REF] Castrec | The dinoflagellate Alexandrium minutum affects development of the oyster Crassostrea gigas, through parental or direct exposure[END_REF][START_REF] Haberkorn | Effects of Alexandrium minutum exposure on nutrition-related processes and reproductive output in oysters Crassostrea gigas[END_REF]. To our knowledge, the respective involvement of PST and BEC in A. minutum toxicity toward C. gigas gametes is not yet clearly established.

In the present study, we investigated the toxicity of A. minutum on C. gigas gametes by measuring their cellular characteristics by flow cytometry and the fertilization success of spermatozoa or oocytes by microscopy. Spermatozoa motility and swimming velocity were analysed by microscopy and image analysis. To determine the respective toxicity of BEC and PST, three A. minutum strains were tested, either producing only PST, only BEC, or both PST and BEC.

Materials and methods

Algal strains

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Three strains of Alexandrium minutum (Halim) were grown in filtered seawater (0.2 µm) supplemented with L1-Si medium [START_REF] Guillard | Stichochrysis immobilis is a diatom, not a chrysophyte[END_REF]) and maintained at 17 ± 1 °C, under a continuous light intensity of 100-110 μmol photons m -2 s -1 . The A. minutum strains were (i) the PST+BEC strain (strain AM89BM, isolated from a bloom in the Bay of Morlaix, France) producing 10.6 fmol PST cell -1 (corresponding to 1.3 pg STX eq. cell -1 ; [START_REF] Fabioux | Exposure to toxic Alexandrium minutum activates the detoxifying and antioxidant systems in gills of the oyster Crassostrea gigas[END_REF]; (ii) the PST strain (strain Da1257, isolated from a bloom in the Bay of Daoulas, France) producing 0.63 fmol PST cell -1 (corresponding to 0.053 pg STX eq. cell -1 ; [START_REF] Pousse | Sources of paralytic shellfish toxin accumulation variability in the Pacific oyster Crassostrea gigas[END_REF]; (iii) the BEC strain (strain CCMI1002, isolated from Irish waters), for which no PST were detected (Borcier et al., 2017).

According to the bioassay developed by Long et al. (2018a), the BEC strain appears four times more cytotoxic than the PST+BEC strain, whereas the PST strain has a negligible cytotoxic potency. Cultures were not axenic, grown without antibiotics, and harvested in exponential growth phase for the experiments. Algal concentrations (cells mL -1 ) were determined by counts using a FACScalibur (BD Sciences, San Jose, CA, USA) flow cytometer equipped with a blue laser (excitation 488 nm) according to [START_REF] Marie | Enumeration of marine viruses in culture and natural samples by flow cytometry[END_REF]. For gamete cellular responses and fertilization experiments, cultures were re-suspended in filtered seawater 24 h prior to the exposures to reach cell concentrations of 2 × 10 1 , 2 × 10 2 , 5 × 10 3 , and 5 × 10 4 cells mL -1 .

Oysters

For the experiment assessing cellular responses of gametes exposed to A. minutum, adult Pacific oysters (n = 5 females and n = 4 males) C. gigas were collected from Daoulas estuary in the Bay of Brest (North Brittany, France). For the fertilization experiment, adult oysters (n = 3 females and n = 3 males) originated from a cohort produced in 2017 according to [START_REF] Petton | Factors influencing diseaseinduced mortality of Pacific oysters Crassostrea gigas[END_REF] and were deployed as early-juveniles (i.e. spat) in the bay of Brest. Gravid oysters were collected during the natural reproduction period (June and July 2018).

