Johanne Teychené

Dalina Didacus-Prins

Nadia Chouini-Lalanne

Valérie Sartor

Christophe Dejugnat
email: dejugnat@chimie.ups-tlse.fr

Dr Christophe Déjugnat

Formulation induces direct DNA UVA photooxidation. Part I. Role of the formulating cationic surfactant

Keywords: surfactant, self-assembly, DNA, formulation, UVA photosensitization

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

Introduction

If gene therapy opens up new therapeutic perspectives in the treatment of inherited deficiency diseases (e. g. cystic fibrosis), acquired diseases (cancer, neurodegenerative diseases) or infectious diseases (hepatitis, AIDS), its success depends on the effective transmission and expression of genetic material within cells. This undoubtedly requires the development of systems capable of efficiently and safely crossing biological barriers on the way to the nucleus and transmitting the drug gene there. Most of the systems used involve recombinant viral vectors, capable of inserting efficiently the transgene into the cells. Although the latter are very effective in the transfer function, their use has a number of disadvantages (production cost, safety, development of immune reactions, and risk of pathogenicity). To avoid them, a number of synthetic vectors have been developed. They are mostly cationic derivatives of a lipidic or polymeric nature capable of interacting with DNA by electrostatic interactions and compacting it to form particles (aggregates). [START_REF] Foldvari | Non-Viral Gene Therapy: Gains and Challenges of Non-Invasive Administration Methods[END_REF] Moreover, since the effective charge of the DNA and its size are reduced, the efficiency of the transfer of the drug gene to its site of action is also improved.

In the case of the in vivo delivery, the compacted gene/vector system can be transferred to the target DNA in two ways: either by the systemic route or by local application. [START_REF] Dunbar | Gene Therapy Comes of Age[END_REF] However, whatever the mode of administration, the gene must be associated with a system capable of protecting it against aggression by the external environment and in particular from UV radiation, one of the main sources of DNA damage at the origin of photocarcinogenesis processes. While the photomutagenic potential of UVB radiation has long been established, that of UVA radiation, which is longer and deeper penetrating the skin, has only recently been recognized. Indeed, the direct formation of cyclobutane pyrimidine dimers (CPD) in DNA under UVA radiation has been widely reported [START_REF] Schuch | Sunlight Damage to Cellular DNA: Focus on Oxidatively Generated Lesions[END_REF][START_REF] Tyrrell | Induction of Pyrimidine Dimers in Bacterial DNA by 365 Nm Radiation[END_REF][START_REF] Kuluncsics | Wavelength Dependence of Ultraviolet-Induced DNA Damage Distribution : Involvement of Direct or Indirect Mechanisms and Possible Artefacts[END_REF][START_REF] Perdiz | Distribution and Repair of Bipyrimidine Photoproducts in Solar UV-Irradiated Mammalian Cells: Possible Role of Dewar Photoproducts in Solar Mutagenesis[END_REF][START_REF] Douki | Bipyrimidine Photoproducts Rather than Oxidative Lesions Are the Main Type of DNA Damage Involved in the Genotoxic Effect of Solar UVA Radiation[END_REF][START_REF] Mouret | Cyclobutane Pyrimidine Dimers Are Predominant DNA Lesions in Whole Human Skin Exposed to UVA Radiation[END_REF][START_REF] Schuch | Development of a DNA-Dosimeter System for Monitoring the Effects of Solar-Ultraviolet Radiation[END_REF][START_REF] Jiang | UVA Generates Pyrimidine Dimers in DNA Directly[END_REF][START_REF] Mouret | UVA-Induced Cyclobutane Pyrimidine Dimers in DNA: A Direct Photochemical Mechanism?[END_REF][START_REF] Cortat | The Relative Roles of DNA Damage Induced by UVA Irradiation in Human Cells[END_REF] and the involvement of UVA radiation in cancer and skin aging processes is now well established. However, no study has been carried out on the direct influence of UVA radiation on DNA in a synthetic vector system. Yet DNA delivery in the skin could be affected by sunlight. The studies carried out in this sense involved the presence of a photosensitizer and focused on studying the influence of the formulation on the formation of photoinduced oxidized damage [START_REF] Rudiuk | Modulation of Photo-Oxidative DNA Damage by Cationic Surfactant Complexation[END_REF] while the direct absorption of UVA radiation by DNA has been widely demonstrated. So, the purpose of this work is to focus on the direct formation of oxidized lesions on DNA formulations under UVA radiation involving as cationic derivatives, a close analog of cetyltrimethylammonium bromide (CTAB), namely cetyltriethylammonium bromide (CTEAB, Figure 1).

Figure 1. Structure of cetyltriethylammonium bromide (CTEAB).

This cationic surfactant presents the advantage of being readily soluble in liquid water at any temperature (TKrafft < 0 °C), [START_REF] Davey | Temperature Depression in Quaternary Ammonium Bromide Surfactants[END_REF] whereas the Krafft temperature of CTAB (TKrafft = 25 °C) [START_REF] Davey | Temperature Depression in Quaternary Ammonium Bromide Surfactants[END_REF] could be the source of troubles when handling it at room temperature (close to the solubility temperature). On the other hand, CTEAB presents a bulkier head group than CTAB and this affects its self-organization properties in pure water due to molecular packing considerations. [START_REF] Israelachvili | Theory of Self-Assembly of Hydrocarbon Amphiphiles into Micelles and Bilayers[END_REF] For example, although they have similar critical micelle concentrations (CMCs) in water, CTAB forms elongated micelles while CTEAB rather self-assembles into much smaller, slightly ellipsoidal micelles. [START_REF] Wasbrough | Control of Mesostructure in Self-Assembled Polymer/Surfactant Films by Rational Micelle Design[END_REF][START_REF] Jaber | Interactions between Quaternary Ammonium Surfactants and Polyethylenimine at High PH in Film Forming Systems[END_REF] Therefore CTEAB has been mainly used as pore directing agent for the preparation of mesoporous materials thanks to its ability to form micellar cubic phases, [START_REF] Anderson | A New Minimal Surface and the Structure of Mesoporous Silicas[END_REF][START_REF] Kruk | Determination of Pore Size and Pore Wall Structure of MCM-41 by Using Nitrogen Adsorption, Transmission Electron Microscopy, and X-Ray Diffraction[END_REF][START_REF] Huo | Generalized Synthesis of Periodic Surfactant/Inorganic Composite Materials[END_REF] but also as adjuvant in enhancing oil recovery technique. [START_REF] Gou | Water-Soluble Complexes of Hydrophobically Modified Polymer and Surface Active Imidazolium-Based Ionic Liquids for Enhancing Oil Recovery[END_REF][START_REF] Li | Oil Detachment from Silica Surface Modified by Carboxy Groups in Aqueous Cetyltriethylammonium Bromide Solution[END_REF] However its interaction with DNA has not been reported yet (few authors sometimes describe the use of cetyltriethylammonium bromide in DNA extraction and purification processes, but a closer look shows that it was a misspelling of cetyltrimethylammonium bromide, which is widely used for decades in reference protocols). Therefore, it is interesting to consider this CTEAB-DNA formulation and to see whether the slight structural change (ethyl vs methyl) due to the replacement of CTAB by CTEAB could induce significant changes or not.

In a first part we present the self-organization properties of CTEAB in the buffer solution used as solvent for DNA. Indeed, aggregation of CTEAB has been depicted in water but the presence of electrolytes (buffer) is known to have an impact on such properties. [START_REF] Rosen | Surfactants and Interfacial Phenomena[END_REF] Therefore the determination of the CMC (by tensiometry and pyrene fluorimetry) and the depiction of the micelles (by scattering experiments) will be carried out. Then the CTEAB-DNA interactions will be characterized to check that CTEAB can also be used to formulate DNA, as an analog of CTAB. For that, the critical aggregation concentrations (CACs) will be determined by complementary techniques (tensiometry, pyrene fluorimetry, agarose gel electrophoresis, UV-Vis absorbance and circular dichroism measurements). Finally, we will investigate the effects of UVA radiation on these formulations (by agarose gel electrophoresis) and will evidence that it can led to direct DNA photosensitization. Experiments conducted in the presence of peculiar scavengers will allow a mechanistic interpretation of the results obtained.

Materials and methods

Materials

Triethylamine (purity 99.9 %) and 1-bromohexadecane (purity 98%) were purchased from VWR (Fontenay Sous Bois, France) and Lancaster (Morecambe, England), respectively. CTEAB was synthesized as described in the literature [START_REF] Kim | Synthesis and Pore Size Control of Cubic Mesoporous Silica SBA-1[END_REF] and purification protocol was improved. Briefly, 1-bromohexadecane (20 g, 65 mmol) was reacted with triethylamine (10 mL, 72 mmol) in 130 mL absolute ethanol for 72 h at 85 °C (reflux). After evaporation to dryness under reduced pressure, the residue was dissolved in chloroform and ethyl acetate was added to induce precipitation. After precipitation was completed at 4 °C, the white solid was collected by filtration and washed with ethyl acetate. Final purification was achieved by solid phase extraction (SPE) on a reverse phase Chromabond C18 ec chromatographic column (70 mL, 10 g) from Macherey-Nagel (first washing with water then elution with methanol). This step ensured full removal of the impurity trimethylamine hydrobromide. Evaporation of methanol afforded CTEAB as a white crystalline solid. Purity was assessed by nuclear magnetic resonance (NMR) and high-resolution mass spectroscopy (HRMS).

(see Supporting Information).

Tris(hydroxymethyl)aminomethane (TRIS, purity 99.8 %) was from Fisher Scientific (Geel, Belgium). Supercoiled plasmid DNA (Form I) pBR322 (4361 base pairs) was purchased from Thermo Fisher Scientific (Vilnius, Lithuania), stored in 10 ×10 -3 mol.L -1 of TRIS/HCL (pH 7.6) and 1×10 -3 mol.L -1 of EDTA. The DNA was used after dilution in a 20 mM TRIS/HCl buffer (pH=7.4) to obtain a stock solution at [DNA-PO4 -] = 4.5×10 -4 mol•L -1 . All the DNA concentration indicated on the manuscript are in mol phosphate•L -1 . Heparin sodium salt (purity 99.8%) was purchased from Alfa Aesar (Heysham, Germany) and Sodium azide (NaN3, purity 99%) from Alfa Aesar (Karlsruhe, Germany). Agarose and tert-butanol ( t BuOH, purity 99.5%) were obtained from Sigma-Aldrich (Saint Louis, USA), while pyrene (purity 98%) was from Acros Organics (Geel, Belgium). Ethidium Bromide (EB) was purchased as a 10 mg•mL -1 aqueous solution from Invitrogen (Carlsbad, USA). D2O (purity 99.9%) was obtained from Eurisotop (Saint Aubin, France) and T4 endonuclease V (pyrimidine dimer glycosylase) from BioLabs (New England, USA). Bromophenol blue was purchased from Sigma Aldrich (Saint Louis, USA).

