Evangelos Balanikas

Akos Banyasz

Thierry Douki

Gérard Baldacchino

Dimitra Markovitsi

Guanine Radicals Induced in DNA by Low-Energy Photoionization

Beyond the biological consequences, photo-generation of electron holes in G-quadruplexes may inspire applications in nano-electronics; although four-stranded structures are currently studied as molecular wires, their behavior as photoconductors has not been explored so far.

In the present Account, after highlighting some key experimental issues, we first describe the photo-ionization process and, then, we focus on radicals. We use as show-cases new results obtained for genomic DNA and Oxytricha G-quadruplexes. Generation and reaction dynamics of G radicals in these systems provide a representative picture of the phenomena reported previously for duplexes and G-quadruplexes, respectively.

CONSPECTUS Figure

CONSPECTUS. Guanine (G) radicals are precursors to DNA oxidative damage, correlated with carcinogenesis and aging. During the past few years, we demonstrated clearly an intriguing effect: G radicals can be generated upon direct absorption of UV radiation with energy significantly lower than the G ionization potential. Using nanosecond transient absorption spectroscopy, we studied the primary species, ejected electrons and guanine radicals, which result from photoionization of various DNA systems in aqueous solution.

The DNA propensity to undergo electron detachment at low photon energies greatly depends on its secondary structure. Non-detected for monomers or unstacked oligomers, it may be one order of magnitude higher for G-quadruplexes than for duplexes. The experimental results point toward non-vertical processes, associated with the relaxation of electronic excited states.

Theoretical studies are required to validate the mechanism and determine the factors that enter in play. In any case, such a mechanism, which may be operative over a broad excitation wavelength range, explains the occurrence of oxidative damage observed upon UVB and UVA irradiation.

Quantification of G radical populations and their time evolution questioned some widespread views. It appeared that G radicals may be generated with the same probability as pyrimidine dimers, which are considered to be the major lesions induced upon absorption of low-energy UV radiation by DNA. As the most important part of the initially created radical cations undergoes deprotonation, the vast majority of the final reaction products is expected to stem from longlived deprotonated radicals. Consequently, the widely used oxidation marker 8-oxodG is not representative of the extent of oxidative damage when this is triggered by generation of radical cations.

Introduction

UV radiation instigates oxidative damage to DNA in an indirect or a direct way. [START_REF] Cadet | Formation of UV-induced DNA damage contributing to skin cancer development[END_REF] The former mechanism involves mediation of other molecules that absorb light and, subsequently, oxidize DNA through release of reactive oxygen species or photosensitized electron abstraction. In the latter, a photon directly absorbed by DNA provokes photo-ionization: an electron is ejected and a hole, that is a radical cation, is created. Regardless the mechanism and the initial location of the electron hole, after charge transfer, [START_REF] Lewis | Tracking Photoinduced Charge Separation in DNA: from Start to Finish[END_REF][START_REF] Angelov | High-intensity UV laser photolysis of DNA and purine 2'-deoxyribonucleosides: Formation of 8-oxopurine damage and oligonucleotide strand cleavage as revealed by HPLC and gel electrophoresis studies[END_REF][START_REF] Meggers | Sequence dependent long range hole transport in DNA[END_REF][START_REF] Saito | Mapping of the hot spots for DNA damage by one-electron oxidation: Efficacy of GG doublets and GGG triplets as a trap in long-range hole migration[END_REF][START_REF] Kanvah | Oxidation of DNA: Damage to Nucleobases[END_REF][START_REF] Genereux | Mechanisms for DNA Charge Transport[END_REF][START_REF] Kawai | Hole Transfer Kinetics of DNA[END_REF] it reaches ultimately a guanine site. This happens because the guanine has the lowest oxidation potential compared to the other nucleobases, sugar and phosphate moieties composing DNA. [START_REF] Palecek | Electrochemistry of Nucleic Acids[END_REF] The present Account describes guanine radical generation via low-energy photo-ionization and discusses their evolution.

As the vertical ionization potential (VIP) of the various DNA components is higher than 6.6 eV [START_REF] Pluharova | Modeling Photoionization of Aqueous DNA and Its Components[END_REF][START_REF] Kumar | One-electron oxidation of ds(5 '-GGG-3 ') and ds(5 '-G(8OG)G-3 ') and the nature of hole distribution: a density functional theory (DFT) study[END_REF] and excitation at the lowest absorption band (Figure 1a) is not expected to provoke onephoton ionization. Therefore, this phenomenon was studied by exciting at 193 nm (6.4 eV). [START_REF] Candeias | Stucture and acid-base properties of one-electronoxidized deoxyguanosine, guanosine, and 1-methylguanosine[END_REF][START_REF] O'neill | Guanine modifications following ionization of DNA occurs predominantly via intra-and not interstrand charge migration: An experimental and theoretical study[END_REF][START_REF] Melvin | 193 nm Light Induces Single-strand Breakage of DNA Predominantly at Guanine[END_REF] Yet, more than a decade ago, two studies reported electron ejection from DNA oligomers, both in aqueous solution [START_REF] Marguet | One and two photon ionization of DNA single and double helices studied by laser flash photolysis at 266 nm[END_REF] and in the gas phase, [START_REF] Gabelica | Base-dependent electron photodetachment from negatively charged DNA strands upon 260-nm laser irradiation[END_REF] at much lower energy (266 nm, 4.7 eV); but these results appeared rather as a curiosity, connected with laser experiments. More recently, some of us showed that low-intensity continuous irradiation of purified genomic DNA at 554 and 295 nm gives rise not only to the well-known oxidation marker 8-oxo-7,8-dihydro-2'-deoxyguanosine (8-oxodG), but also to polyamine-guanine adducts. [START_REF] Gomez-Mendoza | Direct Oxidative Damage of Naked DNA Generated upon Absorption of UV Radiation by Nucleobases[END_REF] While 8-oxodG can be produced by several pathways, including DNA-mediated singlet oxygen generation, [START_REF] Mohammad | Evidence for the photosensitized formation of singlet oxygen by UVB irradiation of 2'-deoxyguanosine 5'-monophosphate[END_REF][START_REF] Yagura | Direct participation of DNA in the formation of singlet oxygen and base damage under UVA irradiation[END_REF] the detected adducts are typical of a mechanism involving the guanine radical cation (G + ) • . In parallel, we have undertaken a study aiming at the quantitative characterization of the related primary species, ejected electrons and guanine radicals, by transient absorption spectroscopy using as excitation source 5 ns laser pulses at 266 nm. Although nanosecond flash photolysis has been a laboratory tool for over half a century now, specific protocols had to be developed for these studies. The reason is that they require detection of very weak signals arising from DNA systems undergoing damage during the measurement.

Our photo-ionization experiments have also proven a unique tool to study the "intrinsic" reaction dynamics of radicals; the term "intrinsic" refers to the absence of any external additive other than the ingredients of the phosphate buffer used as a solvent, which do not react with G radicals. As guanine radical cations (G + )  are known to be metastable undergoing either hydration or loss of a proton, [START_REF] Candeias | Ionization of purine nucleosides and nucleotides and their components by 193-nm laser photolysis in aqueous solution: model studies for oxidative damage of DNA[END_REF] the time-resolved spectra allow us to follow their transformation and evaluate the evolution of their populations. This is an important issue because deprotonated radicals give rise to lesions different from those stemming directly from (G + ) • . [START_REF] Cadet | Formation of UV-induced DNA damage contributing to skin cancer development[END_REF] Consequently, the final type of oxidative damage depends, among others, on the population of (G + ) • that undergoes deprotonation.