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Collection of gametes

Oyster gender determination and gamete quality check, i.e. round shape of oocytes and spermatozoa motility, were performed by examination of 2 μL gonad samples under a light microscope (Leica MZ 125, ×10 objective) before each experiment. Oocytes and spermatozoa were then collected by stripping gonads individually (Boulais et al., 2015a, b). Briefly, gametes were collected in 0.2-µm filtered seawater (FSW; pH 8.12, salinity 34.7, 21 °C) and sieved through 100-µm mesh to eliminate cellular debris. Cell concentrations were determined individually by flow cytometry (FCM) (duplicate, EasyCyte Plus cytometer, Guava Millipore Luminex) according to Le [START_REF] Goïc | Flow cytometric assessment of morphology, viability, and production of reactive oxygen species of Crassostrea gigas oocytes: Application to toxic dinoflagellate (Alexandrium minutum) exposure. Cytom[END_REF][START_REF] Goïc | Flow cytometric assessment of morphology, viability, and production of reactive oxygen species of Crassostrea gigas oocytes: Application to toxic dinoflagellate (Alexandrium minutum) exposure. Cytom[END_REF]. The concentration of oocyte suspensions were adjusted to 1 × 10 5 cells mL -1 with FSW. Spermatozoa suspensions were diluted to 1 × 10 8 cells mL -1 with FSW for movement measurements, and to 2 × 10 6 cells mL -1 for gamete cellular responses and fertilization experiments.

Gamete cellular responses experiment: spermatozoa movement and gamete FCM analyses

For each oyster, 2.5 mL of gamete suspension (see section 2.3) were exposed for 2 hours to 2.5 mL of the A. minutum suspensions (3 A. minutum strains × 4 concentrations) or to 2.5 mL of FSW (control treatment) in 10 mL glass vials for FCM analyses. For spermatozoa motility analyses, 0.5 mL subsample of spermatozoa suspension from each male was transferred in 2 mL glass vials containing 0.5 mL of the A. minutum suspensions or 0.5 mL of FSW (control treatment). After 2 hours of exposure, spermatozoa were sampled for motility measurements.

Final A. minutum concentrations were 10, 10 2 , 2.5 × 10 3 , and 2.5 × 10 4 cells mL -1 . These concentrations were chosen to reflect the range of algal densities observed during natural blooms [START_REF] Chapelle | The Bay of Brest (France), a new risky site for toxic Alexandrium minutum blooms and PSP shellfish contamination[END_REF]. In France, the alert threshold triggering weekly concentration monitoring for A. minutum blooms is 10 cells mL -1 [START_REF] Guallar | Global and local factors driving the phenology of Alexandrium minutum (Halim) blooms and its toxicity[END_REF].

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FCM measurements for spermatozoa and oocytes (i.e. relative cell size and complexity, viability (using Sybr-14 and propidium iodide, final concentration 1 µM and 10 µg L -1 , respectively) and reactive oxygen species production (using DCFH-DA, final concentration 10 µM)), were performed using an EasyCyte Plus cytometer (Guava Millipore Luminex) equipped with standard optics and a 488 nm argon laser according to Le [START_REF] Goïc | Flow cytometric assessment of morphology, viability, and production of reactive oxygen species of Crassostrea gigas oocytes: Application to toxic dinoflagellate (Alexandrium minutum) exposure. Cytom[END_REF][START_REF] Goïc | Flow cytometric assessment of morphology, viability, and production of reactive oxygen species of Crassostrea gigas oocytes: Application to toxic dinoflagellate (Alexandrium minutum) exposure. Cytom[END_REF].

Spermatozoa movement was analyzed under phase contrast microscope coupled to a video camera (Qicam Fast 1394) according to [START_REF] Boulais | pH controls spermatozoa motility in the Pacific oyster (Crassostrea gigas)[END_REF]. Briefly, each spermatozoa suspension was diluted 2 times in FSW containing pluronic acid (final concentration of 1 g L - 1) to avoid spermatozoa sticking to the cell surface. Then, 12 μL of diluted spermatozoa suspension was immediately transferred to a Fast-Read® cell 102 (Fisher Scientific) and the percentage of motile spermatozoa and their velocity (VAP: Velocity of the Average Path)

were assessed on a minimum of 30 spermatozoa for each sample, using the ImageJ software and a CASA plug-in calibrated to Pacific oyster (Boulais et al., 2015b).