Water used in all experiments was produced by a two-stage Milli-Q filtration system from Millipore and had a resistivity higher than 18.2 MΩ•cm.

Surface tension measurements

Surface tension measurements were performed using a Krüss EasyDyne tensiometer using the Wilhelmy plate method. Temperatures were maintained at 25 °C (± 0.1 °C) by circulating thermostated water through a jacketed vessel containing the solution.

For each experiment, surface tension was measured three times (each time ten readings were performed and averaged) after an equilibration time of 30 minutes.

Fluorescence measurements

A stock solution of pyrene (10 -4 mol•L -1 ), was prepared in methanol and stored in glass vials at 4 °C. The solutions for fluorescence probing studies were prepared by adding 1 μL of this pyrene stock solution (10 -4 mol•L -1 ) to 399 μL of the sample solution. Final concentration of pyrene was 2.5×10 -7 mol•L -1 , while the amount of methanol remained very low (0.25 % vol.) Fluorescence measurements were performed on a Fluorolog Horiba spectrofluorimeter equipped with channel multiple tau correlator (auto and cross correlation, 1088 real time channels) and a thermostated cuvette holder at 25 ± 0.1 °C. Excitation wavelength was 335 nm, and the fluorescence emission was recorded between 350 and 500 nm.

UV-Visible absorbance and circular dichroism measurements

Absorption spectra were recorded on a Hewlett Packard HP 8452A Diode Array Spectrophotometer with an optical path length of 1 cm. Circular dichroism spectra were obtained from a circular dichroism spectrometer J-815 from Jasco equipped with a 150 W Xenon arc lamp light source, using a bandwidth of 0.5 nm, with medium sensitivity with a maximum of 200 mdeg. Data acquisition was done in continuous mode.

Multi-angle light scattering experiments

The multi-angle light scattering (MALS) measurements were performed on a 3D LS Spectrometer from LS Instruments (Fribourg, Switzerland) equipped with a 100 mW high performance DPSS Laser (Cobolt) operating at = 660 nm, a two-channel multiple tau correlator (auto and cross correlation, 1088 real time channels), a 3D cross-correlation module, a variable-angle detection system, two high sensitivity APD detectors, an automated laser attenuation system combined with on-line laser intensity measurement, a temperature controllable sample chamber with index matching vat, and an external circulator for temperature control (Julabo CF31).

Before analysis (and otherwise stated), samples were filtered through 0.2 µm hydrophilic PTFE filters into the cylindrical scattering cells.

Measurements were performed at 25°C for scattering angles ranging from 12° to 150°, corresponding to scattering wave vectors q in the range from 2.7×10 -3 to 2.4×10 -2 nm -1 . As CTEAB solutions did not produce multiple scattering, the 3D-cross correlation configuration was not required and the measurement were performed in the classical 2D-pseudo cross configuration.

At each angle, 3 to 10 measurements were carried out and later averaged after having discarded eventual meaningless correlograms. Analysis of both dynamic and static light scattering measurements were performed using the home-made MULTI-STORMS software developed by Dr. C. Mingotaud (see Supporting Information).

Small-Angle X-ray Scattering experiments

SAXS (Small-Angle X-ray Scattering measurements) were conducted at the European Synchrotron Radiation Facility (ESRF, Grenoble, France) at the ID02 beamline. CTEAB solutions (5 to 20 mM) were transferred into glass capillaries before measurements. The sample-to-detector distance was 2.5 m. Using 1 Å X-ray wavelength, the q range covered was 2.9×10 -3 Å -1 < q < 3.1×10 -1 Å -1 . For each solution, 10 scans were recorded and averaged. For each scan, exposure time was kept as low as 100 ms to prevent from radiation damage. The observed intensities I(q) were corrected for transmission, solvent, and detector response. The analysis of the I(q) profiles was performed using the SasView software (http://www.sasview.org/).

Irradiation experiments

DNA irradiation was made with a Mercury Xenon lamp (Oriel instruments, 500W) equipped with a long pass filter λ ≥ 335nm (Newport 20CGA-335 GC505) at 20°C.

The irradiated and non-irradiated sample volume was 100 µL. The final concentrations in TRIS/HCl buffer (20 mM, pH=7.4) were 9×10 -5 mol phosphate•L -1

for the plasmid DNA pBR322, from 0 to 4×10 -3 mol•L -1 for the CTEAB solutions, 10 200×10 -3 mol L -1 for NaN3 and 4% v/v for t BuOH. Each experiment was at least triplicated. (w/w in TRIS/ HCl buffer (20 mM, pH= 7.4) were added.

Agarose gel electrophoresis

To the samples without T4 endonuclease V treatment, 5 µL of bromophenol blue solution, 10 µL of Heparin 20% (w/w in TRIS/ HCl buffer) and 10 µL TRIS/ HCl buffer (20 mM, pH= 7.4) were added.

Electrophoresis and photodensitometry

An aliquot of 40 µL of each sample was deposited into 0.8% agarose gel containing 0.02 % of Ethidium Bromide. Electrophoresis migration was carried out for 4 hours under a constant electric field of 80 mV.

Single strand breaks (SSB) were quantified by photodensitometry using the ImageJ software. To correct the lower efficiency of ethidium bromide binding to Form I DNA with respect to Form II, a coefficient of 1.66 was used. [START_REF] Ciulla | Photosensitization of Single-Strand Breaks in PBR322 DNA by Rose Bengal[END_REF]

Results and discussion

Self-organization of CTEAB in TRIS/HCl buffer

CTEAB surfactant (Figure 1) was synthesized as described in the literature [START_REF] Kim | Synthesis and Pore Size Control of Cubic Mesoporous Silica SBA-1[END_REF] and dissolved in 20 mM TRIS/HCl buffer solutions at pH = 7.4. Determination of the CMC by tensiometry was performed by measuring the variation of the surface tension as a function of the surfactant concentration. In the dilute regime, the surface tension value is close to the one of water and then it decreases when the concentration of surfactant increases. At the threshold value which corresponds to the CMC, the surface tension does not vary much upon increasing surfactant concentration (Figure 2A).

Figure 2. Variation of the surface tension (A) and of the pyrene I1/I3 fluorescence emission ratio (B) of CTEAB solutions as a function of the CTEAB concentration in 20 mM TRIS/HCl buffer (pH = 7.4) at 25 °C.

By this technique the CMC of CTEAB was found to be 1.5 (± 0.2) ×10 -4 mol•L -1 in the 20 mM TRIS/HCl buffer (pH = 7.4) at 25 °C. This value is much lower than the CMC values reported in the literature for CTEAB in water: 7-8×10 -4 mol•L -1 , as determined from tensiometry and conductivity experiments. [START_REF] Wasbrough | Control of Mesostructure in Self-Assembled Polymer/Surfactant Films by Rational Micelle Design[END_REF][START_REF] Jaber | Interactions between Quaternary Ammonium Surfactants and Polyethylenimine at High PH in Film Forming Systems[END_REF][START_REF] Soldi | Arenediazonium Salts: New Probes of the Interfacial Compositions of Association Colloids. 6. Relationships between Interfacial Counterion and Water Concentrations and Surfactant Headgroup Size, Sphere-to-Rod Transitions, and Chemical Reactivity in Cationi[END_REF][START_REF] Bacaloglu | Micellar Enhancements of Rates of SN2 Reactions of Halide Ions. The Effect of Headgroup Size[END_REF][START_REF] Buckingham | Effect of Head-Group Size on Micellization and Phase Behavior in Quaternary Ammonium Surfactant Systems[END_REF][START_REF] Rodríguez | Effects of Head Group Size on Micellization of Cetyltrialkylammonium Bromide Surfactants in Water-Ethylene Glycol Mixtures[END_REF] This decrease of CMC means that the aggregation is favored in TRIS/HCl buffer compared to pure water.

The effect of the electrolyte is to partially screen the repulsion electrostatic interactions between the similar charged head groups of the surfactant and therefore to promote aggregation. Thereby, the CMC is lowering by addition of electrolyte.

In the same way, Haq, Z. and coworkers [START_REF] Haq | Effect of Electrolyte ( NaCl ) and Temperature on the Mechanism of Cetyl Trimethylammonium Bromide Micelles[END_REF] reported a decrease of the CMC of the CTAB from 0.98 mol•L -1 (at 303 K) to 0.90 mol•L -1 at 3 mol•L -1 of NaCl, indicating the significant role of the electrostatic interactions between surfactant and electrolyte.

From the tensiometry curve, one can also estimate the minimal molecular crosssectional area at the air/water interface , at the CMC. [START_REF] Rosen | Surfactants and Interfacial Phenomena[END_REF] This is done using the Gibbs equation which relies the maximal surface excess concentration Γ to the slope of the surface tension vs log C curve before the CMC as follows:

Γ = - 1 2.303 • ( 1
)
where T is the temperature, R the gas constant, C the concentration, and the number of adsorbed species (here = 2, accounting for CTEA + and Br -). Then , can be expressed as (2):

, = 1 Γ (2)
where is the Avogadro number. Applying this to the curve in Figure 2A gives

, = 110 (± 10) Å 2 •molecule -1 .
This value is quite high compared to a surface of 62 Å 2 •molecule -1 reported for CTEAB in pure water, [START_REF] Rodríguez | Effects of Head Group Size on Micellization of Cetyltrialkylammonium Bromide Surfactants in Water-Ethylene Glycol Mixtures[END_REF] suggesting that the distance between the surfactants got increased at the interface in the presence of electrolytes.

