Pascal Roy

Alain Campargue
email: alain.campargue@univ-grenoble-alpes.fr

T A Odintsova

M Yu Tretyakov

A O Zibarova

O Pirali

Far-infrared self-continuum absorption of H 2 16 O and H 2 18 O (15-500 cm -1 )

Keywords: water continuum, far infrared, synchrotron, water dimer, far line wing

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Introduction

The terahertz spectral region (in particular the 10-650 cm -1 interval) offers great potential for astronomy and atmospheric science. The region contains rotational transitions of many minor and major constituents which are significant for atmospheric chemistry and planetary climate. This frequency range covers the major part of the pure rotational band of the water molecule. Although being a minor constituent (≈0.3% of the atmospheric mass), water vapor is the dominant contributor to the atmospheric absorption in this range. In general, the present accuracy of water line parameters (center frequency, intensity and broadening coefficients) presented in spectroscopic database [Gordon2016] fulfills most of the requirements of modern remote sensing experiments. In addition to rotational and rovibrational absorption lines, water vapor exhibits a continuum absorption which has been measured in several infrared regions and in the microwave, but which has been poorly studied in the far IR. Even though the continuum is several orders of magnitude weaker than absorption at the center of absorption lines, its integrated contribution to the total atmospheric absorption is significant and exceeds the contribution of other greenhouse gases, such as CO 2 and CH 4 . Thus, appropriate calculations of radiation balance, modeling of global climate changes and atmosphere remote sensing require accounting for the water vapor continuum. This is confirmed by estimations based on the semi empirical MT-CKD model of the water vapor continuum [START_REF] Mlawer | Development and recent evaluation of the MT_CKD model of continuum absorption[END_REF] http://rtweb.aer.com/continuum_frame.html], that is widely used to take into account water vapor continuum in radiative transfer codes.

Preliminary test-validation of the MT-CKD self-continuum in the terahertz region [Odintsova2017] revealed a significant overestimation. The MT-CKD model is regularly adjusted to available experimental data. For instance, the latest version (V3.2) was adjusted in the 4.0, 2.1, 1.6 and 1.25 µm windows on the basis of accurate measurements by cavity ring down spectroscopy (CRDS) [Campargue2016, Richard2017, Lechevallier2018]). Nevertheless, these empirical adjustments do not insure satisfactory extrapolation capabilities to other spectral intervals or to different thermodynamic conditions. The still missing development of a physically based model is probably the most appropriate approach. Indeed, in spite a long history [Shine, 2012], the nature of the water vapor continuum remains poorly understood. Detailed discussion of this problem can found, for example, in our recent paper [Serov2017] and references therein.

In this paper, we present new measurements of the water vapor continuum absorption in the range covering most part of the pure rotational band. Similarly to the work presented in [Odintsova2017] in the 15-35 cm -1 and 40-200 cm -1 intervals, the spectra were recorded at the SOLEIL synchrotron facility using Fourier Transform Spectroscopy (FTS). Here the spectral range is extended up to 500 cm -1 and a higher signal to noise is achieved allowing decreasing error bars on the retrieved continuum. In addition, the absorption continuum of the H 2 18 O isotopologue is investigated for the first time using the same experimental setup. Such isotopic substitution may give key insights on the physical nature of the water continuum.

Experiment

The experimental approach is mostly identical to that used in [Odintsova2017]. Briefly, water vapor absorption spectra were recorded at the AILES beamline of the SOLEIL synchrotron using the coherent (15-35 cm -1 ) and standard (50-500 cm -1 ) radiation modes and the high resolution Fourier-transform spectrometer (Bruker IFS125-HR) equipped with a multipass White type configuration cell. The total absorption pathlength was 151.75±1.5 m. Spectra were recorded at room temperature 296(2) K. Normal water sample and 18 O enriched water sample (97% enrichment from Euristotop) were used. Detailed experimental conditions of the recordings are presented in Table 1. The experiment provides transmitted light power obtained with cell filled with water vapor, I(ν), or with the cell evacuated, I 0 (ν). The experimental transmittance,

) ( / ) ( 0 ν ν I I , can be approximated by app l f e ⊗ - ) (ν α
where ⍺(v) is the total absorption coefficient and f app is the apparatus function of the considered recording. ⍺(v) is the sum of the contributions of the monomer resonance lines, α res , and of the continuum, α con :

) ( ) ( ) ( ν α ν α ν α con res + =
(1) Considering the smooth frequency dependence of the continuum, the transmittance can be expressed as

app l l f e e res con ⊗ × - - ) ( ) ( ν α ν α
. The apparatus function includes the effect of the finite spectral resolution and finite field of view which were modeled by a sinc and boxcar function, respectively.

The resonance absorption coefficient was calculated as the sum of lines with parameters taken from the HITRAN database [Gordon2016], except for a number of lines, for which more accurate experimental data on collisional broadening and shifting parameters were preferred [Golubiatnikov2005, Golubiatnikov2006, Golubiatnikov2008, Koshelev2007, Koshelev2011a, Tretyakov2013]:

) ( ) ( ν ν α i i i res Φ S ∑ = , ( 2
)
where i is the line index and i S and

) (ν i Φ
the corresponding line intensity and normalized line profile, respectively. For the line profile, we used following expression:

( ) ( ) ( ) ( ) , 2 2 0 2 2 0         ∆ + + ∆ + ∆ + - ∆ = c c c c R Φ ν ν ν ν ν ν ν ν π ν ν (3)
where, ν 0 is the line center frequency and ∆ν с is the collisional width. R(ν) is the general expression for the radiation term suggested in [Clough1989]:

( ) ( ) , 2 tanh 2 tanh 0 0       = kT h kT h R ν ν ν ν ν (4)
where k is the Boltzmann constant and Т the temperature. Formulae (3) reduces at low frequencies to the van Vleck-Weisskopf (VVW) line shape, which is usually preferred in the mm-submm wave range, and at high frequencies, to the Lorentz profile which is generally adopted in the infrared. The range under consideration is an intermediate range where specific frequency dependence of R(ν) should be taken into account. The standard far-wing cut-off at 25 cm -1 from the line center [Clough1989] was applied, the [-25, +25 cm -1 ] "plinth" being excluded and thus contributing to the continuum.

In the case of the spectra recorded with highly 18 O enriched water vapor, the isotopic composition of the sample was determined from the recorded spectra using a number of unsaturated absorption lines. O relative concentration from the stated value of the purchased sample (97 %) is due to the isotopic exchange between gas phase water molecules and normal water molecules adsorbed on the cell walls and in the admission tubes.

The self-continuum cross-section, C S in cm 2 molecule -1 atm -1 , was determined as Synchrotron power transmitted through the empty cell (red), cell filled with water (blue) and simulation corresponding to the resonance absorption only (green). The spectra were recorded with a 0.02 cm -1 resolution.

The coherent mode of the synchrotron radiation allows accessing the 15-35 cm -1 range. Fig. 1 presents a typical example of transmission spectra recorded with the cell filled with natural water vapor and with the empty cell (background spectrum). The water monomer spectrum simulation included in the figure was obtained as the product of the background spectrum with the transmittance factor calculated as described above. Fig. 1 shows that the difference between the recorded spectrum and the simulation vanishes below 15 cm -1 and above 35 cm -1 , indicating that the continuum measurements are not possible in those regions.

Fig.2.

Upper panel: FTS water vapor absorption spectrum recorded at 296 K and 16 mbar in natural isotopic abundance (blue), calculated water resonance absorption spectrum using the HITRAN2016 database [Gordon2016] (green).

Lower panel: Water vapor self-continuum cross-sections derived in this work from the 16 mbar (blue) and 11 mbar (red) recordings and comparison to the values derived in [Odintsova2017] from a spectrum recorded at 15.3 mbar from (grey). Missing values correspond to spectral intervals obscured by strong water lines (optical depth larger than 1.5).

The baseline stability of the spectra is a key criterion for continua retrieval. In the present recordings, the FTS stability was tested from a detailed analysis of several spectra recorded with the cell evacuated (baseline) and with the cell filled with 16 mbar of natural water vapor (sample spectrum). The background and water spectra were recorded successively four times each without any change in the spectrometer regime and data acquisition scheme. The very good coincidence of the series of recordings (down to the noise level) confirmed the long-term stability of the experiment. The average of these four spectra was used for further continuum analysis.