Fertilization experiment

For each oyster, 2.5 mL of gamete suspension (oocytes or spermatozoa, see section 2.3) were exposed for 2 hours to 2.5 mL of the A. minutum culture (3 A. minutum strains × 4 concentrations) or to 2.5 mL of FSW (control treatment) in 10 mL glass vials. Fertilization of exposed oocytes was performed using a pool of control spermatozoa, at 5 × 10 7 cells mL -1 prepared from the initial spermatozoa suspensions of 3 males (see section 2.3). Fertilization of exposed spermatozoa was performed using a pool of control oocytes, at 5 × 10 4 cells mL -1 , prepared from initial oocyte suspensions of 3 female oysters (see section 2.3). After the exposure to A. minutum, exposed oocytes (5 × 10 3 oocytes) were transferred to 24-well microplates (NUNC © ) filled with 2 mL of FSW and 10 µL of the non-exposed spermatozoa pool (100:1 spermatozoa:oocyte ratio). Similarly, exposed spermatozoa (5 × 10 5 spermatozoa) J o u r n a l P r e -p r o o f were transferred to 24-well microplates (NUNC © ) filled with 1.4 mL of FSW and 100 µL of the non-exposed oocytes pool (100:1 spermatozoa:oocyte ratio). After 2 hours of contact between spermatozoa and oocytes, samples were fixed with a formaldehyde-seawater solution (1% final) to estimate the fertilization yield using a light microscope (Leica DM-IRB).

Numbers of fertilized (2-cell or 4-cell embryos) and unfertilized (absence of segmentation) oocytes were counted, on at least 100 oocytes per well. Fertilization yield was defined as number of fertilized oocytes × 100 / number of unfertilized and fertilized oocytes. Each oocytes/spermatozoa fertilization assay was performed in triplicate, the mean of the triplicate fertilizations was used in statistical tests.

Statistical analyses

Statistical analyses and graphical representations were performed using R software (R Core Team, 2012). Differences were considered significant when p < 0.05. All values are expressed as mean ± standard error (SE). Normality and homogeneity of variance were verified by the Shapiro-Wilk and Levene methods, respectively. Cellular characteristics measured by flow cytometry and fertilization yields were compared between the 13 treatments (3 A. minutum strains × 4 concentrations, and the control) for oocytes and spermatozoa using repeated measures ANOVA ('nlme' package), with 'treatment' as a fixed factor and 'oyster' as a random factor. For all models, we checked the assumption of homogeneity of variance and normality of residuals graphically using normal quantilequantile plots and scale-location plots of sqrt(|residuals|). The viability variable was transformed as arcsin(squareroot) before statistical analysis to pass normality, but were presented as non-transformed data in figures. A repeated measures ANOVA was used to test the effect of A. minutum exposure on spermatozoa motility and velocity, accounting for oyster as a random factor. If the effect of treatment was significant, post-hoc analyses were performed using emmeans function with Tukey's correction.

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Results

Gamete cellular responses

The viability of spermatozoa (F = 23.47, p < 10 -12 ) and oocytes (F = 12.76, p < 10 -10 ) were only affected at the highest A. minutum concentration tested, i.e. 2.5 × 10 4 cells mL -1 (Fig. 1A,B). At this concentration, the percentages of viable spermatozoa exposed to the three A. minutum strains were lower than control spermatozoa (94.4 ± 1.4%), the BEC strain having J o u r n a l P r e -p r o o f the strongest effect (-38%) on spermatozoa viability (54.3 ± 9.3%) compared to the PST+BEC (79.4 ± 5.1%, i.e. -14%) and PST strains (78.5 ± 4.8%, i.e. -15%) (Fig. 1A). The viability of oocytes exposed to 2.5 × 10 4 cells mL -1 of the BEC strain (68.4 ± 5.3%) or of the PST+BEC strain (75.4 ± 5.2%) were lower (-21% and -14%, respectively) than control oocytes (91.3 ± 2.1%) (Fig. 1B). The PST strain did not significantly affect oocyte viability compared to control (Fig. 1B).

The production of reactive oxygen species (ROS) of spermatozoa (F = 8.29, p < 10 -6 ) and oocytes (F = 2.70, p < 10 -2 ) were modified by exposure to A. minutum. The ROS production of spermatozoa exposed to 2.5 × 10 4 cells mL -1 of the BEC strain (265.5 ± 37.5 AU) or the PST+BEC strain (228.6 ± 45.0 AU) were higher (+140% and +113%, respectively) than control spermatozoa (72.4 ± 6.0 AU) (Fig. 1C). The ROS production of oocytes exposed to 2.5 × 10 3 cells mL -1 of the BEC strain (783.9 ± 136.8 AU) was higher (+56%) than control oocytes (500.8 ± 61.4 AU) (Fig. 1D). In the other conditions, ROS production of exposed gametes were similar to control (Fig. 1C,D).

