Marie Auvray

Frédéric Bolze

Gilles Clavier

Florence-Mahuteau-Betzer

Silafluorene as a promising core for cell-permeant, highly bright and two-photon excitable fluorescent probes for live-cell imaging

Keywords: Fluorescent probes, Silafluorene, Two-photon absorption, Live-cell imaging

In this study, we report the synthesis, linear and non-linear photophysical studies and live cell imaging of two two-photon activatable probes based on a silafluorene core: SiFluo-V and SiFluo-L. Thanks to their quadrupolar (A-π-D-π-A) design, these probes exhibit respectively good to impressive two-photon cross sections (from 210 GM to 2150 GM). TD-DFT calculations support the experimental evidence that SiFluo-L displays far better two-photon absorption properties than SiFluo-V. Moreover, SiFluo-L possesses all requirements for bioimaging as it is water soluble, cell-permeant and and presents a low cytotoxicity (IC80≥10 µM). It labels mitochondria in live-cell imaging at low laser power with high brightness, contrast and photostability. This study demonstrates that silafluorene is a promising core to develop new two-photon fluorophores for live cell imaging.

Introduction

Despite the growing interest on the development of fluorophores for live cell imaging, challenges to be tackled still remain. [START_REF] Klymchenko | Solvatochromic and Fluorogenic Dyes as Environment-Sensitive Probes: Design and Biological Applications[END_REF][START_REF] Xu | Discerning the Chemistry in Individual Organelles with Small-Molecule Fluorescent Probes[END_REF][START_REF] Gao | Fluorescent probes for organelle-targeted bioactive species imaging[END_REF][START_REF] Zhu | Fluorescent Probes for Sensing and Imaging within Specific Cellular Organelles[END_REF] An ideal fluorescent probe for bioimaging should be water-soluble, cell permeant, photostable and should absorb and emit at wavelengths compatible with live cell imaging, with a high fluorescence quantum yield. Two-photon excitation (2PE) offers a great opportunity as it allows excitation wavelengths in the NIR window where the absorption and diffusion of light by biological samples are minimized. This primordial advantage provides the capability to image deep inside a tissue and avoids autofluorescence as endogeneous fluorophores are not excited by two-photon excitation or only following very specific protocols. [START_REF] Stringari | Multicolor two-photon imaging of endogenous fluorophores in living tissues by wavelength mixing[END_REF] Moreover, 2PE is confined to a small volume at the focal point of the optical system using a fs pulsed laser. Thus, it provides high spatial resolution and limits excitation of the sample reducing photodamages and photobleaching. Furthermore, 2PE requires a lower photon energy compared to one photon excitation and should therefore be less damaging to cells. Unfortunately, most of the available dyes used for two-photon imaging are not designed and optimized for 2PE microscopy. As these dyes do not possess high absorption cross-sections, their imaging by two-photon microscopy requires a high laser power and therefore induces photodamages anyway. Considerable efforts have been carried out to design new fluorophores with high two-photon absorption abilities but the challenge is to strike the right balance between good photophysical properties and the ability to enter the cells. [START_REF] Kim | Small-molecule two-photon probes for bioimaging applications[END_REF] Molecular engineering of twophoton chromophores led to the identification of π-conjugated quadrupolar systems (D-π-A-π-D or A-π-D-π-A) or octupolar systems as excellent two-photon absorbers. [START_REF] Zyss | Nonlinear optics in multipolar media: theory and experiments[END_REF] Indeed, the increase of symmetrical internal charge transfer and the dimensionality of the molecule improves the two-photon absorption abilities. [8][START_REF] Katan | Two-Photon Transitions in Quadrupolar and Branched Chromophores: Experiment and Theory[END_REF] However, strong 2P absorbers are usually extended aromatic structures with high molecular weight and most of them are not biocompatible as they are not water-soluble. Therefore, there is still a strong interest in the development of new scaffolds for 2PE live cell imaging. Another important criterion for an ideal fluorophore for live cell imaging is the high signal-to-noise ratio. Fluorescent turn-on probes fulfill this criterion as they restore their fluorescence through a fluorogenic reaction with cellular analytes (metals, thiols, ROS) [START_REF] Carter | Fluorescent sensors for measuring metal ions in living systems[END_REF][START_REF] Jiao | Small-Molecule Fluorescent Probes for Imaging and Detection of Reactive Oxygen, Nitrogen, and Sulfur Species in Biological Systems[END_REF] or through immobilization/binding to their biological targets. [START_REF] Klymchenko | Solvatochromic and Fluorogenic Dyes as Environment-Sensitive Probes: Design and Biological Applications[END_REF][START_REF] Peveler | More Than a Light Switch: Engineering Unconventional Fluorescent Configurations for Biological Sensing[END_REF] The unbound or unreacted probe is not fluorescent and this improves the sensitivity of the probe by reducing the background signal. Styryl dyes are known to be fluorescent OFF-ON probes for cellular organelles or biomolecules. [START_REF] Rosania | Combinatorial Approach to Organelle-Targeted Fluorescent Library Based on the Styryl Scaffold[END_REF][START_REF] Xie | Asymmetric distyrylpyridinium dyes as red-emitting fluorescent probes for quadruplex DNA[END_REF][START_REF] Naud-Martin | Acri-2,7-Py, a bright red-emitting DNA probe identified through screening of a distyryl dye library[END_REF] In previous papers, our laboratory described the synthesis and optical properties of divinylpyridinium carbazoles [START_REF] Dumat | N-phenyl-carbazole-based two-photon fluorescent probes: strong sequence dependence of the duplex vs quadruplex selectivity[END_REF] or triphenylamines [START_REF] Allain | Vinyl-Pyridinium Triphenylamines: Novel Far-Red Emitters with High Photostability and Two-Photon Absorption Properties for Staining DNA[END_REF] as 2PE fluorescent DNA probes suitable for fixed cell imaging. These quadrupolar structures were efficient two-photon absorbers and were water-soluble and cell permeant thanks to their pyridinium moieties. Recently, silicon containing organic molecules were of growing emphasis for the design of fluorescent dyes for bioimaging. For example, silicon containing xanthene dyes were successfully developed for in vivo tumor imaging, triple-color imaging of neuronal activity in mouse brain slices, live cell protein labeling for super-resolution microscopy, calcium imaging and so on. [START_REF] Egawa | Development of a far-red to near-infrared fluorescence probe for calcium ion and its application to multicolor neuronal imaging[END_REF][START_REF] Kushida | Silicon-substituted xanthene dyes and their applications in bioimaging[END_REF][START_REF] Lukinavičius | A near-infrared fluorophore for live-cell super-resolution microscopy of cellular proteins[END_REF] Surprisingly, very few work was done on the non-linear properties of such molecules, such as their two-photon absorption capabilities. Thus, a silicon-rhodamine based two-photon fluorescent probe for nitric oxide was recently described with two-photon brightness of 75 GM at 820 nm. [START_REF] Mao | Development of a Silicon-Rhodamine Based Near-Infrared Emissive Two-Photon Fluorescent Probe for Nitric Oxide[END_REF] Taking into account the above criteria, we report herein a new class of divinylpyridinium based on a 9silafluorene core. This silicon-bridge analog of fluorene has been mainly used for the development of organic light-emitting diodes. [START_REF] Chan | Poly(2,7-dibenzosilole): A Blue Light Emitting Polymer[END_REF][START_REF] Liu | 9-Silafluorene and 9-germafluorene: novel platforms for highly efficient red phosphorescent organic light-emitting diodes[END_REF][START_REF] Chen | Synthesis and characterization of arylamino end-capped silafluorenes for blue to deep-blue organic light-emitting diodes (OLEDs)[END_REF] Indeed, silafluorene are much more thermostable than fluorene. Moreover, due to a σ*(Si-C)-π * hyperconjugation effect, the incorporation of silicon atoms into π-conjugated systems is expected to decrease the LUMO energy levels. Thus, a red-shift in absorption can be observed by replacing carbon atom with silicon atom in fluorene. [START_REF] Li | Synthesis and photophysical properties of highly emissive compounds containing a dibenzosilole core[END_REF] Synthesis of V-shaped SiFluo-V and linear SiFluo-L substituted silafluorenes was successfully carried out. Both one photon and two-photon photophysical properties were evaluated. These dyes were emissive (from 450-650 nm) in water with good fluorescence quantum yields. Their fluorescence was enhanced when they were immobilized in a viscous solvent suggesting a turn-on probe behavior in cells. Moreover, SiFluo-L displayed high two-photon absorption abilities in the 750-800 nm range leading to an efficient emitting probe for 2PE cell imaging.

Experimental section

General procedures

Reagents were purchased as reagent-grade and used without further purification unless otherwise stated. THF and DCM were freshly distilled before use. Analytical thin-layer chromatographies (TLC) were carried out on Macherey Nagel Alugram Xtra SIL G/UV254 plates using UV light (λ = 254 nm) as visualizing agent. Flash chromatographies were carried out with Macherey Nagel silica gel (40-63 µm) or on CombiFlash Companion from Teledyne Isco equipped with packed silica cartridges from Macherey Nagel. Yields refer to chromatographically and spectroscopically pure compounds. NMR spectra were recorded on Bruker AV300 spectrometer at room temperature. Chemical shifts (δ), which are expressed in part per million (ppm), were determined relative to residual non-deuterated solvent as an internal reference respectively CDCl3 and (CD3)2SO ( 13 C NMR: δ = 77.23; 39.52 ppm; 1 H NMR: δ = 7.26; 2.50 ppm). Coupling constant(s) in hertz (Hz) were measured from one-dimensional spectra and multiplicities were abbreviated as following: s (singlet), d (doublet), t (triplet), q (quadruplet), m (multiplet). MS spectra were recorded on a Waters Micromass ZQ instrument (source voltage 30 kV).

Synthesis

Synthesis of 2,2'-diiodobiphenyl 1:

At -78 °C and under Ar atmosphere, n-BuLi in hexanes (28.0 mL, 1.45 M, 40.5 mmol, 2.3 eq.) was added over 1 hr to a solution of 2,2'-dibromobiphenyl (5.5 g, 17.6 mmol, 1.0 eq.) in dry THF (30 mL). A solution of I2 (10.3 g, 40.5 mmol, 2.3 eq) in dry THF was then added dropwise. The mixture was allowed to warm to room temperature and stirred for 2 hours. A 2 % sodium thiosulfate aqueous solution (100 mL) was used to quench the reaction. The aqueous layer was extracted three times with DCM. Organic layers were combined, washed with brine and dried over MgSO4. The crude was filtered over a small silica plug (Eluent: Cyclohexane) and after concentration, the filtrate was recrystallized in pure heptane to afford the expected product as white crystals (5.40 g, 13.3 mmol,  = 75 %). CAS number [2236-52-4] 1 H NMR (300 MHz, CDCl3): δ = 7.95 (dd, J = 7.5 Hz, J = 1.0 Hz, 2H), 7.42 (td, J = 7.5 Hz, J = 1.0 Hz, 2H), 7.20 (dd, J = 7.5 Hz, J = 1.5 Hz, 2H), 7.09 (td, J = 7.5 Hz, J = 1.5 Hz, 2H). Spectroscopic data were in agreement with those reported in the literature. [START_REF] Chan | Poly(9,9dialkyl-3,6-dibenzosilole)--a high energy gap host for phosphorescent light emitting devices[END_REF]

Synthesis of 5,5'-dibromo-2,2'-diiodobiphenyl 2, p-Br:

Under Ar atmosphere, Br2 (1.43 mL, 27.8 mmol, 2.2 eq.) and iron (106 mg, 1.9 mmol, 0.2 eq.) were added to a solution of 2,2'-diiodobiphenyl 1 (5.15 g, 12.6 mmol, 1.0 eq) in dry DCM (120 mL). The mixture was heated under reflux 2 hours, a 2 % aqueous sodium thiosulfate solution (100 mL) was then used to quench the reaction. The aqueous layer was extracted three times with DCM. Organic layers were combined, washed with brine and dried over MgSO4. The crude was washed with DCM and filtered to afford the expected product as a white powder (5.00 g, 8.87 mmol,  = 70 %). CAS number [852139-02-7] 1 H NMR (300 MHz, CDCl3): δ = 7.78 (d, J = 8.5 Hz, 2H), 7.32 (d, J = 2.5 Hz, 2H), 7.24 (dd, J = 8.5 Hz, J = 2.5 Hz, 2H). Spectroscopic data were in agreement with those reported in the literature. [START_REF] Chan | Poly(9,9dialkyl-3,6-dibenzosilole)--a high energy gap host for phosphorescent light emitting devices[END_REF]

Synthesis of 2,8-dibromo-5,5-dimethyl-5H-dibenzo[b,d]silole 3, p-Br:

At -78 °C and under Ar atmosphere, n-BuLi in hexanes (5.81 mL, 1.45M, 8.42 mmol, 2.0 eq.) was added over 1 hr to a solution of 5,5'-dibromo-2,2'-diiodobiphenyl 2, p-Br (2.38 g, 4.21 mmol, 1.0 eq.) in dry THF (80 mL). After 30 min, dichlorodimethysilane (770 µL, 6.32 mmol, 1.5 eq.) was added dropwise. The mixture was then allowed to warm to room temperature and stirred for 2 hours. Water (100 mL) was introduced to quench the reaction. The aqueous layer was extracted three times with DCM. Organic layers were combined, washed with brine and dried over MgSO4. The crude was filtered over a small silica plug (Eluent: Cyclohexane) and the filtrate was concentrated under reduce pressure. The resulting residue was washed with pentane and filtered to afford the expected product as white crystals (0.96 g, 2.61 mmol,  = 62 %). CAS number [1315321-81-3]. 1 H NMR (300 MHz, CDCl3): δ = 7.90 (d, J = 1.5 Hz, 2H), 7.48 (d, J = 7.5 Hz, 2H), 7.43 (dd, J = 1.5 Hz, J = 7.5 Hz, 2H), 0.41 (s, 6H). 13 C NMR (75 MHz, CDCl3): δ = 148.7, 137.9, 134.2, 130.9, 125.5, 124.6, -3.3. TLC: Rf (Cyclohexane) = 0.59

Synthesis of 3,7-dibromo-5,5-dimethyl-5H-dibenzo[b,d]silole 3, m-Br:

According to the same procedure, n-BuLi in hexanes (0.49 mL, 1.45 M, 0.71 mmol, 2.0 eq.), 4,4'-dibromo-2,2'-diiodobiphenyl (200 mg, 0.35 mmol, 1.0 eq.) and dichlorodimethysilane (65 µL, 0.53 mmol, 1.5 eq.) in dry THF (6 mL) led to the expected product as white crystals (75 mg, 0.20 mmol,  = 57 %). CAS number

Synthesis of 4,4'-((1E,1'E)-(5,5-dimethyl-5H-dibenzo[b,d]silole-2,8-diyl)bis(ethene-2,1-diyl))dipyridine 4, p-Py:

Under Ar atmosphere, a solution of Pd(OAc)2 (3 mg, 14 µmol, 0.1 eq.) and P(o-tol)3 (6.5 mg, 21 µmol, 0.2 eq.) in a freshly degassed Et3N/DMF mixture (2:1, 2 mL) was stirred 15 min and degassed once again. Intermediate 3, p-Br (52 mg, 0.14 mmol, 1.0 eq.) and 4-vinylpyridine (0.04 mL, 0.35 mmol, 2.5 eq.) were added. The mixture was then stirred at 90 °C overnight. The crude was diluted in DCM (25 mL). The organic layer was washed with saturated NaHCO3 and dried over MgSO4. The crude was purified by flash chromatography on silica gel (DCM/EtOH 100:0 to 90:10). The resulting solid was dissolved in DCM. Diethyl ether was added until precipitation of a white solid. The precipitate was filtered under vacuum to afford the expected product as a white powder (23 mg, 55 µmol,  = 39 %). 1

Synthesis of 4,4'-((1E,1'E)-(5,5-dimethyl-5H-dibenzo[b,d]silole-3,7-diyl)bis(ethene-2,1-diyl))dipyridine 4, m-Py:

According to the same procedure, Pd(OAc)2 (4 mg, 18 µmol, 0.1 eq.), P(o-tol)3 (8 mg, 26 µmol, 0.15 eq.) , intermediate 3, m-Br (65 mg, 0.18 mmol, 1.0 eq.) and 4-vinylpyridine (47 µL, 0.44 mmol, 2.5 eq.) in a Et3N/DMF mixture (2:1, 3 mL) led to the expected product as a yellow solid (52 mg, 0.12 mmol,  = 71 %). 1

Synthesis of SiFluo-V:

A large excess of iodomethane (0.3 mL, 100 eq.) was added to a solution of compound 4, p-Py (20 mg, 48 µmol, 1.0 eq.) in a MeOH/DCM (1:1) mixture (2 mL). The reaction was stirred at 30 °C overnight. After addition of diethyl ether, the yellow precipitate was filtered under vacuum to afford the expected product as a pale yellow solid (21 mg, 30 µmol,  = 62 %). 1

Synthesis of SiFluo-L:

According to the same procedure, iodomethane (0.35 mL, 100 eq.) and compound 4, m-Py (20 mg, 48 µmol, 1.0 eq.) in a MeOH/DCM (1:1) mixture (2 mL) led to the expected product as an orange solid (31 mg, 44 µmol,  = 80 %). 1 Fluorescence and UV-visible spectra were respectively recorded using Spex FluoroMax-3 Jobin-Yvon Horiba and Hitachi U-2900 apparatus. Measurements were performed at room temperature with solutions of A < 0.1 to avoid re-absorption of the emitted light, and data were corrected with a blank and from the variations of the detector with the emitted wavelength. Fluorescence quantum yield were measured according to the Crosby method using quinine sulfate (λex = 366 nm, Ф = 0.546) as reference. [START_REF] Brouwer | Standards for photoluminescence quantum yield measurements in solution (IUPAC Technical Report)[END_REF][START_REF] Crosby | Measurement of photoluminescence quantum yields[END_REF]

Molecular Modeling

Geometry optimizations of the ground state were carried out at the B3LYP/6-31G(d) level of theory. A frequency calculation was done in all cases to confirm the true minimum nature (no imaginary frequency) of the converged geometry. TD-DFT calculations were done at the M06-2X/6-311+G(d,p) level of theory using IEFPCM model to include solvent (water) effect. All calculations were done with Gaussian 09 software from Gaussian Inc. and orbitals were plotted with Avogadro.

Two-photon absorption

The two-photon excitation spectra were measured by the fluorescence method by using a Ti:sapphire femtosecond laser Insight DS (680-1300 nm) with pulse width < 120 fs and a repetition rate of 80 MHz (Spectra-Physics) The excitation beam was collimated over the cell length (Helma fluorescence semi-micro 10x4 mm) and the fluorescence, collected at 90° of the excitation beam, was focused into an optical fibre connected to a spectrometer (AvaSpec ULS from Avantes). The incident beam intensity was adjusted to ensure an intensity-squared dependence of the fluorescence over the whole spectral range reported. To avoid reabsorption of emitted light, micro cells are used and the focal point is very close to the edge of the cuvette. This allows elimination of second order filter effects. The concentrations were 5x10 -5 M for SiFluo-L and 10 -4 M for SiFluo-V. Calibration of the spectra was performed by comparison with the published Rhodamine B in MeOH [START_REF] Xu | Measurement of two-photon excitation cross sections of molecular fluorophores with data from 690 to 1050 nm[END_REF][START_REF] Makarov | Two-photon absorption standards in the 550-1600 nm excitation wavelength range[END_REF] in the 750-880 and 930-1000 nm range and Fluorescein in 0.1N NaOH solution in the 880-930 nm range. [START_REF] Makarov | Two-photon absorption standards in the 550-1600 nm excitation wavelength range[END_REF] 2.6 Cell culture and confocal microscopy imaging A549 lung carcinoma cells were cultured in Dulbecco's modified eagle media (DMEM, GIBCO) supplemented with 10% Fetal Bovine Serum (FBS, GIBCO) and 1% Penicillin/Streptomycin (Life Technologies) at 37 °C under 5% CO2, 95 % air and 100 % humidity. Cells were seeded on a 8-well µ-slide from Ibidi (20 000 cells/well). After 24h, cells were incubated 2 hours with the desired compound, washed with PBS once, and observed in Opti-MEM (GIBCO) medium.

For MTT Assay, cells were seeded in 24-well plates from TPP (50 000 cells/well). After 24h, cells were incubated with solutions of various concentrations of both probes (for 0.313 to 10 µM) for 24 hours. Afterwards, 50 μL of MTT solution (previously sterilized with a 0.22 µm filter, 5 mg/mL in PBS) were added in each well. After 1h, the medium was removed and 600 µL of DMSO were added to dissolve MTT formazan. Optical densities were then measured at 562 nm with a FLUOStar Omega plate reader from BMG Labtech.

Every experiment was conducted in duplicate and reproduced three times. Results are represented as means ± SD.

The fluorescence imaging (confocal and biphotonic) was performed using a confocal laser scanning microscope DMI 6000 with a SP5-AOBS unit (both Leica) equipped with a 63x (NA = 1.4) objective (oil immersion), an argon gas laser, a 405 nm diode and helium neon gas laser (633 nm) for one-photon excitation and a Chameleon Ti:Saph laser (Coherent) delivering pulses in the 100 to 200 fs range at an 80 MHz repetition rate with a tunability ranging from 705 to 980 nm for two-photon excitation. The excitation laser power was measured after the objective by a thermal head laser power meter (PM100 S302 ThorLabs). The images were visualized and processed using Image J software (Rasband W.S., U.S. National Institutes of Health, Bethesda, Maryland, USA).

Results and discussion

Synthesis

Compounds SiFluo-V and SiFluo-L were synthesized according to the synthetic pathway shown in Figure 1. A two-step synthesis adapted from a method previously described was performed to afford 5,5'-dibromo-2,2'diiodobiphenyl 2, p-Br. [START_REF] Chan | Poly(9,9dialkyl-3,6-dibenzosilole)--a high energy gap host for phosphorescent light emitting devices[END_REF] Halogen-metal exchange on 2,2'-dibromobiphenyl with n-BuLi in THF followed by the addition of iodine afforded 2,2'-diiodobiphenyl 1 in 75 % yield. Compound 1 was then brominated in dichloromethane in the presence of bromine and iron to provide 5,5'-dibromo-2,2'-diiodobiphenyl 2,p-Br in 2 hours in 70 % yield. For the synthesis of SiFluo-L, the starting material 2, m-Br was commercially available. The silafluorene cores were obtained according to a strategy described in the literature starting with compounds 2-Br. [START_REF] Chan | Poly(2,7-dibenzosilole): A Blue Light Emitting Polymer[END_REF][START_REF] Chen | Synthesis and characterization of arylamino end-capped silafluorenes for blue to deep-blue organic light-emitting diodes (OLEDs)[END_REF] Chemoselective halogen-metal exchanges on dibromo-2,2'-diiodobiphenyls 2-Br on iodine atoms with n-BuLi in THF were followed by nucleophilic substitutions on commercial dichlorodimethylsilane. This afforded brominated silafluorenes 3, m-Br and 3, p-Br with good yields, 57 % and 62 % respectively. A Heck reaction in the presence of 4-vinylpyridine was then performed to give 4, m-Py and 4, p-Py. The moderate yield obtained for 4, p-Py (39 %) could be explained by difficulties met in purification steps. Pyridine moieties were finally methylated to yield pyridinium iodide salts SiFluo-V and SiFluo-L. To sum up, SiFluo-V and SiFluo-L were respectively obtained in 8 % overall yield by a five-step synthesis and in 32 % overall yield by a three-step synthesis.

UV/vis and fluorescent properties

The optical properties of SiFluo-V and SiFluo-L have been investigated in water (μ = 1,002.10 -3 Pa.s at 20 °C) and glycerol (μ = 1,420 Pa.s at 20 °C) at room temperature. All data are summarized in Table 1. These dyes obey Beer Lambert's law up to 180 µM in water (SI, Figure S1) indicating that they do not aggregate in aqueous media and are highly water soluble. SiFluo-V shows an absorbance around 350 nm, whereas SiFluo-L absorbs in the violet region between 416 and 425 m, depending on the solvents (Figure 2 and Table 1). This may reveal a lower degree of conjugation of the V-shaped compound SiFluo-V compared to the linear isomer SiFluo-L originating in its lower rigidity.

In addition, SiFluo-V and SiFluo-L exhibit high molar absorption coefficients which are slightly higher for SiFluo-L (up to 64 200 L.mol-1.cm-1 in glycerol). This difference could also be explained by a more rigid structure for SiFluo-L. In spite of the difference of absorption range, both compounds display a green fluorescence in water and in glycerol. Small shifts observed in absorption and emission in the different solvents are consistent with an intramolecular charge transfer (see 3.4). Furthermore, they display large to impressive Stokes shifts, respectively 5000 cm-1 to 10 000 cm-1 for SiFluo-L and SiFluo-V. These Stokes shifts are about 10 times higher than lots of fluorescent probes used for biological purposes like fluorescein, rhodamine, boron-dipyrromethene or cyanines. That represents a real advantage for one photon excitation imaging, avoiding problems like reabsorption and optical setup implementation. Both dyes are emissive in water, SiFluo-L exhibiting a stronger fluorescence in water than SiFluo-V (13 % versus 3 %). This behavior was quite unexpected as we reported previously that N-phenylcarbazole analogue Cbz-2Py was poorly emissive in water (φF < 0.5%) and restored its fluorescence while binding DNA. [START_REF] Dumat | N-phenyl-carbazole-based two-photon fluorescent probes: strong sequence dependence of the duplex vs quadruplex selectivity[END_REF] In our case, fluorescence could also be enhanced if non-radiative relaxation, such as rotation of the styryl moieties, is inhibited by immobilization inside its cellular target. In order to evaluate the putative increase of fluorescence of SiFluo dyes in a cellular medium, their fluorescent properties were measured in glycerol, a highly viscous solvent (μ = 1.49 Pa.s at 20 °C), that limits the non-radiative relaxation pathways from excited state to ground state through restriction of molecular motions. Both probes exhibit a strong fluorescence in glycerol (φF = 29 % and 31 %), meaning that these probes are responsive to the constraints of the environment. It may indicate that SiFluo-V and SiFluo-L could exhibit a similar fluorescence in cells, immobilized on their biological target.

In addition, both probes show a high and similar brightness in glycerol, which is the figure of merit for imaging. The signal-to-noise ratio could be estimated regarding to the brightness in glycerol compared to the brightness in water. As a consequence, SiFluo-V seems to be a better candidate for bioimaging thanks to its great turn-on properties, but its low absorption wavelength represents a limitation. Overall, these results indicated that SiFluo-V but mostly SiFluo-L thanks to its red-shifted absorption wavelengths, are suitable for cellular imaging.

Two-photon absorption cross-sections

The two-photon absorption properties of SiFluo-V and SiFluo-L have been investigated in water and glycerol solutions at room temperature. Measures were also performed in DMSO in order to compare them with reported cross-section of analogous fluorenes. [START_REF] Suzuki | Efficient Two-Photon Absorption Materials Consisting of Cationic Dyes and Clay Minerals[END_REF] All data are summarized in Table 2. SiFluo-L exhibits outstanding absorption cross-sections, up to 2150 GM regardless of the solvent used, with a maximum around 750 nm (Figure 3). The two-photon induced fluorescent signal for SiFluo-V was unfortunately too low to be precisely quantified at λ > 680 nm in water and in DMSO. Conversely, cross-section values in glycerol were determined and the maximal cross section was about 210 GM at 700 nm (SI, Figure S2). The TPA cross-section of SiFluo-L is about three times higher than the corresponding fluorene (800 GM at 780 nm, DMSO) [START_REF] Suzuki | Efficient Two-Photon Absorption Materials Consisting of Cationic Dyes and Clay Minerals[END_REF] but slightly lower than the corresponding carbazole (2 900 GM at 800 nm, water). [START_REF] Liu | Two-photon fluorescent probe for detecting cell membranal liquid-ordered phase by an aggregate fluorescence method[END_REF] As for the one photon excitation imaging, the figure of merit for non-linear imaging is the two-photon brightness and not the absorption cross-section. The two-photon brightness of our linear silafluorene in water (270 GM at 740 nm) is higher than the two-photon brightness of the corresponding carbazole (87 GM at 800 nm) and other described silicon containing rhodamine (75 GM at 820 nm). [START_REF] Mao | Development of a Silicon-Rhodamine Based Near-Infrared Emissive Two-Photon Fluorescent Probe for Nitric Oxide[END_REF][START_REF] Liu | Two-photon fluorescent probe for detecting cell membranal liquid-ordered phase by an aggregate fluorescence method[END_REF] Unfortunately, the brightnesses in glycerol could not be compared as there is no reported data in this solvent for both carbazole and fluorene. S2). Indeed, for SiFluo-L, there is a strong difference in energy between the first calculated transition (424 nm) and the following one (350 nm). At the opposite, in the case of SiFluo-V, the transitions are very close to each other (367, 347 and 322 nm) and therefore they all contribute to the absorption range 280-400 nm of SiFluo-V. This agreement between experimental data and calculations allows validating the choice of the computational method.

SiFluo-V possesses a higher LUMO and a lower HOMO than SiFluo-L, meaning that the -conjugation is better for 2,7-than 3,6-substitution. These data are consistent with the redshift observed in the absorption spectrum of SiFluo-L. The nature of the transition can be determined looking at shapes of frontiers orbitals (Figure 4). In both cases, the major contribution to the transition from S0 to S1 is HOMO → LUMO (SI, Table S1). The electronic density of the HOMO is mostly located on the silafluorene core for the two probes whereas the electronic density of the LUMO is located on the whole structure in both cases. Nevertheless, HOMO-1 and LUMO+1 play also a role in the transition from S0 to S1. A calculation of the variation of electronic density during the transition from the ground state to the first excited state was thus performed (Figure 5). The increase of the electronic density is shown in blue whereas the decrease is shown in yellow. The electronic density mostly decreases on the silafluorene core whereas it increases on the two branches. It is typical for an internal charge transfer and it is consistent with a A-π-D-π-A design for both probes. To explain their difference in two-photon absorption properties, a calculation of the transition dipole moments 𝜇 𝑆 0 →𝑆 1 and 𝜇 𝑆 1 →𝑆 2 was therefore conducted. For both transitions S0→S1 and S1→S2 the norm of the transition dipole moment is about twice higher for SiFluo-L than SiFluo-V (Table 3 and Tables S2 andS3). As a consequence, the calculated 𝛿 𝑀𝐴𝑋 is 16 times higher for SiFluo-L. This is in line with the respective 2PA cross sections of the compounds. Thus, theoretical calculations support the experimental evidence that SiFluo-L displays by far better two-photon absorption properties than SiFluo-V.

Confocal microscopy

First, the biocompatibility of SiFluo-V and SiFluo-L was evaluated by MTT assay in A549 cells (SI, Figure S4). The probes show no significant effects on cell viability (more than 80% of viable A549 cells at 10 µM) and can be used for live cell imaging. The ability of these two probes for live cells imaging was evaluated through confocal microscopy. After 2h of incubation in A549 cells at 2 µM, images were acquired after one or twophoton excitation.

SiFluo-L exhibits high brightness and contrast at low power of laser under one photon excitation but also under 2PE (3.4 mW laser power) (Figure 7). This value is considered far below the standard noninvasive in vivo two-photon studies. [START_REF] Sacconi | Overcoming photodamage in second-harmonic generation microscopy: real-time optical recording of neuronal action potentials[END_REF][START_REF] Wang | Two-photon microscopy of deep intravital tissues and its merits in clinical research[END_REF] As expected, no autofluorescence was detected at this power (SI, Figure S5).

We took advantage of this high brightness to reduce the concentration of SiFluo-L for live cell imaging. We were able to perform two-photon fluorescence microscopy at only 100 nM increasing laser power to 20 mW (SI, Figure S6). At the opposite, under one photon excitation, SiFluo-V exhibits only moderate brightness and contrast (SI, Figure S7). The poor absorbance of SiFluo-V at 405 nm, the lowest excitation laser on the used confocal microscope, can explain this weak fluorescence. Similarly, the poor two-photon brightness at 705 nm (below 60 GM) does not provide high signal-to-noise ratio images.

These two dyes are localized in the cytoplasm as shown by the brightfield images. To confirm this subcellular localization, we performed a colabeling experiment with SiFluo-L and DRAQ5, a nuclear stainer (Figure 8). Excitation at 633 nm led to the near infra-red fluorescence of DRAQ5 although excitation at 405 nm led to a green to red fluorescence of SiFluo-L. This experiment strongly supports the cytoplasmic localization of SiFluo-L. As lipophilic cations are sequestered in mitochondria due to the mitochondrial membrane potential, SiFluo-L was expected to label mitochondria. A colocalization was performed with a commercially available tracker (Mitotracker Deep Red, λex = 633 nm) to confirm its subcellular localization (Figure 8). The Van Steensel's cross correlation method highlights an overlay between signals from Mitotracker Deep Red and SiFluo-L, that confirms its mitochondrial intracellular labeling (SI, Figure S8).

Conclusion

We designed and synthesized two fluorophores based on a silafluorene core SiFluo-V and SiFluo-L. These two dyes display a strong fluorescence between 450 and 650 nm, despite of their difference in absorption ranges. SiFluo-L exhibits impressive two-photon cross sections (up to 2150 GM) about three times higher than the corresponding fluorene. Thanks to its cell permeability, water solubility and low cytotoxicity (IC80≥10 µM), SiFluo-L is a biocompatible dye. The outstanding combination of optical (high two-photon brightness and photostability) and biological properties makes SiFluo-L an efficient probe for live cell imaging. As it exhibits a large emission spectrum, we were able to perform cellular imaging in the red window (600-700 nm). This should enable the use of SiFluo-L for in vivo labeling experiments. The subcellular localization of this probe was shown to be mitochondrial thanks to colocalization experiments. As silafluorene is a promising core for live cell imaging, next step will be to increase its scope by labeling other organelles. Indeed, there is a real need to design probes suitable to label organelles such as Golgi apparatus or endoplasmic reticulum.

[4] Modification of the acceptor moieties or addition of targeted organelle moieties on the silafluorene core should be envisaged to ensure the design of new fluorophores for different organelle labeling.

Figure 1 .

 1 Figure 1. Synthesis of SiFluo-V and SiFluo-L

[

  1228595-79-6]. 1 H NMR (300 MHz, CDCl3): δ = 7.71 (d, J = 2.0 Hz, 2H), 7.63 (d, J = 8.5 Hz, 2H), 7.54 (dd, J = 8.5, 2.0 Hz, 2H), 0.43 (s, 6H). 13 C NMR (75 MHz, CDCl3): δ = 145.6, 141.5, 135.7, 133.4, 122.6, 122.5, -3.4. TLC:Rf (Cyclohexane) = 0.68. Spectroscopic data were in agreement with those reported in the literature.[START_REF] Chen | Synthesis and characterization of arylamino end-capped silafluorenes for blue to deep-blue organic light-emitting diodes (OLEDs)[END_REF]

  H NMR (300 MHz, CDCl3): δ = 8.62 (d, J = 6.0 Hz, 4H), 8.05 (s, 2H), 7.68 (d, J = 7.5 Hz, 2H), 7.50 (d, J = 7.5 Hz, 2H), 7.43 (d, J = 6.0 Hz, 4H), 7.42 (d, J = 16.5 Hz, 2H), 7.18 (d, J = 16.5 Hz, 2H), 0.46 (s, 6H). 13 C NMR (75 MHz, CDCl3): δ = 150.4, 148.1, 144.6, 140.4, 138.2, 133.5, 133.4, 126.7, 126.5, 121.0, 119.3, -3.1. MS (ES+): m/z = 417.3. HRMS (ES+): calculated for C28H25N2Si + 417.1787, found 417.1784. TLC: Rf (DCM/EtOH, 95:5) = 0.21

  H NMR (300 MHz, CDCl3): δ = 8.58 (d, J = 6.0 Hz, 4H), 7.83 (s, 2H), 7.81 (d, J = 8.0 Hz, 2H), 7.60 (dd, J = 8.0, 1.5 Hz, 2H), 7.37 (d, J = 6.0 Hz, 4H), 7.34 (d, J = 16.0 Hz, 2H), 7.07 (d, J = 16.0 Hz, 2H), 0.50 (s, 6H). 13 C NMR (75 MHz, CDCl3): δ = 150.4, 148.0, 144.8, 140.1, 135.5, 133.1, 131.5, 129.5, 125.8, 121.6, 120.9, -3.1. MS (ES+): m/z = 417.4. HRMS (ES+): calculated for C28H25N2Si + 417.1787, found 417.1779 TLC: Rf (DCM/EtOH, 95:5) = 0.31

  H NMR (300 MHz, DMSO-d6): δ = 8.92 (d, J = 6.0 Hz, 4H), 8.63 (s, 2H), 8.35 (d, J = 6.0 Hz, 4H), 8.12 (d, J = 16.5 Hz, 2H), 7.98 (d, J = 16.5 Hz, 2H), 7.88 (d, J = 7.5 Hz, 2H), 7.65 (d, J = 7.5 Hz, 2H), 4.29 (s, 6H), 0.46 (s, 6H). 13 C NMR (75 MHz, DMSO-d6): δ = 152.4, 147.5, 145.2, 141.8, 140.5, 137.4, 133.9, 128.5, 124.0, 123.6, 119.7, 47.0, -3.4. MS (ES+): m/z = 445.3. HRMS (ES+): calculated for C30H30N2ISi + 573.1223, found 573.1250

  H NMR (300 MHz, DMSO-d6): δ = 8.86 (d, J = 6.5 Hz, 4H), 8.22 (d, J = 6.5 Hz, 4H), 8.19 (d, J = 1.0 Hz, 2H), 8.13 (d, J = 8.0 Hz, 2H), 8.06 (d, J = 16.0 Hz, 2H), 7.85 (dd, J = 8.0, 1.0 Hz, 2H), 7.60 (d, J = 16.0 Hz, 2H), 4.26 (s, 6H), 0.50 (s, 6H). 13 C NMR (75 MHz, DMSO-d6): δ = 152.4, 148.5, 145.1, 140.4, 140.1, 134.7, 132.6, 131.1, 123.4, 123.1, 122.3, 46.9, -3.4. MS (ES+): m/z = 445.1. HRMS (ES+): calculated for C30H30N2ISi + 573.1223, found 573.1227 2.3 Optical measurements Measurements were performed in 0.5 or 1 mL Hellma quartz cuvette (material code QS blue, 200-2000 nm).

Figure 2 .

 2 Figure 2. Absorption (12 µM -solid lines) and emission spectra (λex =λmax, 2 µM -dashed lines) of SiFluo-V (Left) and SiFluo-L (Right) in water (blue lines) and glycerol (grey lines)

Figure 3 .

 3 Figure 3. Nonlinear excitation spectra of SiFluo-L in water (green), glycerol (red) and DMSO (black)

Figure 4 .

 4 Figure 4. Frontiers orbitals of SiFluo-L and SiFluo-V

Figure 5 .

 5 Figure 5. Increase (in blue) and decrease (in yellow) of the electronic density during S0 → S1Two-photon absorption properties are highly dependent of extension of conjugation and charge transfer; and can thus be related to transition dipole moments.[START_REF] Rumi | Structure-Property Relationships for Two-Photon Absorbing Chromophores: Bis-Donor Diphenylpolyene and Bis(styryl)benzene Derivatives[END_REF][START_REF] Pawlicki | Two-photon absorption and the design of twophoton dyes[END_REF] Indeed, in the case of centrosymmetric compound and when S2 is the final state, δMAX is proportional to μS0→S1 and μS1→S2 according to formula (1).

Figure 6 .

 6 Figure 6. Jablonski diagram for centrosymmetric compounds (1PA in blue, 2PA in red) and relationship between maximal twophoton absorption cross-section 𝛿 𝑀𝐴𝑋 and transition dipole moments

Figure 7 .

 7 Figure 7. Confocal microscopy imaging of live A549 cells incubated with SiFluo-L at 2 µM during 2h under one (405 nm) or twophoton excitation (750 nm). Emission slit settings: 500-650 nm. Scale bar: 20 µm

Figure 9 .

 9 Figure 9. Two-photon photostability of SiFLuo-V (triangle) and SiFluo-L (round) -λex = 705 nm and 750 nm respectively

Table 1 .

 1 Photophysical properties of SiFluo-V and SiFluo-L in water and glycerol

	Compound	Solvent	ε (L.mol -1 .cm	-1 )	λ max abs (nm)	λ max em (nm)	Stokes Shift (cm -1 )	Φ	Brightness εΦ (L.mol -1 .cm	-1 )
	SiFluo-V	Water Glycerol	58 600 54 100		345 350	530 510	10 100 9 000	3 % 31 %	1 760 16 770
	SiFluo-L	Water Glycerol	62 900 64 200		416 425	535 530	5 300 4 700	13 % 29 %	8 180 18 610

Table 2 .

 2 Two-photon absorption properties of SiFluo-V and SiFluo-L in water, glycerol and DMSO For both probes, calculated wavelengths of the maximum absorption are close to experimental values, 424 nm versus 416 nm for SiFluo-L and 367 nm versus 345 nm for SiFluo-V. The oscillator strengths are similar for SiFluo-L (2.62) and SiFluo-V (2.79) which is in accordance with their similar extinction coefficients (SI, Table

	Compound	Solvent	λ max,2PA abs (nm)	δ (GM)	Φ	Two-photon brightness δ.Φ (GM)
		Water	-	nd	3 %	-
	SiFluo-V	Glycerol	700	210	31 %	65
		DMSO	-	nd	1 %	-
		Water	740	2100	13 %	270
	SiFluo-L	Glycerol	760	2150	29 %	620
		DMSO	760	2000	25 %	500
	3.4 Molecular Modeling
	TD-DFT calculations in water (M06-2X/6-311+G(d,p) level of theory) were performed to better understand
	the photophysical properties of SiFluo-V and SiFluo-L.

Table 3 .

 3 Transition dipole moments of SiFluo-V and SiFluo-L for S0→S1 and S1 → S2

	Compound	𝜇 𝑆 0 →𝑆 1	𝜇 𝑆 1 →𝑆 2	∆ (eV)	𝜇 𝑆 0 →𝑆 1 2	2 × 𝜇 𝑆 1 →𝑆 2 ∆ 2
	SiFluo-V	3.47	3.02	2.09		25
	SiFluo-L	6.05	5.54	1.66	408

Acknowledgements

M. A. thanks the Ministère de l'Enseignement Supérieur et de la Recherche for her doctoral fellowship. The authors greatly acknowledge the Multimodal Imaging Center-Light Microscopy Facility (Institut Curie, CNRS UMS2016, Inserm US43, Université Paris-Saclay) and particularly Laetitia Besse and Marie-Noëlle Soler for their technical assistance in the use of the Leica confocal SP5 system. This work has benefited from the facilities and expertise of the Small Molecule Mass Spectrometry platform of ICSN (Centre de Recherche de Gif -www.icsn.cnrs-gif.fr).


Malgorzata Tarnowska

Yves Chevalier

Stéphanie Briançon

Claire Bordes

Jacqueline Resende De Azevedo

Delphine Arquier

Thierry Pourcher

Marie-Alexandrine Bolzinger

Małgorzata Tarnowska

Skin absorption of mixed halide anions from concentrated aqueous solutions

Keywords: Skin absorption, Anions absorption, Ionic interactions, Hofmeister series, Halide ions, Experimental design

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

Introduction

Skin plays a key role in separation of human body from external environment. This is mainly due to stratum corneum, the outermost layer made of dead cells (corneocytes) surrounded by a lipid intercellular medium. Stratum corneum is organised into a brick-and-mortar-like structure where the bricks are corneocytes and the mortar is made of the intercellular lipids. Such highly hydrophobic structure protects body from excessive water loss on one hand and from pathogen and xenobiotic absorption on the other. Because of this hydrophobic barrier, skin absorption of simple inorganic ions has long been believed limited, or even impossible [1]. However, several recent studies have proved this concept wrong [2,3]. Recent work by Paweloszek et al. [4] shed new light on the possible mechanisms of halide ion transport across the skin including facilitated transport in viable skin by ionic channels and ion transporters. Skin absorption of ionic species is much more complex than just passive diffusion as described for various hydrophobic molecules because of the complex skin structure organized in layers. Outermost poorly hydrated stratum corneum with high content of lipids could indeed act as a simple passive barrier. On the other hand, viable epidermis is characterised by higher water content (up to 70 %) and living cells producing variety of proteins [5,6]. Similar water content is found in dermis that includes collagen and elastin in the intercellular matrix. Therefore, various types of skin-ion interactions are possible.

Anions interacting with biological systems have been classified in Hofmeister series (F  , Cl  , Br  , NO 3  , I  , SCN  , ClO 4  ) based on their interactions with macromolecules in aqueous solutions [7]. Ions binding to organic materials is related to their "salting in" or "salting out" properties [8]. The Hofmeister series classifies ions that are strongly hydrated in aqueous solution as "kosmotropic" or "water-structure makers". The solubility of neutral organic molecules is reduced in the presence of kosmotropes (saltingout effect). On the other hand, "chaotropic" ions are poorly hydrated in aqueous solution ("waterstructure breakers"). They interact strongly with non-polar substances, which results in their increased solubility (salting-in effect) [7,[9][10][START_REF] Collins | Proc. Natl Acad. Sci. USA[END_REF][START_REF] Collins | [END_REF]. The properties described by Hofmeister series determine various physicochemical phenomena occurring in biological systems. For instance, binding of anions to model phospholipid bilayers was found to increase following the Hofmeister series of anions and binding of chaotropic ions was reported to affect the lipid packing within bilayers [13,14]. Similar effects can be expected within stratum corneum as it has been disclosed by Paweloszek et al. [15]. Moreover, a significant contribution of facilitated transport of tested ions in viable skin was observed [4]. Beyond these observations, the involved physicochemical phenomena still remain poorly understood issues. It is worth noticing that such different phenomena as anion adsorption/absorption to hydrophobic stratum corneum and facilitated anion transport by proteins depend on the nature of anions in the same order: The Hofmeister series.

The present work addresses mixed solutions of anions where non-ideal mixing (interactions with ions of different chemical nature) influence skin absorption. Some clues regarding salts effects have been given in studies of skin absorption of organic molecules from ionic solutions. Thus, Michael-Baruch et al. [16] reported that skin permeation of neostigmine was enhanced in a concentrationdependent manner in the presence of LiCl and NaCl. Soon after, Ko et al. [17] studied transdermal penetration of salicylic acid from mixed water-ethanol medium at pH 2 containing sodium salts of inorganic anions classified in lyotropic Hofmeister. They reported increased skin permeation in the presence of NaBr, NaI and NaSCN while other salts had no or a reverse effect. As a whole, the Hofmeister series was not followed; the authors ascribed the effects to interactions in solution [16].

Absorption of halide ions from concentrated aqueous solutions of single or mixed sodium halides (NaF, NaBr, NaI) into freshly excised skin was investigated. It has been done on excised porcine skin while keeping its metabolism in a suitable survival medium [18]. Young swine skin is the most accurate animal model for human skin in terms of permeation properties [19]. It is recommended for in vitro experiments in diffusion Franz cells. Chloride was excluded from the study because its high endogenous concentration in skin [4,20] causes analysis issues. Indeed, chloride is the most abundant anion in the body, especially in extracellular medium [21]. Cross-effects of halides on one another's on skin absorption were investigated in binary and ternary mixtures. Experimental results were exploited in a {3,2} simplex-lattice design model allowing quantitative statistical analysis.

Materials and Methods

Chemicals

NaF, NaBr and NaI were purchased from Fisher Scientific (Illkirch, France). Aqueous solutions of salts were prepared in ultrapure water (resistivity > 18 MΩꞏcm at 25 °C) by weighing, providing concentrations expressed as molality (molkg 1 ).

Water activity and density measurements

Freezing point depression was measured with a Gonotec Osmomat 3000 freezing point osmometer in order to assess water activity a w . The osmometer was calibrated with pure water. Measurements were performed in triplicate with 50 µL of ionic solutions. The reading expressed in Osmolkg 1 units was converted into water activity as 𝑂𝑠𝑚𝑜𝑙𝑎𝑙𝑖𝑡𝑦 , Eq. 1 where M mol,w is the molar mass of water (0.018 kgmol 1 ).

Densities of ionic solutions needed for the conversion of molality (m, molkg 1 ) into concentration (C, molL 1 ) were measured in triplicate at 32 °C with a 50 cm 3 pycnometer calibrated with pure water at 32 °C (0.995 kgdm 3 ).

Experimental values of densities and osmolalities are given in Table S1 of Supporting Information.

Skin samples preparation

Full-thickness porcine flank skin explants were obtained from five young female pigs (30 ± 1 kg), sacrificed at the École de Chirurgie, University Claude Bernard Lyon 1 (Lyon, France). Freshly excised tissue samples were immediately (< 1 h) used to evaluate skin absorption of anions. The bristles were cut with an electrical clipper, and the explants were rinsed in water. The subcutaneous adipose tissue was carefully removed using a scalpel. Skin samples prepared to the final thickness of 1.35 ± 0.02 mm (Micrometer Mitutoyo) and cut into round sections of 3 cm². Skin integrity was assessed by measuring the Trans Epidermal Water Loss (TEWL) (Tewameter TM210, Monaderm, Monaco). Samples presenting TEWL values larger than 15 gꞏh 1 ꞏm 2 after 1 min measurements were discarded. The average TEWL values of skin samples used for experiments was 9.85 ± 0.50 gꞏh 1 ꞏm 2 .

Permeation and ion distribution in skin layers after 24 h exposure

Skin absorption was carried out for 24 h in static Franz diffusion cells. Skin explants were mounted into two-chamber glass cells [22] (exposure area = 2.54 cm 2 ) with stratum corneum facing up. Acceptor compartment was filled with 10 mL of salt-free survival medium ensuring skin viability over the duration of the experiment. The isotonic survival medium called betaine-glucose (BG) [18] contained glucose 1 gꞏL 1 , betaine 2.99 gꞏL 1 , and halide-free phosphate buffer at pH 7.4 (NaHCO 3 0.35 gꞏL 1 , Na 2 HPO 4 0.048 gꞏL 1 , KH 2 PO 4 0.060 gꞏL -1 ). Mounted Franz cells were placed in a water bath at 37 °C under magnetic stirring, providing a temperature of 32 °C at the skin surface due to heat loss. After 30 min of stabilization, the acceptor fluid was renewed and 1 mL of aqueous solution of sodium halides was placed on the skin surface. Aqueous solutions of NaF, NaBr and NaI alone, in binary and ternary mixtures at the total concentration of 500 mmolkg 1 were studied.

At the end of the experiment, Franz cells were dismantled and skin layers were separated. Stratum corneum (SC) was removed using cyanoacrylate glue (Loctite SuperGlue-3, Henkel) spread on a glass plate, according to the method for cyanoacrylate surface biopsies [23]. Then, the viable epidermis (VE) was separated from the dermis (D) by immersing the sample in water at 60 °C for 45 s. The hot water used for this separation was pooled with the extraction medium of the dermis. The underlying assumption is that extracted ions by hot water mainly came from the dermis, a skin layer of high water content where ions mobility is high. The extraction of ions from each skin layer was performed by sonication for 30 min at 60 Hz followed by extraction with a water/dichloromethane (1:1 v/v) mixture for 17 h. Recovered quantities of ions were measured in the donor medium (DM), the acceptor medium (AM) and the different skin layers. The background amounts coming from endogenous ions was measured in a control experiment without donor fluid under the same conditions as the samples. They were subtracted from the absorbed amounts of the samples. Each measurement was performed on 9 replicates with skin pieces excised from 5 different pigs according to the OECD guidelines [START_REF] Oecd | Guidance Document for the Conduct of Skin Absorption Studies[END_REF].

Analysis of ions concentrations

Collected samples were analysed using ion chromatography (930 Compact IC Flex, Metrohm, Switzerland) equipped with a chemical suppressor and conductivity detection. Elution solvent was 8 mmolꞏL 1 sodium carbonate (Fisher Scientific, Illkirch, France) in ultrapure water. Metrosep A Supp 5 250/4.0 column with an adequate pre-column at a temperature of 35 °C was used for all analyses. Calibration curve was linear from 0.06 to 2000 µmolkg 1 (R² = 0.999).

Data reduction

Results were expressed as recovered quantities in µmolꞏcm 2 . The mean value and standard error of the mean (sem) were calculated from the n = 9 repetitions of each sample. Q abs corresponds to the cumulated absorbed amount of ions recovered in SC + VE + D + AM. Comparison of formulations for their significant differences was performed with a Student t-test (p < 0.05).

Statistical model for ion mixtures

A mixture design approach was used to investigate the influence of the ionic composition on the skin permeation of each ion. Such approach allows regular screening of the entire experimental domain while limiting the number of experiments.

The experimental domain corresponds to the full ternary diagram drawn in mole fractions of the three ions ranging from zero to unity. This simplex experimental domain allows accommodating a polynomial equation that describes the studied phenomenon over all compositions of mixed ions [START_REF] Scheffé | [END_REF][START_REF] Cornell | Experiments with Mixtures: Designs, Models, and the Analysis of Mixture Data[END_REF]. The used {3,2} simplex-lattice consisted of the three vertices and the three binary blends located at the midpoints of the edges. According to the Scheffé's design, six aqueous solutions were tested: three single-anion solutions NaF, NaBr and NaI at the concentration of 500 mmolkg 1 each, (x F ,x Br ,x I ) = (1,0,0), (0,1,0) and (0,0,1), and three binary mixtures made of equal molar amounts of both ions, (x F ,x Br ,x I ) = (1/2,1/2,0), (1/2,0,1/2) and (0,1/2,1/2).

The {3,2} simplex-lattice allows estimating the six coefficients of a {3,2} polynomial equation; i.e. a second-degree model for a three-component system is written as follows:

𝑦 = b 1 x 1 + b 2 x 2 + b 3 x 3 + b 12 x 1 x 2 + b 13 x 1 x 3 + b 23 x 2 x 3 Eq. 2
where 𝑦 is the predicted response for each observed anion, x i are the mole fractions of components i in the mixture (x F + x Br + x I = 1) and the parameters b i x i and b ij x i x j are respectively the linear and nonlinear mixing terms. In a first analysis, responses 𝑦 are measured absorbed amounts per unit skin area (Q abs for F  , Br  and I  ). Thereafter, a second analysis was performed where the ratio of Q abs to ion activity was introduced as a new response. An additional experiment corresponding to the centroid of the simplex (ternary mixture of NaF, NaBr and NaI at 167 mmolkg 1 each, (x F ,x Br ,x I ) = (1/3,1/3,1/3), has been added as a check point to test the adequacy of the model.

Multiple linear regression calculations, analysis of variance (ANOVA) and statistical analyses were performed with Umetrics MODDE 12.0 software (Umetrics, Umeå, Sweden).

Results and discussion

Experimental results

Skin penetration of ions has long been believed limited and most of available research on the subject have considered cations far more often than anions. Previous study by Paweloszek et al. [15] initiated research on cutaneous absorption of halide anions by investigating skin absorption of NaF, NaCl, NaBr and NaI from aqueous solutions of equal mass concentrations. In the present study, molal concentrations were set equal because they are more closely related to thermodynamic parameters such as activity and chemical potential. Chloride was excluded from experiments for the sake of feasibility and reproducibility. Indeed, chloride anions are abundant endogenous ions in the skin tissue; this causes analysis problems for distinguishing endo-and exogenous ions [4,20].

Effect of ionic concentration

The effect of ionic concentration was firstly addressed. Indeed, a higher concentration in the donor side creates a larger concentration gradient through the skin towards the acceptor medium. The amount of ions penetrating skin was very low compared to the amount in the donor solution, so that ion absorption did not significantly deplete the donor fluid; experiments were performed under "infinite dose" conditions. The concentration in the acceptor medium also increased very little compared to that of the donor. As a consequence, the concentration gradient driving passive diffusion was kept constant over the whole experiment duration. Changing the concentration in the donor fluid changes the concentration gradient to the same extent, so that the flux of passive diffusion might be proportional to the concentration in the donor fluid. The sample concentration scale was molality (number of moles of solute per unit mass of solvent, molkg 1 ) throughout the whole paper. As shown in Fig. 1, the total absorbed amount of iodide ions penetrating skin actually did not vary linearly with respect to the concentration. It curved downwards at the highest concentrations. Since the ionic concentrations were fairly high, the activity should be better considered than the concentration. Following Stokes and Robinson [START_REF] Stokes | [END_REF], the activity coefficient of anions, , includes an electrostatic contribution given by the DebyeHückel relationship and a contribution coming from ion hydration expressed with the help of the water activity, a w , in compliance with GibbsDuhem. For a 1:1 electrolyte at 32 °C and concentrations expressed on the molality scale, it reads [28] ln 𝛾 ). Conversion from one into another is made using measured densities. The calculation of the activity of mixed ions is a difficult task because too many parameters have to be taken into account. A clear review of the topic is given by Blandamer et al. [START_REF] Blandamer | [END_REF]. The case is especially dramatic when mixed ions have different valences. In the present case, only monovalent anions having related properties (halides) are mixed; the cationic counter-ion is sodium in every case. The activity coefficients were calculated considering mixed ions as single species.

The relationship between absorbed amount and ion activity in the donor medium was linear (Fig. 1). Since the activity correction only considers interactions taking place in bulk aqueous solution, any supplementary non-ideal behaviour of ions absorption from mixed ionic solutions should come from specific interactions operating inside skin. As a consequence of the linear behaviour with respect to ions activity, it makes sense to consider the ratio of the absorbed amount to ion activity when experiments at different ionic concentrations are compared. Similar ratio has been introduced a long time ago as the permeation coefficient k p defined as the ratio of the permeation flux in steady state regime to the concentration in the donor medium [START_REF] Roberts | Percutaneous Absorption Drugs-Cosmetics-Mechanisms-Methodology[END_REF]. We define here the "absorption coefficient", k abs , as the ratio of the total absorbed amount after 24 h exposure to the activity in the donor solution as:

𝑘

Eq. 4

Absorption of single and mixed anions

The total absorbed quantity of halide anions tested alone at 500 mmolkg 1 did not differ significantly (Fig. 2). The same was observed for concentrations of 250 mmolkg 1 (data not shown). The present results differ from the ones reported previously because the studied solutions were containing the same mass concentration (ppm) for each anion [15] instead of the present molality concentration scale. Given the large differences in molar masses of F (19 gꞏmol 1 ), Br (80 gꞏmol 1 ) and I (127 gꞏmol 1 ), it is easy to notice that conversion into molar concentrations makes the observed variations weaker. Moreover, the survival medium used as the acceptor medium was also different: ultrapure water supplemented with glucose only created a flux of ions towards the hypotonic acceptor solution [15]. In the present study, the acceptor medium was an isotonic composition ensuring equilibrium of osmotic pressure with skin cells and longer viability of skin samples [18]. Investigation of skin permeability for anions in binary mixtures revealed significant differences in their absorption depending on the composition. Synergistic effects were observed for mixtures of NaBr and NaI. The values of k abs of both anions were significantly higher in the case of paired salts than alone. These observations agree with Ko et al. [17] who studied the effects of addition of NaF, NaCl, NaBr, NaI on skin penetration of salicylic acid. They found that addition of NaBr or NaI to the vaseline-based formulation significantly increased absorption of an organic compound through murine skin in vitro and rabbit skin in vivo. On the contrary, addition of NaF and NaCl decreased it. Similarly, the present k abs values for NaI were significantly reduced when mixed with NaF. Skin penetration of fluoride was also impaired in the presence of NaBr and NaI.

Ko et al. [17] also observed that salts increased leaching of sterol off excised skin, thereby impairing the initial hydrophobic barrier. This led to infer that enhanced penetration of salicylic acid in presence of NaBr or NaI might be due to the reduction of the barrier function of stratum corneum by disorganization of the crystalline structure of its lipids, thereby allowing better swelling. According to Elden [START_REF]Biophysical Properties of the Skin[END_REF], lyotropic swelling of collagen also occurs in the order: F  < Cl  < Br  < SCN  . The main presumption from these studies is that penetrating chaotropic ions disorganize the skin barrier and make it more permeable to penetrating ionic or nonionic molecules. There is no experiental evidence of such phenomenon, however. The present study goes deeper into the mechanisms by considering the distribution of anions in skin layers: stratum corneum, viable epidermis, dermis, and acceptor medium (SC, VE, D and AM). Indeed, anions distribution in skin layers after 24 h exposure (Fig. 3) was also altered depending on the composition of tested solution. Simultaneous exposure to Br  and I  led to increased recovery in AM as compared to Br  and I  alone. This was associated with reduced values in D, VE and especially SC, indicating lower tendency for accumulation within the tissues. These observations contradict the postulated idea of a disorganization of skin structure by the presence of absorbed anions. Indeed, structural modification of skin layers would require accumulation of ions inside them. On the other hand, the trends are reversed for iodide distribution in the presence of NaF: recovery in AM slightly decreased for mixed ions and absorbed amount in SC increased. This effect was less pronounced in the case of NaF + NaBr. The observed effects are quite complex because they result from several contributions: interactions between ions in the bulk donor solution, adsorption of ions to the skin surface, transfer into stratum corneum and passive diffusion inside it, facilitated transport in the viable epidermis with the help of membrane proteins in keratinocytes (ion channels, ion transporters).

Interactions in bulk solution are considered non-specific and are accounted for by the activity coefficient involving electrostatic and ion hydration contributions. Facilitated transport in viable skin is predominant; indeed, Paweloszek et al. [4] disclosed a large difference between viable and non-viable skin. Passive diffusion through stratum corneum is necessary for ions to reach viable epidermis where facilitated transport operates. Most elementary steps for ion absorption are interdependent. Transport phenomena depend on ion type in the same way according to Hofmeister series. The best strategy for addressing such a complexity is a global approach undertaken here using an experimental design.

Statistical Modelling

An alternative way to exploit experimental results consists in fitting them to statistical models. The beneficial input of such data analysis is a rigorous statistical framework. The outcome is a quantitative parametric assessment of non-ideal behaviour through the coefficients of the Scheffé {3,2} polynomial equation (Eq. 2). The 𝑦 -responses are either absorbed amounts Q abs or absorption coefficients k abs = Q abs /m. Experimental values of Q abs and k abs are given in Table S2 of Supporting Information. They must fully fill a matrix containing absorption data of ions thought some of them are not present in the solution of mixed ions. As example, a binary mixture of fluoride and bromide does not contain iodide, but the matrix for iodide absorption data does contain a figure pertaining to iodide absorption from a mixed solution of fluoride and bromide. This is mandatory to fully fill the 𝑦 -response matrix in the mathematical framework of Scheffé simplex-lattice design. This is easy to manage when Q abs is considered as a response: Q abs is zero when the anion is not present. When responses are absorption coefficients, the correct values are lim →  . They were obtained by extrapolation from experiments at several concentrations. Although those concentrations were fairly high (> 100 mM) for ensuring enough experimental accuracy, extrapolation to infinite dilution was quite robust, owing to the almost linear dependence of Q abs with respect to m in the low concentration range. A first approach was to determine the coefficients of the polynomial using the six experiments of the {3,2} simplex-lattice design for the skin absorption of each anion. Since there are mixtures where some ions are absent, their coefficient in the polynomial is undetermined, and it has been removed from the polynomial model. Keeping these coefficients led to statistically non-significant values (p > 0.75). As example, because there is no I  in a binary mixture of F  and Br  , the term containing the coefficient b FBr was removed from the polynomial pertaining to Q abs or k abs of iodide. The modified Eq. 2 became the set of Eqs 5 to 7 for Q abs and Eqs 8 to 10 for k abs :

Q abs (F  ) = a F x F + a Br x Br + a I x I + a FBr x F x Br + a FI x F x I Eq. 5 Q abs (Br  ) = a F x F + a Br x Br + a I x I + a FBr x F x Br + a BrI x Br x I Eq. 6 Q abs (I  ) = a F x F + a Br x Br + a I x I + a FI x F x I + a BrI x Br x I Eq. 7 k abs (F  ) = b F x F + b Br x Br + b I x I + b FBr x F x Br + b FI x F x I Eq. 8 k abs (Br  ) = b F x F + b Br x Br + b I x I + b FBr x F x Br + b BrI x Br x I Eq. 9 k abs (I  ) = b F x F + b Br x Br + b I x I + b FI x F x I + b BrI x Br x I Eq. 10
Q abs was first analysed because this was the actually measured parameter. The models for Q abs (Eqs 5, 6 and 7) were first used to predict the amounts of absorbed ions for the centroid experiment (ternary mixture) as a validation tool of the model: residuals of 0.5, -1.6 and -1.3 µmolꞏcm 2 were respectively obtained for Q abs (F  ), Q abs (Br  ) and Q abs (I  ). They were considered satisfactory compared to the experimental standard deviation. The centroid experiment was then used in combination with the 6 experiments of the simplex-lattice design to fit once again the models for Q abs and k abs to the full experimental data. The best statistical models (characterized by highest values of R 2 ) are presented in Table 1. For each model, ANOVA analysis indicated the high significance of the fits (p < 0.05); and the corresponding determination coefficient R² greater than 0.97 (Table 1) also showed their satisfactory adequacy.

Once validated, the models were used to plot the estimated surface contours of the studied responses in the investigated experimental domain, i.e. in a classical ternary diagram in mole fractions of ions (Fig. 4) where the colour scale stands for Q abs .

The variation of Q abs of F  in Fig. 4 shows a continuous increase of Q abs as the mole fraction of fluoride increases, which is the obvious consequence of the increase of fluoride concentration in the donor solution. The iso-Q abs lines are almost horizontal in the triangular presentation where pure fluoride is at the apex, showing that the effects of bromide and iodide ions are identical and negligible. As a whole, there is no specific effect of mixed anions. Conversely, absorptions of bromide and iodide anions show a maximum in the presence of the other. There is no apparent effect of fluoride. The statistical analysis disclosed a specific interaction between bromide and iodide that caused enhanced skin absorption of these anions. The maxima of absorption occur when the solution is rich in the observed anion because of the trivial effect of the higher concentration of the observed anion as the corner of pure anion is approached. This analysis considering Q abs includes contributions of the concentration of observed anions and specific interactions with their partners. A quantitative approach is to consider the a ij coefficients (Table 1) that have statistical significance. The a F , a Br and a I coefficients of the same anions (e.g. a F for Q abs of F  ) are highly significant (p  0.01) and positive. They reflect the trivial effects of increased absorption as a function of concentration. The a F , a Br and a I coefficients of different anions (e.g. a F for Q abs of Br  ) are statistically not significant (SD is larger than the coefficient value and p = 0.93). a FBr , and a FI negative coefficients are also not significant owing the large SD and p-value. The striking feature is the large and significant positive values of a BrI , showing a specific interaction between bromide and iodide anions.

Table 1

Coefficients a ij (µmolꞏcm 2 ) of the {3,2} polynomial models of absorbed amounts Q abs (Eqs 5, 6 and 7) together with the corresponding determination coefficient R², standard deviation (SD) and p-value of the ANOVA test between brackets. All values are given with two digits with no consideration to their statistical significance.

Ions (i,j)

F  aij (SD, p) The global statistical analysis of skin absorption of mixed anions disclosed a specific interaction between them, but neither had it allowed inferring the nature of the interactions, nor the location of them in the complex layered structure of skin (donor solution, stratum corneum, viable epidermis and dermis). A refined analysis was performed considering the absorption coefficient k abs = Q abs /m in place of Q abs . This suppresses the effects of the concentration of observed anion and interactions taking place in the bulk donor solution through the activity coefficient. The same statistical analysis as for Q abs was made. Results are given in Table 2 and Fig. 5.

Br  aij (SD,
Substitution of k abs for Q abs eliminates the effects of ion concentrations in a similar way as applying a background flattening image processing to the triangular composition maps of Fig. 4. The sole remaining effects are specific cross-interactions. The contour plot for fluoride is almost flat with a constant value of k abs = 0.1 kgꞏm 2 (Fig. 5). This feature shows the overall absence of specific interactions of bromide and iodide with fluoride. Conversely again, the k abs maps of bromide and iodide anions show a maximum at the centre of the bottom side. Substitution of k abs for Q abs shifted the location of the absorption maximum at the bottom side of the triangle from close to the vertex of adsorbed ion to the mid-point of the BrI axis, (x F ,x Br ,x I ) = (0,1/2,1/2). Such symmetrical position suggests a 1:1 stoichiometry of specific interaction between bromide and iodide anions that could not be detected in the raw Q abs map. Many of the b ij coefficients (Table 2) A specific interaction operating between bromide and iodide was already inferred from the raw experimental data. The statistical analysis showed that this was the sole significant specific interaction.

The absorption coefficient k abs of Br  in the presence of an equal amount of I  was 0.41 kgm 2 against 0.21 kgm 2 for Br  alone (Table S2 andFig 2), which was twice an absorption enhancement caused by non-ideal mixing. In the same symmetrical case, k abs of I  increased by a factor of three in the presence of an equal amount of Br  (k abs = 0.44 kgm 2 against 0.146 kgm 2 for I  alone). Such interactions between bromide and iodide caused an absorption enhancement of their partner by a factor of 2-3 with respect to the case of ideal mixing.

Discussion

The location of disclosed interactions is difficult to discuss in details despite the distribution of ions stored in the different skin layers has been measured (Fig. 3). As main the feature, very few figures show significant differences. The main contributions to differences of total absorbed amount Q abs come from the amounts that reached the acceptor medium. The very small differences of amounts in SC suggest that SC is just a passive diffusion barrier where permeation is only driven by the concentration gradient. There is no accumulation of ions inside SC, showing that there is no specific binding of anions there. There are also small differences of ion amounts in viable epidermis and dermis. It is known that these skin layers are not passive diffusion barriers because they contain ion transporters contributing a lot to the overall absorption [15]. The absorbed amounts per unit skin area can be converted into concentrations in mmolꞏL 1 taking the thickness of SC, VE and D as 20 µm, 50 µm and 1.25 mm. The result is a smooth concentration gradient along skin depth in all cases (Fig. 6). One consequence is that concentrations in different layers are interdependent. There is no indication of accumulation coming either from specific interactions with skin materials or any ion-specific barrier in SC or VE. The nature of interactions operating in skin absorption experiments cannot be inferred from the present data analysis that remains a global approach. Non-specific electrostatic interactions do operate in the concentrated donor solution; they have been accounted for by considering the activity coefficients. Ions absorption cannot contribute to electrostatic effects inside skin because the concentrations of penetrating ions inside skin layers were low with respect to the concentrations of endogenous ions [4]. As example taking the thickness of viable epidermis as 50 µm and that of dermis as 1.3 mm, the mean concentration of endogenous chloride in viable epidermis and dermis are respectively 200 mmolꞏL 1 and 15 mmolꞏL 1 ; the concentrations of sodium are three times larger and those of potassium are also larger than those of chloride [4]. All presently measured anions concentrations were less than 50 mmolꞏL 1 in viable epidermis and less than 10 mmolꞏL 1 in dermis.

A specific interaction between bromide and iodide ions should be considered. These two anions are chaotropic in the Hofmeister series of halides because of their large size and high polarizability allowing strong attractive dispersion interactions and their poor hydration. Hydration of ions [START_REF] Ruckenstein | [END_REF]34] and dispersion interactions [35] are the two main rationalizing factors for the Hofmeister series. As outlined early by Fajans [36], both phenomena are interrelated as they originate from the size and polarizability of ions [37][38][39]. Both Hofmeister and anti-Hofmeister behaviours have been reported [40,41]; their concomitance may lead to compensation of effects and even reversal of the global balance. Owing to the poor current knowledge on skin ultrastructure and interactions operating inside skin layers, going farther would require a full account of many interactions before a simplified view retaining only the predominant interactions could be reached. A recent study of water sorption by wood is a successful example of such an approach [42]. Electrostatic repulsions act against association of Br  and I  anions, so that a cation is necessarily involved in the association. Possible complex species may result from the association of Br  , I  and Na + ions as the NaBrI  monovalent anion. Another option is the association with endogenous magnesium or calcium cations by formation of the neutral MgBrI and CaBrI species. Indeed, magnesium and calcium are abundant endogenous ions inside skin, with the presence of a Ca 2+ gradient from the stratum basale to the stratum granulosum where it peaks before declining in stratum corneum [43]. On the basis of size and polarizability of ionic partners, Mg 2+ , Ca 2+ , Br  and I  [37-39], such complex association with magnesium or calcium looks quite a likely mechanism for anions to pass through the stratum corneum.

Conclusion

Skin absorption of mixed halide ions shows synergistic effects between chaotropic bromide and iodide anions. This has been clearly disclosed by a statistical analysis of absorption experiments on excised pig skin mounted in diffusion Franz cells. Statistical analysis allowed identification of interacting anions pairs from skin absorption experiments that show a large variability. Considering the ratio of the absorbed amounts to the ion activity discards the trivial contributions of ion concentration and non-specific effects of electrostatic interactions in the aqueous solution; such data reduction process highlights the effects of specific interactions.

It has been inferred that polarizable hydrophobic anions associate in the stratum corneum as complex species together with cations, in particular with magnesium and calcium, in order to counterbalance their electrostatic repulsions.

The present results together with our previous work [15], definitely show that ionic species do penetrate skin. They are of relevance to practical ionic solutions such as spring waters used in cosmetic products.

  ln 1 𝑀 , 𝑛 2 𝑚 Eq. 3 where symbols have their usual meaning. 𝐼 𝟐 ∑ 𝒛 𝒊 𝟐 𝑪 𝒊 𝒊𝒐𝒏𝒔 is the ionic strength; b is a constant taken as 1.2 L 1/2 mol 1/2 [28]; M mol,w = 0.018 kgmol 1 is the molar mass of water; and m is the molality of solutions. There is a large variability of experimental values of hydration numbers. The hydration number of sodium halides, n, was taken from mean values compiled by Israelachvili [29]: n = 7 for NaF, n = 6 for NaBr and n = 5 for NaI. Hydration numbers are close to each other because the main contribution comes from the hydration of the sodium cation. The mean value of n = 6 was taken for the mixtures of all sodium halides. It is noticed that the DebyeHückel part of Eq. 3 is expressed as a function of molarity (C i , moldm 3 ) whereas the two other terms are functions of the molality (m, molkg 1

Fig. 1 .

 1 Fig. 1. Total absorbed amount of iodide ions (µmolꞏcm 2 ) after 24 h exposure to sodium iodide solutions as a function of iodide concentration (blue) and iodide activity (red).

Fig. 2 .

 2 Fig. 2. Absorption coefficient k abs = Q abs /m (kgꞏm 2 ) after 24 h exposure time for skin exposed to binary and ternary mixtures of halide salts compared to single halide salt as control. Data represent mean ± sem carried out on n = 9 individual skin explants taken from 5 different pigs. Asterisks (*) indicate p < 0.05 in t-test analysis.

Fig. 3 .

 3 Fig. 3. Distribution of halide anions in skin layers after 24 h exposure. Data represent mean value of absorbed amount expressed as a percentage of the total absorbed amount Q abs . Results are means of n = 9 independent measurements.

Fig. 4 .

 4 Fig. 4. Contour plots of the predicted absorbed amounts (Q abs , µmolꞏcm 2 ) of F  , Br  and I  ions after 24 h exposure in the composition space of ionic mixtures expressed in mole fractions.

  (0.3, 0.93) -0.08 (0.9, 0.93) 7.20 (0.78, 0.01) F -/Br - -3.53 (1.4, 0.13) -6.50 (4.3, 0.27)  F -/I - 5.65 (1.4, 0.06)  -10.1 (3.6, 0.11) Br -/I -  12.7 (4.3, 0.10) -10.1 (3.6, 0.11)

  have poor statistical significance. So, the significance of outcoming b ij coefficients is first discussed. The distribution of p-values was definitely bimodal with either very large or moderate values. p < 0.1 was taken for claiming significance in the present case instead of the classical criterion p < 0.05 for the full population of low/moderate p-values is taken as significant. Under this condition, the b F , b Br and b I coefficients are significant (p < 0.07). The b BrI and b IBr are also of medium significance; they assume a high positive value. The negative b FBr and b FI coefficients involving the F -anion are not significant. They nevertheless give a contribution to other coefficients in the statistical model. Thus, it is clear from the flat F  map (Fig. 5) that skin absorption of fluoride was not influenced by the presence of other ions, so that the positive values of b F coefficients contradicted the overall features of the F  map of k abs . It is suspected that the effects of the positive values of b F and the negative values of b FBr and b FI compensated such that the balance is null. Because of the lack of statistical significance of b FBr and b FI coefficients for absorption of all anions, it is considered that the positive values of b F are biases coming from a too large variability of skin absorption measurements. Such high variability is intrinsic of experiments performed on skin and living matter in general.

Fig. 5 .

 5 Fig. 5. Contour plots of the predicted absorption coefficients (k abs = Q abs /C, kgꞏm 2 ) of F  , Br  and I  ions after 24 h exposure in the composition space of ionic mixtures expressed in mole fractions.

  Refinement of the analysis by considering k abs may allow discrimination between the ion effects coming from alteration of the medium (ionic strength, dielectric properties…) through the b F , b Br and b I coefficients, and from specific interactions through the b FBr , b FI and b BrI coefficients. This was successful and led to supplementary conclusions: -Owing to the linear dependence of Q abs with respect to activity for F -, Br -and I -(Fig. 1), the values of b F , b Br and b I should be null. The positive values of b F , b Br and b I ( 0.2 kgꞏm 2 for all anions) cannot be considered as a non-specific effect of the presence of other ions inside skin. Their contribution is compensated by negative b ij coefficients that are not significant as it has been shown from the flat k abs map for F  absorption. -The high positive values of b BrI indicates a strong specific interaction between bromide and iodide. This is the main outcome of the statistical analysis.

Fig. 6 .

 6 Fig. 6. Concentration profile of iodide ions inside skin layers (mmolꞏL 1 ) as a function of depth showing the concentration gradient from the surface to the acceptor medium. Concentrations are taken homogeneous in each skin layer, Stratum corneum (SC), Viable epidermis (VE), Dermis (D) and Acceptor medium (AM).

Table 2

 2 Coefficients b ij (kgꞏm 2 ) of the {3,2} polynomial models of absorption coefficients k abs (Eqs 8, 9 and 10) together with the corresponding determination coefficient R², standard deviation (SD) and p-value of the ANOVA test between brackets. All values are given with two digits with no consideration to their statistical significance.

	Ions (i,j)	F  bij (SD, p)	Br  bij (SD, p)	I  bij (SD, p)
	F -	0.17 (0.017, 0.010)	0.17 (0.048, 0.071)	0.17 (0.041, 0.051)
	Br -	0.12 (0.016, 0.016)	0.22 (0.053, 0.056)	0.17 (0.041, 0.051)
	I -	0.12 (0.016, 0.016)	0.17 (0.048, 0.071)	0.18 (0.044, 0.055)
	F -/Br -F -/I -Br -/I -	-0.14 (0.080, 0.21) 0.20 (0.080, 0.13) 	-0.28 (0.24, 0.37)  0.76 (0.24, 0.089)	 -0.48 (0.20, 0.14) 0.96 (0.20, 0.042)
	R 2	0.86	0.88	0.95

Acknowledgements

MT acknowledges a PhD grant from the University of Lyon.

Declaration of competing interest

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

Appendix A. Supplementary data

Supplementary material related to this article can be found in the on line version of Supporting Information file