Our studies revealed that the secondary DNA structure plays a key role both in the generation of guanine radicals by low-energy photo-ionization and in their evolution. Here, we discuss our previous studies on model duplexes [START_REF] Banyasz | UV-induced Adenine Radicals Induced in DNA A-tracts: Spectral and Dynamical Characterization[END_REF][START_REF] Banyasz | Adenine radicals generated in alternating AT duplexes by direct absorption of low-energy UV radiation[END_REF][START_REF] Banyasz | Radicals generated in alternating guanine-cytosine duplexes by direct absorption of low-energy UV radiation[END_REF][START_REF] Balanikas | Populations and Dynamics of Guanine Radicals in DNA strands: Direct versus Indirect Generation[END_REF] and present new results on calf thymus (CT-DNA), showing that genomic DNA exhibits the same behavior as small size systems. In addition, we exemplify the behavior of G-quadruplexes (G4), whose building blocks are guanine tetrads (Conspectus Figure), by presenting new data obtained for Oxytricha G4. The latter, obtained by association of two single strands GGGGTTTTGGGG (OXY), [START_REF] Schultze | The effect of sodium, potassium and ammonium ions on the conformation of the dimeric quadruplex formed by the Oxytricha nova telomere repeat oligonucleotide d(G(4)T(4)G(4))[END_REF] confirm previous studies reported for monomolecular [START_REF] Balanikas | Populations and Dynamics of Guanine Radicals in DNA strands: Direct versus Indirect Generation[END_REF][START_REF] Banyasz | Absorption of Low-Energy UV Radiation by Human Telomere G-Quadruplexes Generates Long-Lived Guanine Radical Cations[END_REF][START_REF] Balanikas | Guanine Radicals Generated in Telomeric G-quadruplexes by Direct Absorption of Low-Energy UV Photons: Effect of Potassium Ions[END_REF] and tetramolecular systems. [START_REF] Banyasz | Radicals generated in tetramolecular guanine quadruplexes by photoionization: spectral and dynamical features[END_REF][START_REF] Behmand | Potassium Ions Enhance Guanine Radical Generation upon Absorption of Low-Energy Photons by G-quadruplexes and Modify Their Reactivity[END_REF][START_REF] Behmand | Correction to "Potassium Ions Enhance Guanine Radical Generation upon Absorption of Low-Energy Photons by G-quadruplexes and Modify Their Reactivity[END_REF] Our G4 are formed and studied in the presence of Na + or K + cations. These cations, are not only part of the bulk solvent; they are also located in the central cavity of G4, being constitutive elements of their structure. [START_REF] Hud | The role of cations in determining quadruplex structure and stability[END_REF] Therefore, when referring to G4, we always indicate the type of metal cations, for example: OXY/Na + and OXY/K + .

Key experimental points

Experimental details are given in the Supporting Information (SI-Section 1). Here, we simply highlight a few points that are crucial for these studies.

Materials. Both synthetic oligomers and genomic DNA were extensively purified. Moreover, the purity of the chemicals used for the preparation of the buffer was 99.99%. This is an important requirement for avoiding photo-ionization of impurities, on the one hand, and their reaction with radicals, on the other. The buffer (pH 7) was composed of an equimolar mixture of MH 2 PO 4 , and M 2 HPO 4 , where M + is either Na + or K + . In most experiments, their concentration was high (0.15 mol•L -1 ) so that to scavenge the ejected electrons, [START_REF] Von Sonntag | Free-Radical-Induced DNA damage and its Repair[END_REF] preventing their interaction with DNA. Furthermore, the corresponding high ionic strength helped stabilizing short duplexes.

During the measurement, the solution was frequently renewed so that to avoid that successive laser pulses excite already damaged DNA; typically, for a complete study of a given system, 300-500 mL were needed. Spectroscopic measurements. The challenge was to work with low-excitation intensities, leading to very weak transient absorption signals, so that to avoid two-photon ionization of the buffer, saturation effects in electron ejection (SI-Section 2), interaction among radicals and minimize two-photon ionization of DNA. Transient absorption signals were optimized by using orthogonal exciting and probing beams whose path-lengths though the sample were, respectively, 0.1 cm and 1 cm; the absorbance of the solution on the excitation side was 0.25 ± 0.02, corresponding to a base concentration of the order of 10 -4 mol•L -1 . The incident pulse intensity did not exceed, depending on the system, 2×10 6 or 3×10 6 W•cm -2 (SI-Section 2). In this way, the transient absorption decays are not influenced by the incident excitation intensity (Figure S2). Finally, the concentration of photons absorbed in the probed volume of the studied solution [h] was determined using a NIST traceable power-meter and counterchecked via an actinometer (SI-Section 1). In all experiments, the concentration of generated radicals was three orders of magnitude lower than the base concentration.

Characterization of ejected electrons

Electrons issued from photo-ionization in aqueous solution are known to be hydrated (e hyd -) and exhibit a broad absorption band peaking around 720 nm. Such a band is indeed present in the transient absorption spectrum recorded for CT-DNA at 30 ns, corresponding to the 30-ns time resolution of our experimental setup (Figure 1b). Based on this property and taking into account a maximum molar absorption coefficient ε of 19700 mol -1 •L•cm -1 reported for e hyd -, [START_REF] Torche | Direct Evaluation of the Molar Absorption Coefficient of Hydrated Electron by the Isosbestic Point Method[END_REF] we quantify the ejected electrons by probing their transient absorption on the sub-microsecond timescale. (c) Normalized transient absorption decay at 700 nm; it is compared with the corresponding signal obtained under the same conditions for a short duplex (cyan; S1S2, [START_REF] Balanikas | Populations and Dynamics of Guanine Radicals in DNA strands: Direct versus Indirect Generation[END_REF] In our experimental conditions, e hyd -disappear within a few µs, reacting with H 2 PO 4 -ions [START_REF] Von Sonntag | Free-Radical-Induced DNA damage and its Repair[END_REF] present in high concentration. Their decay rate is the same for all the small DNA systems (Figure S3), depending only on the buffer concentration. In contrast, for the same buffer concentration, e hyd -stemming from CT-DNA decay significantly faster (Figures 1c), revealing the existence of additional reaction paths, involving DNA. [START_REF] Kumar | Reaction of Electrons with DNA: Radiation Damage to Radiosensitization[END_REF] Such reactions could be favored by the flexibility of the very long duplex, [START_REF] Peters | DNA curvature and flexibility in vitro and in vivo[END_REF] increasing locally the encounter probability between nucleic acid components and e hyd -produced by the same helix.

Although we use low excitation intensities, two-photon ionization, resulting from absorption of a second photon by a long-lived electronic excited state, cannot be completely prevented. To disentangle one-and two-photon events, we vary the excitation intensity, thus changing the concentration of absorbed photons. Subsequently, we plot [e hyd -] 0 /[hν] versus [hν], obtaining the so-called ionization curve (Figure 1d). The determination of [e hyd -] 0 is illustrated in Figure S3: We did not detect one-photon ionization (φ 1 ≤3×10 -4 ) for mononucleotides and small single strands characterized by poor base stacking, such as the 6-mer telomere repeat TTAGGG [START_REF] Banyasz | Absorption of Low-Energy UV Radiation by Human Telomere G-Quadruplexes Generates Long-Lived Guanine Radical Cations[END_REF] or thymine single strands (dT) 20 . [START_REF] Marguet | One and two photon ionization of DNA single and double helices studied by laser flash photolysis at 266 nm[END_REF] In contrast, for adenine single strands, known to adopt a helical structure, a φ 1 value of (1.0 ± 0.1)×10 -3 was found. [START_REF] Banyasz | UV-induced Adenine Radicals Induced in DNA A-tracts: Spectral and Dynamical Characterization[END_REF] Those determined for various duplexes and G4 are gathered on Table 1. In the case of duplexes, φ 1 ranges from 1.0×10 -3 to 2.0×10 -3 . [START_REF] Banyasz | UV-induced Adenine Radicals Induced in DNA A-tracts: Spectral and Dynamical Characterization[END_REF][START_REF] Banyasz | Adenine radicals generated in alternating AT duplexes by direct absorption of low-energy UV radiation[END_REF][START_REF] Banyasz | Radicals generated in alternating guanine-cytosine duplexes by direct absorption of low-energy UV radiation[END_REF][START_REF] Balanikas | Populations and Dynamics of Guanine Radicals in DNA strands: Direct versus Indirect Generation[END_REF] This concerns also icosamers containing only adenines and thymines in alternating [START_REF] Banyasz | Adenine radicals generated in alternating AT duplexes by direct absorption of low-energy UV radiation[END_REF] or homopolymeric sequence. [START_REF] Banyasz | UV-induced Adenine Radicals Induced in DNA A-tracts: Spectral and Dynamical Characterization[END_REF] Clearly higher values, which may approach 10 -2 , are observed for G4. [START_REF] Balanikas | Populations and Dynamics of Guanine Radicals in DNA strands: Direct versus Indirect Generation[END_REF][START_REF] Banyasz | Absorption of Low-Energy UV Radiation by Human Telomere G-Quadruplexes Generates Long-Lived Guanine Radical Cations[END_REF][START_REF] Banyasz | Radicals generated in tetramolecular guanine quadruplexes by photoionization: spectral and dynamical features[END_REF][START_REF] Behmand | Potassium Ions Enhance Guanine Radical Generation upon Absorption of Low-Energy Photons by G-quadruplexes and Modify Their Reactivity[END_REF][START_REF] Behmand | Correction to "Potassium Ions Enhance Guanine Radical Generation upon Absorption of Low-Energy Photons by G-quadruplexes and Modify Their Reactivity[END_REF] In this family, topology and molecularity seem to play a rather minor role: the behavior of tetramolecular (TG 4 T) 4 /Na + and monomolecular TEL21/Na + systems is similar although their guanines adopt, respectively, parallel and antiparallel orientations in respect to the glyosidic bonds. [START_REF] Banyasz | Absorption of Low-Energy UV Radiation by Human Telomere G-Quadruplexes Generates Long-Lived Guanine Radical Cations[END_REF][START_REF] Banyasz | Radicals generated in tetramolecular guanine quadruplexes by photoionization: spectral and dynamical features[END_REF] In contrast, the metal cation used in the buffer in which G4 are formed and studied, has an important effect: the values found in the case of K + are significantly higher compared to Na + .

Table 1. Quantum yields (φ 1 ×10 3 ) of one-photon ionization at 266 nm and guanine/adenine radical halflives (ms, in brackets) determined for duplexes and G4 in phosphate buffer. 1.2 ± 0.2 [START_REF] Banyasz | Radicals generated in alternating guanine-cytosine duplexes by direct absorption of low-energy UV radiation[END_REF] (2.5 ± 0.2)

2.1 ± 0.4 [START_REF] Balanikas | Populations and Dynamics of Guanine Radicals in DNA strands: Direct versus Indirect Generation[END_REF] (4 ± 0.2)

1.5 ± 0.3 [START_REF] Banyasz | Adenine radicals generated in alternating AT duplexes by direct absorption of low-energy UV radiation[END_REF] (2.0 ± 0.1)

1.1 ± 0.3 21 (4.0 ± 1.0) K +
1.9 ± 0.1

(3.6± 0.2) - - - M + TEL21 e TEL25 f OXY g (TG 4 T) 4 h G4 Na +
4.5 ± 0.6 [START_REF] Banyasz | Absorption of Low-Energy UV Radiation by Human Telomere G-Quadruplexes Generates Long-Lived Guanine Radical Cations[END_REF] (6.7 ± 0.5)

5.2 ± 0.3 [START_REF] Balanikas | Populations and Dynamics of Guanine Radicals in DNA strands: Direct versus Indirect Generation[END_REF] (3.5± 0.2)

6.0 ± 0.2 (4.1 ± 0.2)
3.5±0.5 [START_REF] Banyasz | Radicals generated in tetramolecular guanine quadruplexes by photoionization: spectral and dynamical features[END_REF] (6.0 ± 0.5)

K +
9.4 ± 0.1 [START_REF] Balanikas | Guanine Radicals Generated in Telomeric G-quadruplexes by Direct Absorption of Low-Energy UV Photons: Effect of Potassium Ions[END_REF] (1.4± 0.1) -7.9 ± 0.1

(2.1± 0.2)
8.1 ± 0.5 [START_REF] Behmand | Potassium Ions Enhance Guanine Radical Generation upon Absorption of Low-Energy Photons by G-quadruplexes and Modify Their Reactivity[END_REF][START_REF] Behmand | Correction to "Potassium Ions Enhance Guanine Radical Generation upon Absorption of Low-Energy Photons by G-quadruplexes and Modify Their Reactivity[END_REF] (3.1± 0.2) a) alternating guanine-cytosine; b) S1: 5'-CGTACTCTTTGGTGGGTCGGTTCTTTCTAT-3'/ S2: 3'-GCATGAGAAACCACCCAGCCAAGAAAGATA-5', c) alternating adenine-thymine; d) homopolymeric adeninethymine; e) monomolecular: GGG(TTAGGG) 3 ; f) monomolecular: TAGGG(TTAGGG) 3 TT; g) bimolecular: 2×(GGGGTTTTGGGG); h) tetramolecular: 4×(TGGGGT).

Evidence for a non-vertical photo-ionization mechanism?

The effect of metal ions on the propensity of G4 to undergo low-energy photo-ionization points towards non-vertical electron ejection. This conclusion was drawn, in particular, by comparing (TG 4 T) 4 /Na + and (TG 4 T) 4 /K + , [START_REF] Banyasz | Radicals generated in tetramolecular guanine quadruplexes by photoionization: spectral and dynamical features[END_REF][START_REF] Behmand | Potassium Ions Enhance Guanine Radical Generation upon Absorption of Low-Energy Photons by G-quadruplexes and Modify Their Reactivity[END_REF][START_REF] Behmand | Correction to "Potassium Ions Enhance Guanine Radical Generation upon Absorption of Low-Energy Photons by G-quadruplexes and Modify Their Reactivity[END_REF] in which the static arrangement of nucleobases is the same. Although the VIP of these two systems, computed by quantum chemistry methods, are practically identical, [START_REF] Yagura | Direct participation of DNA in the formation of singlet oxygen and base damage under UVA irradiation[END_REF] we observe a twofold increase in φ 1 upon replacing Na + by K + cations.

Hence, a complex mechanism, associated with the excited state relaxation, was proposed. The first step implies population of an excited charge transfer (CT) state, either between a thymine and a guanine or between two guanines. In a second step (charge separation), the positive charge is trapped by the guanine core, where it may be delocalized, [START_REF] Kumar | One-electron oxidation of ds(5 '-GGG-3 ') and ds(5 '-G(8OG)G-3 ') and the nature of hole distribution: a density functional theory (DFT) study[END_REF][START_REF] Capobianco | Delocalized Hole Domains in Guanine-Rich DNA Oligonucleotides[END_REF][START_REF] Sun | Effects of G-Quadruplex Topology on Electronic Transfer Integrals[END_REF][START_REF] Martinez-Fernandez | Topology controls the electronic absorption delocalization of electron hole in guanine quadruplexes[END_REF] while the negative one is born by a thymine. This process is tentatively described as:

T -G + GGGT  T -(GGGG) + T or TGG -G + GT  T -(GGGG) + T,
where the radical sign was omitted for simplicity. Finally, electron ejection, assisted by conformational motions, occurs from the thymine anion, whose VIP in the gas phase is lower than 0.1 eV. [START_REF] Schiedt | Anion spectroscopy of uracil, thymine and the amino-oxo and amino-hydroxy tautomers of cytosine and their water clusters[END_REF] In the frame of such a scenario, Na + cations, smaller and more mobile than K + , [START_REF] Ida | Direct NMR detection of alkali metal ions bound to G-quadruplex DNA[END_REF] allow the geometrical arrangement accompanying stabilization of CT states, [START_REF] Hua | Cation Effect on the Electronic Excited States of Guanine Nanostructures Studied by Time-Resolved Fluorescence Spectroscopy[END_REF] and, hence, reducing the probability of charge separation.

Population of excited CT states both in duplexes [START_REF] Chen | Excited states in DNA strands investigated by ultrafast laser spectroscopy[END_REF][START_REF] Markovitsi | UV-induced DNA Damage: The Role of Electronic Excited States[END_REF][START_REF] Schreier | Early Events of DNA Photodamage[END_REF] and G4 [START_REF] Hua | Cation Effect on the Electronic Excited States of Guanine Nanostructures Studied by Time-Resolved Fluorescence Spectroscopy[END_REF][START_REF] Martinez-Fernandez | A Comprehensive Study of Guanine Excited State Relaxation and Photoreactivity in G-Quadruplexes[END_REF][START_REF] Ma | Realtime Monitoring Excitation Dynamics of Human Telomeric Guanine Quadruplexes: Effect of Folding Topology, Metal Cation, and Confinement by Nanocavity Water Pool[END_REF] is well documented. The occurrence of charge separation along DNA strands has also been reported. [START_REF] Bucher | Charge separation and charge delocalization identified in long-living states of photoexcited DNA[END_REF] The higher φ 1 in G4, could be due to more efficient trapping of the positive charge within stacked guanine tetrads (Conspectus Figure); in this way, charge separation becomes more efficient, increasing the probability of electron ejection from a base located outside the guanine core. Another important difference is that guanine tetrads interact directly with dehydrated cations. [START_REF] Hud | The role of cations in determining quadruplex structure and stability[END_REF] Such interaction is not encountered in duplexes, explaining why the φ 1 of CT-DNA is not significantly different in presence of Na + or K + cations in contrast to G4 scaffolds (Table 1).