Spermatozoa motility was significantly affected by A. minutum exposure (F = 19.66, p < 10 -11 ). Exposure to 2.5 × 10 4 cells mL -1 of the BEC strain totally inhibited spermatozoa movement (Fig. 1E). The percentage of motile spermatozoa in spermatozoa exposed to 2.5 × 10 3 cells mL -1 of the BEC strain (38.3 ± 8.0%) was lower (-36%) than in control spermatozoa (59.8 ± 4.1%) (Fig. 1E). The motility of spermatozoa in the other conditions were similar to control (Fig. 1E). The velocity of motile spermatozoa (VAP: Velocity of the Average Path)

were not significantly affected by A. minutum exposure (Fig. 1F), except for the VAP of spermatozoa exposed to 2.5 × 10 4 cells mL -1 of the BEC strain, which could not be measured since spermatozoa movement was totally inhibited (Fig. 1E).

Fertilization of exposed oocytes or spermatozoa

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Pre-exposure of oocytes or spermatozoa to A. minutum, prior to gamete contact for fertilization test, significantly affected fertilization yields (spermatozoa: F = 10.78, p < 10 -6 ; oocytes: F = 29.60, p < 10 -10 ). The fertilization yields obtained using spermatozoa exposed to the BEC strain at the two highest concentrations tested (2.5 × 10 4 and 2.5 × 10 3 cells mL -1 ) were significantly lower (1.4 ± 1.4% and 24.5 ± 18.2%, i.e. -98 and -73%, respectively) than fertilization yield obtained using control spermatozoa (92.3 ± 0.5%). Similarly, spermatozoa exposure to the highest concentration (2.5 × 10 4 cells mL -1 ) of the PST+BEC strain or the PST strain significantly decreased fertilization yields (12.6 ± 10.8% and 21.6 ± 14.4%, i.e. -86% and -77%, respectively) compared to control (Fig. 2A). Exposure of oocytes also induced lower fertilization yields compared to control oocytes (90.9 ± 2.7%) when exposed to the two highest concentrations tested (2.5 × 10 4 and 2.5 × 10 3 cells mL -1 ) of the BEC strain (0.1 ± 0.1% and 49.0 ± 13.5%, i.e. -99 and -46%, respectively), and to 2.5 × 10 4 cells mL -1 of the PST+BEC strain (32.3 ± 3.9%, i.e. -64%) or the PST strain (62.3 ± 1.3%, i.e. -31%) (Fig. 2B). The other concentrations of the A. minutum strains induced similar responses than control condition. Error bars denote ± standard error. Letters denote significant groupings (p < 0.05).

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Discussion

The present study evidences that concentrations of 2.5 × 10 3 cells mL -1 of Alexandrium minutum induced sublethal defects on oyster gametes after only two hours of in vitro exposure. The extent of the effects depended on the A. minutum strain, the toxic compound they produced and exposure concentration. Cellular damages on spermatozoa or oocytes were associated to significant decreases in fertilization yields, the ultimate phenotype translating the quality of gametes. The highest concentrations tested (up to 2.5 × 10 4 cells mL -1 ) are in the range of values observed during severe A. minutum blooms in France, Spain, Egypt, and South Africa [START_REF] Chapelle | The Bay of Brest (France), a new risky site for toxic Alexandrium minutum blooms and PSP shellfish contamination[END_REF][START_REF] Garcés | Relationship between vegetative cells and cyst production during Alexandrium minutum bloom in Arenys de Mar harbour (NW Mediterranean)[END_REF][START_REF] Labib | Diel vertical migration and toxicity of Alexandrium minutum Halim red tide, in Alexandria, Egypt[END_REF][START_REF] Pitcher | The dinoflagellate Alexandrium minutum in Cape Town harbour (South Africa): Bloom characteristics, phylogenetic analysis and toxin composition[END_REF] and demonstrate the potentiality of ecological consequences of A. minutum blooms for wild and cultivated bivalve populations.