The coincidence of the cross-section values derived from recordings at different pressures is another way to check both the baseline stability and the quadratic pressure dependence of the self-continuum which is a key test of the quality of the obtained results. Due to the limited beam time granted for these measurements, in addition to the 16 mbar recordings, FTS spectra could be recorded at a single additional pressure (about 11 mbar and 13 mbar for natural water and H 2 18 O, respectively, roughly corresponding to a two times smaller continuum compared to 16 mbar). One hundred raw spectra were co-added for natural water at this pressure, which resulted in a somewhat lower SNR compared to the 16 mbar recordings (1520 raw spectra in total). However, the C S values derived at 11 mbar and 16 mbar are found in very good coincidence as illustrated in. Fig. 2. A similar agreement is achieved for the two sets of data acquired for 18 O-enriched water sample (Fig. 3, lower panel) confirming the square pressure dependence of the measured continua. 18 O (94.1% enrichment) recorded at 296 K and 16 mbar (blue), corresponding water resonance absorption spectrum simulated using the HITRAN2016 database [Gordon2016] (green). Lower panel: Water vapor self-continuum cross-section of H 2 18 O derived from the 16 mbar (blue) and 13 mbar (red) recordings.

Comparison to literature data. Discussion.

Previous experimental studies of the water vapor self-continuum below 50 cm -1 [Koshelev2011b, Kuhn2002, Slocum2015, Burch1982, Odintsova2017, Podobedov2008, Koshelev2018] are reviewed in Table 2 which provides, for each of them, the experimental technique, spectral range and temperature conditions. An overview comparison of the literature results to the present measurements is presented in Fig. 4. In order to take into account the frequency dependence corresponding to the radiation term, the spectral function, C S (ν)/ν 2 (also known as spectral density, spectral profile, spectral shape, [Frommhold2006, Hartmann2008]), is plotted. All the data correspond to 296 K. Continuum measurements for a number of temperatures (293, 313, 333 K) were performed in [Podobedov2008]. These data were recalculated to 296 K using the temperature exponent determined in [Podobedov2008].

The spectral function of the water dimer, (H 2 16 O) 2 , included in Fig. 4, was calculated from the ab initio absorption spectrum presented in Fig. 8 from [Scribano2007]. Indeed, water vapor continuum in the 15-35 cm -1 range is of particular interest since spectral signature of bound water dimer has been predicted in this region by ab initio [Scribano2007] and classical [Vigasin1983, Viktorova1970] calculations. Rotationally resolved water dimer spectrum at close to atmospheric conditions was recorded and unambiguously identified in the 3.5-8.5 cm -1 range [Tretyakov2012, Serov2014, Koshelev2018]. Sequence of observed rotational peaks consists from a large number of overlapped lines (E-type transitions) corresponding to the end over end rotation of water dimer [Odintsova2014]. Peaks are observed separated by the dimer rotational constant 2B ~ 12.32 GHz (≈ 0.4 cm -1 ) [Fraser1989]. At room temperature, the sequence is supposed to reach a broad maximum located around 20 cm -1 . This maximum is predicted to be superposed to a broad absorption pedestal smoothly increasing with frequency, due to the overlapping of lines of A-and B-type transitions of bound water dimer (see e.g. Fig. 1 of [Odintsova2014]). In real water vapor similar smooth pedestal from quasibound states is expected. Such deviation of the water vapor continuum frequency dependence from a quadratic function (expected in earlier studies in mm [Koshelev2011b] and far IR [Podobedov2008] ranges) was tentatively evidenced in our preliminary work [Odintsova2017]. This conclusion relying on a single pressure recorded at 15.3 mbar (see Fig. 2 of Ref. [Odintsova2017]) is fully confirmed by the present results. In Fig. 4, the broad absorption maximum due to the dimer rotational absorption near 20 cm -1 is transformed into a characteristic sharp slope of the spectral function. Our experimental data are found in very good agreement with the water dimer predictions in the 15-35 cm -1 region. This confirms the dominant contribution of the water dimer absorption to the continuum in this region. Note the very good agreement with literature data, especially with quite reliable data recently reported by Slocum [Slocum2015] near 50 cm -1 and unpublished results obtained by Bohlander within 14 microwindows of transparency in the range of 14-50 cm -1 presented by Burch [Burch1982].

Let us underline that the water dimer contribution is dominating up to about 25 cm -1 only. This is mostly due to the intense rotational spectrum of the dimer with a maximum around 15 cm -1 . In the range of maximum of the monomer rotational spectrum, the predicted dimer spectrum is mostly due to four low-lying fundamental vibrational bands (at about 88, 103, 108 and 143 cm -1 ) and their multiple overtones and combination bands, all populated at room temperature. The resulting calculated spectrum is similar to the observed continuum [Scribano2007]. However, the relative importance of dimers decreases at higher wavenumbers. For example, in the 100-200 cm -1 range, dimers are responsible for only about one half of the observed continuum [Odintsova2017, Serov2017] and far wings of monomer lines come into the play. In the millimeter-wave range (below about 10 cm -1 ), far wings contribution to the spectral function is almost negligible because the monomer spectrum 9 maximum is located at about 150 cm -1 , far above the dimer rotational spectrum maximum. As detailed below, this is not the case in the 50-500 cm -1 interval studied with the standard synchrotron mode. The MT-CKD values of C S (ν)/ν 2 plotted in Fig. 4 are mostly frequency independent up to 60 cm -1 . Although the MT-CKD average value is within the range of the observations, the frequency dependence is not reproduced. The MT-CKD empirical model is based on the assumption that the continuum originates from far wings of the monomer lines. It is thus not surprising that the MT-CKD predictions deviate from the observations in the considered spectral region where the dimer contribution dominates. O and H 2 18 O selfcontinua are expected to be close. This is confirmed by the comparison presented in Fig. 5. The coincidence within the experimental noise confirms the above mentioned non-quadratic frequency dependence of water vapor continuum in this spectral range. In principle a small isotopic shift to lower energy is expected for the heavier H 2 18 O dimer. The end-over-end rotation spectrum of (H 2 18 O) 2 dimer can be roughly predicted shifted by about 1-2 cm -1 . However, the SNR of our data is not sufficient to evidence such small isotopic shift of the continuum.

We have plotted in Fig. 5, curves corresponding to a smoothing of the measured normalized self-continuum cross-sections. The corresponding values sampled with 0.5 cm -1 step are provided as Supplementary Material.

Standard synchrotron mode (50-500 cm -1 ) 4.1 Cross-section retrieval

The standard mode of the SOLEIL synchrotron allowed for recording the H 2 16 O and H 2 18 O spectra in the 50-500 cm -1 range. The overview of the FTS spectrum of natural water is presented in Fig. 6 together with the background spectrum recorded with the cell evacuated. Note the noisy appearance of the background spectrum. This quite regular spectral structure due to multiple interferences of radiation inside the spectrometer elements is very stable (see insert in Fig. 6) and thus strongly reduced when divided by the spectrum recorded with the water sample.

Two values of spectral resolution were chosen for the recordings (see Table 1). A first series consists of spectra recorded at intermediate resolution (0.02 cm -1 , ~30 minutes acquisition time) with different water vapor pressures of natural and 18 O enriched water, between 2 and 6 mbar. This set of measurements allowed controlling the quadratic pressure dependence of the continuum. The second series consists of H 2 16 O and H 2 18 O spectra recorded with the maximum resolution (0.002 cm -1 ) at about 3 and 6 mbar. These spectra allow investigating in detail the shape of continuum absorption, that is necessary for further analysis of its physical nature. The high intensity of the monomer transitions and the insufficient accuracy of individual line parameters (in particular for H 2 18 O) prevented the global retrieval of the continuum by difference between the measured spectrum and the simulation of the monomer spectrum (Eq. 3). So, unlike to the 15-35 cm -1 range, the continuum was determined only at about one hundred frequency points corresponding to micro-windows of transparency between resonance lines. At the chosen spectral points, the monomer contribution (up to 50% of the total measured absorption) was simulated on the basis of the HITRAN database and subtracted.

As illustrated in Fig. 7 for a few of the chosen spectral points, a very good quadratic pressure dependence of the resulting absorption continuum is achieved. Self-continuum crosssections and their statistical uncertainty were derived from a linear fit of the continuum absorption coefficient versus pressure squared (Eq. 6). The derived values for H 2 16 O (118 points) and H 2 18 O (127 points) are provided as Supplementary Material and plotted in Fig. 8. This data treatment was applied to the spectra recorded at resolution of 0.02 cm -1 for which about six pressure conditions were at disposal. The continuum cross-sections were also derived from the spectrum recorded at the highest resolution at a single pressure of 6 mbar and 4 mbar for H 2 16 O and H 2 18 O, respectively. The narrower instrumental function allowed accounting better for the monomer contribution and thus enlarging the number of spectral points (about 6000). The C S values obtained from the high resolution spectra are included in Fig. 8. They show an excellent agreement with the values derived from the pressure dependence analysis providing a mutual validation of the two approaches, in particular of the approximations concerning treatment of the apparatus function (see above).