In contrast to the vertical ionization process, whose quantum yield decreases rapidly when moving away from the VIP, the proposed mechanism is expected to be operative over a broader range of excitation energy, provided that CT states are populated and charge separation achieved. This is supported by the fact that similar quantum yields for 8-oxodG formation were obtained for UVC and UVB irradiation. [START_REF] Gomez-Mendoza | Direct Oxidative Damage of Naked DNA Generated upon Absorption of UV Radiation by Nucleobases[END_REF] Furthermore, strand breaks were observed upon UVA irradiation, [START_REF] Teychene | Formulation induces direct DNA UVA photooxidation. Part I. Role of the formulating cationic surfactant[END_REF] where the weakly absorbing excited states [START_REF] Sutherland | Absorption spectrum of DNA for wavelengths greater than 300 nm[END_REF][START_REF] Banyasz | Base-pairing enhances fluorescence and favors cyclobutane dimer formation induced upon absorption of UVA radiation by DNA[END_REF] have partial charge transfer character. 50,51

Radicals

General considerations. The spectral fingerprints of radicals are determined after the decay of e hyd -. We identify them by comparison with the corresponding spectra reported for monomeric guanosine derivatives (Figure 2a). We checked experimentally the validity of this comparison for (G + )  , for which stronger interactions with neighboring bases are expected than for deprotonated radicals, because of the presence of a positive charge. To this end, we recorded time-resolved spectra of G4 at pH3, where deprotonation of (G + )  is hindered. [START_REF] Candeias | Stucture and acid-base properties of one-electronoxidized deoxyguanosine, guanosine, and 1-methylguanosine[END_REF] This is shown in Figure 2b in the case of (TG 4 T) 4 /Na + : [START_REF] Banyasz | Radicals generated in tetramolecular guanine quadruplexes by photoionization: spectral and dynamical features[END_REF] the agreement with the monomeric radical spectrum is satisfactory in the 450-700 nm domain, not only regarding the spectral shape but also the extinction coefficients determined by dividing the observed transient absorption A at 2.5 µs by [e hyd -] 0 , which corresponds to that of generated electron holes. As predicted by quantum chemistry calculations, lower  values were found for the band at 400 nm. [START_REF] Banyasz | Absorption of Low-Energy UV Radiation by Human Telomere G-Quadruplexes Generates Long-Lived Guanine Radical Cations[END_REF][START_REF] Banyasz | Radicals generated in tetramolecular guanine quadruplexes by photoionization: spectral and dynamical features[END_REF] Below this wavelength, it was impossible to determine reliable spectra due to strong photodegradation occurring in acidic solutions during the measurements. Reference monomeric G radicals. Absorption spectra of monomeric radical cation (G + )  (red), [START_REF] Candeias | Stucture and acid-base properties of one-electronoxidized deoxyguanosine, guanosine, and 1-methylguanosine[END_REF] and deprotonated (G-H1)  radical (blue) [START_REF] Candeias | Stucture and acid-base properties of one-electronoxidized deoxyguanosine, guanosine, and 1-methylguanosine[END_REF] and (G-H2)  radicals (green), [START_REF] Chatgilialoglu | Tautomerism in the guanyl radical[END_REF] resulting, respectively, from loss of the protons at position 1 or 2 (Conspectus Figure ); the black square indicates the spectral region where the  values of all three radicals are similar (< 100 mol -1 •L•cm -1 ). [START_REF] Balanikas | Guanine Radicals Generated in Telomeric G-quadruplexes by Direct Absorption of Low-Energy UV Photons: Effect of Potassium Ions[END_REF] (b) Transient absorption spectrum obtained for (TG 4 T) 4 /Na + in pH 3 at 2.5 µs (circles); A is divided by [e hyd -] 0 , determined in the same experiment; the spectrum of the monomeric (G + )  (red) [START_REF] Banyasz | Radicals generated in tetramolecular guanine quadruplexes by photoionization: spectral and dynamical features[END_REF] is represented with values.

In Figure 2a, we remark the existence of a quasi-isosbestic point around 500-515 nm. Thus, regardless the radical evolution in a given system, the total radical concentration at time t, [R] t , may be obtained from the A value at this wavelength range. We found that for all the examined systems, [R] t at 3 µs matches the concentration of hydrated ejected electrons, corresponding to the initially created electron holes ([R] 0 = [e hyd -] 0 ). This means that only a small fraction of the radical population, associated with our experimental error (5-10%, depending on the system), reacts at earlier times. Consequently, the survival probability of the total radical population is given by the decays recorded at the quasi-isosbestic point, setting A at 3 µs equal to 1. The survival probabilities determined for CT-DNA and OXY/K + are shown in Figure 3. The radical half-lives  1/2 , that is the time at which [R] t /[R] 0 = 0.5, are of a few milliseconds in both duplexes and G4 (Table 1). The  1/2 found for the duplex S1S2 (4 ms) is twice as long than those determined for the two parent single strands. [START_REF] Balanikas | Populations and Dynamics of Guanine Radicals in DNA strands: Direct versus Indirect Generation[END_REF] A similar increase in  1/2 upon base-pairing is observed for adenine radicals in A-tracts. [START_REF] Banyasz | UV-induced Adenine Radicals Induced in DNA A-tracts: Spectral and Dynamical Characterization[END_REF] Larger conformational motions in single strands probably allow the systems to adopt more rapidly reactive conformations, increasing the reaction rate. Finally, we remark in Table 1 that  1/2 of G4 is much shorter in the presence of K + compared to Na + . The reasons underlying this effect are not clear yet.

CT-DNA. The transient absorption spectrum determined for CT-DNA at 50 µs is shown in Figure 4a. It strongly resembles that of (G-H1)  radical reported for dGMP; [START_REF] Candeias | Stucture and acid-base properties of one-electronoxidized deoxyguanosine, guanosine, and 1-methylguanosine[END_REF] the agreement is quantitative, reproducing the  values. However, as in the case of short duplexes, [START_REF] Balanikas | Populations and Dynamics of Guanine Radicals in DNA strands: Direct versus Indirect Generation[END_REF] the relative intensity at 700 nm in respect to that at 500 nm (0.6) is higher than that characterizing the

CT-DNA

OXY/K + monomer spectrum (0.4). Such an enhanced absorption at the red part is predicted by quantum chemistry calculations for guanine radicals within G-C pairs. [START_REF] Banyasz | Radicals generated in alternating guanine-cytosine duplexes by direct absorption of low-energy UV radiation[END_REF][START_REF] Kumar | Excited States of One-Electron Oxidized Guanine-Cytosine Base Pair Radicals: A Time Dependent Density Functional Theory Study[END_REF] It was shown, in particular, that when the proton is transferred to the bulk water instead of cytosine, a weak intensity band appears around 650 nm. [START_REF] Kumar | Excited States of One-Electron Oxidized Guanine-Cytosine Base Pair Radicals: A Time Dependent Density Functional Theory Study[END_REF] We determined the deprotonation dynamics in CT-DNA by monitoring the transient absorption at 700 nm because only (G-H1)  absorbs at this wavelength (Figure 2a). To this end, we eliminated the much stronger absorption of e hyd -using efficient electron scavengers (N 2 O and NO 3 -). [START_REF] Von Sonntag | Free-Radical-Induced DNA damage and its Repair[END_REF] Under these conditions, we observed a rise which is completed within 2 µs (Figure 4b); it can be approximated with a monoexponential function with a time constant of 0.3 µs, in line with the fast deprotonation rate obtained for short duplexes using pulse radiolysis. [START_REF] Kobayashi | Direct observation of guanine radical cation deprotonation in duplex DNA using pulse radiolysis[END_REF] Subsequently, we found that the signal starts decaying slowly on the µs time-scale (Figure 4c), with a rate similar to that at 500 nm (Figure 3a). The indirect oxidation study reported instead a slow rise corresponding to a time constant of 7 µs. [START_REF] Kobayashi | Direct observation of guanine radical cation deprotonation in duplex DNA using pulse radiolysis[END_REF] This discrepancy probably arises from anisotropic reaction kinetics between the oxidant and DNA bases in the duplex, as discussed in detail in reference 24. The  values of the (G-H1)  at 700 nm have not been determined experimentally for duplexes.

However, the spectral shape in Figure 4a, in analogy with the computed spectra, [START_REF] Kumar | Excited States of One-Electron Oxidized Guanine-Cytosine Base Pair Radicals: A Time Dependent Density Functional Theory Study[END_REF] as well as the extent of rise in Figure 4b, strongly suggest that the quasi-entire population of (G + )  undergoes deprotonation within 2 µs.

Radicals in G4.