Sublethal cellular damages and consequences on fertilization were most severe with the BEC-producing A. minutum strain, illustrating the high toxicity of bioactive extracellular compounds to oyster gametes. This strain significantly decreased fertilization when spermatozoa (-73%) or oocytes (-49%) were exposed at 2.5 × 10 3 cells mL -1 and almost totally inhibited it for gamete exposure at 2.5 × 10 4 cells mL -1 . This strain was also characterized as the most allelopathic, i.e. cytotoxic, for diatoms (Long et al., 2018a) and oyster embryos [START_REF] Castrec | The toxic dinoflagellate Alexandrium minutum impairs the performance of oyster embryos and larvae[END_REF].

In addition to a high cellular mortality rate (45.7%), inhibition of spermatozoa motility likely explain the drastic decrease in fertilization yield following spermatozoa exposure to the BEC strain since concentration of motile spermatozoa is a pivotal factor for successful fertilization in free-spawning marine invertebrates [START_REF] Nice | Sperm motility in the Pacific oyster (Crassostrea gigas) is affected by nonylphenol[END_REF][START_REF] Styan | Polyspermy, egg size, and the fertilization kinetics of free-spawning marine invertebrates[END_REF]. The motility was significantly reduced after an exposure to 2.5 × 10 3 A. minutum cells mL -1 and totally at 2.5 × 10 4 cells mL -1 . Alteration of spermatozoa movement could result from membrane alteration or sub-cellular cytotoxic effects. Long et al. (2018b) highlighted the deleterious J o u r n a l P r e -p r o o f effects of extracellular bioactive compounds produced by the BEC strain of A. minutum on membranes of the diatom Chaetoceros muelleri, with modifications of the proportion of lipid classes, pigments, and of the photosynthetic chain suggesting an alteration of membrane integrity, associated with an increase of internal ROS production of the diatom. In human, oxidative stress is largely implicated in reproductive physiopathology. An excessive ROS production was demonstrated to be deleterious for sperm membrane integrity, motility, and fertility [START_REF] Agarwal | Role of reactive oxygen species in the pathophysiology of human reproduction[END_REF], by inducing peroxidative damage to the plasma membrane and DNA fragmentation [START_REF] Sanocka | Reactive oxygen species and sperm cells[END_REF]. Consequently, higher ROS production in spermatozoa exposed to 2.5 × 10 4 cells mL -1 of the BEC strain or the PST+BEC strain could be another element to explain spermatozoa reduced motility and viability. The increase in ROS production in oocytes exposed to 2.5 × 10 3 cells mL -1 of the BEC strain could be associated with BEC, as ROS generation in cells can be triggered by exposure to xenobiotic or toxins [START_REF] Manduzio | The point about oxidative stress in molluscs[END_REF]. As proposed by Le [START_REF] Goïc | Flow cytometric assessment of morphology, viability, and production of reactive oxygen species of Crassostrea gigas oocytes: Application to toxic dinoflagellate (Alexandrium minutum) exposure. Cytom[END_REF], ROS generation in oocytes exposed to A. minutum could lead to cellular damages and subsequently alter fertilization processes. High concentrations of intracellular ROS in human oocytes are responsible for detrimental effects such as disruption of Ca 2+ homeostasis [START_REF] Martín-Romero | Contribution of culture media to oxidative stress and its effect on human oocytes[END_REF][START_REF] Takahashi | Impact of oxidative stress in aged mouse oocytes on calcium oscillations at fertilization[END_REF], impaired fertilization, and altered cleavage [START_REF] Bedaiwy | Relationship between oxidative stress and embryotoxicity of hydrosalpingeal fluid[END_REF][START_REF] Hu | Effects of low O2 and ageing on spindles and chromosomes in mouse oocytes from pre-antral follicle culture[END_REF].