The fact that the interface occupation appears less compact (and the surfactants bulkier) might be due to the accumulation of species (like water or ions) between the surfactants.

The aggregation properties of CTEAB in TRIS/HCl buffer have also been studied by pyrene fluorescence measurements. Pyrene is a hydrophobic fluorescent probe that has been widely used for the characterization of self-assembling systems due to the specific variation of its emission fluorescence as a function of the local polarity. [START_REF] Kalyanasundaram | Environmental Effects on Vibronic Band Intensities in Pyrene Monomer Fluorescence and Their Application in Studies of Micellar Systems[END_REF] In its specific multi-peak emission spectrum, the I1/I3 intensity ratio between the first and third peaks (I1 at 372 nm and I3 at 383 nm respectively) is decreasing if the polarity decreases. In surfactant systems, this I1/I3 ratio varies as a function of the surfactant concentration with a sharp decrease at the CMC, from a high value (below CMC, pyrene located in water) to a lower one (above CMC, pyrene located in the hydrophobic inner core of the micelles). The results regarding pyrene fluorescence as a function of CTEAB concentration in TRIS/HCl buffer are represented in Figure 2B.

The variation of the I1/I3 ratio has been adjusted by a sigmoidal Boltzmann function to determinate the CMC. [START_REF] Aguiar | On the Determination of the Critical Micelle Concentration by the Pyrene 1:3 Ratio Method[END_REF] From this fluorescence measurements, the aggregation of CTEAB in TRIS/HCl buffer occurs at CMC = 1.6 (± 0.2) ×10 -4 mol•L -1 , which is in good accordance with tensiometry measurements (using this quick technique we also checked the CMC of CTEAB in pure water and found 7.1 (± 0.2) ×10 -4 mol•L -1 , which is very close to the values reported in the literature, [START_REF] Wasbrough | Control of Mesostructure in Self-Assembled Polymer/Surfactant Films by Rational Micelle Design[END_REF][START_REF] Jaber | Interactions between Quaternary Ammonium Surfactants and Polyethylenimine at High PH in Film Forming Systems[END_REF][START_REF] Soldi | Arenediazonium Salts: New Probes of the Interfacial Compositions of Association Colloids. 6. Relationships between Interfacial Counterion and Water Concentrations and Surfactant Headgroup Size, Sphere-to-Rod Transitions, and Chemical Reactivity in Cationi[END_REF][START_REF] Bacaloglu | Micellar Enhancements of Rates of SN2 Reactions of Halide Ions. The Effect of Headgroup Size[END_REF][START_REF] Buckingham | Effect of Head-Group Size on Micellization and Phase Behavior in Quaternary Ammonium Surfactant Systems[END_REF][START_REF] Rodríguez | Effects of Head Group Size on Micellization of Cetyltrialkylammonium Bromide Surfactants in Water-Ethylene Glycol Mixtures[END_REF] see Supporting Information, Figure S3). In addition, the intrinsic value of the I1/I3 ratio is directly related to local micropolarity: a low ratio value (<1) indicates that pyrene is surrounded by a nonpolar environment, while higher ratio values (>1) show that the pyrene environment is polar. [START_REF] Kalyanasundaram | Environmental Effects on Vibronic Band Intensities in Pyrene Monomer Fluorescence and Their Application in Studies of Micellar Systems[END_REF] This ratio has been shown to vary from about 0.6 in alkanes to 1.2-1.6 in alcohols and up to 1.9 in water. [START_REF] Kalyanasundaram | Environmental Effects on Vibronic Band Intensities in Pyrene Monomer Fluorescence and Their Application in Studies of Micellar Systems[END_REF][START_REF] Dong | The Py Scale of Solvent Polarities[END_REF] In the present case of CTEAB, we observed a decrease of the I1/I3 ratio from 2.0 to 1.5 at the CMC. This shows that even when located in micelles, the pyrene probe is still in a rather polar environment. This suggest that water molecules have partially penetrated the inner micellar cores, leading to an increase of the I1/I3 ratio. [START_REF] Kalyanasundaram | Environmental Effects on Vibronic Band Intensities in Pyrene Monomer Fluorescence and Their Application in Studies of Micellar Systems[END_REF][START_REF] Lianos | Fluorescence-Probe Study of Oil-in-Water Microemulsions. 3. Further Investigations Involving Other Surfactants and Oil Mixtures[END_REF] This is directly related to the surfactants head groups: bulky heads induce less compact interfaces and allow penetration of water, which is here consistent with large polar surface areas determined for CTEAB from tensiometry measurements.

In order to get more insights on the structure of the aggregates formed by CTEAB in aqueous TRIS/HCl solutions, both multi-angle static-and dynamic light scattering (MASLS and MADLS) experiments were performed at different concentrations ([CTEAB] = 5 to 30×10 -3 mol•L -1 ). Small angle X-Ray scattering (SAXS) measurements were also carried out.

In light scattering experiments, the scattering wave vector is defined as a function of the scattering angle as described by equation (3).

= 4" sin& /2( (3)
where is the refractive index of the medium and the wavelength of the incident light.

In MASLS, the excess of scattered intensity by a sample with respect to the solvent is converted into absolute intensity (Rayleigh ratio ) , in cm -1 ) using toluene as a reference (see Supporting Information). Absolute Rayleigh excess ratios of CTEAB solutions were measured in the 2.6×10 -4 -2.5×10 -3 Å -1 q range. In all cases, flat plateaus were obtained meaning that the scattering was isotropic and that the aggregates formed by CTEAB were very small in size (see Supporting Information, Figure S4). As a consequence, the radius of gyration Rg could not be determined due to the q-independent form factor in this q range. However, the variation of the Rayleigh ratio as a function of the CTEAB concentration could allow Debye analysis (see Supporting Information, Figure S5). Therefore, the apparent mass of the aggregates was determined to be Mw = 41.1 ± 1.6 kDa. From this value and using the molar weight of CTEAB, it was possible to calculate the aggregation number (Nagg)

which was found to be Nagg = 101 ± 4. This value is larger or equal to those reported for CTEAB in pure water (Nagg = 49-100), [START_REF] Jaber | Interactions between Quaternary Ammonium Surfactants and Polyethylenimine at High PH in Film Forming Systems[END_REF][START_REF] Rodríguez | Effects of Head Group Size on Micellization of Cetyltrialkylammonium Bromide Surfactants in Water-Ethylene Glycol Mixtures[END_REF] confirming that micellization in TRIS buffer is favored and allows a larger number of surfactant molecules to aggregate.

What is measured experimentally in

where Γ = ; < * is the decay rate and ; < is the translational diffusion coefficient of the particles. The hydrodynamic radius of equivalent sphere ( = ) is then obtained by the Stokes-Einstein relationship: = = > 6"@; < (7) where > is the Boltzmann constant, the absolute temperature, and @ the solvent viscosity.

Experimentally, simple scattering was always observed (no multiple scattering) from the clear, transparent CTEAB solutions. In all cases, the autocorrelation functions were well fitted using a Cumulant analysis [START_REF] Frisken | Revisiting the Method of Cumulants for the Analysis of Dynamic Light-Scattering Data[END_REF] (see Supporting Information, Figure S6), affording the intensity-weighted decay rates Γ. Plotting decay rates as a function of * afforded linear profiles Γ = ; AA * (Figure 3A), meaning that single relaxation mechanisms were observed associated to single apparent translational diffusion coefficients (; AA ).

Figure 3. Linear variations of decay rates as a function of q 2 (A). Variation of the apparent diffusion coefficient B CDD as a function of the micelle concentration (B).

The apparent diffusion coefficients showed a linear dependence as a function of the micelle concentration (ie CCTEAB-CMCCTEAB) (Figure 3B):

; AA = ; < + >& EFG H -I EFG H ( (8)
This reflects inter-particle interactions (probably electrostatic repulsions between positively charged aggregates of cationic surfactants). Extrapolation at infinite dilution afforded ; < = 8.68×10 7 nm 2 •s -1 and =,< = 2.83 nm from the Stockes-Einstein relationship. This hydrodynamic radius is comparable to the dimensions of micelles formed by CTEAB in pure water. [START_REF] Wasbrough | Control of Mesostructure in Self-Assembled Polymer/Surfactant Films by Rational Micelle Design[END_REF][START_REF] Jaber | Interactions between Quaternary Ammonium Surfactants and Polyethylenimine at High PH in Film Forming Systems[END_REF] Knowing the radius of the micelles, the determination of their surface gives 101 nm [START_REF] Dunbar | Gene Therapy Comes of Age[END_REF] , and dividing it by the aggregation number, the surface occupied by one surfactant head group is 1 nm 2 , which is consistent with the surface estimated from tensiometry measurements. It was also possible to determine the volume occupied per surfactant at 0.94 nm [START_REF] Schuch | Sunlight Damage to Cellular DNA: Focus on Oxidatively Generated Lesions[END_REF] . The comparison of this value to the molecular volume of CTEAB (0.64 nm [START_REF] Schuch | Sunlight Damage to Cellular DNA: Focus on Oxidatively Generated Lesions[END_REF] ) indicates that about 10 water molecules are present around each CTEAB molecule, confirming that CTEAB micelles are highly hydrated.

Complementary SAXS experiments were also carried out to get more information on CTEAB micelles. The general expression of the scattered intensity

,& ( is:

,& ( = Φ • V • &ΔM( * • N& ( • O& ( (9)
where = P4" sin& /2(Q/ is the scattering vector ( is the scattering angle), Φ is the volume fraction of the scatterers, V is their volume, and ΔM is their difference in scattering length density (SLD) with respect to the solvent. N& ( is the scatterers' form factor for which analytical expressions have been reported for various geometries. [START_REF] Pedersen | Analysis of Small-Angle Scattering Data from Colloids and Polymer Solutions: Modeling and Least-Squares Fitting[END_REF][START_REF] Pedersen | Modelling of Small-Angle Scattering Date from Colloids and Polymer Systems[END_REF] O& ( is the structure factor accounting for inter-particle interactions, for which different models are also available. [START_REF] Pedersen | Analysis of Small-Angle Scattering Data from Colloids and Polymer Solutions: Modeling and Least-Squares Fitting[END_REF][START_REF] Pedersen | Modelling of Small-Angle Scattering Date from Colloids and Polymer Systems[END_REF] Regarding the CTEAB solutions, the scattering intensities were very low, indicating a weak electronic contrast between the solvent and the aggregates. Moreover, the profiles of the scattering curves suggested a spherical shape for the aggregates, as illustrated in Figure 4 (full curves and fitting parameters are reported in the Supporting Information). Indeed, the data were efficiently adjusted using a P(q) spherical model, whereas the ellipsoidal model used by others to describe CTEAB micelles in pure water was not convenient here. [START_REF] Wasbrough | Control of Mesostructure in Self-Assembled Polymer/Surfactant Films by Rational Micelle Design[END_REF][START_REF] Jaber | Interactions between Quaternary Ammonium Surfactants and Polyethylenimine at High PH in Film Forming Systems[END_REF] In addition, a structure factor S(q) was included, which corresponded to a charged hard sphere model to take into account electrostatic repulsions between positively charged micelles (visible at low as a decline of ,& ( in the SAXS curve). However, the classical core-shell structure could not be evidenced contrary to analogous cationic surfactants. [START_REF] Müller | How Do Anions Affect Self-Assembly and Solubility of Cetylpyridinium Surfactants in Water[END_REF] Instead, the SAXS profiles rather corresponded to small spherical shapes (R = 14 Å) with a scattering contrast that was the one of pure hydrophobic alkyl chains. This indicates that only a part of the inner core of the micelles could be observed by this technique, and it is again in accordance with a possible penetration of water towards the inner, "hydrophobic" core of the aggregates.

Interaction between CTEAB and DNA

Cationic surfactants have been considered for a few decades as potential non-viral vectors for gene delivery, thanks to their ability to easily form complexes with DNA.

This complexation induces the formation of highly organized assemblies, involving various intermolecular interactions (electrostatic, hydrophobic, etc.) and highly cooperative binding. [START_REF] Liu | DNA-Surfactant Complexes: Self-Assembly Properties and Applications[END_REF][START_REF] Dias | DNA and Surfactants in Bulk and at Interfaces[END_REF] In this field, CTAB was one of the most studied cationic increase, with the re-apparition of a not-so-well defined band. This could indicate the formation of another type of CTEAB-DNA complex in the presence of a large excess of CTEAB and notably a decompaction process of DNA. In the litterature, this process was ascribed to the presence of an excess of the cationic surfactant, which promotes the DNA decompaction. [START_REF] Li | Studying Compaction-Decompaction of DNA Molecules Induced by Surfactants[END_REF][START_REF] Xu | Compaction and Decompaction of DNA Dominated by the Competition between Counterions and DNA Associating with Cationic Aggregates[END_REF][START_REF] Feng | Controlled Compaction and Decompaction of DNA by Zwitterionic Surfactants[END_REF] To go futher into the understanding of the interaction mechanisms between DNA and CTEAB, circular dichroism spectroscopy (CD) was realized. The DNA circular dichroic spectrum exhibits two peaks. The first one is a negative band at 245 nm, due to the helicity of DNA. The second one, at 278 nm is a positive band corresponding to the base stacking, as shown in Figure 6. [START_REF] Wang | Magnetic Fullerene-DNA / Hyaluronic Acid Nanovehicles with Magnetism / Reduction Dual-Responsive Triggered Release[END_REF][START_REF] Wang | Nanocapsules of Magnetic Au Self-Assembly for DNA Migration and Secondary Self-Assembly[END_REF][START_REF] Wang | Versatile Self-Assembly and Biosensing Applications of DNA and Carbon Quantum Dots Coordinated Cerium Ions[END_REF][START_REF] Wang | Fluorescent Hybrid Nanospheres Induced by Single-Stranded DNA and Magnetic Carbon Quantum Dots[END_REF]

Figure 6. Circular dichroism spectra in CTEAB-DNA solutions for various CTEAB concentrations ([DNA-PO4 -] = 9×10 -5 mol•L -1 , 20 mM TRIS/HCl buffer, pH = 7.4) at 25 °C.

The CTEAB-DNA complexes, in the two phase regions, present a red-shift of the positive signal from 278 nm to 284 nm, for [CTEAB] > 15×10 -5 mol.L -1 . This suggests a minor changing of interactions between the DNA bases and the evidence of the DNA compaction process in presence of CTEAB surfactant. [START_REF] Wang | Versatile Self-Assembly and Biosensing Applications of DNA and Carbon Quantum Dots Coordinated Cerium Ions[END_REF] The observed transition could be due by the reduction of the DNA hydration layer, caused by a helical enhancement and a pitch shortening. [START_REF] Wang | Versatile Self-Assembly and Biosensing Applications of DNA and Carbon Quantum Dots Coordinated Cerium Ions[END_REF][START_REF] Wang | Fluorescent Hybrid Nanospheres Induced by Single-Stranded DNA and Magnetic Carbon Quantum Dots[END_REF] With further CTEAB concentration increase (from 100×10 -5 mol.L -1 ), there is a blue shift of the positive band and the position and intensity of that band recovers as DNA bands. It shows that CTEAB can decompact DNA with excessive amount of surfactant as it was already described in the literature for other surfactants. [START_REF] Li | Studying Compaction-Decompaction of DNA Molecules Induced by Surfactants[END_REF][START_REF] Xu | Compaction and Decompaction of DNA Dominated by the Competition between Counterions and DNA Associating with Cationic Aggregates[END_REF][START_REF] Feng | Controlled Compaction and Decompaction of DNA by Zwitterionic Surfactants[END_REF] These two peculiar CTEAB concentrations are on the same range that the ones find with the electrophoresis experiment.

CTEAB-DNA interactions were also evidenced by surface tension measurements. Figure 7A shows the variation of the surface tension of the DNA solution as a function of the CTEAB concentration. meaning that this phenomenon does not correspond to the formation of micelles. This rather shows the synergistic interaction between oppositely charged species that leads to the formation of highly surface active CTEAB-DNA complexes located at the air/water interface, as proposed by others. [START_REF] Di Profio | Interaction between DNA and Cationic Amphiphiles: A Multi-Technique Study[END_REF][START_REF] Mcloughlin | Surface Complexation of DNA with a Cationic Surfactant[END_REF][START_REF] Moradi | Surface Tension and Dilation Rheology of DNA Solutions in Mixtures with Azobenzene-Containing Cationic Surfactant[END_REF][START_REF] Lyadinskaya | Phase Transitions in DNA/Surfactant Adsorption Layers[END_REF] This complexation is driven both by electrostatic interactions but also by hydrophobic interactions between the surfactant and the biopolymer. [START_REF] Di Profio | Interaction between DNA and Cationic Amphiphiles: A Multi-Technique Study[END_REF] In this concentration range, the CTEAB molecules are believed to gradually decorate the DNA strand by progressive charge neutralization. Then, upon increasing CTEAB concentration, the surface tension rises to a local maximum and finally decreases again and reaches the curve of pure CTEAB. This could be attributed to a partial desorption of the CTEAB-DNA complexes from the interface as they accumulate in the bulk solution upon adsorption of further surfactant, potentially forming new types of aggregates. Finally, the transition to a "plateau" coincides with the apparition of a turbid solution and is observed at

Figure 7. Variation of the surface tension (A), and of the pyrene I1/I3 fluorescence emission ratio (B) of CTEAB solutions as a function of CTEAB concentration, in the presence of DNA ([DNA-PO4 -] = 9×10

[CTEAB] = 20×10 -5 mol•L -1 ([CTEAB]/[DNA] = 2.
2). At this point the polyanion is saturated with surfactant and the complex formed corresponds to formulated DNA. As the air/water interface is now only occupied by surfactants, surface tension monitors then only the micellization of CTEAB upon further addition of surfactant.

In a complementary way, pyrene fluorescence was studied at different

[CTEAB]/[DNA] ratios as previously conducted for CTEAB alone. In Figure 7B is presented the variation of the pyrene I1/I3 emission fluorescence ratio as a function of the CTEAB concentration in a DNA solution. We observed a classical sigmoidal shape referring to a phase transition and the formation of hydrophobic domains.

Below the phase transition, the I1/I3 ratio was found to be 1.93 versus 2.03 in the case of pure CTEAB. This slight decrease means that, even if pyrene is largely in contact with water or in polar environment, it has found some more hydrophobic places to locate. Indeed, it is known that pyrene can interact with DNA via partial intercalation at the grooves. [START_REF] Jumbri | An Insight into Structure and Stability of DNA in and Experimental Studies[END_REF][START_REF] Wang | Binding Gibbs Energy of Ionic Liquids to Calf Thymus DNA: A Fluorescence Spectroscopy Study[END_REF] Then the phase transition occurred at

[CTEAB] = 2.8×10 -5 mol•L -1 ([CTEAB]/[DNA] = 0.31)
. This critical concentration is much lower than the CMC of pure CTEAB and refers here to a critical aggregation concentration (CAC) evidencing again the synergistic aggregation of CTEAB and DNA. This point is believed to refer to the transition between a state where DNA is decorated by individual surfactant molecules (neutralization phase) and a state where CTEAB molecules form local hydrophobic domains on the DNA strand (compaction phase).

Pyrene can locate in these aggregates and the I1/I3 ratio drops to the 1.51 value, which is almost identical to what observed with CTEAB alone (1.50). This means that pyrene still remains in a quite hydrated environment like in the case of CTEAB micelles, where bulky head groups allow penetration of water. Note that the limited decrease of the pyrene I1/I3 ratio does not allow the detection of further transitions as observed for other DNA-cationic surfactant systems. [START_REF] Petrov | Structural and Thermodynamic Features of Complexes Formed by DNA and Synthetic Polynucleotides with Dodecylamine and Dodecyltrimethylammonium Bromide[END_REF][START_REF] Zhang | Micellization of Lactosylammonium Surfactants with Di Ff Erent Counter Ions and Their Interaction with DNA[END_REF] The steric hindrance of the triethylammonium moiety could also explain why the transition occurs at a

[CTEAB]/[DNA] ratio which is much lower than in the case of CTAB (0.31 vs. about 0.70) [START_REF] Mel'nikov | Transition of Double-Stranded DNA Chains between Random Coil and Compact Globule States Induced by Cooperative Binding of Cationic Surfactant[END_REF] . Indeed, the neutralization phase is limited by the available space along the DNA strand and depends on the size of the complexing cationic surfactant.

The effect of the surfactant on DNA compaction can also be followed by UV-Vis spectrometry. Thus, DNA adsorption is performed at 260 nm for different CTEAB concentrations (Figure 8). It can be observed that absorption of CTEAB-DNA complex sharply decreases until a CTEAB concentration corresponding to 20-30×10 -

5 mol•L -1 .
The increase in turbidity is due to strong electrostatic interactions between the DNA and the surfactant. This result suggests that DNA is fully compacted.

CTEAB surfactant induces the reduction of the repulsive forces between the phosphate groups of DNA leading to the formation of CTEAB-DNA agregates. No longer time of irradiation was used because of the appearance of secondary DNA strand breaks and the formation of pBR322 plasmid DNA linear form (data not show).

Control UVA irradiation of DNA alone also shows SSB damage that increase with irradiation time, but twice less than in the lipoplex (see agarose gel and photodensitometry quantification in the Supporting Information). DNA damage by UVA light were already described in the literature and different hypothesis were made to explain how DNA can be cleaved by UVA radiation whereas the nucleotides do not absorb at these wavelengths. [START_REF] Mouret | UVA-Induced Cyclobutane Pyrimidine Dimers in DNA: A Direct Photochemical Mechanism?[END_REF][START_REF] Sutherland | Absorption Spectrum of DNA for Wavelengths Greater than 300 Nm[END_REF][START_REF] Ikehata | Mechanistic Considerations on the Wavelength-Dependent Variations of UVR Genotoxicity and Mutagenesis in Skin : The Discrimination of UVA-Signature from UV-Signature Mutation[END_REF][START_REF] Markovitsi | UV-Induced DNA Damage: The Role of Electronic Excited States[END_REF] It has been shown that DNA solution presents a slight and broad absorbance band in UVA range which could be enough to induce UVA deterioration of DNA. [START_REF] Mouret | UVA-Induced Cyclobutane Pyrimidine Dimers in DNA: A Direct Photochemical Mechanism?[END_REF][START_REF] Sutherland | Absorption Spectrum of DNA for Wavelengths Greater than 300 Nm[END_REF] Recently, Markovitsi implied the existence of "collective" excited states in UVA photon absorption by DNA and speculated that condensed DNA enhanced the collective character of electronic excitations. [START_REF] Markovitsi | UV-Induced DNA Damage: The Role of Electronic Excited States[END_REF] The CTEAB lipoplex made with the plasmid DNA pBR322 raises significantly the SSB ratio. The effect of the compaction of DNA induced by CTEAB could explain the increase of the DNA cleavage in the presence of surfactant. Indeed, Merindol and al.

have shown the appearance of an absorption band on UVA wavelengths when DNA was aggregated by temperature. [START_REF] Merindol | Pathway-Controlled Formation of Mesostructured All-DNA Colloids and Superstructures[END_REF] To confirm this hypothesis, UV spectrum of the CTEAB-DNA complex was performed (see Supporting Information): a UVA absorption band appears in the presence of CTEAB. However, as the solution is turbid, the light scattering produced by the colloidal dispersion of the lipoplexes contributes to the UV-Vis spectrum and does not allow to differentiate the absorbance of the lipoplex from the scattering and to quantify each contribution. The effect of the CTEAB concentration on the DNA photodamage was also studied and the irradiation time was fixed to 10 min. Indeed, this time allows to see well the formation of SSB while avoiding overbreaks. The CTEAB concentration range was from 0 to 7×10 -4 mol•L -1 and corresponds to the lanes 2* to 9* on the electrophoresis agarose gel shown in figure 11A. In figure 11B, the enhancement of the SSB ratio is shown with the increase of the CTEAB concentration. To go further on the study of the mechanism involved in the formation of SSB, peculiar scavengers have been used. CTEAB-DNA lipoplex was first irradiated in presence of sodium azide NaN3 (lane 11*), a well-known singlet oxygen quencher. [START_REF] Bancirova | Sodium Azide as a Specific Quencher of Singlet Oxygen during Chemiluminescent Detection by Luminol and Cypridina Luciferin Analogues[END_REF] Under irradiation, the single-strand break ratio drops in presence of NaN3 (Figure 12B). It means that the singlet oxygen is involved on the oxidized damage. To confirm it, the CTEAB-DNA lipoplex solution was also prepared in D2O TRIS/DCl buffer and irradiated for 10 min (lane 13*). Indeed, D2O increases the life time of the singlet oxygen, [START_REF] Merkel | Deuterium Effects on Singlet Oxygen Lifetimes in Solutions. New Test of Singlet Oxygen Reactions[END_REF][START_REF] Merkel | Radiationless Decay of Singlet Molecular Oxygen in Solution. Experimental and Theoretical Study of Electronic-to-Vibrational Energy Transfer[END_REF] and as expected an enhancement of SSB ratio is obtained (lane 13*). These results highlight the involvement of a type II mechanism by energy transfer from the DNA molecule itself, acting as a chromophore, [START_REF] Yagura | Free Radical Biology and Medicine Direct Participation of DNA in the Formation of Singlet Oxygen and Base Damage under UVA Irradiation[END_REF] to the ground state of the molecular oxygen to produce the singlet oxygen responsible of these direct oxidized photodamage under UVA radiation. Finally, the lipoplex irradiation was performed with 4 % of tert-butanol ( t BuOH, lane 12*), as a OH radical scavenger. [START_REF] Billen | The Role of Hydroxyl Radical Scavengers in Preventing DNA Strand Breaks Induced by X Irradiation of Toluene-Treated Escherichia Coli[END_REF][START_REF] Staehelln | Decomposition of Ozone in Water in the Presence of Organic Solutes Acting as Promoters and Inhibitors of Radical Chain Reactions[END_REF] No decrease of the SSB ratio is observable in the presence of t BuOH suggesting the non-intervention of the type I mechanism involving hydroxyl radicals in these processes.

In conclusion, UVA irradiation of DNA-CTEAB lipoplex induces the direct formation of oxidized damage involving singlet oxygen and implementing energy transfer.

However, it does not lead to the formation of CPD. The compaction of the plasmid pBR322 by the positive CTEAB surfactant is probably the cause of the increase in photooxidized DNA damage.

Conclusion

Cationic surfactants or polymers have been shown to be efficient complexing agents

2. 8 . 1 .

 81 Sample preparation 50 µL of the sample solution were used on the T4 endonuclease V experiment. It consists to add 10 µL of T4 endonuclease V (10000U/ml) and to incubate the solution 30 minutes at 37°C. 5 µL of bromophenol blue solution and 10 µL of Heparin 20%

5 * 4 ≤ 1 ( 5 )

 5415 MADLS is the autocorrelation function &*( & , +( of the scattered intensity ,& , -(, normalized over time (4): &*( & , +( = .,& , -(,& , -+ +(0 〈,& , -(〉 * (4) This latter is also related to the correlation function of the electric field &3( & , +( by the Siegert relationship (5): &*( & , +( = 1 + 45 &3( & , +(For monodisperse spherical particles under Brownian motion, the autocorrelation function decays exponentially over time (6): &3( & , +( = e 89:

Figure 4 .

 4 Figure 4. SAXS profile of 20 mM CTEAB solution in 20 mM TRIS/HCl (pH = 7.4)

  surfactants. It has been shown that combination of electrostatic and hydrophobic interactions between CTAB and DNA induces functional and morphological changes of the biopolymer, particularly DNA compaction.[START_REF] Di Profio | Interaction between DNA and Cationic Amphiphiles: A Multi-Technique Study[END_REF][START_REF] Grueso | Compaction and Decompaction of DNA Induced by the Cationic Surfactant CTAB[END_REF][START_REF] Zhou | Nanostructures of Complexes Formed by Calf Thymus DNA Interacting with Cationic Surfactants[END_REF][START_REF] Dias | Coil-Globule Transition of DNA Molecules Induced by Cationic Surfactants: A Dynamic Light Scattering Study[END_REF][START_REF] Zhu | Molecular Mechanism and Thermodynamics Study of Plasmid DNA and Cationic Surfactants Interactions[END_REF][START_REF] Guo | Investigation on Interaction of DNA and Several Cationic Surfactants with Different Head Groups by Spectroscopy, Gel Electrophoresis and Viscosity Technologies[END_REF][START_REF] Li | Studying Compaction-Decompaction of DNA Molecules Induced by Surfactants[END_REF][START_REF] Mel'nikov | Transition of Double-Stranded DNA Chains between Random Coil and Compact Globule States Induced by Cooperative Binding of Cationic Surfactant[END_REF][START_REF] Mel'nikov | Discrete Coil-Globule Transition of Large DNA Induced by Cationic Surfactant[END_REF][START_REF] Mel'nikov | Cooperativity or Phase Transition ? Unfolding Transition of DNA Cationic Surfactant Complex Cooperativity or Phase Transition ? Unfolding Transition of DNA Cationic Surfactant Complex[END_REF][START_REF] Sergeyev | How Does Alcohol Dissolve the Complex of DNA with a Cationic Surfactant?[END_REF][START_REF] Clamme | Gene Transfer by Cationic Surfactants Is Essentially Limited by the Trapping of the Surfactant/DNA Complexes onto the Cell Membrane: A Fluorescence Investigation[END_REF][START_REF] Dias | DNA Phase Behavior in the Presence of Oppositely Charged Surfactants[END_REF] Considering CTEAB as a potential non-viral vector, it is therefore important to characterize the interactions occurring between the surfactant and the nucleic acid involved in such DNA formulations. It is especially interesting to study the effect of replacing CTAB by CTEAB on the different phase transitions, as we have shown that these structurally close surfactants differ, however, in their micellization properties. Three macroscopic states were observed on CTEAB-DNA solutions depending on the CTEAB concentration. For [CTEAB] < 20-30×10 -5 mol•L -1 clear solutions were observed. Between 20-30×10 -5 mol.L -1 and 100-200 ×10 -5 mol.L -1 , turbid solutions appear. For higher CTEAB concentrations ([CTEAB] > 100-200 ×10 -5 mol.L -1 ), turbid solutions turned to clear. Therefore, complementary techniques (agarose gel electrophoresis, tensiometry, fluorimetry, UV-Visible spectrometry and circular dichroism) were used to study the binary system made of CTEAB and the supercoiled plasmid DNA pBR322 at various molar ratios. 20 Agarose gel electrophoresis was first carried out to study CTEAB-DNA interactions with CTEAB concentrations ranging from 0 to 4×10 -3 mol•L -1 (Figure5).

Figure 5 .

 5 Figure 5. Electrophoresis agarose gel of plasmid DNA in the presence of

  buffer, pH = 7.4) at 25 °C. Dashed lines refer to CTEAB alone, for comparison. The curve profile obtained in the presence of DNA is more complex than the one for surfactant alone. Indeed, surface tension started to decrease at very low CTEAB concentrations (< 10 -6 mol•L -1 ) to reach a first minimum at [CTEAB] = 0.16×10 -5 mol•L -1 ([CTEAB]/[DNA] = 0.02). It occurs well below the CMC of CTEAB,

Figure 8 .

 8 Figure 8. Variation of the absorbance of CTEAB-DNA solutions for various

Figure 9 . 3 . 3 .

 933 Figure 9. CTEAB concentrations (10 -5 mol•L -1 ) at which different phase

Figure 10 .

 10 Figure 10. DNA cleavage for different irradiation times at λ ≥ 335nm and 20 °C (*

Figure 11 .

 11 Figure 11. DNA cleavage for different CTEAB concentrations for 10 min

Figure 12 .

 12 Figure 12. DNA cleavage for 10 min of irradiation at λ ≥ 335nm and 20°C with

  and transporters of DNA to cells. In this study, CTEAB surfactant was used to complex a DNA model, the plasmid pBR322. The self-organization properties of the CTEAB were studied by different physico-chemical characterizations (tensiometry, pyrene fluorimetry and scattering experiments). Results show that CTEAB molecules form small spherical and highly hydrated micelles in TRIS/HCl buffer solution. The study of the interactions between CTEAB and plasmid DNA has highlighted different phases, the DNA neutralization, the gradual until the full DNA compaction and the decompaction process of DNA. Furthermore, formulated CTEAB-DNA lipoplexes were irradiated under UVA light. With the increase of the irradiation time and of the CTEAB concentration, an increase of DNA damage was observed. The involvement of singlet oxygen has been shown to be responsible for these damage. The compaction of DNA by CTEAB may be the cause of the increase in photooxidized DNA damage. This study has investigated the DNA compaction by the cationic surfactant CTEAB and pointed out its role on DNA photodamage under UVA irradiation. Further work is currently under progress to show what could be the effect of adding anti-oxidant drug such as vitamin E on the photodamage observed in this system.

  [START_REF] Wang | Magnetic Fullerene-DNA / Hyaluronic Acid Nanovehicles with Magnetism / Reduction Dual-Responsive Triggered Release[END_REF][START_REF] Wang | Nanocapsules of Magnetic Au Self-Assembly for DNA Migration and Secondary Self-Assembly[END_REF]

Acknowledgements

This work benefited from the use of the SasView application, originally developed under NSF award DMR-0520547. SasView contains code developed with funding from the European Union's Horizon 2020 research and innovation program under the SINE2020 project, grant agreement No 654000. Dr. C. Mingotaud is thanked for help in MULTI-STORMS use and for SAXS measurements.


Maude Ferrari
email: maude.ferrari@univ-lorraine.fr

Christian Moyne

Daniel Canet

Proton Nutation Spectroscopy. Application to the Quantitation of Water in a Kaolinite Sample

Nutation consists in monitoring the motion of nuclear magnetization under the application of a radio-frequency field. Depending on the amplitude of the rf field, the nutation frequency may be sensitive to the two longitudinal and transverse relaxation rates R1 and R2, hence the possibility of differentiating species having the same resonance frequency in the laboratory frame (the Larmor frequency) but differing by their relaxation rates, as it may occur for the composite proton NMR signal of water in complex systems. Thus, Fourier transform of the nutation curve should provide separate peaks associated with the different species involved in a composite classical NMR signal. As nutation peaks may be close to zero frequency (or even at zero frequency), their full observation requires a complex Fourier transform. This implies a second nutation curve, de-phased by 90° with respect to the first one, achieved here by a second nutation experiment preceded by a 90° hard pulse. Eventually, more accurate parameters are obtained by a non-linear leastsquares analysis of the simple nutation experiment. This methodology is applied to water in a natural clay (kaolinite) and reveals the unexpected presence of two peaks which can be characterized by the relaxation rates derived from the line-widths of the nutation signals.

Introduction

The first NMR nutation experiments and the underlying theory can be found in the pioneering work of Torrey [START_REF] Torrey | Transient nutations in nuclear magnetic resonance[END_REF]. Since then, nutation experiments were mainly applied to solid state NMR for determining the quadrupolar coupling constant of quadrupolar nuclei [START_REF] Veeman | Quadrupole nutation NMR in solids[END_REF] and are still nowadays used for that purpose [START_REF] Blaakmeer | Quadrupolar nutation NMR to discriminate central and satellite transitions: Spectral assignments for a Ziegler-Natta catalyst[END_REF] [START_REF] Franssen | High radio-frequency field strength nutation NMR of quadrupolar nuclei[END_REF]. It was also demonstrated that nutation experiments, through their dependence on relaxation parameters (R1, the longitudinal relaxation rate and R2, the transverse relaxation rate), were able to discriminate the different types of water in clays [START_REF] Trausch | Separation of a 1 H composite signal by nutation experiments under low amplitude radio-frequency fields. Application to water in clays[END_REF]- [START_REF] Fleury | Water orientation in smectites using NMR nutation experiments[END_REF].

Furthermore, it was shown recently that pseudo-echo nutation experiments are able to provide accurately the value very short transverse relaxation times [START_REF] Ferrari | Measurement of short transverse relaxation times by pseudoecho nutation experiments[END_REF] when classical methods turned out to be inadequate or even fail.

A nutation experiment consists in observing the motion of nuclear magnetization in the presence of a radio-frequency (rf) field B1 applied continuously. Viewed from the so-called rotating frame (the frame rotating around the direction of the static magnetic field , at the frequency of the field B1), this motion is similar to precession as it is merely a rotation around the B1 field which is stationary in the rotating frame. Still viewed from the rotating frame, this B1 field is the only magnetic field, as far as on-resonance conditions are fulfilled. Thus, the NMR signal, as a function of the duration of application of the B1 field, oscillates at a frequency equal to 2 ( being the gyromagnetic ratio and, in this latter expression, being the amplitude of the rf field).

However, it turns out that, depending on B1, the nutation curve may also depend on the longitudinal and transverse relaxation rates R1 and R2. In fact, the nutation frequency may become smaller than 2 , depending on = ( -)/2 while the damping factor remains equal to = ( + )/2. Thus, if the classical NMR signal is composite (involving several resonances which differ by their relaxation rates, as this is often the case for the water signal in complex systems like clays), the nutation curve is a sort of fid (free induction decay) constituted of several damped cosine functions. This should be amenable to Fourier transform. The problem is that it is a real Fourier transform which, by essence, leads to peaks only at positive frequencies.

Although frequencies of nutation peaks are indeed positive (they may even be zero in some cases, as shown in the theoretical section), their linewidths are such that the corresponding line-shapes generally extend largely toward the negative part of the frequency domain. For properly visualizing the nutation peaks, one remedy is to resort to a complex Fourier transform. This requires however two different fids, one involving a cosine modulation (the normal nutation experiment), the other with a sine modulation (obtained in this work by a hard 90° pulse preceding the normal nutation experiment). Another possibility is to model the nutation curve (of the simple experiment) with one or several damped cosine functions and to search their characteristics by non-linear least squares. These different strategies will be detailed in the first section of this paper. The second section will be devoted to a complete theoretical treatment of what can be called nutation spectroscopy with emphasis on its specificities regarding relaxation parameters as well as the possibility of quantifying the different contributions involved in the nutation curves. A special attention will be paid to nutation signals at zero frequency which may be observed when R2 becomes very large and much larger than R1. It will be especially shown that, in that case, the damping factor is no longer equal to RS.

As a matter of fact, the present work is part of a project concerning the characterization of water in clays. This is a wide subject [START_REF] Olphen | An Introduction to Clay Colloid Chemistry: For Clay Technologists, Geologists, and Soil Scientists[END_REF] [10] related to many systems involving different types of water which cannot be differentiated by their chemical shifts, i.e. giving rise to a single NMR signal (more or less broadened). In this paper, a study by nutation spectroscopy will be applied to a natural clay (kaolinite). Kaolinite is a layered silicate mineral, with each layer made of an alternation of tetrahedral sheet of silica and of octahedral sheet of alumina forming particles of some thirty layers. After hydration, the water present in the kaolinite is not localized between the layers but only between the particles. In this system, only one type of water is expected while nutation spectroscopy reveals two different populations of water.

Displaying the whole nutation spectrum in the negative and positive frequency domain

As explained above, a complex Fourier transform requires the combination of two experiments with a 90° phase difference. These experiments are schematized in figure 1. Experiment A is the normal nutation experiment while experiment B involves an initial π/2 hard pulse which ensures the 90° dephasing of the nutation curve. The following notations, with the quantities already defined, will be used

= (1) = - (2)
Provided that is larger than , is the frequency (in rad s -1 ) of a given nutation signal characterized by the relaxation parameter (see reference [START_REF] Ferrari | Measurement of short transverse relaxation times by pseudoecho nutation experiments[END_REF] and the theoretical section below). This effective frequency is the basis of nutation spectroscopy since different 's will lead to different peaks in the Fourier transform of the nutation curve. Note that the case < leads to a signal at zero frequency considered in detail in the next section. Anticipating the theoretical developments of this section and recognizing that it is the longitudinal component of the nuclear magnetization which is actually measured (longitudinal magnetization has been selected for sensitivity reasons), one has for the experiment A of figure 1:

( = cos( + ! " + #$ (3)
It will be shown that the amplitude is proportional to the equilibrium magnetization , that the phase is generally weak (smaller than π/6) and that the dc component Frequencies of nutation spectra are, by nature, close to zero. Thus, the real Fourier transform of a simple nutation curve yields peaks close to zero, hardly legible and generally truncated on the left (see figure 2-center) because a real Fourier transform provides exclusively one side of the frequency domain (either the positive side, or the negative side which is its mirror image).

Fortunately, experiment B provides a sine modulation while experiment A provides a cosine modulation. The nutation curve corresponding to experiment B has for expression (see the theoretical section below):

% ( = % sin( + % ! " + #$ (4)
and % may be different but this can be tentatively corrected so that ( and % ( share approximately the same amplitude a. If the dc component is (also approximately) removed from the two A and B nutation curves and if ≅ % = (this is not always the case, see below), we can combine experiments A and B for obtaining the following complex function.

)( = ( + * % ( = +, - .// " +0 ! " (5)
The complex Fourier transform of )( yields a peak at frequency (in Hz) 1 = + /2 and of linewidth at half-height equal to / . The spectrum extends between -1 345 /2 and +1 345 /2

with 1 345 = 1/278, 78 being the sampling interval of the nutation curve (figure 2-right). The phase can be corrected according to the usual procedure which combines real (Re) and imaginary (Im) parts of the Fourier transform aiming at an absorption spectrum. However, this procedure was found difficult to deal with when several peaks of different phases are present. In that case, we found useful to use the alternative method of the power spectrum equal to (Re) 2 +(Im) 2 . It can be shown that the power spectrum does not exhibit any dephasing but has the same line-shape and linewidth as the absorption spectrum [START_REF] Guenneau | Measurement of longitudinal and rotating-frame relaxation times through fully J-decoupled homonuclear spectra[END_REF]. Evidently, quantitation is lost because the height is the square of the absorption spectrum height. More precisely, for the power spectrum. As will be observed in the examples given below for spectra involving two lines, the relative heights of the two peaks may be deceptive because a smaller may be compensated by a smaller , or vice versa. Nevertheless, quantitation will be retrieved by a least-squares analysis of experiment A (see below), the aim of this complex Fourier transform being the visualization of the nutation spectrum in terms of number of lines, of their frequency and of their line-width. Now, if and % are significantly different, some complications occur. Equation ( 5) must now be rewritten as

)( = ( + * % ( = ! " [ +, - .// " ;< => ;< ? + +, - .// " ;< = ;< ? ] (6)
The power spectrum is unchanged as far as positive frequencies are concerned. However, it appears spurious image signals at negative frequencies whose intensity increases with the difference of the two phases and % . Now, it must be recognized that the useful information is indeed contained in experiment A (and equation ( 3) corrected for #$ . Therefore, for extracting the information relevant to A B+C # lines in the nutation spectrum (constituted of A DE+C$# data points F G at time G = H78). The calculated pseudo fid can be expressed as

I G = ∑ + cos( + G + + !; " K C L;M.N +O (7)
The various parameters can be deduced from a standard non-linear least-squares (NLLS) procedure and used thereafter for re-constructing an absorption spectrum from -1 345 /2 to +1 345 /2 as a superposition of Lorentzian functions:

P(1 = ∑ 4 =; / !;
>QR 9 (S S -;

.// 9 / !; 9 C L;M.N +O [START_REF] Ferrari | Measurement of short transverse relaxation times by pseudoecho nutation experiments[END_REF] This procedure has proved very efficient as illustrated in figure 3. It can be noticed that + provides directly the area under the corresponding Lorentzian line, thus the contribution (proportion) of species i. In fact, the spectra of figure 3 correspond to a favorable situation for which ≅ % in such a way that the spurious image at negative frequencies is hardly visible. In that case (a single line), the power spectrum and the reconstructed spectrum appear very similar. Another spurious signal (of very weak amplitude) is observed at zero frequency. It reflects a slightly imperfect balance between A and B nutation curves.

A full theory of nutation spectroscopy

Nutation takes place in the rotating frame (rotating around the fixed z axis) which is a frame in which the radio-frequency (rf) field (denoted B1) appears stationary. The nutation process consists of a rotation around the 1 B field (if on-resonance conditions are met, as assumed throughout). If we call x the axis of the rotating frame along which lies the 1 B field, nutation takes place in the zy plane. At equilibrium, that is before the application of the rf field, nuclear magnetization lies along the z axis and will be denoted by 0 m . In a general way, the components of the nuclear magnetization in the rotating frame will be denoted by (

z y x m m m , ,
).

As will be seen below, when the amplitude 1 B of the rf field is sufficiently large, is simply the nutation frequency. The aim of the forthcoming calculations is to show that, with appropriate 1 B values, the actual nutation frequency may be smaller because it will depend on the relaxation rates 1 R and 2 R . Under on-resonance conditions (the carrier frequency being identical to the resonance frequency), the x m component is not created by the rf field. One has thus to consider only the z m and y m components which obey the following differential equations (Bloch equations).

T3 U T$ = ( - - V (9a)
T3 W T$ = - V + (9b)
It has been found that, for sensitivity reasons, it was advisable to probe rather than V .

Hence, the observing 90° hard pulse, after the nutation interval, in the experiments sketched in figure 1 and the differential equation built from (9a) and (9b):

T 9 3 U T$ 9 + ( + T3 U T$ + ( + ( -#$ = 0 (10)
with

#$ = -9
, - 9 > -9

The following notations regarding the sum and the difference of the relaxation rates are recalled for convenience:

, = ( ± (11)
From the characteristic equation of [START_REF] Chipera | Baseline studies of the clay minerals society source clays: powder X-ray diffraction analysis[END_REF], two situations must be envisaged: > and <

.

1) \ ] > ^_

The solution of ( 10) is oscillatory:

(` = #$ + ! $ a[ (0 -#$ ] cos `+ , - .// [ ( -#$ + ( (0 - - V (0 ] sin `b (12)
Experiment A:

(0 = , V (0 = 0 (` -#$ = ! $ cosc `+ d = ( -#$ e 1 + ( ! , - .// (13) tan = -! , - .// Experiment B: (0 = 0, V (0 = (` -#$ = -% ! $ sinc `+ % d % = e ( #$ + ( , - .// - - - #$ ] (14)
tan % = -3 U Nh , - .// ( ! i , -3 j ! 3 U

Nh

From these expressions, it can be seen that, if is sufficiently large with respect to the relaxation rates, one has effectively: #$ ≅ 0 , ≅ % ≅ and ≅ % ≅ 0. Otherwise, one has to face the problems mentioned in the previous section. In any event, the numerical analysis of experiment A, as described in the previous section, seems to be the method of choice as far as quantitation is required ( remains in all instances close to ). On the other hand, the linewidth at half height will provide :

k8 = ! R (15)
As could in principle be deduced from (see equation [START_REF] Veeman | Quadrupole nutation NMR in solids[END_REF]; this would however require an accurate calibration of the field), a precise analysis of experiment A should lead to , and again in principle to and .

2) \ ] < ^_

This condition is encountered in some instances, especially when becomes very large and much larger than . The solution of ( 10) is no longer oscillatory and the frequency of the nutation signal is zero. One has

(` -#$ = N $ ( i .// $ + l > i .// $ (16) with = - (17)
and l are determined from the initial conditions (0 and ( Assuming that is much larger than and , we can see that N i .// i .// is close to zero and use the following approximation (neglecting further #$ with respect to )

m n m` `=0 : = -N i .// i .// [ (0 -#$ ] -- i .// [ -(0 ] + , - i .// V (0 (18)
l = o1 + N i .// i .// p [ (0 -#$ ] + - i .// [ -(0 ] - , - i .// V (0 (19)
(` -#$ ≅ - ( N i .// $ (20)
Therefore, can be approximately deduced from experiment A which can be again considered as quantitative.

Moreover, still assuming that is much larger than and performing first order expansions, we obtain for the two exponents of eq. ( 16) : $ , this latter term decreasing very rapidly. Thus, the linewidth at half height can be approximated as

( N i .// $ ≅ ( -> 1
k8 ≅ R ( + , - 9 i (21)
It can be seen that the linewidth should decrease when decreases. Moreover, carrying out at least two experiment with different values should lead to the two relaxation rates, provided that is known with a reasonable accuracy.

Experiment B:

(0 = 0, V (0 = = 1 -- i .// + N i .// i .// #$ and l = -1 -- i .// -(1 + N i .// i .// #$ .
With the same approximations as above, one has

≅ -l ≅ , -- i .// .
The resulting expression is somewhat more complicated than for experiment A and not really amenable to the determination of pertinent parameters. Thus, experiment B will serve (as usual) to construct, along with experiment A, a set of complex data, the Fourier transform of which being used for visualizing purposes.

Results

The sample of kaolinite which is investigated is supposed to involve only one type of water. It turns out that the nutation spectrum contains the expected signal with relaxation parameters usual for water in clays but also an additional signal at zero frequency characteristic of a very large transverse relaxation rate, still much larger than the longitudinal relaxation rate. This is shown in The fact that the power spectrum is somewhat close to the reconstructed spectrum is here especially deceptive. As explained in the first section, this is due for the peak at zero frequency (in the power spectrum) to a smaller compensating a smaller amplitude. In any event, as shown above, reliable parameters are preferentially obtained from the least-squares analysis of experiment A. It is particularly interesting to notice that, in agreement with theory, the line at zero frequency is paradoxically sharp. As shown In the theory section, this is due to the fact that the linewidth is dominated by and not (with here ≪ ). Now and as stated above, the amplitudes + are nothing else than the peak areas. Using the values obtained from the least-squares analysis of experiment A, we arrive at the conclusion that the peak at zero frequency represents about 30% of the total amount of water (this proportion has been calculated from

4 - 4 ->4 9
. This is the amazing result of this study. A single nutation peak was expected (the high frequency peak with relaxation rates around 3 ms -1 ) corresponding to water interacting with the clay surface. In addition, a peak at zero frequency is observed implying a very large transverse relaxation rate (R2>40 ms -1 ) the origin of which, as indicated by recent observations, originate from an heterogeneous distribution of paramagnetic species which are responsible for the spin relaxation phenomena affecting water in these systems. The composition of the actual kaolinite sample confirms the presence of paramagnetic species such as Fe2O3 or TiO2 [START_REF] Mermut | Baseline studies of the clay minerals society source clays: chemical analyses of major elements[END_REF]- [START_REF] Chipera | Baseline studies of the clay minerals society source clays: powder X-ray diffraction analysis[END_REF]. This signal tends to weaken several weeks after the sample has been hydrated (proportions go from 30:70 to 10:90) and that, at the same time, the relaxation rate corresponding to the signal at a positive frequency tends to increase. This is illustrated by the series of spectra shown in figure 5.

The rf amplitude is not sufficient for satisfying the condition > and thus moving to higher frequency the signal at zero frequency. After several months, the signal at zero frequency has almost totally disappeared indicating that the clay sample tends to become homogeneous (see figure 5b).

Figure 5. a) Spectra obtained two months after the one of figure 4. From bottom to top: =20%, 30% and 50% of the maximum available value. Blue dots: nutation power spectra obtained from the complex Fourier transform of experiments A and B. Red: reconstructed nutation spectra resulting from the least squares analysis of experiment A; For visualization purposes, the power spectrum and the reconstructed spectrum have been normalized to the same maximum value. b) Spectra showing the sample evolution after its initial hydration for =20% : time zero (--), three months (-.-), five months (-).

Concerning the spectra of figure 5, some differences occur between the power spectrum and the recalculated spectrum (resulting from the least-squares analysis). This is in agreement with the previous considerations: contrary to the spectrum of figure 4, the weaker amplitude of the signal at zero frequency is no longer compensated for by its transverse relaxation rate. Data corresponding to the spectra of figures 4 and 5 are gathered in table 1

where and l refer to two different values of the B1 field. Using the data at B1=20% and B1=50%, we obtain for a value around 2600 ms -1 and then, directly from (21), a value for around 1ms -1 . Owing to this latter value, can be safely assimilated to /2, thus =5200 ms -1 , an extraordinary large value which can only arise from paramagnetic relaxation. We turn now to the peak at positive frequencies, the linewidth of which is equal to ! R (equation ( 15)) yielding values around 4 ms -1 , still assuming ≪ (this has been checked by a direct measurement of from the normal NMR spectrum in which water corresponding to this peak is exclusively visible, because the nutation peak at zero frequency is much too broad to be visible).

Finally, assuming dipolar relaxation and the same relaxation mechanism for both peaks (affecting the water protons located at a distance w from the unpaired electron of the paramagnetic species) implies a dependence in 1/w x . The ratio of the two values (5200 : 4) can be used to derive an estimate of the ratio of the distances between water and the location of paramagnetic species within the clay material. We obtain w /w around 0.3, meaning that water molecules corresponding to the peak at zero frequency are roughly three times closer to the paramagnetic species than those corresponding to the peak at positive frequencies. This is however a crude estimate which should be refined with regard to the sample heterogeneity.

Experimental

The NMR experiments were performed with a spectrometer equipped with a 4. Minerals Society). The elemental composition of this clay minerals has been described in several publications [START_REF] Mermut | Baseline studies of the clay minerals society source clays: chemical analyses of major elements[END_REF]- [START_REF] Chipera | Baseline studies of the clay minerals society source clays: powder X-ray diffraction analysis[END_REF]. The sample is prepared and packaged as described in the article of Porion et al. [START_REF] P;Porion | Water mobility within compacted clay samples: multi-scale analysis exploiting 1 H NMR pulsed gradient spin echo and magnetic resonance imagingof water density profiles[END_REF]. The sample of kaolinite used for these first measurements was hydrated at 100 %.

Nutation curves were obtained with 512 data points, the sampling interval (increment of the duration of the rf field application) being 10ms. Experiments were carried out at different values as indicated in the text.

In all these experiments, when a rf field is applied for a non-negligible time interval (contrary to hard pulses), sample temperature may be a problem. Several points can be mentioned which explain why no disturbance was observed even at large τ values (see figure 1): i) the transmit coil is designed for 10 mm o.d. sample tubes whereas 5 mm o.d. sample tubes are used for the present experiments making the rf source relatively far from the sample (initially, for avoiding radiation damping effects), ii) an air flow is systematically employed, iii) large rf amplitudes were not used so as to prevent dielectric heating and amplifier dips. The latter could actually be avoided by using a coil of smaller diameter but at the risk of dielectric heating. Also, with the present probe, inhomogeneity is negligible for our current experiments (as shown previously [START_REF] Ferrari | Measurement of short transverse relaxation times by pseudoecho nutation experiments[END_REF]). Finally, inhomogeneity of course affects experiments involving precession but is known to have little effect on nutation experiments.

Conclusion

The aim of this study was to devise an appropriate methodology for obtaining nutation spectra, i.e. a series of peaks when the nutation curve arises from a single NMR signal involving several contributions which differ by their relaxation rates. We have emphasized that a simple (real) Fourier transform is not convenient because it does not provide the negative part of the frequency domain and, as a consequence, would lead to severely truncated peaks. The idea was then to use a complementary experiment affording a sine modulation while the simple nutation experiment involves a cosine modulation. This is easily accomplished by adding a hard 90° pulse at the beginning of the simple nutation experiment. Combining these two experiments permits a complex Fourier transform yielding clear spectra including the negative part of the frequency domain. This is especially valuable for a signal at zero frequency which can occur whenever is very large and much larger than . However, as shown theoretically, an accurate quantitation is not attainable by this method which in addition generates small artefacts. Thus, the complex Fourier transform serves merely for visualizing purposes, that is for determining the number of contributions to the nutation curve and obtaining a first estimate of their characteristics.

Thereafter, the method of choice for arriving at quantitative and reliable results is to analyse the simple nutation experiment by least-squares and to reconstruct an appropriate spectrum. This was successfully applied to the clay sample investigated in this study (which constitutes a good test since, fortunately, it involves two signals, including a signal at zero frequency). A further advantage of such a method is its ability to separate signals which would overlap in the spectrum obtained by Fourier transform. It can be further noticed that the discrimination of neighboring signals can be improved by changing the amplitude of the rf field (see figure 5). Concerning spin relaxation, the method provides a very good estimate of both relaxation rates and , as far as one has to deal with a signal at zero frequency. By contrast, for signals at positive frequencies, the method provides only half the sum of and . If both relaxation rates are required, it can be anticipated that combining inversion-recovery or saturation-recovery with the simple nutation experiment would easily yield the value for each signal. Concerning the clay sample serving as an example in this study, these relaxation rates have allowed us to characterize the possible

Figure 1 .

 1 Figure 1. a): The simple nutation experiment: a weak rf field is applied along the x axis of the rotating frame for inducing nutation of the nuclear magnetization, assumed to be at thermal equilibrium (along the z axis) at the onset. The hard (π/2)x pulse allows one to select the longitudinal magnetization. b): The normal nutation experiment with an initial (π/2)x pulse for obtaining a 90° dephasing of the nutation curve.

Figure 2 .

 2 Figure 2. a) A typical nutation curve (pseudo fids: blue: experiment A; black; experiment B) of a water sample doped with a paramagnetic species (MnCl2, 60mM) for a B1 field leading to low frequency oscillations. b) The real Fourier transform of experiment A. c) The complex Fourier transform spectrum obtained through the combination of experiments A and B.

  signal (of amplitude ) in the absorption spectrum, one has ( 4 9

Figure 3 .

 3 Figure 3. a) A typical nutation curve (experiment A) of a water sample doped with a paramagnetic species (MnCl2, 10mM) for a B1 field leading to more pronounced oscillations than in figure 2. Blue: experimental data points; red; reconstructed pseudo-fit with parameters obtained through a least-squares analysis. b) Blue dots: nutation power spectrum obtained from the complex Fourier transform of experiments A and B. Red: reconstructed nutation spectrum resulting from the least squares analysis of experiment A. For visualization purposes, both spectra have been normalized to the same maximum value. In this figure and in the following, the point size represents roughly the experimental uncertainty.

Figure 4 .

 4 Figure 4. a): Kaolinite nutation curve (experiment A, data points in blue) for =20% of the maximum available value ( q3.3 kHz) clearly showing oscillations superposed to a contribution at zero frequency. The dashed black curves correspond to the reconstructed (from a least-squares analysis) nutation curves of both contributions. b) The experimental nutation curve (blue dots) with the total pseudo-fid (red curve) reconstructed from the least-squares analysis. c) Corresponding nutation spectra. Blue dots: nutation power spectrum obtained from the complex Fourier transform of experiments A and B. Red: reconstructed nutation spectra resulting from the least squares analysis of experiment A. For visualization purposes, both spectra have been normalized to the same maximum value.

  7 T Oxford magnet (proton resonance frequency: 200 MHz) and an NMR cube console manufactured by RS 2 D. The 90° pulse duration is 24µs (corresponding to 85% of the maximum field). All experiments were carried out at 298K. The kaolinite clay sample come from Warren County in Georgia in USA (KGa-2 kaolinite reference from the Source Clay Repository of The Clay

  .

		experiment	p1	lw1 (kHz)	ν2 (kHz)	lw2 (kHz)
		fig. 4		0.33±0.03	0.30±0.01	3.22±0.01	0.56±0.01
		B1 : : 20%
		fig. 5		0.12±0.05	0.33±0.01	3.20±0.01	0.72±0.01
		B1 : : 20%
		fig. 5		0.11±0.05	0.36±0.01	4.68±0.01	0.74±0.01
		B1 : : 30%
		fig. 5		0.10±0.09	0.43±0.02	7.37±0.02	0.77±0.01
		B1 : : 50%
	Table 1. Peak at zero frequency: p1=a1/(a1+a2); lw1: linewidth at half-height. lw2: linewidth at
	half-height of peak at frequency ν2.
	Some information concerning relaxation rates can be deduced from the data of table 1. From
	equation (21) where	can be replaced by 2 1 , we can write for the peak at zero frequency
	= 2	S 9t 9 Bv -t Bv -u S 9u 9

Acknowledgment

The authors thank Thomas Dabat et Eric Ferrage (IC2MP, Poitiers, France) for the packaging of kaolinite samples.

The Carnot Institute ICEEL by project: MultiEC-HYDRO and the CNRS interdisciplinary "défi Needs" through its "MiPor" program (Project TRANSREAC) are acknowledged for providing financial support for this study.

heterogeneity of the sample and to delineate the interactions between water and the paramagnetic species present in the clay material.