Going from duplexes to four-stranded structures, the spectra recorded at 3 µs exhibit a broad absorption band in the visible, attributed to the coexistence of (G + )  and (G-H2)  radicals. As the hydrogen at position 1 of guanines (Conspectus Figure ) is engaged in hydrogen bonding within the tetrads, deprotonation occurs at position 2. The existence of long-lived (G + )  in G4 and their deprotonation toward (G-H2)  , was reported in a study performed via photosensitization. [START_REF] Wu | Direct Observation of Guanine Radical Cation Deprotonation in G-Quadruplex DNA[END_REF] In our studies, we quantified the population of these long-lived (G + )  . To this end, we reconstructed the time-resolved spectra with linear combinations of the spectra of monomeric radicals. An example is shown in Figure 5a, where the reconstruction of the transient absorption spectrum obtained for OXY/K + at 3 µs is presented. The fraction of the radical population persisting as electron holes at 3 µs ranges from 0.25 to 0.50, depending on the G4 structure. [START_REF] Balanikas | Populations and Dynamics of Guanine Radicals in DNA strands: Direct versus Indirect Generation[END_REF][START_REF] Banyasz | Absorption of Low-Energy UV Radiation by Human Telomere G-Quadruplexes Generates Long-Lived Guanine Radical Cations[END_REF][START_REF] Balanikas | Guanine Radicals Generated in Telomeric G-quadruplexes by Direct Absorption of Low-Energy UV Photons: Effect of Potassium Ions[END_REF][START_REF] Banyasz | Radicals generated in tetramolecular guanine quadruplexes by photoionization: spectral and dynamical features[END_REF][START_REF] Behmand | Potassium Ions Enhance Guanine Radical Generation upon Absorption of Low-Energy Photons by G-quadruplexes and Modify Their Reactivity[END_REF][START_REF] Behmand | Correction to "Potassium Ions Enhance Guanine Radical Generation upon Absorption of Low-Energy Photons by G-quadruplexes and Modify Their Reactivity[END_REF] Figure 5. G radicals in OXY/K + . Transient absorption spectra (circles) at 3 µs (a, [R] t = [R] 0 ) and 10 ms (c, [R] t = 0.3[R] 0 ) determined for aerated solutions; the green line in (a) is a linear combination of the spectra corresponding to (G + )  (30%) [START_REF] Candeias | Stucture and acid-base properties of one-electronoxidized deoxyguanosine, guanosine, and 1-methylguanosine[END_REF] and the (G-H2)  (70%) [START_REF] Chatgilialoglu | Tautomerism in the guanyl radical[END_REF] radicals of monomeric guanosine; the blue line in (c) corresponds to the spectrum (G-H1)  of dGMP. 12 (b) Transient absorption trace at 620 nm recorded for N 2 O saturated solutions (green); the red line corresponds to the fit with a monoexponential rise. Incident excitation intensity: 2.0×10 6 W•cm -2 .

The (G + )   (G-H2)  deprotonation in G4 spans several decades of time. It can be observed by the rise of the transient absorption signal at 600-620 nm, where the difference between the two radical spectra is particularly important (Figure 2a). The fastest part (Figure 5b) is probably related with outer tetrads that are most exposed to bulk water. Completion of the (G + )  deprotonation ranges from few decades of microseconds in tetramolecular G4 [START_REF] Banyasz | Radicals generated in tetramolecular guanine quadruplexes by photoionization: spectral and dynamical features[END_REF][START_REF] Behmand | Potassium Ions Enhance Guanine Radical Generation upon Absorption of Low-Energy Photons by G-quadruplexes and Modify Their Reactivity[END_REF][START_REF] Behmand | Correction to "Potassium Ions Enhance Guanine Radical Generation upon Absorption of Low-Energy Photons by G-quadruplexes and Modify Their Reactivity[END_REF] to a few milliseconds in TEL21/Na + . [START_REF] Banyasz | Absorption of Low-Energy UV Radiation by Human Telomere G-Quadruplexes Generates Long-Lived Guanine Radical Cations[END_REF] In most cases, (G + )   (G-H2)  deprotonation is followed by (G- )   (G-H1)  tautomerization. [START_REF] Balanikas | Populations and Dynamics of Guanine Radicals in DNA strands: Direct versus Indirect Generation[END_REF][START_REF] Banyasz | Absorption of Low-Energy UV Radiation by Human Telomere G-Quadruplexes Generates Long-Lived Guanine Radical Cations[END_REF][START_REF] Balanikas | Guanine Radicals Generated in Telomeric G-quadruplexes by Direct Absorption of Low-Energy UV Photons: Effect of Potassium Ions[END_REF][START_REF] Banyasz | Radicals generated in tetramolecular guanine quadruplexes by photoionization: spectral and dynamical features[END_REF] An example is shown in Figure 5c, where the OXY/K + spectrum at 10 ms in the visible spectral domain corresponds to that of (G-H1)  in a concentration equal to 30% of [R] 0 (Figure 3d). Below 400 nm we observe the fingerprint of an unknown reaction intermediate, also detected for monomolecular G4. [START_REF] Balanikas | Populations and Dynamics of Guanine Radicals in DNA strands: Direct versus Indirect Generation[END_REF][START_REF] Balanikas | Guanine Radicals Generated in Telomeric G-quadruplexes by Direct Absorption of Low-Energy UV Photons: Effect of Potassium Ions[END_REF] Tautomerization is not observed in (TG4T) 4 /K + , where (G-H2)  radicals react rapidly through some other, currently unexplored, reaction path. [START_REF] Candeias | Ionization of purine nucleosides and nucleotides and their components by 193-nm laser photolysis in aqueous solution: model studies for oxidative damage of DNA[END_REF]

Correlation with final lesions

Although the present study deals with primary processes, our findings shed some light upon final lesions. For example, the formation of 8-oxodG, known to stem from hydration of (G + )  , is in competition with the deprotonation process. Consequently, the level of 8-oxodG will be determined by the relative rates of these two reactions. This effect is illustrated by a comparative study on TEL21/Na + and (TG 4 T) 4 /Na + , for which 8-oxodG was analyzed by high performance liquid chromatography coupled to mass spectrometry following irradiation at 266 nm. [START_REF] Banyasz | Absorption of Low-Energy UV Radiation by Human Telomere G-Quadruplexes Generates Long-Lived Guanine Radical Cations[END_REF][START_REF] Banyasz | Radicals generated in tetramolecular guanine quadruplexes by photoionization: spectral and dynamical features[END_REF] The quantum yield for 8-oxodG formation φ ox was found to be 3.2×10 -4 for TEL21/Na + and lower than 10 -5 for (TG4T) 4 /Na + . For the former system, in which part of the (G + )  population survives on the millisecond time-scale, φ ox represents 7% of the photo-ionization quantum yield ϕ 1 .

Deprotonation is much faster in (TG4T) 4 /Na + , being completed within 20 µs, thus rendering the reaction path leading to 8-oxodG less probable (φ ox /φ 1 < 0.003).

As we mentioned above, we found that the largest part of the initially generated (G + )  population in the examined systems undergoes deprotonation. Therefore, we expect the major oxidative damage to arise from deprotonated radicals. As neither the radical concentration nor the decay patterns are affected by the buffer concentration (Figure S4a), we conclude that their reactions do not involve buffer ingredients. Furthermore, no significant difference was found between the transient signals recorded for aerated and argon saturated solutions (Figure S4b). The latter observation rules out formation of imidazolone and oxazolone, known to be formed from (G-H1)  radicals exclusively in the presence of oxygen. In contrast, the formation of oxidized bases and strand breaks are not affected by oxygen. [START_REF] Melvin | Induction of strand breaks in single-stranded polyribonucleotides and DNA by photoionization: One electron oxidized nucleobase radicals as precursors[END_REF][START_REF] Ravanat | Direct and indirect effects of UV radiation on DNA and its components[END_REF] In the case of plasmid DNA, the yield of oxidized bases was found to be 20-fold higher than strand breaks. [START_REF] Melvin | Induction of strand breaks in single-stranded polyribonucleotides and DNA by photoionization: One electron oxidized nucleobase radicals as precursors[END_REF] Interestingly, strand breaks were detected in plasmid DNA following direct absorption of low-energy radiation, [START_REF] Teychene | Formulation induces direct DNA UVA photooxidation. Part I. Role of the formulating cationic surfactant[END_REF] but quantum yields were not determined.

Our studies, performed without external additives, show that deprotonated radicals react mostly on the millisecond time-scale in an "intrinsic" way. This means that G radicals disappear reacting with other parts of the nucleic acids and/or water molecules. Evidently, the reaction path may be altered by the presence of other chemical species in their vicinity, as happens in cells.

The outcome will depend on the relative reaction rates of "extrinsic" and "intrinsic" paths, the final lesions being controlled by the faster process. The same reasoning is valid for the photoejected electrons which, in our experimental conditions appear to interact with genomic DNA, but may be scavenged by other chemical species present in biological conditions.

Conclusions and Outlook

The studies presented in this Account have challenged two widely accepted ideas regarding DNA damage and lead to important questions.

Firstly, we showed that direct absorption of low-energy UV radiation by DNA does generate guanine radicals. In the case of genomic DNA, the quantum yield of this process at 266 nm (2.0×10 -3 ) is similar to the sum of the quantum yields of all types of dimeric pyrimidine photoproducts, both cyclobutane dimers and (6-4) adducts, following 254 nm irradiation (1.3×10 -3 ). [START_REF] Douki | Effect of denaturation on the photochemistry of pyrimidine bases in isolated DNA[END_REF] The generation of guanine radicals via direct photo-oxidation, occurring without the mediation of photosensitizers, has important repercussion on preventive measures: administration of antioxidants to protect DNA damage from low-energy UVB and UVA radiation, although proved efficient for indirect damage, cannot be operative for direct UVinduced radical generation.

Secondly, we demonstrated that 8-oxodG, a widely used oxidation marker, is not representative of the extent of oxidative damage when this is triggered by generation of radical cations. In this case, the major oxidative lesions should stem from deprotonated radicals and be context dependent, because of the long lifetime of these species. Photo-ionization quantum yields provide an estimation for the expected total amount of oxidative lesions. In association with analytical methods, they could contribute to quantify the various types of final reaction products and, possibly, lead to characterization of new ones. For example, the lesions resulting from (G-H2)  radicals, detected in all G4 structures, remain to be identified.

To explain photo-ionization by low-energy UV photons, we proposed a complex path, encompassing recent knowledge of the electronic excited states in DNA. This hypothesis is supported by a series of observations associating photo-ionization with DNA secondary structure. It also explains the detection of 8-oxodG and strand breaks after UVB and UVA irradiation of DNA. A non-vertical mechanism is also suggested by electron detachment studies on DNA polyanions in the gas phase. [START_REF] Daly | Electronic spectroscopy of isolated DNA polyanions[END_REF] However, more effort is needed for its validation, fully characterizing the various steps that lead to electron photo-detachment and assessing the electronic, geometrical and dynamical factors that enter in play. We hope that this Account will motivate theoretical studies which will explore this phenomenon in detail and provide a comprehensive picture.

An important question concerns the sites on which oxidative lesions are formed. This issue was tackled by a photo-sensitization study on telomeric G4. [START_REF] Fleming | G-Quadruplex Folds of the Human Telomere Sequence Alter the Site Reactivity and Reaction Pathway of Guanine Oxidation Compared to Duplex DNA[END_REF] It would be interesting to explore whether the reactive sites created by external oxidants are similar to those generated through direct UV-induced oxidation.

Finally, beyond the biological issues discussed above, the larger propensity of G4 to undergo low-energy photo-ionization, compared to duplex DNA, deserves attention. G4 structures appear appealing for applications in the field of nanotechnology. [START_REF] Mergny | DNA Quadruple Helices in Nanotechnology[END_REF] Their behavior as molecular wires, connected to external electric circuits, was reported. [START_REF] Livshits | Long-range charge transport in single G-quadruplex DNA molecules[END_REF][START_REF] Sha | Charge splitters and charge transport junctions based on guanine quadruplexes[END_REF] But so far, their properties as photoconductors have been not explored. In this respect, our results could have an impact on the design of optoelectronic devices inspired by four-stranded scaffolds, potentially containing other functional groups.

ASSOCIATED CONTENT

Supporting Information: Experimental Details; Saturation Effect; Additional Figures. interchromophore interactions. During the past two decades she focused her efforts on the study of UV-induced processes in DNA, from photon absorption to excited state relaxation and reaction dynamics.

Figure 1 .

 1 Figure 1. CT-DNA (blue) in phosphate buffer (0.015 mol•L -1 NaH 2 PO 4 / 0.015 mol•L -1 Na 2 HPO 4 ). (a) Steady-state absorption spectrum; the vertical violet line indicates the excitation wavelength at 266 nm. (b) Transient absorption spectrum recorded at 30 ns with incident excitation intensity of 2.0×10 6 W•cm -2 .(c) Normalized transient absorption decay at 700 nm; it is compared with the corresponding signal obtained under the same conditions for a short duplex (cyan; S1S2,[START_REF] Balanikas | Populations and Dynamics of Guanine Radicals in DNA strands: Direct versus Indirect Generation[END_REF] Table 1). (d) Ionization curve; [h] and [e hyd

-] 0

 0 denote, respectively, the concentration of absorbed photons per laser pulse and the initial concentration of hydrated electrons; the red line is the fit with a linear model function. (b-d): argon saturated solutions.

  the e hyd -decay is fitted with a model function A 1 +A 0 exp(-t/  ); subsequently, [e hyd -] 0 is obtained from the A 0 value using the corresponding molar absorption coefficient. The fit of the experimental points in Figure 1d with a linear function [e hyd -] 0 /[hν] = φ 1 + α[hν] provides the quantum yield for one-photon ionization φ 1 , while the contribution of two-photon ionization α[hν] is given by the slope of the curve.

2 ( 3 .

 23 7± 0.2)

Figure 2 .

 2 Figure 2.Reference monomeric G radicals. Absorption spectra of monomeric radical cation (G + )  (red),[START_REF] Candeias | Stucture and acid-base properties of one-electronoxidized deoxyguanosine, guanosine, and 1-methylguanosine[END_REF] and deprotonated (G-H1)  radical (blue)[START_REF] Candeias | Stucture and acid-base properties of one-electronoxidized deoxyguanosine, guanosine, and 1-methylguanosine[END_REF] and (G-H2)  radicals (green),[START_REF] Chatgilialoglu | Tautomerism in the guanyl radical[END_REF] resulting, respectively, from loss of the protons at position 1 or 2 (Conspectus Figure); the black square indicates the spectral region where the  values of all three radicals are similar (< 100 mol -1 •L•cm -1 ).[START_REF] Balanikas | Guanine Radicals Generated in Telomeric G-quadruplexes by Direct Absorption of Low-Energy UV Photons: Effect of Potassium Ions[END_REF] (b) Transient absorption spectrum obtained for (TG 4 T) 4 /Na + in pH 3 at 2.5 µs (circles); A is divided by [e hyd

Figure 3 .

 3 Figure 3. Survival probability of the total G radical population in CT-DNA (a and b) and OXY/K + (c and d). Experimental decays (green) recorded at 500 nm (a and b) and 512 nm (c and d) are fitted with multiexponential functions (red). The vertical yellow lines indicate  1/2 .

Figure 4 .

 4 Figure 4. Guanine radicals in CT-DNA. (a) Transient absorption spectrum determined for aerated solutions at 50 µs (red circles); A was divided by [R] t . The blue line corresponds to the deprotonated radical of dGMP attributed to (G-H1) • , represented with  values. 12 (b and c) Transient absorption signals recorded for N 2 O saturated solutions at 700 nm; yellow lines are derived from fits with monoexponential rise/decay; incident excitation intensity: 2.0×10 6 W·cm -2 .

Table 1 )

 1 . (d) Ionization curve; [h] and [e hyd

Funding Sources

The authors thank the European Programme H2020 MSCA ITN [grant No. 765266 -LightDyNAmics project] and the French National Research Agency (N° ANR-12-BS08-0001-01, OPHID project).

AUTHOR INFORMATION

Corresponding Author E-mail: Dimitra.markovitsi@cea.fr ORCID : 0000-0002-2726-305X

Biographies


Duc Tan Vu

Ngac Ky Nguyen

Eric Semail

Thi Thanh

Current Harmonic Eliminations for Seven-phase Non-sinusoidal PMSM Drives applying Artificial Neurons

Keywords: Multiphase machine, seven-phase PMSM, non-sinusoidal back-EMF, current harmonics, ADALINE, artificial intelligence

This study is to deal with unwanted current harmonics in rotating (dq) frames of a 7-phase non-sinusoidal permanent magnet synchronous machine (PMSM) in a wye-connected winding topology. The machine is supplied by a 7leg voltage source inverter (VSI) fed by a DC-bus voltage. In control, current responses are expected to properly track their references. However, several unwanted harmonics of the non-sinusoidal back electromotive force (back-EMF) and the inverter nonlinearity generate unwanted harmonic components in d-q currents. These current harmonics cannot be nullified by controllers such as conventional proportional-integral (PI) controllers. Consequently, the current responses cannot track their references. In this study, a combination of conventional PI controllers and simple adaptive linear neurons (ADALINEs) is proposed to eliminate these current harmonics, improving current control quality of the drive. The effectiveness of the proposed control structure is verified by experimental results.

Introduction

Electric multiphase drives have become more interesting due to their advantages over the conventional three-phase drives such as higher reliability and lower power per phase rating [START_REF] Barrero | Recent Advances in the Design, Modeling, and Control of Multiphase Machines Part I[END_REF]. In an electric drive, machine design and inverter nonlinearity can affect current control quality [START_REF] Hwang | The Current Harmonics Elimination Control Strategy for Six-Leg Three-Phase Permanent Magnet Synchronous Motor Drives[END_REF][START_REF] Vu | Control strategies for nonsinusoidal multiphase PMSM drives in faulty modes under constraints on copper losses and peak phase voltage[END_REF]. Owing to the multi-reference frame theory [START_REF] Semail | Right harmonic spectrum for the backelectromotive force of an n-phase synchronous motor[END_REF], only one harmonic of back-EMF should be associated with each d-q frame. As a result, all currents and back-EMFs in d-q frames are constant, creating constant torques. It means that there are no current harmonics in d-q frames. In general, a n-phase machine should contain only (n-1)/2 harmonics in its back-EMF. For example, a 7-phase machine has three d-q and one zero-sequence frames. Therefore, three is the maximum number of harmonics that should exist in the back-EMF to create constant torques with constant d-q currents. Nevertheless, because of machine design, more than one back-EMF harmonic can be associated with each d-q frame. These unwanted back-EMF harmonics cause not only current harmonics in d-q frames but also torque ripples. In addition, extra current harmonics in d-q frames are generated by the inverter nonlinearity with dead-time voltages. These dead-time voltages are analyzed in [START_REF] Grandi | Analysis of dead-time effects in multi-phase voltage source inverters[END_REF] for inverters with different numbers of legs. To eliminate current harmonics, study [START_REF] Liu | Selective Current Harmonic Suppression for High-Speed PMSM Based on High-Precision Harmonic Detection Method[END_REF] uses low-pass filters (LPFs) to obtain harmonics from winding currents. However, the computation is complicated. Hence, study [START_REF] Wang | Current Harmonics Suppression Strategy for PMSM with Non-Sinusoidal Back-EMF Based on Adaptive Linear Neuron Method[END_REF] applies simple ADALINEs to compensate the unwanted back-EMFs and the dead-time voltages for 3-phase machines. For multiphase machines, there have been some studies [START_REF] Li | An Improved Model Predictive Direct Torque Control Strategy for Reducing Harmonic Currents and Torque Ripples of Five-Phase Permanent Magnet Synchronous Motors[END_REF][START_REF] Karttunen | Current Harmonic Compensation in Dual Three-Phase PMSMs Using a Disturbance Observer[END_REF] applying either an improved model predictive control strategy or an inverse model-based disturbance observer to reduce the voltage and current harmonics for 5-phase or dual 3-phase machines. However, existing high-frequency components in [START_REF] Li | An Improved Model Predictive Direct Torque Control Strategy for Reducing Harmonic Currents and Torque Ripples of Five-Phase Permanent Magnet Synchronous Motors[END_REF] and calculating complications in [START_REF] Karttunen | Current Harmonic Compensation in Dual Three-Phase PMSMs Using a Disturbance Observer[END_REF] are several drawbacks.

In this study, ADALINEs, with self-learning ability, fast convergence and simplicity as discussed in [START_REF] Wang | Current Harmonics Suppression Strategy for PMSM with Non-Sinusoidal Back-EMF Based on Adaptive Linear Neuron Method[END_REF][START_REF] Sediki | ADALINE approach for induction motor mechanical parameters identification[END_REF][START_REF] Nguyen | Adaline Neural Networks-based sensorless control of five-phase PMSM drives[END_REF], are added to conventional PI controllers for current harmonic eliminations in d-q frames of a 7-phase non-sinusoidal PMSM drive. Current control improvements are verified with experimental results under the presence of the unwanted harmonics of back-EMF and dead-time voltages from the inverter nonlinearity.

This paper is organized as follows. The modeling of a 7-phase drive is presented in section 2. Origins of current harmonics are analyzed in section 3. Solutions are discussed in section 4. A verification with experimental results is presented in section 5.

2

Modeling of a seven-phase PMSM Fig. 1. Schematic diagram of a seven-phase drive in a wye-connected winding topology.

A seven-phase drive with a 7-leg VSI fed by a DC-bus voltage VDC is shown in Fig. 1. Several assumptions of a 7-phase PMSM in the considered drive are described as follows: the 1 st , 3 rd , and 9 th harmonics of its back-EMF account for highest proportions; unwanted harmonics such as 11 th , 13 th , and 19 th have small but unneglected proportions in the back-EMF; 7 phase windings of the machine are equally shifted and wye-connected. The 7-dimensional phase voltage vector v of the machine can be expressed in (1).

 

s di v = R i + + e dt L ( 1
)
where i and e are the 7-dimensional vectors of phase currents and back-EMFs, respectively; Rs is the resistance of one phase of stator; [L] is a 7 by 7 stator inductance matrix.

V DC + - A B C D E F G VSI
To control the machine drive using the field-oriented control (FOC), Clarke and Park matrices are applied to convert the machine parameters from natural frame into d-q frames. For example, the transformation for currents is presented in [START_REF] Hwang | The Current Harmonics Elimination Control Strategy for Six-Leg Three-Phase Permanent Magnet Synchronous Motor Drives[END_REF].

      1 1 9 9 3 3 T T d q d q d q z A B C D E F G i i i i i i i i i i i i i i = PC (2)   ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
                                    = C 1 2 1 2 1 2 1 2 1 2 1 2         ;   cos( ) sin( ) 0 0 0 0 0 sin( ) cos( ) 0 0 0 0 0 0 0 cos(9 ) sin(9 ) 0 0 0 0 0 sin(9 ) cos(9 ) 0 0 0 0 0 0 0 cos(3 ) sin(3 ) 0 0 0 0 0 sin(3 ) cos(3 ) 0 0 0 0 0 0 0 1         -     =   -     -     P
where [C] is the Clarke matrix; δ is the spatial phase shift angle 2π/7; [P] is the Park matrix associated with the 1 st , 9 th , and 3 rd harmonics due to the assumptions of the considered back-EMF; θ is the electrical position of the machine. In d-q frames, the 7-phase machine is decomposed into three fictitious 2-phase machines (FM1, FM2, FM3) with decoupled frames (d1-q1), (d9-q9), and (d3-q3), respectively, and one zero-sequence machine (ZM) with reference frame z [START_REF] Semail | Right harmonic spectrum for the backelectromotive force of an n-phase synchronous motor[END_REF]. Due to wyeconnected stator windings, impacts of the zero-sequence component on current control and torque performances are eliminated. A fictitious machine with its corresponding dq frame is associated with a group of harmonics as presented in Table 1.

Table 1. Fictitious machines and associated harmonics of a 7-phase machine (odd harmonics).

Fictitious machine

Frame Associated harmonic ( 3

Current harmonic analyses

According to the multi-reference frame theory [START_REF] Semail | Right harmonic spectrum for the backelectromotive force of an n-phase synchronous motor[END_REF], the back-EMF of a 7-phase machine should have only 3 harmonics (1 st , 9 th , and 3 rd , for example) associated with 3 d-q frames. However, in Table 1, two harmonics (1 st , 13 th ) are associated with (d1-q1) while two harmonics (9 th , 19 th ) harmonics are associated with (d9-q9). Then, two harmonics (3 rd , 11 th ) are associated with (d3-q3). The back-EMF of a phase is described in (3).

(

( )

1
E j E j φ E j + φ e E j + φ E j + φ E j + φ                    -- + -- + + -- +               =           -- + -- + --                 ( 3
)
where ej is the back-EMF of phase j (from 1 to 7, representing phases A to G); (E1, E3, E9, E11, E13, E19) and (φ3, φ9, φ11, φ13, φ19) are the amplitudes and phase shift angles of the harmonic components of the back-EMF. By applying the classical Clarke and Park transformations, back-EMFs in d-q frames can be expressed as follows:

(

( )

1
d q d q d q eEφ e E E φ eEφ e E E φ eEφ e E E φ        =+   = + +   =+    = + +    =+   = + +   (4)
All d-q back-EMFs in (4) are not constant because of the existing unwanted back-EMF harmonics. The back-EMFs have frequencies 14θ in (d1-q1), 28θ in (d9-q9), and 14θ in (d3-q3). Especially, these back-EMF harmonics generate corresponding current harmonics in d-q frames. The current harmonic amplitudes in d-q frames depend on the harmonic distribution in the back-EMFs, and especially on the rotating speed.