Bioactive extracellular compounds produced by different dinoflagellate species generally appear highly toxic for gametes (this study) and early developmental stages of bivalves, not protected by a shell [START_REF] Banno | Deleterious effects of harmful dinoflagellates and raphidophytes on egg viability and spermatozoa swimming velocity in the Japanese pearl oyster Pinctada fucata martensii[END_REF][START_REF] Basti | Differential inimical effects of Alexandrium spp. and Karenia spp. on cleavage, hatching, and two larval stages of Japanese pearl oyster Pinctada fucata martensii[END_REF][START_REF] Castrec | The toxic dinoflagellate Alexandrium minutum impairs the performance of oyster embryos and larvae[END_REF][START_REF] Rolton | Susceptibility of gametes and embryos of the eastern oyster, Crassostrea virginica, to Karenia brevis and its toxins[END_REF]. It is urgent to consider these uncharacterized bioactive compounds in studies assessing the effects of HAB on marine species, to characterize them, and to decipher the mechanisms underlying their toxicity.

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Exposure of spermatozoa or oocytes to the PST-producing A. minutum strain at 2.5 × 10 4 cells mL -1 also altered fertilization and induced mortality in spermatozoa. Although PST is mainly intracellular in dinoflagellates, low levels of extracellular PST have been measured in the culture media of some Alexandrium spp. isolates [START_REF] Lefebvre | Characterization of intracellular and extracellular saxitoxin levels in both field and cultured Alexandrium spp. samples from Sequim Bay, Washington[END_REF]. Extracellular PST might have been present in the PST strain culture media and could be involved in the toxic effects observed. Saxitoxin, binding to Na + and Ca 2+ channels [START_REF] Llewellyn | Saxitoxin, a toxic marine natural product that targets a multitude of receptors[END_REF], likely modifies fluxes of these ions in cells. Saxitoxin could therefore alter cellular processes involving Ca 2+ , such as spermatozoa motility [START_REF] Boulais | ATP content and viability of spermatozoa drive variability of fertilization success in the Pacific oyster (Crassostrea gigas)[END_REF], oocyte maturation [START_REF] Leclerc | Role of dihydropyridine-sensitive calcium channels in meiosis and fertilization in the bivalve molluscs Ruditapes philippinarum and Crassostrea gigas[END_REF] and, fertilization [START_REF] Togo | Impacts of Deepwater Horizon oil and associated dispersant on early development of the Eastern oyster Crassostrea virginica[END_REF] in C. gigas. Further studies should investigate the effects of oyster gamete exposure to purified PST, assessing cellular integrity using electronic microscopy, cellular physiology including spermatozoa motility or oocyte maturation, and the consequences on fertilization processes.

In addition to the toxicity of BEC and PST, repeated contacts between oyster gametes and motile thecate dinoflagellates at high concentration (2.5 × 10 4 cells mL -1 ) also likely contribute to alter oocytes and spermatozoa cellular integrity, reducing their fertilization capacity. Physical contact with algal cells seems to be an important mechanism involved in the toxicity of HAB species to bivalve gametes and embryos, and has been suggested for Alexandrium species such as A. tamarense, A. taylori and A. affine [START_REF] Basti | Differential inimical effects of Alexandrium spp. and Karenia spp. on cleavage, hatching, and two larval stages of Japanese pearl oyster Pinctada fucata martensii[END_REF][START_REF] Matsuyama | Effects of harmful algae on the early planktonic larvae of the oyster, Crassostrea gigas[END_REF][START_REF] Yan | Inhibition of egg hatching success and larvae survival of the scallop, Chlamys farreri, associated with exposure to cells and cell fragments of the dinoflagellate Alexandrium tamarense[END_REF].

In our experiments, A. minutum cells and their toxins were still present during fertilization since oocytes and spermatozoa were not filtered following exposure to remove algal cells. Therefore, algal concentrations during fertilization ranged from 2.5 to 6.25 × 10 3 cells mL -1 when performed with previously exposed spermatozoa and from 0.5 to 1.25 × 10 3 cells mL -1 with previously exposed oocytes. Thus, A. minutum toxins could have directly impaired fertilization process or prevent first cleavage of embryos. Indeed, some Alexandrium strains, J o u r n a l P r e -p r o o f i.e. A. catenella and A. affine, affected the first and second cleavages of the Japanese pearl oyster P. fucata martensii embryos [START_REF] Basti | Differential inimical effects of Alexandrium spp. and Karenia spp. on cleavage, hatching, and two larval stages of Japanese pearl oyster Pinctada fucata martensii[END_REF].