Fig. 7.

Continuum absorption coefficient of H 2 16 O, (upper row) and H 2 18 O (lower row) versus pressure squared in three selected micro-windows. Error bars correspond to one standard deviation of the noisy signal from its mean value within current micro-window.

Fig. 8.

Self-continuum cross-sections of H 2 16 O (upper panel) and H 2 18 O (lower panel) retrieved from high resolution water vapor spectra at 4 mbar (grey squares). The red circles correspond to values derived from the analysis of the quadratic pressure dependence of the absorption in micro-windows selected in lower resolution recordings. Error bars correspond to one standard deviation of the noisy signal from its mean value within current micro-window.

Comparison to literature data. Discussion.

An overview of the literature data is presented in Fig. 9 for natural water (see also Table 2). The new H 2 16 O C S values agree with our previous FTS measurements limited to the 40-200 cm -1 range [Odintsova2017]. The overall agreement with Burch above 350 cm -1 [Burch1982] is satisfactory although Burch's values are systematically larger than ours. The present measurements fill the 200-350 cm -1 gap where the water vapor continuum was not measured before. The data confirm that the widely used MT-CKD model [Mlawer2012] overestimates the continuum amplitude by a percentage between 30% and 100 % in the range of the rotational band of H 2 O. As expected the H 2 16 O and H 2 18 O absorption continua are very similar in shape and magnitude (Fig. 8). We would like to point out and discuss the non-smooth frequency dependence of the H 2 16 O and H 2 18 O continua, which manifests itself as significant fluctuations of C S values between nearby micro-windows. These fluctuations are reproducible and significantly larger than the experimental noise. Let us recall that the continuum involves contributions from monomolecular and bimolecular absorptions [Serov2017]. In our experimental conditions, the contribution of free molecular pairs is negligible [Vigasin1991]. So only bound and quasibound water dimers contribute to the bimolecular absorption and their contributions have a similar amplitude [Odintsova2017, Serov2017]. Regarding frequency irregularity of the dimer spectrum in our region the reader is referred to [Scribano2007] for results of quantum chemical calculations. Note that in [Scribano2007], the pressure broadening parameter value (0.12 cm -1 ) used for computing the dimer spectrum was overestimated by about one order of magnitude [Serov2014]. Even though, one may see on Fig. 8 of [Scribano2007] that, within the 100-200 cm -1 range, the dimer absorption shows some sharp irregular features with amplitude representing up to 10% of the unresolved broadband absorption. In our case, the bound dimer absorption should be superimposed on the contribution of the quasibound dimer which is broadened by metastable states lifetime. This should somewhat broaden the sharp structures in the total bimolecular spectrum. Nevertheless, taking into account the small water vapor pressure in our experiment, we cannot completely exclude the bimolecular absorption as a source of the observed irregular frequency dependence of the retrieved C S values.

The subtraction of the resonance lines may also be responsible of the observed dispersion of the C S values. Two mechanisms may contribute: (i) the uncertainty of line shape parameters taken from the HITRAN database (mostly the intensity and the self-broadening parameter) and (ii) inadequate resonance line shape modeling of the intermediate wings (at about 5-10 cm -1 from the line center). In the following, we analyze the potential impact of both mechanisms.

In our region, the HITRAN database provides resonance line intensities with uncertainty ranging from 1 to 20%. However, it is believed that these error bars are conservative estimates and that the real uncertainty is about 1% [Conway2018, Birk2017], at least for the most intense lines. Such error bars have a marginal impact on the resonance absorption simulation and thus can hardly explain the observed non-smooth frequency dependence. On the contrary, the HITRAN uncertainty of the self-broadening parameter can be large (20%), even for some of the most intense lines. Possible impact of this uncertainty on the retrieved continuum was estimated from the following procedure:

(i) self-broadening parameter of all water lines were independently and randomly varied within the HITRAN uncertainty range and 80 sets of broadenings were generated for our line list;

(ii) water vapor absorption was simulated as the sum of the continuum and the resonance absorption, the first one was modeled as a smooth curve, that roughly reproduce our experimental data (blue curve in Fig. 10), and the second one was modeled as a line by line sum using their parameters from HITRAN database except for self-broadening parameters for which values as described in (i) were used;

(iii) the continuum spectra were determined by subtraction of the resonance absorption modeled using unperturbed HITRAN values from water vapor absorption data simulated at previous step (ii);

(iv) maximum and minimum values of the continuum obtained from the 80 statistically spread data at each selected absorption micro-window frequency were found. They are presented in Fig. 10 (black curves) together with experimental data (red circles). This figure demonstrates that the line width uncertainty may lead to fluctuations from a smooth function with an amplitude comparable to the observations. The self-broadening coefficient of water lines is thus an important source in the error budget on C S values. The impact of inadequate resonance line shape modeling (i.e. important deviations from the assumed line shape function), at large detuning from the line center was also considered. The total observed continuum absorption was approximated by a smooth function as before and a simple model was used to account for super-and sub-Lorentzian effects in the intermediate wings [Serov2017]. It is worth mentioning that practically the same approach was used in [Tran2017]. The model includes two variable parameters: the intermediate wing amplitude, A, and the characteristic width of the wing, ∆ν wing . In [Serov2017], the best modeling of the continuum spectrum in the 40-200 cm -1 range was achieved by setting the parameter ∆ν wing to 11 cm -1 , the value of the A parameter was determined from the fit of the continuum model to experimental data. The C S values at the selected spectral points, calculated following this approach are plotted in Fig. 11. A negative correlation exists between the A and ∆ν wing parameters of the model: similar fit quality can be obtained by a simultaneous increase of ∆ν wing and decrease of A and vice versa. As expected, larger ∆ν wing values lead to a smooth cumulative contribution of the wings (∆ν wing ) and smaller values of ∆ν wing entail irregular sharper structure similar to those observed in our experiment. This is illustrated in Fig. 11 by two simulations corresponding to ∆ν wing equal to 88 and 5.5 cm -1 . Note that the smaller ∆ν wing value is more reasonable taking into account the mean collision duration between two water molecules evaluated in [Serov2017]. We thus conclude that uncertainties of intermediate and far line wings of the water resonance lines can also be a reason of the non-smooth frequency dependence of water vapor continuum.

Conclusions

The self-continuum absorption of water vapor for the two main isotopologues (H 2 16 O and H 2 18 O) was investigated at the SOLEIL synchrotron in two frequency domains: 15-35 cm - 1 and 50-500 cm -1 . These spectral intervals are attractive for understanding the continuum origin by comparison to the unique quantum chemical calculations of the water dimer spectrum [Scribano2007]. To the best of our knowledge, the retrieved continua are the first ever reported for the H 2 18 O isotopologue and for natural water in the 200-350 cm -1 interval. The pressure squared dependence of the measured continua was systematically checked and used as criterion to validate the reported cross-section values.

The H 2 16 O continuum in the 15-35 cm -1 range together with literature results in the 3-50 cm -1 range [Burch1982, Furashov1985, Kuhn2002, Podobedov2008, Koshelev2011b, Slocum2015, Odintsova2017, Koshelev2018] agree with ab initio calculations of the water dimer spectrum [START_REF] Scribano | Contribution of water dimer absorption to the millimeter and far infrared atmospheric water continuum[END_REF]]. This agreement confirms the dominant contribution of water dimer absorption to the observed continuum in this domain. The SNR of the spectra and the absence of ab initio calculations of (H 2 18 O) 2 spectrum prevented to evidence the small isotopic red-shift of the H 2 18 O continuum. The MT-CKD model does not account for the frequency dependence water self-continuum in this range.

The large 50-500 cm -1 coverage of our spectra allows for comparison to various previous experimental investigations with more limited spectral coverage [Burch1982, Furashov1996, Podobedov2008, Slocum2015, Odintsova2017]. An overall general agreement is achieved for natural water while the MT-CKD model [Mlawer2012] significantly overestimates the continuum in this region. On the basis of spectra simulations, the inadequate description of the line shapes in the range of the intermediate wings (detuning of 5-10 cm -1 from line center) and the uncertainties on the self-broadening coefficients of water monomer lines are identified as possible mechanisms responsible of the obtained irregular frequency dependence of the retrieved C S values. The development of a more rigorous model of the intermediate line wings of water vapor appears to be a critical step to improve the analysis. In this context, the investigation of the isotopic dependence of the continuum in the rotational range may give insights to test the contribution of intermediate wings of resonance lines.

  Synchrotron Mode (15-35 cm -1 ) 3.1 Cross-section retrieval

Fig

  Fig.1.Synchrotron power transmitted through the empty cell (red), cell filled with water (blue) and simulation corresponding to the resonance absorption only (green). The spectra were recorded with a 0.02 cm -1 resolution.

Fig. 3 .

 3 Fig.3.Upper panel: FTS absorption spectrum of H 2 18 O (94.1% enrichment) recorded at 296 K and 16 mbar (blue), corresponding water resonance absorption spectrum simulated using the HITRAN2016 database[Gordon2016] (green). Lower panel: Water vapor self-continuum cross-section of H 2 18 O derived from the 16 mbar (blue) and 13 mbar (red) recordings.

Fig. 4 .

 4 Fig. 4.Overview comparison of the experimental values of the normalized self-continuum cross-section of water vapor, C S (ν)/ν 2 , to the spectral function of water dimer at room temperature (brown solid line) calculated ab initio[START_REF] Scribano | Contribution of water dimer absorption to the millimeter and far infrared atmospheric water continuum[END_REF]] and the MT-CKD_3.2 model (dashed black line).

Fig. 5 .

 5 Fig. 5. Comparison of H 2 16 O and H 2 18 O normalized self-continuum cross-sections, C S (ν)/ν 2 . Blue and red symbols correspond to H 2 16 O and H 2 18 O, respectively (both obtained from water vapor recording at 16 mbar). Light blue and magenta curves correspond to a smoothing of the H 2 16 O and H 2 18 O data, respectively.

Fig. 6 .

 6 Fig. 6.Transmission spectrum of natural water (blue) at a pressure of 6 mbar and corresponding background spectrum recorded with the empty cell (red).

Fig. 9 .

 9 Fig. 9. Comparison of the water vapor self-continuum derived in this work to previous experimental studies [Burch1982, Furashov1996, Odintsova2017, Podobedov2008, Slocum2015,] and to the MT-CKD_3.2 model [Mlawer2012].

Fig. 10 .

 10 Fig. 10. Estimated influence of the uncertainty of self-broadening parameters listed in HITRAN to the retrieved self-continuum cross sections (black curves), experimental values (red circles). The blue curve corresponds to a smoothing of the experimental values.

Fig. 11 .

 11 Fig.11. Continuum model based on the line shape approach of [Serov2017] for different values of the ∆ν wing parameter and comparison to experimental continuum (red circles).

Table 1 .

 1 Experimental conditions of the recordings (151.75 m path length).

	Freq. Range, cm -1	P, mbar	Resolution, cm -1	Number of acquisitions
			H 2 16 O
	15-35	16.00	0.02	1520
		11.03		100
	40-650	6.099	0.02	200
		5.495
		4.999
		4.000
		2.995
		5.993	0.002	380
			H 2 18 O
	15-35	15.94	0.02	1060
		13.13		1340
	40-650	6.018	0.02	200
		5.450
		5.000
		4.500
		3.993
		3.497
		2.994
		1.985
		3.991	0.002	200
		5.982

Table 2 .

 2 Experimental conditions and techniques of previous continuum measurements.

	Reference	Technique	T	Spectral interval, cm -1
	Burch1982	Interferometer	296	14-50 and 350-800
	Kuhn2002	Resonator spectrometer	296-356 5.1-11.7
	Podobedov2008	FTS	293-333 20-90
	Koshelev2011b	Resonator spectrometer	261-328 3.5-4.8
	Slocum2015	Video-spectrometer	296	50
	Odintsova2017	FTS	297	14-35 and 40-200
	Koshelev2018	Resonator spectrometer	296	3.5-8.5
	This work	FTS	297	15-35 and 50-500

Acknowledgements

This work became possible due to the Project No 20180347 supported by SOLEIL Synchrotron Team. TAO, AOZ and MYT acknowledge Russian Foundation for Basic Research. The sub-THz range data treatment and the continuum retrieval was supported by project № 18-05-00698; the FIR data analysis was performed within the project № 18-02-00705; water dimer contribution in sub-THz range was analyzed within RAS program № 0035-2018-00002. PR and OP aknowledge partial support from CNRS-RFBR project 18-55_16006. The authors are grateful to C. Leforestier for numerical data related to ab initio calculations of water dimer absorption.


Jérôme Cleach

Philippe Pasdois

Philippe Marchetti

Denis Watier

Guillaume Duflos

Emmanuelle Goffier

Anne-Sophie Lacoste

Christian Slomianny

Thierry Grard
email: thierry.grard@univ-littoral.fr

Philippe Lencel

Jérôme Cléach

Mitochondrial activity as an indicator of fish freshness

Keywords: Mitochondrial membrane potential (ΔΨm), mitochondrial respiration, fish freshness, gilthead sea bream (Sparus aurata)

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

Introduction

The quality of aquatic products is defined by objective criteria such as food safety, nutritional quality, origin, and traceability of the products (G Olafsdottir, Martinsdóttir, [START_REF] Olafsdottir | Methods to evaluate fish freshness in research and industry[END_REF][START_REF] Olafsdottir | Multisensor for fish quality determination[END_REF]. It also depends on less objective criteria such as the organoleptic properties and the freshness of the products.

Fish freshness is "dependent on different biological and processing factors" (Gudrun [START_REF] Olafsdottir | Multisensor for fish quality determination[END_REF].

To meet expectations in terms of freshness, the fishing industry is trying to improve information on the date of capture of the product. However, treatments and storage conditions can vary greatly, strongly affecting quality and fish freshness. Seafood 4/25 products are highly perishable and processing factors determine the quality of the product [START_REF] Cheng | Texture and structure measurements and analyses for evaluation of fish and fillet freshness quality: a review[END_REF][START_REF] Mendes | Technological processing of fresh gilthead seabream (Sparus aurata): A review of quality changes[END_REF].

Consumers are becoming more attentive and demanding concerning the quality of food, including seafood. By definition, a fish can be considered fresh when its organoleptic, physical and chemical characteristics are very close to those of a living fish [START_REF] Oehlenschläger | Criteria of fish freshness and quality aspects[END_REF]. Savvy consumers or experts are able to discriminate fresh products by a sensory approach. Sensory evaluation grids have been developed to train a less experienced audience. However, these approaches remain highly dependent on the consumer's level of perception and knowledge of the product.

Further research is required to develop methods to evaluate fish freshness, and there are still many challenges. Microbiological, organoleptic and chemical methods are used routinely in the fishing industry to evaluate fish freshness. As an example, the total volatile base nitrogen (TVB-N) level increases significantly during the late stages of storage (10-20 days of storage), and is therefore a limited freshness indicator [START_REF] Castro | Total volatile base nitrogen and its use to assess freshness in European sea bass stored in ice[END_REF][START_REF] Parlapani | Microbiological spoilage and investigation of volatile profile during storage of sea bream fillets under various conditions[END_REF], but should rather be seen as an advanced spoilage indicator. Moreover, TVB-N/total biogenic amines (TBA) analyses are not applicable to all fish species. Therefore, research in this area and the development of new fish freshness indicators are still a challenge for scientists and industry.

Many studies have shown post mortem structural changes in myofibrillar proteins (Delbarre-Ladrat, Chéret, [START_REF] Delbarre-Ladrat | Trends in postmortem aging in fish: understanding of proteolysis and disorganization of the myofibrillar structure[END_REF]. These changes in muscle tissue have often been correlated with the mechanical properties of the tissues (texture, elasticity, suppleness, hardness, cohesion, etc.) [START_REF] Taylor | Salmon fillet texture is determined by myofiber-myofiber and myofiber-myocommata attachment[END_REF]. The level of myofibrillar protein degradation can be correlated with fish alteration. In some of these studies, the structural changes in myofibrillar proteins have been associated with 5/25 structural changes in post mortem mitochondria (María Dolores [START_REF] Ayala | Muscle tissue structural changes and texture development in sea bream, Sparus aurata L., during post-mortem storage[END_REF][START_REF] Parsons | Mitochondria in cell death[END_REF]. Studies using electron microscopy have reported post mortem morphological mitochondrial changes such as swelling and disrupted cristae in muscle in cold storage from the gilthead sea bream (Sparus aurata) (María Dolores [START_REF] Ayala | Muscle tissue structural changes and texture development in sea bream, Sparus aurata L., during post-mortem storage[END_REF] and the Pacific bluefin tuna (Thunnus orientalis) [START_REF] Roy | Structural and ultrastructural changes of full-cycle cultured Pacific bluefin tuna (Thunnus orientalis) muscle slices during chilled storage[END_REF]. We focused on mitochondria to study their structural and functional changes in sea bream fillets stored at +4°C. Mitochondria play a central role in cell death mechanisms such as apoptosis and necrosis [START_REF] Parsons | Mitochondria in cell death[END_REF]. Several studies have shown that mitochondrial activity was still present post mortem in storage conditions of +4°C in bovine, murine and human models [START_REF] Barksdale | Mitochondrial viability in mouse and human postmortem brain[END_REF][START_REF] Cheah | Post-mortem changes in structure and function of ox muscle mitochondria. 1. Electron microscopic and polarographic investigations[END_REF][START_REF] Tang | Postmortem oxygen consumption by mitochondria and its effects on myoglobin form and stability[END_REF]. Mitochondrial activity in fish has been studied in the areas of eco-physiology [START_REF] Blier | Mitochondrial activity in rainbow trout red muscle: the effect of temperature on the ADP-dependence of ATP synthesis[END_REF][START_REF] Hilton | Temperature sensitivity of cardiac mitochondria in intertidal and subtidal triplefin fishes[END_REF][START_REF] Lionetti | High-lard and high-fish-oil diets differ in their effects on function and dynamic behaviour of rat hepatic mitochondria[END_REF] and eco-toxicology [START_REF] Cambier | At environmental doses, dietary methylmercury inhibits mitochondrial energy metabolism in skeletal muscles of the zebra fish (Danio rerio)[END_REF][START_REF] Soares | Mitochondria as a target for decavanadate toxicity in Sparus aurata heart[END_REF][START_REF] Van Den Thillart | The effect of acclimation temperature on the activation energies of state III respiration and on the unsaturation of membrane lipids of goldfish mitochondria[END_REF]. However, to our knowledge, there are currently no studies on the impact of storage at +4°C on post mortem changes in fish mitochondrial structure and function.

The purpose of this study was therefore to evaluate whether mitochondrial structure and function could be considered reliable and early markers of fish freshness.

To determine post mortem changes in mitochondrial structure and function, two approaches were used: firstly, morphological changes were analysed by transmission electron microscopy; and secondly, a functional analysis was performed to assess the 6/25 oxygen consumption and membrane potential (ΔΨm) of mitochondria isolated from gilthead sea bream fillets stored at +4°C.

Materials and methods

Reagents and materials

Rhodamine 123 (Rh123), carbonyl cyanide 3-chlorophenylhydrazone (CCCP), Tris (hydroxymethyl)aminomethane (Trizma ® base), ethylene-bis(oxyethylenenitrilo)tetraacetic acid (EGTA), proteinase type XXIV, bovine serum albumin (BSA), 4morpholinepropanesulfonic acid (MOPS), malate, succinate, adenosine 5′-diphosphate (ADP), carboxyatractyloside (CAT) and cytochrome c from equine heart were purchased from Sigma-Aldrich (St. Louis, MO, USA). Potassium chloride (KCl) and glutamate were acquired from Fisher Labosi (Paris, France). Sucrose, magnesium chloride (MgCl2), and potassium dihydrogen phosphate (KH2PO4) were purchased from Acros Organics (Morris, NJ, USA). Rh123 and CCCP were prepared in dimethyl sulfoxide (DMSO) purchased from Thermo Scientific (San Diego, CA, USA).

Fish muscle origin and storage

The gilthead sea bream (300-400 g) were sourced from Aquanord sea farm (Gravelines, France). This farmed fish model was chosen in order to obtain accurate data on living conditions, slaughter, and storage, which influence the study of freshness. Breeding conditions were: temperature 18 ± 6°C, pH 8.2, total ammonia < 30 pmol/L, and dissolved oxygen 99 % (v/v) to saturation (7 ppm). Within the Aquanord sea farm, the fish were killed by asphyxiation/hypothermia and kept on ice (0 to 2°C) in expanded polystyrene boxes for 4 hours of transport. We bought the fish from the company after their death. Upon arrival at the laboratory, the fish were immediately skinned and filleted. The fillets were stored on ice in a cold room (+4°C) for 5 days and used for experiments every 24 hours over 6 days: Day 0,

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Day 1, Day 2, Day 3, Day 4 and Day 6. The ice was renewed every day. Plastic wrapping was used to avoid contact between the fillets and the ice or the accumulated water.

Sample preparation and transmission electron microscopy

To prepare samples, as previously described [START_REF] Michalec | Short-term exposure to gold nanoparticle suspension impairs swimming behavior in a widespread calanoid copepod[END_REF], 3 mm 3 pieces of muscle were cut from fillets and fixed in 2.5% glutaraldehyde (Merck KGaA, Darmstadt, Germany) buffered with 0.1M sodium cacodylate (Sigma-Aldrich), postfixed in 1% osmium tetroxide (Sigma-Aldrich) in the same buffer and "en bloc" stained with 2% uranyl acetate (Agar Scientific, Stansted, Essex, UK). After acetonitrile dehydration (Sigma-Aldrich), samples were embedded in epon-like resin (Embed-812). Ultrathin sections (90 nm) were cut using a Leica UC7 ultra-microtome and collected on 150 mesh hexagonal barred copper grids. After staining with 2% uranyl acetate prepared in 50% ethanol (Fisher, Loughborough, Leicester, UK) and incubation with a lead citrate solution, sections were observed on a Hitachi H-600 transmission electron microscope equipped with a W electron source (operated at 75kV) and a side mounted Hamamatsu C4742-95 digital camera.

Mitochondrial isolation from fish fillets

The method for mitochondrial isolation was adapted from [START_REF] Pasdois | The role of oxidized cytochrome c in regulating mitochondrial reactive oxygen species production and its perturbation in ischaemia[END_REF]. All the steps in mitochondrial isolation were performed in a cold room at +4°C. Red muscle was dissected from the fillet (10 g) and finely diced with scissors. The fine pieces obtained (2-3 mm 3 ) were incubated at +4°C for 7 minutes under stirring in 20 mL of isolation buffer (180 mM KCl, 80 mM sucrose, 5 mM MgCl2, 10 mM Tris, 2 mM EGTA, pH 7.2 at +4°C) supplemented with 0.1 mg/mL of bacterial proteinase type XXIV. The resulting tissue suspension was poured into a 30 mL glass Potter homogeniser and homogenised for 3 min using a motorised Teflon pestle at 300 rpm. The homogenate was centrifuged at 7 500 g 8/25

for 10 minutes. The resulting pellet was first washed and then resuspended in 20 mL isolation buffer containing 2 mg/mL of fatty acid free BSA and homogenised for 3 minutes at 150 rpm.

The homogenate was then centrifuged at 700 g for 10 min. The supernatant was centrifuged at 1500 g for 10 min. The resulting supernatant was centrifuged again at 7 000 g for 10 min. The mitochondrial pellet obtained was resuspended with a low volume (50 µL) of isolation buffer in order to obtain a concentrated mitochondrial suspension. The protein concentration was determined using a Bio-Rad protein assay kit, derived from the Bradford method (1976), using BSA as a standard. Mitochondria were kept on ice at a final concentration of 60-100 mg/mL for not more than 4 h.

Measurement of mitochondrial ΔΨm

A Xenius XC spectrofluorometer (SAFAS, Monaco) was used to monitor the fluorescence of Rh123 [START_REF] Emaus | Rhodamine 123 as a probe of transmembrane potential in isolated rat-liver mitochondria: spectral and metabolic properties[END_REF] in order to evaluate changes in mitochondrial ΔΨm of isolated mitochondria extracted at different storage times (Day 0, Day 1, Day 2, Day 3 and Day 4). Importantly, this experimental approach does not enable the user to measure ΔΨm but gives a qualitative index of mitochondrial polarisation. 1 mL of respiration buffer (KCl 125 mM, MOPS 20 mM, Tris 10 mM, EGTA 10 µM, KH2PO4 2.5 mM, fatty acid free BSA 2 mg/mL, pH 7.2) at 25°C was added to a 3 mL plastic cuvette. Rh123 (50 nM final) and respiratory substrates -glutamate (5 mM), malate (2 mM) and succinate (5 mM) -were added sequentially. The baseline fluorescence of free Rh123 was recorded during 2 minutes and mitochondria (0.2 mg/mL) were then added. The generation of ΔΨm leads to accumulation of Rh123 in the mitochondrial matrix and consequent fluorescence quenching (dye stacking). To evaluate mitochondrial function, the following additions were performed sequentially. ADP (1 mM), CAT (5 µM) and CCCP (2 µM). The sampling rate was 1 Hz, bandwidth 15 nm at excitation and emission, and photomultiplier tube voltage was 700 V.

Samples were excited at 500 nm and fluorescence was collected at 535 nm.

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The Rh123 fluorescence intensities recorded at different states of respiration (basal (substrates only), state 3 (ADP addition), and CAT) were normalised to the fluorescence recorded after CCCP addition, according to the following formula:

Where: X = Rh123 fluorescence intensity after CCCP addition Y = Rh123 fluorescence intensity after mitochondria or ADP or CAT addition CCCP at 2 µM completely depolarised mitochondria by consuming all the proton gradient established by the respiratory chain. Thus, the fluorescence intensity obtained after its addition corresponded only to the dissipation of ΔΨm and enabled us to take into account the non-specific binding of the dye.

Respiration assay

Oxygraphy (Rank Brothers digital model 10, Cambridge, United Kingdom) was used to monitor the oxygen consumption of isolated mitochondria at 25°C [START_REF] Frezza | Organelle isolation: functional mitochondria from mouse liver, muscle and cultured filroblasts[END_REF]. Firstly, 2.1 mL of respiration buffer (composition previously described) were added to the oxygraphic chamber supplemented with a mixture of glutamate (5 mM), malate (2 mM) and succinate (5 mM). Then, mitochondria were added at a final concentration of 0.2 mg/mL. Oxygen consumption rates were assessed without and with ADP (1 mM) (basal and state 3, respectively). Then, CAT (5 µM) was added to block the oxygen consumption linked to ATP synthesis. In order to evaluate the permeability of the mitochondrial outer membrane, 10 µM of exogenous cytochrome c from equine heart were added. At the end of the acquisition, CCCP was added to disrupt mitochondrial ΔΨm and to uncouple the respiratory chain, leading to an increase in oxygen consumption. The medium was stirred continuously during measurement. Calibration using sodium dithionite was performed to reach zero oxygen in the oxygraphic chamber.

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Oxygen consumption rates were determined at each day of storage in the different experimental conditions (basal, state 3, and CAT). As an index of mitochondrial coupling, the respiratory control index (RCI) was calculated according to the following formula:

Where state 3 is the respiration rate during maximum ATP synthesis and CAT is the respiration rate not linked to ATP synthesis. The integrity of the outer membrane was evaluated by calculating the percentage of oxygen consumption not linked to ATP synthesis stimulated following the addition of exogenous cytochrome c.

Statistical analysis

The statistical analysis and graphs were generated with SPSS 17 software. Each experiment was performed at least in triplicate. Data are expressed as mean + standard deviation.

Unpaired two-sample t-tests were used to express the significance of difference (p < 0.05) between means, and Levene's test was used to determine the homogeneity of variance.

Results

Ultrastructural analysis of post mortem fish muscle at different times of storage

In order to study post mortem (PM) cell structural changes, the ultrastructure of gilthead sea bream muscle tissue was observed by transmission electron microscopy (TEM) from Day 0 to Day 6: Day 0 (6 h PM: Fig. 1a), Day 3 (72 h PM: Fig. 1b), Day 4 (96 h PM: Fig. 1c), Day 6 (144 h PM: Fig. 1d).

At Day 0, myofibrils were characterised by intact and well organised bands (I-bands and Abands) and lines (Z-lines and M-lines). The myofilaments of actin and myosin, which constitute the sarcomere, were well defined and their alignment was parallel.

The disorganisation of the I-bands was observed from Day 3 of storage, and it was amplified at Day 4 (Fig. The micrograph of gilthead sea bream muscle at Day 0 showed intact mitochondria with a dense matrix. The cristae compartments were compact and well organised. For the majority of the mitochondria, the double layer membranes were visible, with an intact and regular shape.

From Day 3, mitochondrial morphology began to change: mitochondria appeared swollen.

The shape of the membranes was discontinuous and in some places damaged. The cristae were elongated, tubular, disorganised and had almost disappeared in some mitochondria. The matrix had a more electron lucent appearance with the presence of a few dense granules (Fig. From a general point of view, gilthead sea bream fillet muscle cells underwent several major structural changes from 3 days post mortem at +4°C. The mitochondria seemed to show profound structural damage from the third day. The correlation between structural damage and mitochondrial activity post mortem in fish fillet muscle was studied in the subsequent experiments.

Post mortem assessment of mitochondrial function

Here, we studied mitochondrial oxygen consumption in gilthead sea bream fillet muscle by oxygraphy at different times of storage at +4°C (Fig. 2.a-e).

Figure 2 shows typical oxygraphic recordings of the changes in mitochondrial function from Day 0 to Day 4 (a: Day 0; b: Day 1; c: Day 2; d: Day 3; e: Day 4). At Day 0 (Fig. 2a), basal respiration (substrates only) reached 13.9 nmol O2/min/mg proteins. Following ADP addition, 12/25 mitochondrial respiration was stimulated (39.95 nmol O2/min/mg proteins), due to the consumption of the proton gradient by the ATP synthase. Addition of CAT inhibited the adenine nucleotides translocator and consequently ATP synthesis. As a consequence, oxygen consumption decreased to reach a new steady state of respiration not coupled to ATP synthesis (7 nmol O2/min/mg proteins). The addition of cytochrome c, showing the integrity of the outer membrane of mitochondria by measuring the effect on respiration, demonstrated that the endogenous cytochrome c had no effect on respiration. The mitochondrial outer membrane was intact. Finally, the decoupling agent CCCP was added. The respiration rate strongly increased during a very short time, illustrating an increase of respiratory activity to maintain the disruption of ΔΨm (Fig. 2a.b.c.d.). That was not the case for Day 4 (Fig. 2e).

The results for mitochondrial oxygen consumption at Day 0 were compared with mitochondrial oxygen consumption at Day 1 (Fig. to Day 4 (Fig. 2.e), the respiration rate at state 3 decreased gradually from 39.95 nmol O2/min/mg proteins to 24.225 nmol O2/min/mg proteins. From Day 0 (Fig. 2.a) to Day 3 (Fig. 2.d), the difference between the basal respiration rate and state 3 respiration rate was important. At Day 4 (Fig. 2.e), differences between the basal respiration rate (17.54 nmol O2/min/mg proteins) and the state 3 respiration rate (24.22 nmol O2/min/mg proteins) were very weak, demonstrating that ADP addition had barely effect.

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Figure 3.a illustrates the repeatability of results from Figure 2, according to 3-5 independent experiments. Changes in respiration (basal, state 3 and after CAT addition) are illustrated in Figure 3a. From Day 0 to Day 3, no difference in basal respiration and a slight decrease of the state 3 respiration rate were observed. By Day 4 (Fig. 3a), the basal respiratory rate had increased by 45% (10.48 ± 3.10 nmol O2/min/mg proteins to 15.93 ± 5.38 nmol O2/min/mg proteins, p < 0.05). At Day 4, an increase in the respiration rate after CAT addition was observed (8.88 ± 2.36 nmol O2/min/mg proteins to 15.66 ± 5.66 nmol O2/min/mg proteins, p < 0.05). At Day 4, mitochondria were not responding to ADP addition, indicating either dysfunction of the ATP synthasome or increased permeability of the inner membrane to protons.

The respiratory control index (RCI = state3/CAT) was calculated for each day (Fig. 3a). At Day 0, RCI was 3.17 ± 0.71. RCI decreased from Day 0 to Day 4 to reach 1.30 ± 0.15, illustrating a significant difference between Day 0 and Day 4 (p < 0.05).

External membrane integrity was measured by the addition of exogenous cytochrome c (Fig.

3.b).

From Day 0 to Day 2, an elevation of the respiration rate was observed between 0.70 and 8%. An increase induced by cytochrome c was considered normal and acceptable when it is between 5 and 15% [START_REF] Kuznetsov | Analysis of mitochondrial function in situ in permeabilized muscle fibers, tissues and cells[END_REF]. From Day 3, more than 30% stimulation of the respiratory rate was observed (38.5% ± 21.19 at Day 3 and 35% ± 19.06 at Day 4), illustrating that the outer membrane of mitochondria was damaged.

Post mortem assessment of mitochondrial ΔΨm

To further characterise changes in mitochondrial function post mortem, a qualitative assessment of mitochondrial ΔΨm was performed (Fig. 4). ΔΨm, being generated by the electron transport chain, is correlated to mitochondrial function and integrity [START_REF] Zorova | Mitochondrial membrane potential[END_REF]. The potentiometric dye

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Rh123 was used to qualitatively assess ΔΨm. Rh123 accumulates in the mitochondrial compartment as a function of ΔΨm. The higher the potential, the more dye will enter the matrix. Following accumulation and stacking of the dye within the matrix, its fluorescence is quenched. Modulation of the electron transport chain activity by ADP, CAT or CCCP leads to changes in ΔΨm and consequent movement of the dye across the mitochondrial inner membrane.

At Day 0 (Fig. 4.a), the addition of mitochondria to the buffer led to a strong fluorescence intensity decrease (quenching). Then, when ADP was added (state 3), the Rh123 fluorescence increased due to the release of the probe from the matrix in the surrounding buffer. ADP addition led to a decrease in ΔΨm. In contrast, addition of CAT restored ΔΨm, and consequently led to a decrease in fluorescence intensity. At the end of the experiment (Day 0;

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The action of CCCP (increased fluorescence due to Rh123 release) was related to the level of probe incorporation, and was more visible at Days 0, 1, 2, and 3 (Fig. 4.a-d) than at Day 4 (Fig. 4.e). The results obtained at Day 4 revealed that ΔΨm is disrupted.

In order to obtain an overall view of changes in ΔΨm at different storage times post mortem, the recorded fluorescence intensity was analysed at different states of respiration (Fig. 5). The fluorescence associated with different states of respiration (basal/ADP/CAT) was normalised by the fluorescence associated with CCCP treatment (as described in Materials and methods).

From Day 0 to Day 2, the effects of ADP and CAT on Rh123 fluorescence were significant.

From Day 3 to Day 4, neither ADP nor CAT affected Rh123 fluorescence, demonstrating severe mitochondrial dysfunction.

From Day 3 to Day 4, the normalised Rh123 fluorescence was significantly higher for each state of respiration in comparison with Days 0, 1, and 2. This increase reflected a lower intake of Rh123 in the mitochondria, and consequently a fall in ΔΨm. On the basis of these results, we can conclude that after 72 h of storage (Day 3) at +4°C, ΔΨm started to decline and became significantly disrupted after 96 hours (Day 4).

Discussion

The research of early markers of freshness is still a current challenge. This study focused, for the first time, on mitochondria function as reliable indicator of fish freshness. Mitochondrial activity was studied in fish skeletal muscle at different time points of post mortem storage at +4°C in order to show structural and functional changes in post mortem mitochondria. The structural changes were described based on electron microscopy images. A dual approach to mitochondrial functionality (oxymetric approach and mitochondrial potential approach (ΔΨm)) enabled us to better understand the alterations affecting the mitochondria in sea bream fillet muscle. This research showed that mitochondria undergo profound post mortem changes, which may be a relevant finding for assessment of food product freshness.

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Post mortem structural changes in fish skeletal muscle

Electron microscopy images were used to study the structural changes in mitochondria in fish fillets stored post mortem at +4°C over 6 days. By choosing Days 3 and 4, we aimed to check whether the observed mitochondrial activity changes were associated with major structural changes. At Day 0 (6 hours post mortem), fish cell muscle retained its structural integrity. The myofibril arrangement was conserved and well organised. No gaps between sarcomeres were observable and collagen was still visible. These observations were consistent with those in other studies, which described good preservation of muscle myofilaments in gilthead sea bream fillet at Day 0 (María Dolores [START_REF] Ayala | Muscle tissue structural changes and texture development in sea bream, Sparus aurata L., during post-mortem storage[END_REF]María Dolores Ayala, Santaella, Martínez, Periago, Blanco, Vázquez, et al., 2011;[START_REF] Caballero | Post mortem changes produced in the muscle of sea bream (Sparus aurata) during ice storage[END_REF]. The majority of mitochondria were intact with nonaltered membranes and a network of compact and well organised cristae. Some authors who have studied changes in myofilament structure in fish muscle have also been able to observe changes in mitochondria (María Dolores [START_REF] Ayala | Muscle tissue structural changes and texture development in sea bream, Sparus aurata L., during post-mortem storage[END_REF]. For example, in gilthead sea bream fillet (kept at +4°C), these authors observed swelling of some organelles, such as mitochondria and sarcoplasmic reticulum 3 hours post mortem. Another study on sea bass, carried out by the same authors, showed rapid changes in mitochondrial structure (with swelling) 3 hours post mortem (Ma D [START_REF] Ayala | Structural and ultrastructural changes on muscle tissue of sea bass, Dicentrarchus labrax L., after cooking and freezing[END_REF]. Similarly, Roy, Ando, Itoh, and Tsukamasa (2012) described altered mitochondria with swollen cristae in Pacific bluefin tuna muscle cells at Day 0. Studies specifically focused on mammalian mitochondria showed good mitochondrial structure preservation several hours post mortem. From a structural point of view, it appears that gilthead sea bream mitochondria (like for mammalian mitochondria: [START_REF] Barksdale | Mitochondrial viability in mouse and human postmortem brain[END_REF]) undergo few changes within a few hours of the animal's death. From Day 3 to Day 6 (72 h -144 h post mortem), several forms of structural damage in muscle 17/25 myofilaments were observed in gilthead sea bream fillet, with general disorganisation of myofibril alignment, showing several gaps. The same observations were reported from Day 5 in gilthead sea bream muscle, such as alterations of sarcomeres at the I-band level, alteration of actin filaments, and disruption of Z-lines (María Dolores [START_REF] Ayala | Muscle tissue structure and flesh texture in gilthead sea bream, Sparus aurata L., fillets preserved by refrigeration and by vacuum packaging[END_REF].

Mitochondria were swollen with disrupted membranes and dense granules in the mitochondrial matrix. Dense granules were also observed (María Dolores [START_REF] Ayala | Muscle tissue structural changes and texture development in sea bream, Sparus aurata L., during post-mortem storage[END_REF] on gilthead sea bream mitochondria from 5 days post mortem. These granules have also been observed post mortem in mammalian mitochondria [START_REF] Kuypers | Post-mortem elemental redistribution in rat studied by X-ray microanalysis and electron microscopy[END_REF]. Importantly, an explanation was offered for the appearance of dense granules in mitochondria [START_REF] Wolf | 3D visualization of mitochondrial solid-phase calcium stores in whole cells[END_REF]. These authors showed that the granules resulted from the accumulation and precipitation of calcium in the mitochondrial matrix. During cell death processes, calcium homeostasis is profoundly disturbed, leading to massive calcium entry into the mitochondria [START_REF] Dong | Calcium in cell injury and death[END_REF]. This flux initially caused swelling of the organelles and then precipitation of calcium as insoluble phosphate and hydroxyapatite, which participated in mitochondrial damage and cell death [START_REF] Dong | Calcium in cell injury and death[END_REF]. The calcium aggregation in ischaemic conditions described by these authors could be similar to that found post mortem in muscle cells, which were also deprived of oxygen.

Mitochondrial activity: an early fish freshness indicator

In the second part of our study, we focused on mitochondrial activity post mortem in fish muscle cells at different storage time points at +4°C: Day 0 (6 h), Day 1 (24 h), Day 2 (48 h), Day 3 (72 h), and Day 4 (96 h). Two approaches based on oxygraphy and fluorescence enabled us to investigate mitochondrial activity.

Mitochondria maintained significant respiratory activity for the first 3 days of storage (Day 0 to Day 3). From Day 4, respiratory activity declined significantly (96 hours post mortem):

18/25 RCI (1.30 ± 0.15) was significantly lower than at Day 0 (3.17 ± 0.71). RCI is a useful measure to assess mitochondrial function in isolated mitochondria, and its decrease is associated with mitochondrial dysfunction [START_REF] Brand | Assessing mitochondrial dysfunction in cells[END_REF]. This mitochondrial dysfunction resulted from electron transport chain alteration, and this activity can be explored with different substrates (ADP, CAT, cytochrome C, and CCCP). On the fourth day (Day 4), decoupling agents such as CCCP and ADP had no action on mitochondrial respiration (no increase in respiratory activity), showing the inability of respiratory chains to adapt to the loss of mitochondrial potential (via ADP or CCCP addition). Mitochondrial decoupling at Day 4 could be due to mitochondrial membrane permeabilisation. Alteration of the mitochondrial outer membrane was confirmed by the activating effect of exogenous cytochrome c on respiration activity (30% at Day 4).

The fluorescent probe Rh123 was used to evaluate the ΔΨm of isolated mitochondria. By comparing findings with oxygraphic results, we can clearly observe the uncoupling action of ADP and CCCP on mitochondria isolated from sea bream fillets stored at +4°C (Day 0, Day 1, and Day 2). ADP and CCCP led to dissipation of mitochondrial potential, which decreased the uptake of the probe and thus increased the overall fluorescence in the surrounding buffer.

From Day 3, ADP and CCCP additions had no significant effects on Rh123 fluorescence intensity, indicating mitochondrial decoupling. In addition, the intensity of Rh123 fluorescence increased from Day 3 for all states of respiration. This increase was associated with a decrease in Rh123 quenching. The high values for standard deviations obtained at Day 3, representative of eight independent experiments, highlighted the marked heterogeneity of the results at this precise time compared to Day 4. Overall, the results obtained with the Rh123 fluorescent probe demonstrated that ΔΨm was strongly and significantly disrupted from Day 4. This disruption was correlated to the decline in mitochondrial activity, and consequently to cell health and mitochondrial membrane integrity [START_REF] Zorova | Mitochondrial membrane potential[END_REF].

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The two approaches (oxygraphic and fluorescence) coincided well and showed that isolated mitochondria of sea bream fillets stored at +4°C retained activity 2 to 3 days post mortem.

From Day 3/Day 4, mitochondrial respiratory activity and ΔΨm strongly decreased. On the basis of the concept developed by [START_REF] Cheah | Post-mortem changes in structure and function of ox muscle mitochondria. 1. Electron microscopic and polarographic investigations[END_REF], the "critical storage time" was between 72 hours (Day 3) and 96 hours (Day 4) for the Sparus aurata model stored on ice at +4°C. Maintenance of mitochondrial activity has been demonstrated in other studies in ox neck muscle [START_REF] Cheah | Post-mortem changes in structure and function of ox muscle mitochondria. 1. Electron microscopic and polarographic investigations[END_REF][START_REF] Cheah | Properties of mitochondria from ox neck muscle after storage in situ[END_REF] and in mouse and human brain tissue [START_REF] Barksdale | Mitochondrial viability in mouse and human postmortem brain[END_REF].

In stress conditions of anoxia present after death, calcium homeostasis is disrupted and calcium levels increase in the sarcoplasm. Mitochondria have the ability to maintain their activity post mortem. This maintenance occurs because mitochondrial ATP synthase can run in reverse, hydrolysing ATP generated by glycolysis in order to maintain ΔΨm (St-Pierre, [START_REF] St-Pierre | Mitochondria as ATP consumers: cellular treason in anoxia[END_REF]. Sarcoplasmic calcium enters mitochondria through the maintained ΔΨm. From Day 3/Day 4, marked calcium accumulation in mitochondria was found and appeared in the form of dense granules by electron microscopy. Mitochondrial calcium overload developed, leading to ΔΨm disruption and mitochondrial membrane permeabilisation [START_REF] Dong | Calcium in cell injury and death[END_REF]. Membrane permeabilisation may be associated with the formation of mitochondrial permeability transition pores, leading to the release of cell death-inducing factors, cytochrome c, and huge amounts of calcium in the sarcoplasm. This release probably plays a role in integrating death signals and may participate in proteolytic enzyme activation (via the release of cytochrome c and mitochondrial calpain activation) [START_REF] Boudida | Muscle to meat conversion in common carp (cyprinus carpio): new insights involving apoptosis[END_REF][START_REF] Smith | Calpains, mitochondria, and apoptosis[END_REF].

Day 4 is a crucial storage time point in gilthead sea bream muscle cells, and is the starting point of marked cell alteration. From Day 4, it has been reported that insoluble collagen 20/25 decreased strongly, leading to a loss of firmness and an increase in the water-holding capacity [START_REF] Suárez | Changes in muscle collagen content during post mortem storage of farmed sea bream (Sparus aurata): influence on textural properties[END_REF]. At Day 4, the molecule dystrophin, which provides a link between cytoskeletal actin and the extracellular matrix, almost disappeared, while actin and desmin were detected in fish muscle at early stages of alteration post mortem (14 days). Loss of dystrophin is correlated to detachment myofibres and myocommata, and a reduction in flesh hardness [START_REF] Caballero | Post mortem changes produced in the muscle of sea bream (Sparus aurata) during ice storage[END_REF]. From Day 4, free LDH activity released from sea bream muscle strongly increased, demonstrating an increase of fish autolysis after 4 days of storage at +4°C [START_REF] Diop | Assessment of freshness and freeze-thawing of sea bream fillets (Sparus aurata) by a cytosolic enzyme: Lactate dehydrogenase[END_REF].

In future studies, it would be interesting to assess whether mitochondrial activity is maintained for a longer period of time in other experimental conditions, such as a storage temperature of +0°C/+2°C, the use of natural additives, or modified atmosphere packaging.

Conclusion

The mitochondrial structural changes (swelling, membrane and cristae alteration, and accumulation of dense granules) were correlated with an increase in permeability (sensitivity to cytochrome c), ΔΨm disruption, and a decrease in respiratory activity. The mitochondria of sea bream fillets stored at +4°C maintained significant respiratory activity for the first three days of storage. Therefore, mitochondria could be useful targets for evaluating the freshness of seafood, and the starting point for the development of a fish freshness kit concerning the first stages of spoilage. It would be very interesting to determine whether these structural and physiological mitochondrial changes in a fresh seafood product (such as fish fillets) have an influence on perceptions and the health of consumers. mitochondria (Mito.) (0.2 mg/mL), the molecules ADP (2 mM), CAT (5 µM) and CCCP (2 µM) were added to a 3 mL cuvette. These graphs are representative of one experiment.

Figure captions

  Figures 1a to 1d also illustrate the effects of post mortem storage on mitochondrial structures.

  1.b). The number of granules increased over time (few granules on Day 3, many granules on Day 6 (Fig 1.d)). At Day 6, dense granules were located in nearly all mitochondria.

  2.b), Day 2 (Fig. 2.c), Day 3 (Fig. 2.d), and Day 4 (Fig. 2.e). From Day 0 (Fig. 2.a) to Day 3 (Fig. 2.d), the mean basal respiration rate was around 13.67 nmol O2/min/mg proteins. From Day 4 (Fig. 2.e), the respiration rate increased to reach 17.75 nmol O2/min/mg proteins. From Day 0 to Day 3 (Figs. 2.a-d), ADP, CAT and CCCP produced an effect on oxygen consumption. From Day 4 (Fig. 2.e), the effect of these compounds was very weak, which showed mitochondrial decoupling. From Day 0 (Fig. 2.a)

Fig. 4

 4 Fig. 4.a), addition of CCCP disrupted ΔΨm and led to a rapid increase in fluorescence. The

Figure 1 :

 1 Figure 1: Longitudinal sections of gilthead sea bream muscle at different post mortem times:

Figure 2 :

 2 Figure 2: Post mortem assessment of respiratory activity of gilthead sea bream isolated

Figure 3 :

 3 Figure 3: Evaluation of mitochondrial intactness parameters

Figure 4 :

 4 Figure 4: Post mortem assessment of the mitochondrial membrane potential of gilthead sea

Figure 5 :

 5 Figure 5: Summary graphs of Rh123 fluorescence levels at different states of respiration

Acknowledgements

Jérôme Cléach would like to thank the Pôle Métropolitain de la Côte d'Opale council and PFI Nouvelles Vagues for their financial support of his PhD studies.

-Tris (hydroxymethyl)aminomethane (PubChem CID: 6503) -Ethylene-bis(oxyethylenenitrilo)tetraacetic acid (PubChem CID: 6207) -4-Morpholinepropanesulfonic acid (PubChem CID: 70807) -Malate (PubChem CID: 525) -Succinate (PubChem CID 160419) -Glutamate (PubChem CID: 33032) -Adenosine 5′-diphosphate (PubChem CID: 128882) -Carboxyatractyloside (PubChem CID: 20055804) 3/25 -Cytochrome c (PubChem CID 16057918) -Potassium chloride (PubChem CID: 4873) -Sucrose (PubChem CID: 5988) -Magnesium chloride (PubChem CID: 5360315) -Potassium dihydrogen phosphate (PubChem CID: 516951) -Dimethyl sulfoxide (PubChem CID: 679) -Glutaraldehyde (PubChem CID: 3485) -Sodium cacodylate (PubChem CID: 2724247) -Osmium tetroxide (PubChem CID: 30318) -Uranyl acetate (PubChem CID: 10915) -Acetonitrile (PubChem CID: 6342)

Funding

This study was funded by the French government and the Hauts-de-France region in the framework of the CPER 2014-2020 MARCO project. This research was also funded by FranceAgrimer in the framework of the Altfish project.