The 7-leg VSI supplying the 7-phase machine creates extra current harmonics in dq frames due to its nonlinearity. Indeed, the dead time, a time interval in which both switches of one inverter leg are off, mainly causes the VSI nonlinearity. According to [START_REF] Grandi | Analysis of dead-time effects in multi-phase voltage source inverters[END_REF], the dead-time voltage in a phase of the VSI can be generally expressed in [START_REF] Grandi | Analysis of dead-time effects in multi-phase voltage source inverters[END_REF]. where vj_dead is the dead-time voltage of phase j; Vdead is a constant voltage; Tdead is the dead time; TPWM is the switching period of the inverter; VDC is the DC-bus voltage. The harmonic amplitudes are inversely proportional to their orders so the considered harmonics can be up to 19θ. The dead-time voltages in d-q frames are presented in [START_REF] Liu | Selective Current Harmonic Suppression for High-Speed PMSM Based on High-Precision Harmonic Detection Method[END_REF].

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2
j j j v V j j j jj                     -- + -- + -- +                 = - -- + -- + -- +                 -- + --       ( ) 12 sin 19 ( 1) 19 7 j                  + --           (5)
( )   ( ) ( )    ( )   ( )  ( ) ( ) ( )  ( ) ( )   ( )   ( ) ( ) 1
d               ++   (6)
In [START_REF] Liu | Selective Current Harmonic Suppression for High-Speed PMSM Based on High-Precision Harmonic Detection Method[END_REF], the dead-time voltages in (d1-q1) and (d3-q3) frames have a frequency of 14θ while the voltages in (d9-q9) have two frequencies of 14θ and 28θ. Therefore, current harmonics in d-q frames are also caused by the inverter nonlinearity with the dead-time voltages. The amplitudes of these current harmonics do not depend on the rotating speed but Vdead. Voltage Vdead is related to Tdead, TPWM, and VDC as described in [START_REF] Grandi | Analysis of dead-time effects in multi-phase voltage source inverters[END_REF].

Finally, unwanted current harmonics in d-q frames caused by the unwanted back-EMF harmonics in (4) and the dead-time voltages in [START_REF] Liu | Selective Current Harmonic Suppression for High-Speed PMSM Based on High-Precision Harmonic Detection Method[END_REF] are summarized in Table 2.

Table 2. Current harmonics in d-q frames caused by the unwanted back-EMF harmonics and the inverter nonlinearity with dead-time voltages in a 7-phase PMSM drive.

Frame Current harmonics caused by unwanted back-EMF harmonics

Current harmonics caused by dead-time voltages

d1-q1 14θ 14θ d9-q9 28θ 14θ, 28θ d3-q3 14θ 14θ 4
Eliminations of current harmonics with ADALINEs Fig. 2. The proposed control structure for current ix with the ADALINE compensation.

As described in Table 2, current harmonics in d-q frames have frequencies of 14θ and 28θ. Due to the complexity of the experimental drive, these values need to be automatically learned in real time to correctly eliminate these current harmonics. A current control structure is proposed in Fig. 2 in which current ix (can be id1, iq1, id9, iq9, id3, or iq3) is controlled by a PI controller with an adaptive compensating voltage (𝑣 𝑥_𝑐𝑜𝑚 ). A fictitious machine is represented by a transfer function with inductance Lx, resistance Rs and Laplace operator s. By using 𝑣 𝑥_𝑐𝑜𝑚 , all current harmonics in d-q frames described in Table 2 can be eliminated. Voltage 𝑣 𝑥_𝑐𝑜𝑚 for current ix is generated by an ADALINE, hence, there are 6 ADALINEs for 6 d-q currents (id1, iq1, id9, iq9, id3, or iq3) in the considered 7-phase drive. The general structure of an ADALINE in Fig. 2 is based on current harmonics in Table 2. The ADALINE output (𝑣 𝑥_𝑐𝑜𝑚 ) is generally calculated from ADALINE inputs with harmonics 14θ and 28θ, as described in [START_REF] Wang | Current Harmonics Suppression Strategy for PMSM with Non-Sinusoidal Back-EMF Based on Adaptive Linear Neuron Method[END_REF].

_ cos( 14) sin( 14) cos( 28) sin( 28)

x com 1_x 2_x 3_x 4_x v w w w w         = + + +     ( 7
)
where harmonic weights w1_x and w2_x are associated with harmonic 14θ; w3_x and w4_x are used for harmonic 28θ. In Fig. 2, weights of a harmonic are updated by Least Mean Square rule with learning rate η, current error ierror, and the corresponding harmonic. An increase in η can shorten the learning time but η should be between 0 and 1 to guarantee the weight convergence and the stability of the drive. According to Table 2, if x is d1, q1, d3 or q3, the ADALINE structure only has two weights for harmonic 14θ.



Updating laws 1_x cos( 14) sin( 14) cos( 28) sin( 28)

error error error error         = + = + = + = + 1_x 1_x 2_x 2_x 3_x 3_x 4_x 4_x w w i w w i w w i w w i -+ -+ Transfer function PI w 2_x w 3_x w 4_x + + +
Meanwhile, if x is d9 or q9, the ADALINE uses four weights for both harmonics 14θ and 28θ. Therefore, the number of weights is optimized to avoid the calculation burden.

Experimental results

The proposed control structure in Fig. 2 is verified by an experimental drive as described in Fig. 3a and Table 3. The experimental 7-phase PMSM is mechanically connected to a load drive that is an industrial three-phase synchronous machine. The load drive is controlled to tune the rotating speed of the 7-phase PMSM. A 7-leg VSI with insulated gate bipolar transistors (IGBTs) supplies the 7-phase PMSM. Its switching frequency is set to 10 kHz. A dSPACE 1005 board with I/O interface is used to transfer PWM signals to the IGBT driver of the inverter and collect the measured data of speed and currents. The experimental 7-phase PMSM is introduced in [START_REF] Locment | Design and study of a multiphase axial-flux machine[END_REF]. This machine has an axial flux with double rotors. When the two rotors have different numbers of poles and spatially shifted an angle of 7 degrees, the back-EMF waveform and its specific harmonics are presented in Fig. 3b. Proportions of the back-EMF harmonics over the 1 st harmonic are 32.3% for the 3 rd , 12.5% for the 9 th , 10.3% for the 11 th , 5.02% for the 13 th , 1.98% for the 19 th . The current harmonics in d-q frames of the considered experimental drive have been discussed in [START_REF] Vu | Control strategies for nonsinusoidal multiphase PMSM drives in faulty modes under constraints on copper losses and peak phase voltage[END_REF]. In this study, current harmonic eliminations of the proposed control structure with ADALINE compensation are shown in Fig. 4. Current control quality is significantly improved, especially in (d9-q9) and (d3-q3) frames.

Conclusion

This paper has introduced an option to improve control quality of a non-sinusoidal multiphase machine drive. Simple adaptive linear neurons combined with PI controllers have eliminated most current harmonics in d-q frames caused by the unwanted back-EMF harmonics and the inverter nonlinearity. Dynamic performances have been validated with sudden variations in the rotating speed or current references. The proposed control structure can be further applied to an industrial drive thanks to its adaptivity and easy implementation.

Fig. 3 .

 3 Fig. 3. The experimental drive (a), the speed-normalized back-EMF and its harmonic spectrum of the experimental 7-phase PMSM (b).

Fig. 4 .Fig. 5 .Fig. 6 .

 456 Fig. 4. (Experimental result) Currents in (d1-q1) frame (a), currents in (d9-q9) frame (b), currents in (d3-q3) frame (c) without (No. comp.) and with the ADALINE compensation at 20 rad/s.

Fig. 7 .Fig. 8 .

 78 Fig. 7. (Experimental result) Phase-A current without (iA_no_com) and with (iA_com) the ADALINE compensation (a), harmonic spectrums of iA_no_com (b) and iA_com (c) at 20 rad/s.Variations of the rotating speed (from 20 to 10 and 30 rad/s) in Fig.8aand changes in current references in Fig.8bhave modest effects on current control quality in (d9-q9) frame. The current control performance in (d1-q1) and (d3-q3) frames is similar. The performance validates the dynamic responses of the proposed control structure.

Table 3 .

 3 Electrical parameters of the experimental 7-phase PMSM drive.

	Parameter	Unit	Value
	Stator resistance Rs	Ω	1.4
	Self-inductance L	mH	14.7
	Inductance Ld1= Lq1	mH	30.5
	Inductance Ld9= Lq9	mH	7.1
	Inductance Ld3= Lq3

Acknowledgment

We would like to thank Thai Nguyen University of Technology, Thai Nguyen city, Vietnam, and the CE2I project of European Union for the financial support.