Conclusion

This experiment clearly highlights the toxicity of A. minutum on C. gigas gametes and their fertilization capacity and suggests that A. minutum blooms could have negative consequences on oyster recruitment. The most striking effects were observed following exposure of oyster gametes to the BEC-producing A. minutum strain, which decreased spermatozoa motility, increased gamete ROS production, and virtually inhibited the subsequent fertilization, thus confirming a PST-independent toxicity of A. minutum. Results illustrate that negative effects of A. minutum on oyster gametes, as well as on embryos and larvae, as we demonstrated previously [START_REF] Castrec | The toxic dinoflagellate Alexandrium minutum impairs the performance of oyster embryos and larvae[END_REF], are strain specific and mainly caused by uncharacterized bioactive extracellular compounds, released as exudates and/or associated to algal cell membranes. Further research is necessary to determine the chemical identity of these bioactive compounds produced by A. minutum and the mechanism by which Alexandrium spp. toxins affect bivalve gametes and embryos. These results also participate to illustrate that toxicity vary substantially among clones of the same Alexandrium species [START_REF] Castrec | Bioactive extracellular compounds produced by the dinoflagellate Alexandrium minutum are highly detrimental for oysters[END_REF]Long et al., 2018a;[START_REF] Togo | Impacts of Deepwater Horizon oil and associated dispersant on early development of the Eastern oyster Crassostrea virginica[END_REF]. As suggested for A. ostenfeldii [START_REF] Brandenburg | Intraspecific trait variation and trade-offs within and across populations of a toxic dinoflagellate[END_REF], this intraspecific trait variation could be an advantage for development and resilience of A. minutum blooms.

CRediT authorship contribution statement

Fig. 1 .

 1 Fig. 1. Effects of three A. minutum strains producing BEC, PST+BEC, or PST, on cellular features of C. gigas gametes after a 2-hour exposure of spermatozoa (n = 4 males) or oocytes (n = 5 females) to 10 ( ), 10 2 ( ), 2.5 × 10 3 ( ), and 2.5 × 10 4 ( ) cells mL -1 of A. minutum or to seawater ( ) (control). Percentage of viable spermatozoa (A) and oocytes (B), reactive oxygen species (ROS) production of spermatozoa (C) and oocytes (D), spermatozoa motility (E) and velocity of the average path (VAP) (F). *: VAP of spermatozoa exposed to 2.5 × 10 4 cells mL -1 of the BEC strain was 0, as movement was totally inhibited. AU: arbitrary unit. Error bars denote ± standard error. Letters denote significant groupings (p < 0.05).

Fig. 2 .

 2 Fig. 2. Effects of three A. minutum strains producing BEC, PST+BEC, or PST, on C. gigas fertilization yield after a 2-hour exposure of spermatozoa (n = 3 males) or oocytes (n = 3 females) to 10 ( ), 10 2 ( ), 2.5 × 10 3 ( ), and 2.5 × 10 4 ( ) cells mL -1 of A. minutum (Pre-fertilization experiment) or to seawater ( ) (control). Fertilization yields of exposed spermatozoa (A) and exposed oocytes (B).

Justine Castrec :

 Castrec Conceptualization, Methodology, Investigation, Writing -Original Draft, Formal analysis, Visualization. Caroline Fabioux: Conceptualization, Investigation, Supervision, Writing -Review & Editing. Nelly Le Goïc: Investigation, Resources, Writing -Review & Editing. Myrina Boulais: Conceptualization, Methodology, Investigation, Writing J o u r n a l P r e -p r o o f

-Review & Editing. Philippe Soudant: Supervision, Writing -Review & Editing. Hélène Hégaret: Conceptualization, Investigation, Writing -Review & Editing, Supervision.

Acknowledgments

This work was supported by the French National Research Agency ANR CESA, which founded the ACCUTOX project ANR-13-CESA-0019 (2013)(2014)(2015)(2016)(2017). This work was also cofunded by grants from the Regional Council of the Région Bretagne and Brest Métropole. The funding sources had no involvement in study design, collection, analysis and interpretation of the data. The authors gratefully acknowledge all the colleagues who provided a valuable help during the experiment, dissections, discussions and advices: Christophe Lambert, Sylvain Gaillard, and Kevin Tallec.

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Declaration of interests

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

☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: