Z Elekes

Á Kripkó

D Sohler

K Sieja

K Ogata

K Yoshida

P Doornenbal

A Obertelli

G Authelet

H Baba

D Calvet

F Château

A Corsi

A Delbart

J.-M Gheller

A Gillibert

T Isobe

V Lapoux

M Matsushita

S Momiyama

T Motobayashi

H Otsu

C Péron

A Peyaud

E C Pollacco

J.-Y Roussé

H Sakurai

C Santamaria

Y Shiga

S Takeuchi

R Taniuchi

T Uesaka

H Wang

K Yoneda

F Browne

L X Chung

Zs Dombrádi

F Flavigny

S Franchoo

F Giacoppo

A Gottardo

K Hadyńska-Klęk

Z Korkulu

S Koyama

Y Kubota

J Lee

M Lettmann

C Louchart

R Lozeva

K Matsui

T Miyazaki

M Niikura

S Nishimura

L Olivier

S Ota

Z Patel

E Sahin

C Shand

P.-A Söderström

I Stefan

D Steppenbeck

T Sumikama

D Suzuki

Zs Vajta

V Werner

J Wu

Z Xu

Nuclear structure of 76 Ni by (p,2p) reaction

The nuclear structure of the 76 Ni nucleus was investigated by (p,2p) reaction using a NaI(Tl) array to detect the deexciting prompt γ rays. A new transition with an energy of 2227 keV was identified by γγ and γγγ coincidences. According to these coincidence spectra the observed transition connects a new state at 4147 keV and the previously known 4 + 1 state at 1920 keV. Two weaker transitions were also obtained at 2441 keV and 2838 keV, which could be tentatively placed to feed the known 2 + 1 state at 990 keV. Our shell model calculations using the LNPS interaction produced good candidates for the experimental proton hole states in the observed energy region, and the theoretical cross sections showed good agreement with the experimental values. Although we could not assign all the experimental states to the theoretical ones unambiguously, the results are consistent with a reasonably large Z=28 shell gap for nickel isotopes in accordance with previous studies.

I. INTRODUCTION

Since the discovery of magic neutron and proton numbers in stable nuclei and the seminal works by Maria Göppert-Mayer on the interpretation of this structural property by the nuclear shell model [1,2], scientists were interested in whether the location of single particle states and the magic numbers change away from stability. In the past thirty years, by the widespread use of beams of ions with nuclei of exotic neutron-to-proton ratios it has become evident that the magic numbers among extremely neutron rich and proton rich isotopes may in-deed differ from those close to the stability. Extraordinary experimental effort was devoted to uncover this phenomenon especially for the neutron number (N) 20 (see e.g., [3][4][5][6][7]). For larger neutron numbers the magicity of N=28 was also proved to be soft for example in the 42 Si nucleus [8,9]. Regarding the protons, there are accumulating pieces of evidence for a new magic number at 6 in addition to 8 for neutron rich carbon isotopes [10]. On the proton rich side of the nuclear chart there were indications for a new magic number at 16 instead of 20 in 28 S nucleus [11], as well.

For these structural changes, mainly the Tokyo theo-retical group developed an explanation that is connected to the monopole part of the neutron-proton interaction (see, e.g., [12,13]). This concept was applied for the larger magic numbers, especially for neutron number 50 and proton number (Z) 28 (see, e.g., [14][15][16][17]), which inspired many spectroscopic experiments when this region became available by the radioactive ion beam facilities (see e.g., [18][19][20][21][22][23][24]) to approach the possibly doubly-magic nucleus 78 Ni.

Just two neutrons away from 78 Ni, the even-even nucleus 76 Ni is an ideal candidate to investigate the shell evolution. Especially the Z=28 shell gap can be surveyed by proton knock-out reactions, therefore we carried out a γ spectroscopy experiment via the 77 Cu(p,2p) 76 Ni reaction to explore proton hole states in 76 Ni and to investigate the proton shell gap 28. The yrast band of 76 Ni up to the 8 + level is relatively well-known from previous studies [18]. In addition to this yrast band, another γ ray was detected in the β decay of the assumed ground state of 76 Co [25], tentatively placed to feed the 2 + 1 state. Beyond this we step into terra incognita regarding the low-energy level structure of 76 Ni.

II. EXPERIMENT

The experiment was carried out at the Radioactive Isotope Beam Factory (RIBF) maintained by the RIKEN Nishina Center and the Center for Nuclear Study of the University of Tokyo. As a first step to get the radioactive beam, 238 U ions were produced by an Electron Cyclotron Resonance Ion Source and were fed into the linear accelerator RILAC of RIBF. The ions were then further accelerated by the four coupled cyclotrons of RIBF, RRC, fRC, IRC and SRC ending up with a beam energy of 345 MeV/nucleon and a beam intensity of 12 pnA. The 238 U beam was transported to a 9 Be primary target with a thickness of 3 mm placed at the entrance of the Bi-gRIPS separator [26] in order to induce in-flight fission. From the produced radioactive isotopes of many different kinds, the constituents of the secondary beam were selected by the Bρ-∆E -Bρ method (Bρ: magnetic rigidity, ∆E: energy loss) using slits and an aluminum wedged degrader at the first focal plane F1, located between the two dipole magnets D1 and D2 of BigRIPS. The different radioactive ions of the resulting cocktail beam were then tagged between focal planes F3 and F7 by time-of-flight (TOF ), energy loss and magnetic rigidity measurements. TOF was determined by plastic scintillators at F3 and F7 providing a time resolution of about 40 ps [27], while ∆E was yielded by a tilted electrode gas ionization chamber at F7 [28]. The trajectory of the particles was monitored by several sets of parallel plate avalanche counters (PPAC) at F3, F5 and F7 [29,30].

The 76 Ni isotopes to be studied were produced through nucleon removal reactions by using the MINOS device [31], which consisted of a liquid hydrogen target surrounded by a cylindrical time-projection chamber (TPC).

The liquid hydrogen with a temperature of 20 K was placed inside a polyethylene terephthalate cell, which had an entrance window diameter and thickness of 38 mm and 110 µm, respectively. The ions left the target through an exit window of 52 mm diameter and 150 µm thickness. The effective target length was measured to be 102(1) mm. The length, the inner diameter and the outer diameter of the TPC were 300 mm, 80 mm and 178.8 mm, respectively. The TPC chamber was filled with a gas mixture of argon, CF 4 and isobutane at room temperature and atmospheric pressure. The vertex position was reconstructed either by using the scattered and the removed protons or one of the protons and the projected trajectory of the radioactive ions (the former method was preferred when both data were available). An overall efficiency of 95% and a resolution of 5 mm (FWHM) along the beam axis was achieved for the events when at least one proton was recorded by the TPC.

For the detection of prompt γ rays 186 NaI(Tl) crystals of DALI2 [9] were built around the MINOS device. The arrangement of the scintillators was optimized for total photopeak efficiency and resolution. Therefore, they were packed in 10 cylindrical layers with 10-14 units, while in the forward direction a wall of 64 detectors served to observe the γ rays. The beginning of the liquid hydrogen target was just 8 mm upstream of the edge of the first layer of the DALI2 array. The beam-like heavy ions leaving the target were identified by the ZeroDegree spectrometer [26] operated in large acceptance mode using the same principles applied at BigRIPS [27]. The elements of the ZeroDegree spectrometer were similar to the BigRIPS separator while its length was 36.5 m and included four focal planes (F8, F9, F10, F11) where the beamline detectors were placed to measure the properties of the ions. The TOF was taken between F8 and F11 by plastic scintillators and the ∆E was measured by an ionization chamber at F11. PPACs were applied at F8, F9 and F11 to provide information of the trajectory of the ions. In total 5.5×10 3 particles hit the liquid hydrogen target every second while the intensity of 77 Cu ions was only 10 pps. In Figure 1 the particle identification plot of the incoming ions can be seen incoincidence with outgoing 76 Ni ions tagged by the ZeroDegree spectrometer. This shows that the 76 Ni ions mainly originated from nucleon removal reactions on 81 Ga, 79 Zn, 80 Zn, 77 Cu, 78 Cu, 79 Cu nuclei, and many unreacted nuclei passed through the target. Figure 2 is also a particle identification plot but with an additional coincidence on protons detected by the MINOS device. The 77 Cu(p,2p) 76 Ni reaction amounted to about 7% of the 76 Ni producing events and occurred at a mean energy of 229 MeV/nucleon.

III. RESULTS AND DISCUSSION

The energy calibration of the DALI2 detectors was done several times during the collection of the data by 60 Co, 137 Cs and 88 Y radioactive sources. The Doppler correction was performed by using the vertex information from the MINOS TPC. In order to extract this position information, a tracking algorithm [32] was applied, and the change in the drift velocity during the time of the experiment was also taken into account. The efficiency of the DALI2 array was increased by the add back method, which reconstructs the total energy of the γ rays hitting the neighboring NaI(Tl) units, putting the events of Compton scattering and pair production to the photopeak in the γ ray spectrum. Figure 3 demonstrates the results for 76 Ni. The upper panel shows the singles spectrum. The experimental data are represented by dots with error bars and shaded area. The known transitions with energies of 930 keV and 990 keV [25] appear in the spectrum as an unre-solved peak. However, a small peak around 2.8 MeV is also present as well as a peak-like structure around 2.0-2.5 MeV not observed previously. In order to investigate the origin of the new peaks, γγ and γγγ matrices were generated. The middle panel shows a one dimensional projection of the γγ coincidences with an energy cut that corresponds to the peak of 930+990 keV. This clearly shows that the transitions with energies of 930 keV and 990 keV form a cascade, which is expected from previous studies [18,25,33,34]. The spectrum also provides an even more pronounced high energy peak structure at around 2.0-2.5 MeV as well as a peak at 2.8 MeV. From the known energy resolution of the setup we can conclude that there must be at least two γ rays involved in the structure around 2.0-2.5 MeV. A high-energy fit with three peaks provides the energy of the transitions to be 2227 (35) keV, 2441(50) keV and 2838(69) keV. The energy uncertainties are mainly coming from statistics since the uncertainty due to the calibration is just 5 keV. The statistical confidence of the three peaks is 5.5σ, 3.3σ and 2.3σ, respectively. These transitions are in coincidence with either the transition with an energy of 990 keV or with both the 930 keV and the 990 keV ones. The lower panel in Figure 3 clarifies the situation because it shows a one dimensional projection of the γγγ coincidences with two energy cuts on the unresolved 930+990 keV peak. A peak at around 2.3 MeV also appears in this spectrum, which proves that the transition of 2227 keV forms a cascade with the transitions of 930 keV and 990 keV, and this new γ ray most probably feeds the known state at 1920 keV (4 + 1 ). It cannot populate the known state at 2275 keV (6 + 1 ) because we did not observe a γ ray of 355 keV connecting 6 + 1 and 4 + 1 states (see the discussion on the partial half life for the 355 keV photon later). The two other new γ rays (2441 keV, 2838 keV) can be tentatively placed to connect new states at 3431 keV and 3828 keV and the known 2 + 1 state. Probably, they do not populate the 4 + 1 and the 6 + 1 states strongly because we do not observe them in the spectrum of γγγ coincidences. The relative intensities of the detected γ rays were deduced to be 100(12)%, 70(15)%, 62(22)%, 35 (17)% and 20(9)% for 990 keV, 930 keV, 2227 keV, 2441 keV and 2838 keV, respectively.

In order to check whether the experimental spectra can be matched to the expected response of the DALI2 array using such a γ ray cascade (right part of Figure 4), a simulation was performed with the Geant4 code [35]. The resolution of the DALI2 detectors were adjusted in the simulation to equal the values in the experimental spectra taken with the radioactive sources. The simulation results are represented as red lines in the figures. The blue line in Figure 3 is an exponential function added to the simulated response in order to mimic the background (originating from unresolved transitions, particles hitting the detectors and other materials followed by γ emission) present in the experimental spectrum. Magenta color is used to show the experimental background spectrum for the coincidence events produced using energy cuts near the peaks. The inclusive cross section was determined to be 8.4(4) mb, while the exclusive cross sections could be extracted to be 0.65 (33) mb for the 3431 keV state, 0.38 (16) mb for the 3828 keV state and 1.17 (25) mb for the 4147 keV state. Finally, it could be concluded that the exclusive cross section is 6.9 mb for the ground state, 0.57 mb for the first excited state and 0.68 mb for the second excited state. In a simple approach, we can suppose that the observed excited states correspond to the multiplet of 1 + -6 + levels created by elevating a proton from f 7/2 to f 5/2 orbital across the Z=28 shell gap.

In order to see how the observed level and decay scheme compares with theory as well as to shed light on the fate of the shell closure Z=28, large scale shell model calculations were performed in the valence space comprising neutron (f 5/2 p 1/2 g 9/2 d 5/2 ) and proton fp orbitals. The Hamiltonian employed here was the one based on the LNPS interaction [36], which was used recently to study the copper isotopes from 69 Cu to 77 Cu [37][38][39]. Due to the large size of the configuration space, the calculations were truncated to 8p-8h excitations across Z=28 and N=40 gaps, which assured, however, a good convergence of the calculated spectra for 76 Ni. The diagonalization of the Hamiltonian matrices was achieved using the Strasbourg shell model code ANTOINE [40,41]. To get theoretical branching ratios, the E2/M1 reduced transitions rates were obtained using effective charges e p =1.31, e n =0.46 for B(E2)'s and g n l =-0.1, g n s =-2.87, g p l =1.1, g p s =4.19 for the B(M1)'s. The output of the shell model calculations regarding the level and decay scheme can be seen in the left part of Figure 4. The three lowest excited states (2 + 1 , 4 + 1 , 6 + 1 ) are known from previous studies and can be unambiguously connected to the experimental levels. The calculation also provides four states (2 + 2 , 4 + 2 , 5 + 2 , 6 + 2 ) associated with mainly neutron excitations not populated by (p,2p) reaction in the experiment. However, the wave function of the colored (green-4 + 3 , brown-5 + 1 , cyan-6 + 3 ) states shows dominance of proton excitations in Table I (mainly f 7/2 →f 5/2 ) which are generally accessible by our experimental probe. This means that the shell model provides good candidates for our experimental proton hole states in the energy range of 3.5-4.1 MeV. According to the calculations the 6 + 3 state essentially decays to the 6 + 1 state. The 6 + 1 state decays to the 4 + 1 state by emitting a γ ray of 355 keV. Considering the calculated B(E2), the partial half life for the 355 keV photon emission is 1.8 ns, which would imply a smeared but visible peak around 300-350 keV in the experimental spectrum. Also, in this case the 4 + 1 → 2 + 1 and the 2 + 1 → 0 + 1 transitions would include a long lived component, which can be excluded from their lineshape. Therefore, probably none of our experimental states should correspond to the 6 + 3 state. Both of the 5 + 1 and 4 + 3 states decay to the 4 + 1 state. Thus, they are good candidates for the experimental 4147 keV level. However, the calculation suggests significant decay to the 6 + 1 state from the 5 + 1 state and to the 2 + 1 state from the 4 + 3 state, which would results in strong γ rays of and add back procedure (upper panel: singles, middle panel: projection of γγ coincidences, lower panel: projection of γγγ coincidences). The data with error bars and shaded area represent the experimental spectrum, the red line is the simulation plus an exponential background, and the latter function (exponential background) is also plotted separately as a blue line. Magenta color stands for spectra of coincidence events (γγ and γγγ) with cuts on the background close to the peaks.

355 keV and 1872 keV for the first case and a significant γ ray of 3157 keV for the second case. Our simulations show that the upper limits on the number of counts for either the 5 + 1 → 6 + 1 or the 4 + 3 → 2 + 1 transitions would make them at most 20% branches not as significant as in the theoretical calculations.

In order to compare the deduced exclusive cross sections for the proton hole states, we calculated the single particle cross sections for the (p,2p) reaction by integrating the differential cross section of the distorted wave impulse approximation (DWIA) framework given I. Occupation numbers of proton orbits for the lowest three theoretical states (E th ) and for the strongest proton hole states from our shell model calculations in Eq. (3.52) of Ref. [42] over

E th J π Proton orbits (MeV) f 7/2 f 5/2 p 3/
E L 1 , Ω L 1 , Ω L 2
, and divided by 2. The single-particle wave function and the nuclear density were obtained by the Bohr-Mottelson single particle potential [START_REF] Bohr | Nuclear Structure[END_REF]. The optical potentials for the distorted waves in the initial and final channels were constructed by the microscopic folding model [START_REF] Toyokawa | [END_REF] with the Melbourne g-matrix interaction [45] and the calculated nuclear density. The spin-orbit part of each distorting potential was disregarded. As for the pp interaction, the Franey-Love effective interaction [46] was adopted. These theoretical cross sections were combined with the spectroscopic factors of our shell model calculations and averaged over the beam energy covered by our target similar to the experimental exclusive cross sections. The resulting theoretical cross sections for the relevant states are listed in Table II. If we add the cross sections up to the estimated neutron separation energy of 5.4 MeV for 76 Ni [47] taking into account knock-out from f 7/2 and f 5/2 single particle states, we end up with 7.4 mb. This value is very close to our experimental inclusive cross section of 8.4(4) mb. Furthermore, the calculated exclusive cross sections for the 2 + 1 , the 4 + 1 and the 6 + 1 states are consistent with the experimental findings. The theoretical cross sections for the 4 + 3 , the 5 + 1 and the 6 + 3 states are 1.08 mb, 1.02 mb and 0.86 mb, respectively. These values are comparable to our experimental cross sections for the proton hole states (3431 keV, 3828 keV, 4147 keV) indicated in Fig- ure 4. All in all, a good agreement was achieved between the experimental and the theoretical cross sections taking into account the uncertainties. It must be noted, however, that a small value of 0.74 mb was calculated for the ground state while we could give a much higher experimental upper limit. This indicates that some excited states may remained unobserved due to the modest resolution of the DALI2 array.

Although further theoretical efforts are needed to fully understand the experimental data, our results shows consistency with a strong proton shell closure for nickel isotopes since the employed shell model interaction assumes a proton gap of 5.2 MeV, a value compatible with the most recent theoretical and experimental studies in the region [22,48]. ) associated with mainly neutron excitations in the energy region of the observed states not populated in the (p,2p) reaction. The colored (green, brown, cyan) theoretical levels are proton hole states that are good candidates for the experimental states. and 2838 keV. The γγ and γγγ coincidence spectra showed that the first γ ray was in coincidence with both the known 930 keV and 990 keV transitions of the 4 + 1 → 2 + 1 → 0 + 1 cascade. This established a new excited state at 4147 keV. The two other new transitions could be tentatively placed feeding the 2 + 1 state, which implied two possible new states at 3431 keV and 3828 keV. Comparing the experimental results to shell model calculations the experimental state at 4147 keV could be assigned to either the 5 + 1 or the 4 + 3 theoretical proton hole states. Besides, the calculated cross sections agree quite well with the experimental ones, and our results suggest a substantial Z=28 shell closure in the region.

E th J π Spectroscopic

2 χ

 2 fit: simulation+exponential bg. fit: exponential bg.

Figure 3 .

 3 Figure 3. Doppler corrected γ ray spectra of 76 Ni using vertex reconstruction (requiring only a single proton in the TPC) and add back procedure (upper panel: singles, middle panel: projection of γγ coincidences, lower panel: projection of γγγ coincidences). The data with error bars and shaded area represent the experimental spectrum, the red line is the simulation plus an exponential background, and the latter function (exponential background) is also plotted separately as a blue line. Magenta color stands for spectra of coincidence events (γγ and γγγ) with cuts on the background close to the peaks.

81 Zn 79 Zn 80 Cu 77 Cu 78 Cu 79 Ni 76

  Figure 1. Particle identification of the incoming cocktail beam in coincidence with outgoing 76 Ni ions tagged in the ZeroDegree spectrometer.

	Z
	31	Ga
	30
	29
	28
		2.6	2.65	2.7	2.75
					A/Q
	Z
	31	Ga
	30
	29
	28
		2.6	2.65	2.7	2.75
					A/Q

81 Zn 79 Zn 80 Cu 77 Cu 78 Cu 79 Ni 76

Figure 2. Particle identification of the incoming cocktail beam in coincidence with outgoing 76 Ni ions tagged in the ZeroDegree spectrometer and protons detected in the MINOS device.

Table II

 II The low-energy level structure of76 Ni nucleus was investigated by proton knock-out reactions. The γ spectroscopy study in the 77 Cu(p,2p) 76 Ni channel revealed three new transitions with energies of 2227 keV, 2441 keV Figure 4. Partial level and decay scheme of 76 Ni showing the two known, lowest-lying transitions with energies of 930 keV and 990 keV. The newly established proton hole state at 4147 keV (magenta) decaying with a γ ray of 2227 keV to the second excited state (4 + 1 ) is also drawn. The observed two other γ rays are tentatively placed to feed the 2 + 1 state, resulting in excited proton hole states at 3431 keV (red) and 3828 keV (blue). The numbers on the right hand side of the levels indicate the extracted exclusive cross section of the states in the 77 Cu(p,2p) 76 Ni reaction. The experimental data are compared with our shell model calculations. The three lowest excited levels can be unambiguously matched with the experimental states. The calculation provides four states (2 + 2 , 4 + 2 , 5 + 2 , 6 + 2

	3046 3393 3727 4007	2 2 + 4 2 + 5 2 + 6 2 +	2913 3550 3603 4164	52% 45%	54% 42%	73%	22%	6 1 + 4 3 + 5 1 + 6 3 +	2441γ 35(17) 3431 3828 4147	2227γ 62(22)	2838γ 20(9) (4 + ,5 + )	0.65(33) mb 0.38(16) mb 1.17(25) mb
							100%
			2038					4 1 +	1920 2275		(4 + ) (6 + )	≤0.68 mb
							100%		930γ 70(15)
			846					2 1 +	990		(2 + )	≤0.57 mb
							100%		990γ 100(12)
			0					0 1 +	0		0 +	≤6.9 mb
					Shell model				Experiment
									. Theoretical level energies (E th ), spectroscopic fac-
							tors, (p,2p) exclusive cross sections (σ th ) together with exper-
							imental level energies (Eexp) and cross sections (σexp). The
							level energies and the spectroscopic factors originate from our
							shell model calculations while the cross sections were derived
							by combining DWIA cross sections and the spectroscopic fac-
							tors. The uncertainty in the DWIA framework and its input
							is about 20% as discussed in Ref. [42]. Above 4 MeV, only
							those excited states are shown for which the theoretical cross
							section exceeds 0.1 mb. Regarding the experimental data,
							only the first four states could be unambiguously assigned to
							theoretical levels. The experimental 4147 keV state and the
							corresponding experimental (p,2p) cross section is shown to-
							gether with the theoretical 4 + 3 level, however the 4147 keV state may also belong to the theoretical 5 + 1 level.
									IV. SUMMARY

ACKNOWLEDGMENTS

The authors are thankful to the RIBF and BigRIPS teams for the stable operation and high intensity of the uranium primary beam, and production of secondary beams during the experiment. The development of MI-NOS and the core MINOS team have been supported by the European Research Council through the ERC Grant No. MINOS-258567. A. O. was supported by JSPS longterm fellowship L-13520 from September 2013 to June 2014 at the RIKEN Nishina Center. A. O. deeply thanks the ERC and JSPS for their support. C. S. was supported by the IPA program at the RIKEN Nishina Center. A. O. and C. S. are grateful to the RIKEN Nishina Center for its hospitality. This work was supported by JSPS Grantin-Aid for a JSPS Research Fellow (No. 268718). Z. E. was supported by the NKFIH-NN11454 contract and Á. K. by ÚNKP program of the Ministry of Human Capacities. L. X. C. would like to thank MOST for its support through the Physics Development Program Grant No. DTDLCN.25/18. M. L. and V. W. acknowledge the German BMBF with the supporting No. 05P15RDFN1 and No. 05P12RDFN8. D. S. and Zs. D. were partly supported by the GINOP-2.3.3-15-2016-00034 contract.


Melha Benlebna

Laurence Balas

Béatrice Bonafos

Laurence Pessemesse

Gilles Fouret

Claire Vigor

Sylvie Gaillet

Jacques Grober

Florence Bernex

Jean-Francois Landrier

Jean-Franç Landrier

Ondrej Kuda

Thierry Durand

Charles Coudray

François Casas

Christine Feillet-Coudray

Long-term intake of 9-PAHPA or 9-OAHPA modulates favorably the basal metabolism and exerts an insulin sensitizing effect in obesogenic diet-fed mice

Keywords: FAHFA, Basal metabolism, Insulin sensitivity, Liver steatosis, Mitochondria, Oxidative stress mice

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

Introduction

The burden of nutrition-related chronic diseases is rapidly increasing worldwide [START_REF] Ng | Global, regional, and national prevalence of overweight and obesity in children and adults during 1980-2013: a systematic analysis for the Global Burden of Disease Study 2013[END_REF]. It is well known that the excessive energy consumption and the reduction of physical activity are determining factors in the prevalence of these diseases.

An energy-rich diet such as a diet high in fats and sugars, combined with sedentarily, may induce an energy imbalance responsible for weight gain and obesity. Overweight and obesity are the main causes of the development of metabolic disorders such as type 2 diabetes, hepatic steatosis and cardiovascular diseases, which can lead to significant morbidity and mortality [START_REF] Alberti | The metabolic syndrome-a new worldwide definition[END_REF]. Recently, the International Diabetes Federation estimated that 463 million people in 2019 were affected diabetes worldwide, representing approximately 4.2 million deaths and an estimated $760 billion in health care costs [START_REF] Saeedi | Global and regional diabetes prevalence estimates for 2019 and projections for 2030 and 2045: Results from the International Diabetes Federation Diabetes Atlas, 9(th) edition[END_REF]4]. Non-alcoholic fatty liver disease (NAFLD) is an other emerging global health issue which represents a potential risk factor for insulin resistance and type 2 diabetes [5]. Indeed, over 75% of patients with type 2 diabetes are afflicted of NAFLD [START_REF] Angulo | Nonalcoholic fatty liver disease[END_REF].

Recently, Branched Fatty Acid esters of Hydroxy Fatty Acids (FAHFAs), a class of endogenous bioactive lipids in mammals, has emerged as a new opportunity of treatment for diabetes and inflammatory diseases. FAHFAs are present in many foods [START_REF] Yore | Discovery of a class of endogenous mammalian lipids with anti-diabetic and anti-inflammatory effects[END_REF][START_REF] Balas | Branched fatty acyl esters of hydroxyl fatty acids (FAHFAs), appealing beneficial endogenous fat against obesity and type-2 diabetes[END_REF]. As there are naturally many fatty acids (FAs) and many hydroxylated fatty acids (HFAs), multiple possible combinations exist and about 50 families of FAHFAs have been recently identified [START_REF] Yore | Discovery of a class of endogenous mammalian lipids with anti-diabetic and anti-inflammatory effects[END_REF][START_REF] Kuda | Docosahexaenoic acid-derived fatty acid esters of hydroxy fatty acids (FAHFAs) with anti-inflammatory properties[END_REF]. Interestingly, important biological effects of some FAHFAs have been reported. In particular, 5-PAHSA and 9-PAHSA have been shown to have anti-diabetic and anti-inflammatory activity in humans and rodents [START_REF] Yore | Discovery of a class of endogenous mammalian lipids with anti-diabetic and anti-inflammatory effects[END_REF][START_REF] Bandak | Microfluidic-enabled quantitative measurements of insulin release dynamics from single islets of Langerhans in response to 5-palmitic acid hydroxy stearic acid[END_REF]. We have also recently reported that the long-term intake of 9-PAHPA or 9-OAHPA increased basal metabolism and insulin sensitivity in healthy mice fed a control diet [START_REF] Benlebna | Long-term high intake of 9-PAHPA or 9-OAHPA increases metabolism and insulin sensitivity but disrupts liver homeostasis in healthy mice[END_REF]. However, there are still many questions about the biological roles of others FAHFAs in different physio-pathological states.

The objective of this work was to explore whether a longterm intake of 9-PAHPA or 9-OAHPA may induce similar effects in obesogenic diet-fed mice. To address this question, C57Bl6 mice were fed for 12 weeks with a high fathigh sugar (HFHS) diet supplemented with 9-PAHPA or 9-OAHPA and whole-body metabolism was explored with a particular focus on the liver functions as a key metabolic organ regarding insulin action, glucose production and its homeostatic control.

Materials and methods

Animals and diets

Forty 6-week-old male C57BL/6 J mice (Charles River, L'Arbresle, France), weighing about 22 g, were housed (5 per cage) under conditions of constant temperature (20-22 °C), humidity (45-50%) and a standard dark cycle (20.00-08.00 h). The mice were randomized, according to their initial weight, into four groups of ten animals and fed for 12 weeks with one of the four following semi-purified diets: (1) control diet, (2) HFHS diet, (3) HFHS + 9-PAHPA, (4) HFHS + 9-OAHPA.

The detailed composition of the diets is given in the supplementary Table 1. The control diet contains 5% lipids as a mixture of rapeseed oil, high oleic sunflower oil, sunflower oil and linseed oil (oil mixture of Carrefour), the HFHS diets contain 25% lipids (5% of a mixture of rapeseed oil, high oleic sunflower oil, sunflower oil and linseed oil and 20% of lard) and 30% sucrose. The lipid fraction of the control diet was composed of 12.2% saturated fatty acids (SFA), 60.6% monounsaturated fatty acids (MUFA) and 27.3% polyunsaturated fatty acids (PUFA) and that of the HFHS diet was composed of 30.4% SFA, 53.4% MUFA and 16.3% PUFA (supplementary Table 2).

The 9-PAHPA (molecular mass = 510.5) or the 9-OAHPA (molecular mass = 537) was incorporated into the diet after dissolution in the combined table oils (oil mixture of Carrefour) and the final content of each FAHFA was set at 300 µmol/kg diet. For a mouse of 25 g that eats about 2.5 g diet/day, this corresponds to a FAHFA intake of about 30 µmol/day/kg b.w. of mice (i.e., about 15 mg/day/kg). The administered dosage of the studied FAHFAs was based on the work of Yore et al. 2014 [START_REF] Yore | Discovery of a class of endogenous mammalian lipids with anti-diabetic and anti-inflammatory effects[END_REF] as well as on the recent work of Paluchova et al. 2019 [START_REF] Paluchova | Lipokine 5-PAHSA is regulated by adipose triglyceride lipase and primes adipocytes for de novo lipogenesis in mice[END_REF]. The synthesis of 9-PAHPA and 9-OAHPA was performed using our previously reported procedure [START_REF] Balas | Regiocontrolled syntheses of FAHFAs and LC-MS/MS differentiation of regioisomers[END_REF].

Throughout the study, mice were given free access to tap water and to their respective diets. Mice body weight was followed weekly and food consumption was determined every 2 days (during the week) or 3 days (the week-end). Our institution guidelines for the care and use of laboratory animals were observed and all experimental procedures were approved by the local ethical committee in Montpellier, France (Reference APAFIS#12759-2017121912214385). A detailed scheme of the study design is provided in Fig. 1.

Body composition and metabolic analyses

Mice whole-body composition (fat and lean masses) was measured every 2 weeks throughout the study using an EchoMRI-700 whole-body composition analyzer (Echo Medical Systems, Houston, TX), according to the manufacturer's instructions.

Oxygen consumption and carbon dioxide production were measured using a Comprehensive Lab Animal Monitoring System (CLAMS) (Columbus Instruments, Columbus, OH). Mice were housed in individual cage inside a controlled cabinet. Mice were acclimatized individually in metabolic cages at 22 °C with ad libitum access to food and water for 24-h, prior to a 24-h period of automated recordings. Sampled air from individual cages was passed through sensors to determine O 2 and CO 2 content. Sensors were calibrated before each experiment with commercial gas mixtures of accurately determined composition (20.5% O2, 0.5% CO2 and 79% N2). Volume of O 2 (VO 2 ) and VCO 2 were measured 111 times in about 24 h. The respiratory exchange ratio (RER) was calculated as the volume of CO 2 vs. volume of O 2 (VCO 2 /VO 2 ) ratio [START_REF] Marvyn | Data on oxygen consumption rate, respiratory exchange ratio, and movement in C57BL/6J female mice on the third day of consuming a high-fat diet[END_REF].

Oral glucose tolerance test (OGTT) and insulin tolerance test (ITT)

Following an overnight fasting (16 h), mice were administrated glucose solution (2 g/kg) by oral gavage, and blood were collected from the tail vein at the indicated times for glucose and insulin determination. Insulin tolerance was also assessed after 2 h fasting by administration of human insulin (0.75 U/kg) and blood glucose monitoring. Glycemia was measured using an OneTouch Verio glucometer (Lifescan).

Sampling and routine biochemical analyses

Four to five days after the OGTT or the ITT, blood from 12 h-fasted mice was collected from the retro-orbital sinus and distributed into heparinized tubes. Blood tubes were centrifuged at 1000 g for 10 min at 4 °C, plasma was collected and stored at -80 °C until analysis. After cervical dislocation of mice, liver was removed, rinsed with 0.9% NaCl, weighed, cut into several parts, plunged into liquid nitrogen and then kept at -80 °C until analysis. In addition, liver fresh samples were frozen in Tissue-Tek (Microm Microtech) for histological analysis and stored at -80 °C. Moreover, white adipose tissue (WAT) was removed, rinsed with 0.9% NaCl and kept at -80 °C until analysis.

Plasma levels of glucose, total cholesterol, triglycerides and free fatty acids as well as enzymatic activity of alanine aminotransferase (ALT) were measured at the ANEXPLO/ CREFRE analysis platform (CHU RANGUEIL-BP 84225, France). Plasma levels of insulin, leptin and IL-6 were quantified with ELISA kits (Merck Millipore, Darmstadt, Germany; Crystal Chem, Zaandam, Netherlands; Abcam, Paris, France, respectively).

Liver neutral lipids measurement and histological study

Liver samples were homogenized in NaCl solution (9 g/L) and Triton X-100 (0.1%) and free fatty acids, triglycerides and total cholesterol levels were quantified on the tissue homogenate by enzymatic methods (Wako-NEFA-C kit, Oxoid, Dardilly, France; Cholesterol CHOD-PAP SOBI-ODA kit and triglycerides LQ SOBIODA kit, Sobioda 38330 Montbonnot-Saint-Martin, France) [START_REF] Coudray | A mitochondrial-targeted ubiquinone modulates muscle lipid profile and improves mitochondrial respiration in obesogenic diet-fed rats[END_REF].

Histological liver analysis was performed on ten μm cryostat sections, stained with Oil Red O or Sirius Red. For Oil Red O staining, the sections were fixed in PBS, 4% Fig. 1 Design of the study. Forty 6-week-old male C57BL/6 were fed for 12 weeks either a control diet, a high fat-high sucrose diet (HFHS), a HFHS diet + 9-PAHPA or a HFHS diet + 9-OAHPA. Whole body composition was measured every 2 weeks using an EchoMRI-700 analyzer. Mice oxygen consumption and carbon dioxide production were measured using a Comprehensive Lab Animal Monitoring System the last weeks of the study. Oral glucose tolerance test and insulin tolerance test were performed the last weeks of the study. At the end of the study, blood was collected from retro-orbital sinus for biochemical analyses. After cervical dislocation, the liver was removed, rinsed, cut into several parts and frozen into liquid nitrogen until analyses paraformaldehyde at room temperature for 5 min, washed in H 2 O, incubated with 60% isopropanol for 5 min and then incubated in oil Red O solution (0.6%) for 7 min. The sections were then briefly washed with 60% isopropanol, incubated with Harris's Hematoxylin for 30 s, washed in H 2 O for 3 min, and mounted.

For Sirius Red staining, the sections were fixed in PBS, 4% PFA at room temperature 5 min, washed in H 2 O and incubated in 0.01% Sirius Red F3B 1 h. The sections were then washed twice in acidified water, dehydrated thrice in 100% ethanol, then cleared in xylene and mounted. For the morphometric analysis, liver sections were scanned using a NanoZoomer (Hamamatsu Photonics, Japan) with a 20 × objective. The degree of hepatic steatosis and liver fibrosis were, respectively, evaluated on Oil Red O and Sirius Red stained slides, and scored using Image J software as described [START_REF] Standish | An appraisal of the histopathological assessment of liver fibrosis[END_REF].

Liver oxidative stress status

Liver samples were homogenized in phosphate buffer (50 mM, pH 7) 1 g for 9 ml buffer, using a Polytron homogenizer and long-established oxidative stress parameters were performed. The liver thiobarbituric acid reactive substances (TBARS) and total glutathione (GSH) levels were measured in homogenate according to the methods of Sunderman [START_REF] Sunderman | Increased lipid peroxidation in tissues of nickel chloridetreated rats[END_REF] and Griffith [START_REF] Griffith | Determination of glutathione and glutathione disulfide using glutathione reductase and 2-vinylpyridine[END_REF], respectively. The remaining homogenate was centrifuged at 1000 g for 10 min at 4 °C and the supernatant was used for the analyses of oxidative stress. Protein oxidation was assessed by measurement of thiol groups [START_REF] Faure | Measurement of plasma sulfhydryl and carbonyl groups as a possible indicator of protein oxidation[END_REF]. Catalase activity was measured according to the method of Beers and Sizer [START_REF] Beers Rf | A spectrophotometric method for measuring the breakdown of hydrogen peroxide by catalase[END_REF]. Glutathione peroxidase (GPx) was measured according to the method of Flohe and Gunzler [START_REF] Flohe | Assays of glutathione peroxidase[END_REF]. Total superoxide dismutase (SOD) was measured according to the method of Marklund [START_REF] Marklund | Spectrophotometric study of spontaneous disproportionation of superoxide anion radical and sensitive direct assay for superoxide dismutase[END_REF].

The liver isoprostanoid levels, considered as a reference method of lipid peroxidation, were measured based on micro-LC-MS/MS technique [START_REF] Dupuy | Simultaneous quantitative profiling of 20 isoprostanoids from omega-3 and omega-6 polyunsaturated fatty acids by LC-MS/MS in various biological samples[END_REF]. Briefly, after lipid extraction with Folch mixture, the extracts were mixed with a cocktail of internal standards, and an alkaline hydrolysis was performed. The metabolites were concentrated thanks to a solid phase extraction step conducted on weak-anion exchange materials. The metabolites were then analyzed by micro-LC-MS/MS. Mass spectrometry analysis was performed with an AB Sciex QTRAP5500 (Sciex Applied Biosystems), using electrospray in negative mode as the ionization source. Detection of the fragmentation ion products from each deprotonated molecule was performed in the multiple reaction monitoring modes. Metabolites quantification was done, using MultiQuant 3.0 software, by measuring the ratio of area under the specific metabolite peak/area under the internal standard peak and compared to the ratio of area under the metabolite calibration peak/area under the internal standard peak.

Liver mitochondrial enzymatic activities

The enzymatic activity of the different mitochondrial respiratory complexes was determined as previously described [START_REF] Feillet-Coudray | Oxidative stress in rats fed a high-fat high-sucrose diet and preventive effect of polyphenols: involvement of mitochondrial and NAD(P)H oxidase systems[END_REF]. Citrate synthase (CS) activity was measured according to Srere [25]: the activity of the enzyme is measured by following the color of 5-thio-2-nitrobenzoic acid, which is generated from 5,5′-dithiobis-2-nitrobenzoic acid present in the reaction of citrate synthesis, and caused by the deacetylation of Acetyl-CoA. Complex I activity was measured spectrophotometrically at 600 nm during 45 s by following the reduction of 2,6-dichloroindophenol by electrons accepted from decylubiquinol, itself reduced after oxidation of NADH by complex I [START_REF] Janssen | Spectrophotometric assay for complex I of the respiratory chain in tissue samples and cultured fibroblasts[END_REF]. Complex II (CII) activity was measured spectrophotometrically at 600 nm by following the reduction of 2,6-dichloroindophenol by the succinate during 120 s [START_REF] Feillet-Coudray | Oxidative stress in rats fed a high-fat high-sucrose diet and preventive effect of polyphenols: involvement of mitochondrial and NAD(P)H oxidase systems[END_REF]. Complex II + III (CII + CIII) activities were measured spectrophotometrically by following the oxidation of oxidation of cytochrome c at 550 nm during 90 s [27]. Cytochrome c oxidase (COX) activity was measured spectrophotometrically by following the oxidation of reduced cytochrome c at 550 nm during 30 s [START_REF] Wharton | Cytochrome oxidase from beef heart mitochondria[END_REF]. In addition, mitochondrial β-hydroxyacyl-CoA dehydrogenase (β-HAD), a marker of last step of mitochondrial β-oxidation activity, was determined spectrophotometrically according to the procedure described by Clayton et al. [START_REF] Clayton | Hyperinsulinism in short-chain L-3-hydroxyacyl-CoA dehydrogenase deficiency reveals the importance of beta-oxidation in insulin secretion[END_REF].

Protein isolation and western blotting analysis

Frozen liver samples were homogenized using an Ultra Turax homogenizer in an ice cold extraction buffer containing 20 mM Tris-HCL, 150 mM NaCl, 1 mM EDTA, 0.5% Triton X-100, 0.1% SDS, 1 mM PMSF, 10 µM leupeptin, and 1 µM pepstatin. Proteins (50 µg) were separated with 6-15% SDS-PAGE and then transferred to a nitrocellulose membrane (120 min, 100 V). Membranes were blocked in 5% fat-free milk for 1 h at room temperature. Then, membranes were incubated overnight with primary antibody against ChREBP, GLK, GLUT2, PEPCK, p-ACC, ACC, FAS, FATP4, PGC1α, L-CPT1, IL-6, and TNF-α in blocking buffer (See supplementary Table 3). After washes in TBS/Tween under gentle agitation, membranes were incubated for 1 h with horseradish peroxidase-labeled antibody. After further washes, blots were treated with enhanced chemiluminescence detection reagents (ThermoScientific, Illkirch, France). β-actin or α-tubulin was used as loading references, and blot intensities were measured using Image Lab™ Software 5.2.1 (Bio-Rad Laboratories, Marnes-la-Coquette, France).

Real-time quantitative RT-qPCR analysis

Real-time Quantitative Polymerase Chain Reaction (RT-qPCR) was used to measure target genes mRNA expression in liver. Total RNA was extracted with Trizol reagent (Invitrogen Life Technologies, Cergy Pontoise, France). Reverse transcription reaction was performed with 2 μg total RNA. cDNA was synthesized with the use of PrimeScript RT reagent Kit (Perfect Real Time) (TAKARA) and Oligo (dT) primers + Randoms 6 mers. The mRNA expressions of target genes were determined by RT-qPCR, using a Step One Plus detection system (AB Applied Biosystems) and SYBR Premix Ex Taq II (TAKARA). Results were normalized with the gene encoding RPS9 used as the reference. The primer sequences used for real-time RT-PCR are given in the supplementary Table 4.

Real-time Quantitative Polymerase Chain Reaction (RT-qPCR) was also applied to measure genes mRNA expression in the adipose tissue. RNA from WAT was extracted with Trizol reagent (Invitrogen Life Technologies, Cergy Pontoise, France). Reverse transcription reaction was performed with 1 μg total RNA. cDNA was synthesized with the use of moloney murine leukemia virus reverse transcriptase for first strand cDNA synthesis and random primers. The mRNA expressions of target genes were determined by RT-qPCR. RT-qPCR analysis was performed using SYBR Green Mastermix (Eurogentec, liege, Belgium) with a Mx3005P Real-Time PCR System (Stratagene, La Jolla, CA). Results were normalized with the gene encoding 18S. For the primer sequences used for real-time RT-PCR, see supplementary Table 4.

Statistical analysis

The number of mice required for this study was based on the expected difference in OGTT between the control and the HFHS groups. As the starting hypothesis was that the HFHS diet would increase the OGTT, we expected a 30% increase in OGTT in the HFHS group compared to the control group with a possible standard deviation of 20% of the higher mean value. Thus, for a type 1 risk α of 0.05 and a power (1-β) of 85%, the number of mice required was 7 per group. However, because we have 4 experimental groups this study was designed with 10 mice/group.

Results were expressed as means ± SD. HFHS diet vs. control diet was tested by a student t test; *p < 0.05 for HFHS vs. control diet. Inside the three HFHS diets, the effects of FAHFA intake was tested by a one-way ANOVA test, followed up by a Fisher's Least Significant Difference test. The means not sharing the same letter significantly differ. Correlations were performed with the Spearman method. The limit of statistical significance was set at p < 0.05. Statistical analyses were performed using the StatView program (SAS Institute, Cary, NC, USA).

Results

9-PAHPA and 9-OAHPA intake had no effect on obesity and hyperlipidemia induced by the HFHS diet

We observed that mice mean food intake decreased in the HFHS diet-fed mice (Control: 2.79 ± 0.06 g/mice/ day, HFHS: 2.55 ± 0.13 g/mice/day, HFHS + 9-PAHPA: 2.51 ± 0.4 g/mice/day, HFHS + 9-OAHPA: 2.72 ± 0.12 g/ mice/day). However, mice being housed 5 per cage, the sample size (n = 2) was too small to perform statistical analysis. The final body weight and fat mass, as well as lean mass, were significantly increased with the HFHS diet by comparison to controls. No specific effect of 9-PAHPA or 9-OAHPA intake was observed on any of these parameters. As expected, plasma leptin level was significantly increased in mice fed the HFHS diet, while plasma IL6 level was not modified (Fig. 2a). In addition, plasma triglycerides and total cholesterol levels were significantly increased with HFHS diet reflecting hyperlipidemia induced by this diet (Fig. 2a). However, no specific effect of 9-PAHPA or 9-OAHPA intake was observed on any of these parameters.

9-PAHPA and/or 9-OAHPA intake modulated basal metabolism and carbohydrate oxidation

Mice basal metabolism was investigated by measuring oxygen consumption (VO 2 ) and carbon dioxide production (VCO 2 ) using CLAMS system. VO 2 reflecting the basal metabolism was significantly decreased with HFHS diet (Fig. 2b). Interestingly, while supplementation with 9-OAHPA had no impact on VO 2 , 9-PAHPA intake restored VO 2 to control values. VCO 2 was also significantly decreased with HFHS diet, while 9-PAHPA and 9-OAHPA intake limited this decreases (Fig. 2c). Moreover, HFHS diet significantly decreased RER (VCO 2 /VO 2 ) compared to the control diet, suggesting a higher preference for lipid oxidation (Fig. 2d). Interestingly, both 9-PAHPA and 9-OAHPA intake significantly increased RER by comparison to HFHS diet, thus favouring carbohydrate oxidation, however, without reaching the carbohydrate oxidation value obtained with the control diet (Fig. 2d). It is worth to notice that RER value was higher in mice supplemented with 9-OAHPA by comparison to 9-PAHPA (Fig. 2d). It should be pointed out that the HFHS phenotype obtained in this study was not extreme enough to unmask everything, explaining probably why FAHFAs has no marked effect on body weight and fat mass and non-significant change in food intake, while energy expenditure is decreased. At least, it is possible that 9-PAHPA and 9-OAHPA exerted lipid remodeling/ futile substrate cycling burning energy as we have seen with 5-PAHSA [START_REF] Paluchova | Lipokine 5-PAHSA is regulated by adipose triglyceride lipase and primes adipocytes for de novo lipogenesis in mice[END_REF].

9-PAHPA and 9-OAHPA intake ameliorated peripheral insulin resistance but had no effect on glucose intolerance induced by HFHS diet

Insulin tolerance test (ITT) reflects mainly insulin-stimulated peripheral utilization of glucose by tissues (in particular muscle) but also insulin ability to suppress (more or less completely) glucose production by the liver [START_REF] Rabasa-Lhoret | How to measure insulin sensitivity in clinical practice?[END_REF]. This test confirmed that HFHS diet induced insulin resistance in mice, and showed that both 9-PAHPA and 9-OAHPA intake increased insulin sensitivity in comparison to HFHS diet alone, yet without recovering the control values (Fig. 3a).

The oral glucose tolerance test (OGTT) is the reference method for the assessment of glucose tolerance [START_REF] Rabasa-Lhoret | How to measure insulin sensitivity in clinical practice?[END_REF]. It reflects the ability of the pancreas to secrete insulin and the responsiveness of the whole body in response to blood glucose levels. We observed that the HFHS diets, with or without 9-PAHPA or 9-OAHPA, rendered the mice diabetic as evidenced by the fasting hyperglycemia found in HFHS diet-fed mice (Fig. 3b). Nevertheless, neither 9-PAHPA nor 9-OAHPA showed any effect on glucose tolerance (Fig. 3b).

Fasted plasma glucose was increased with HFHS diet (Fig. 3c). In addition, insulin levels were up regulated with HFHS diet both in fast and in fed conditions (Fig. 3c) but no specific effect of 9-PAHPA or 9-OAHPA were observed by comparison to HFHS alone. Moreover, HOMA index, reflecting mainly hepatic insulin resistance [START_REF] Rabasa-Lhoret | How to measure insulin sensitivity in clinical practice?[END_REF], was significantly increased HFHS diet to controls. Surprisingly, no specific effects of 9-PAHPA or 9-OAHPA intake were observed on any of these parameters, suggesting increased peripheral utilization of glucose with these FAHFAs but no modification of liver glucose production or pancreas insulin secretion. Fasting level of plasma total GLP-1, an incretin promoting insulin secretion, was not modified whatever the diet (Fig. 3c), but was, however, positively correlated with fasted plasma insulin level (r = 0.520, p = 0.0038). Regarding the abundance of proteins involved in the glucose metabolism, liver expression of glucose transporter GLUT2 was decreased with the HFHS diet, while the expression of phosphoenolpyruvate carboxykinase (PEPCK), a key enzyme of gluconeogenesis, glucokinase (GLK) and the glucose-activated transcription factor (CHREB) remained unchanged whatever the diet (Fig. 3d).

No specific effect of 9-PAHPA or 9-OAHPA intake was observed on the expression of any of these proteins.

9-PAHPA and 9-OAHPA intake had no effect on liver steatosis nor fibrosis

Liver triglycerides, total cholesterol, free fatty acid and total lipid contents were measured in liver samples by colorimetric method. No modification was observed whatever the group of diets (Fig. 4b). Furthermore, histologic analysis revealed a slight increase in hepatic steatosis with the HFHS diet by comparison to controls. However, no significant impact of 9-PAHPA or 9-OAHPA intake was observed (Fig. 4c). However, it should be noticed that liver slices for Inside the three HFHS diets, the effects of FAHFA intake was tested by a one-way ANOVA test, followed up by a Fisher's Least Significant Difference test. The means not sharing the same letter significantly differ. The limit of statistical significance was set at p < 0.05. GLP-1: glucagon like peptide-1, GLUT2: glucose transporter 2, PEPCK: phosphoenol pyruvate kinase, GLK: glucokinase, ChREBP: carbohydrate-responsive element-binding protein histological analysis were cut from the edge of the liver lobe and that such a sample is prone to smearing of lipid bodies [START_REF] Levene | Quantifying hepatic steatosismore than meets the eye[END_REF][START_REF] Gerspach | Variation in fat content between liver lobes and comparison with histopathological scores in dairy cows with fatty liver[END_REF]. Accordingly, at necropsy macroscopical normal livers were observed independently of 9-PAHPA or intake not shown), a fatty liver was not recorded unlike to our previous observations with FAHFA supplementation of healthy mice [START_REF] Benlebna | Long-term high intake of 9-PAHPA or 9-OAHPA increases metabolism and insulin sensitivity but disrupts liver homeostasis in healthy mice[END_REF]. In addition, liver gene expression of major players in hepatic de novo lipogenesis, fatty acid synthase (FAS) and peroxisome proliferator-activated (PPAR) α and δ, were unchanged whatever the diet Moreover, protein expression of longacid transport 4 (FATP-4), palmitoyltransferase I (L-CPT1), essential in the β-oxidation chain fatty acids, PGC1-α, a master regulator of mitochondrial biogenesis, as liver 3-hydroxyacyl CoA activity (β-HAD), in β-oxidation remained unmodified whatever the diet (Fig. 4e). The p-ACC/ACC ratio (Acetyl-CoA carboxylase), involved in the biosynthesis of fatty acids was significantly decreased with the HFHS diet. However, 9-PAHPA or 9-OAHPA supplementation could not prevent these p-ACC/ACC ratios from decreasing (Fig. 4f).

Fibrosis was also investigated using Sirius red staining (Fig. 5a). Fibrosis in percentage, evaluated by analysis imagen was not modified with HFHS diet (Fig. 5b) and no significant impact of 9-PAHPA or 9-OAHPA intake was observed. Plasma ALAT activity, a biochemical marker of hepatic lysis/ fibrosis, was significantly increased with the HFHS diet, but with no significant effect of 9-PAHPA or 9-OAHPA intake (Fig. 5c). No modification of gene expression of major players Results were expressed as means ± SD, n = 9-10 animals per group. HFHS diet vs. control diet was tested by a student t test; *p < 0.05 for HFHS vs control diet. Inside the three HFHS diets, the effects of FAHFA intake was tested by a one-way ANOVA test, followed up by a Fisher's Least Significant Difference test. The means not sharing the same letter significantly differ. The limit of statistical significance was set at p < Representative Oil Red O (D) of livers from all the mice (magnification × 10), n = 10 animals per group. β-HAD β-hydroxyacyl-CoA dehydrogenase, PPARα peroxisome proliferatoractivated receptor alpha, PPARγ peroxisome proliferator-activated receptor gamma, ACC acetyl-CoA carboxylase, FAS/Fasn fatty acid synthase involved in liver fibrosis was observed whatever the group of diet, for collagen Col1A1 that increased with the diet but without specific effect of 9-PAHPA or 9-OAHPA 5d). All these results reflect little or no fibrosis with the HFHS diets.

Finally, no liver inflammation was as liver gene expression of TNF-α and MCP1 and liver expression of TNF-α and IL-6 remained unchanged whatever the (Fig. 5e,f).

9-PAHPA and 9-OAHPA intake had little effects on mitochondrial activity and liver oxidative stress alteration induced by HFHS diet

Mitochondrial dysfunction and oxidative stress are interconnected known be involved in the development of steatosis to steatohepatitis and fibrosis [START_REF] Manne | Pathophysiology of nonalcoholic fatty liver disease/nonalcoholic steatohepatitis[END_REF]. No modification of mitochondrial respiratory chain complexes activity was observed with the HFHS diet (Fig. 6a). However, citrate synthase (CS), a marker of mitochondrial activity, was significantly decreased with the HFHS diet by comparison to control (Fig. 6b), most likely to limit de novo lipogenesis [34]. 9-PAHPA intake had no impact. However, 9-OAHPA intake significantly decreased liver CS activity by comparison to HFHS diet alone (Fig. 6b). Liver GSH and contents, but not GSH/GSSG ratio (data not shown) were increased with HFHS diet, with no significant effect of 9-PAHPA or 9-OAHPA (Fig. 6e). The other markers of oxidative stress measured in this study (antioxidant enzymes, oxidized and proteins) were not modified with HFHS (Fig. 6c,d,f).

9-OAHPA not 9-PAHPA intake induced thermogenic phenotype in WAT

Certain depots of WAT, in response to appropriate stimuli such as chronic cold exposure or certain pharmacologic treatments, undergo a known as browning [START_REF] Lim | Depot-specific UCP1 expression in human white adipose tissue and its association with obesity-related markers[END_REF]. expression of three markers of thermogenic fat cells, UCP1, PRDM16 and Cidea, was determined in epididymal WAT (Fig. 7a-c). UCP1 and Cidea gene expression were increased with HFHS diet with no significant effect of 9-PAHPA or 9-OAHPA (Fig. 7a,b). PRDM16 was not modified with the HFHS diet by comparison to controls but Results were expressed as means ± SD, n = 10 animals per group. HFHS diet vs. control diet was tested by a student t test; *p < 0.05 for HFHS vs. control diet. Inside the three HFHS diets, the effects of FAHFA intake was tested by a one-way ANOVA test, followed up by a Fisher's Least Significant Difference test. The means not sharing the same letter significantly differ. The limit of statistical significance was set at p < 0.05. CI complex I, CII complex II, CII + III complexes II + III, COX cytochrome c oxidase, CS citrate synthase, SOD total superoxide dismutase, MnSOD manganese superoxide dismutase, GPx glutathione peroxidase, TBARS thiobarbituric acid reactive substances, -SH thiols, GSH reduced glutathione, GSSG oxidised glutathione, Phytoprostanes: ent-16-B 1t -phytoprostane, ent-9-L 1t -phytoprostane; Phytofuran: ent-16(RS)-13-epi-ST-Δ 14 -9phytofuran; Isoprostanes: 15(S)-15-F 2t -isoprostane, 15(R)-15-F 2tisoprostane, 5(RS)-5-F 2t -isoprostane, 5(RS)-5-F 2c -isoprostane; Neuroprostanes: 10(S)-10-F 4t -neuroprostane, 10(R)-10-F 4t -neuroprostane, 4(RS)-4-F 4t -neuroprostane was significantly increased with 9-OAHPA while not with 9-PAHPA (Fig. 7c).

Discussion

The "FAHFAs" has been introduced in 2014 for bioactive lipids found in with potential antidiabetic and anti-inflammatory properties [START_REF] Yore | Discovery of a class of endogenous mammalian lipids with anti-diabetic and anti-inflammatory effects[END_REF][START_REF] Balas | Branched fatty acyl esters of hydroxyl fatty acids (FAHFAs), appealing beneficial endogenous fat against obesity and type-2 diabetes[END_REF]. Branched FAHFAs are biosynthesized and stored in adipose tissue as nonesterified FAHFAs and FAHFA-containing triacylglycerols (FAHFAs-TG), FAHFA-TGs serving most likely as a storage form of FAHFAs under nutrient-rich conditions [START_REF] Paluchova | Lipokine 5-PAHSA is regulated by adipose triglyceride lipase and primes adipocytes for de novo lipogenesis in mice[END_REF][START_REF] Tan | Discovery of FAHFAcontaining triacylglycerols and metabolic regulation[END_REF]. FAHFAs were also detected in many others tissues [START_REF] Yore | Discovery of a class of endogenous mammalian lipids with anti-diabetic and anti-inflammatory effects[END_REF][START_REF] Balas | Branched fatty acyl esters of hydroxyl fatty acids (FAHFAs), appealing beneficial endogenous fat against obesity and type-2 diabetes[END_REF]. To date, of the saturated FAHFAs studied are branched regioisomers of Palmitic Acid Hydroxyl Stearic Acid (PAHSA) and nearly all of these studies indicated that both and 9-PAHSA may have anti-diabetic and anti-inflammatory activity in humans and rodents [START_REF] Yore | Discovery of a class of endogenous mammalian lipids with anti-diabetic and anti-inflammatory effects[END_REF][START_REF] Balas | Branched fatty acyl esters of hydroxyl fatty acids (FAHFAs), appealing beneficial endogenous fat against obesity and type-2 diabetes[END_REF][START_REF] Bandak | Microfluidic-enabled quantitative measurements of insulin release dynamics from single islets of Langerhans in response to 5-palmitic acid hydroxy stearic acid[END_REF]]. Yet, some disparate results have been recently reported, probably because of design differences in the experimental and analytical methodologies [START_REF] Pflimlin | Acute and repeated treatment with 5-PAHSA or 9-PAHSA isomers not improve glucose control in mice[END_REF][START_REF] Kuda | On the complexity of PAHSA research[END_REF][START_REF] Syed | Methodological issues in studying PAHSA biology: masking PAHSA effects[END_REF]. Some isomers of docosahexaenoic acid-derived fatty acid esters of hydroxy fatty acids and of linoleic acid acid-derived fatty acid esters of hydroxy fatty acids were also studied and it was observed that both 13(S)-DHAHLA and 13-LAHLA exerted antiinflammatory properties [START_REF] Kuda | Docosahexaenoic acid-derived fatty acid esters of hydroxy fatty acids (FAHFAs) with anti-inflammatory properties[END_REF][START_REF] Kolar | Linoleic acid esters of hydroxy linoleic acids are anti-inflammatory lipids found in plants and mammals[END_REF]. We have recently reported that other saturated branched FAHFAs may exhibit bioactive properties and insulin sensitizing effects. Indeed, long-term intake of 9-PAHPA or 9-OAHPA has been shown to increase basal metabolic rate and insulin sensitivity in healthy control diet-fed mice [START_REF] Syed | Methodological issues in studying PAHSA biology: masking PAHSA effects[END_REF]. However, the insulin sensitizing effect of specific FAHFAs was associated with slight adverse metabolic effects, as liver steatosis and fibrosis development in some of these mice. Regarding the great interest of these issues in the obesity and diabetic states, whether a long-term intake of 9-PAHPA or 9-OAHPA may induce similar effects in obesogenic diet-fed mice was explored in the present study.

9-PAHPA and 9-OAHPA intake modulated basal metabolic rate in obesogenic diet-fed mice

Compared to the control mice, the HFHS diet-fed mice had higher calorie intake associated with a decrease in their basal metabolism. Accordingly, this positive energy balance resulted in an increased body weight and in obesity. Moreover, HFHS diet-fed mice exhibited lower respiratory exchange ratio (RER) than control mice, indicating a switch from carbohydrate to fat as the major energy source. In fact, a high RER suggests that carbohydrates are being predominantly utilized as source of fuel, whereas a low RER indicates fatty acid oxidation preference. Such an effect of HFHS diet has been already largely reported in the literature [START_REF] Burchfield | High dietary fat and sucrose results in an extensive and time-dependent deterioration in health of multiple physiological systems in mice[END_REF].

In a previous study, we reported that 9-PAHPA and 9-OAHPA intake increased basal metabolic rate in the healthy control diet-fed mice [START_REF] Benlebna | Long-term high intake of 9-PAHPA or 9-OAHPA increases metabolism and insulin sensitivity but disrupts liver homeostasis in healthy mice[END_REF]. In the present study, the intake of 9-PAHPA but not the 9-OAHPA restored basal metabolism in the HFHS diet-fed mice to the level of control mice. It has been reported that increased energy expenditure contributes to body weight loss and protects against dietinduced obesity [START_REF] Schneider | Increased energy expenditure, Ucp1 expression, and resistance to diet-induced obesity in mice lacking nuclear factor-erythroid-2-related transcription factor-2 (Nrf2)[END_REF]. However, although its favorable effect on basal metabolism, 9-PAHPA intake did not modify body weight, fat mass and lean mass. This is in agreement with a recent report indicating that PAHSA treatment had no effect on body weight and fat mass [START_REF] Zhou | PAHSAs enhance hepatic and systemic insulin sensitivity through direct and indirect mechanisms[END_REF]. Interestingly, 9-PAHPA or 9-OAHPA intake attenuated the preferential use of fatty acids over glucose as energy source observed in the HFHS diet-fed mice alone, as previously observed in healthy mice, and this effect was most pronounced with 9-OAHPA. The results indicate also that 9-PAHPA and 9-OAHPA modulate basal metabolism and substrates oxidation in HFHS diet-fed mice. To our knowledge, the effect of others FAHFAs on parameters has not yet been reported. A tentative explanation may be find in the browning of white fat. Indeed, recent data indicate that some FAHFAs (from the PAHSAs family) can promote browning of white fat tissues [START_REF] Wang | 9-PAHSA promotes browning of white fat via activating G-protein-coupled receptor 120 and inhibiting lipopolysaccharide / NF-kappa B pathway[END_REF] and it was shown that enhanced brown adipose tissue metabolic function could lead increased oxygen consumption [START_REF] Zou | Raspberry promotes brown and beige adipocyte development in mice fed high-fat diet through activation of AMP-activated protein kinase (AMPK) alpha1[END_REF]. Interestingly, we observed that 9-OAHPA intake, but not that of 9-PAHPA, led to an increased PRDM16 gene expression, known as an inducer of thermogenic phenotype fat cells [START_REF] Ishibashi | Functions of Prdm16 in thermogenic fat cells[END_REF].

9-PAHPA and 9-OAHPA intake increased insulin sensitivity in obesogenic diet-fed mice

Various methods exist to investigate glucose metabolism and insulin resistance, including the glucose and insulin tolerance tests, and the homeostasis model assessment (HOMA) index. Our present study indicated that the HFHS diet-fed mice developed hyperglycaemia and insulin resistance, and, therefore, diabetes, in line with the decreased RER observed in these mice. This observation was expected as the mouse model of diet-induced obesity is a well described model of obesity and insulin resistance [START_REF] Fernandes-Santos | Pan-PPAR agonist beneficial effects in overweight mice fed a high-fat high-sucrose diet[END_REF]. However, intake of 9-PAHPA or 9-OAHPA did not prevent or protect from hyperglycemia and hyperinsulinemia observed with the HFHS diet. However, these both studied FAHFAs nicely increased insulin sensitivity as measured in ITT. The OGTT and ITT in this work do not assess the same aspect of carbohydrate homeostasis. While the OGTT reflects the ability of the pancreas to secrete insulin and the responsiveness of the whole body in response to high blood glucose levels, HOMA index reflects hepatic insulin resistance and ITT measures mainly insulin-stimulated peripheral utilization of glucose by muscle [START_REF] Rabasa-Lhoret | How to measure insulin sensitivity in clinical practice?[END_REF]. The pyruvate tolerance test (PTT) is also used to evaluate hepatic gluconeogenesis. However, this is an oversimplification as pyruvate is utilized by many other tissues. Analysis of neoglucogenesis with only PTT may make interpretation hazardous. Indeed, the optimal method to assess gluconeogenesis is the measurement of endogenous glucose fluxes with use of tracers. However, this involves the generation of a set of mice dedicated only to this experiment which is not possible because of the quantity of FAHFAs needed on the one hand and the number of additional animals which poses an ethical problem on the other hand. While exploring molecular glucose metabolism in the liver, we observed that HFHS diet altered the expression of the glucose transporter GLUT 2 but not of other proteins involved in glucose metabolism and we observed that neither 9-PAHPA nor 9-OAHPA had any impact on their expression. In healthy mice, we previously showed that glucose tolerance was not changed by any diet although intake of 9-PAHPA or 9-OAHPA nicely increased the insulin sensitivity too. A possible explanation may be that the innate glucose tolerance is satisfactory and sufficient in healthy mice [START_REF] Benlebna | Long-term high intake of 9-PAHPA or 9-OAHPA increases metabolism and insulin sensitivity but disrupts liver homeostasis in healthy mice[END_REF].

The results obtained in the HFHS diet-fed mice may suggest that the insulin sensitizing effect of 9-PAHPA and 9-OAHPA may be exerted mainly on some peripheral tissues (skeletal muscle and heart). Zhou et al. [START_REF] Zhou | PAHSAs enhance hepatic and systemic insulin sensitivity through direct and indirect mechanisms[END_REF] have recently reported that 5-PAHSA and 9-PAHSA enhance both hepatic and systemic insulin sensitivity. Moreover, 5-PAHSA and 9-PAHSA were previously shown to enhance glucose tolerance and insulin-sensitivity, insulin and GLP-1 secretion in chow-and high fat-diet fed mice, and to augment glucosestimulated insulin secretion in human islets from healthy or diabetic people [START_REF] Yore | Discovery of a class of endogenous mammalian lipids with anti-diabetic and anti-inflammatory effects[END_REF][START_REF] Syed | Palmitic acid hydroxystearic acids activate GPR40, which is involved in their beneficial effects on glucose homeostasis[END_REF][START_REF] Moraes-Vieira | GLUT4 expression in adipocytes regulates de novo lipogenesis and levels of a novel class of lipids with antidiabetic and anti-inflammatory effects[END_REF].

9-PAHPA and 9-OAHPA intake did not affect hepatic steatosis or fibrosis in obesogenic diet-fed mice

Measurement of liver lipid content in HFHS diet-fed mice by biochemical methods did not show any difference with control mice for liver free fatty acids, cholesterol and triglycerides contents. Inflammation, mitochondrial dysfunction and oxidative stress were shown to be implicated in the progression of liver steatosis into steatohepatitis and fibrosis [START_REF] Fujii | Inflammation and fibrogenesis in steatohepatitis[END_REF][START_REF] Masarone | Role of oxidative stress in pathophysiology of nonalcoholic fatty liver disease[END_REF]. However, no major change in plasma or liver inflammation marker was observed in mice fed with the HFHS diet. There was also no major change in mitochondrial or oxidative stress markers. Moreover, no fibrosis marker was modified with HFHS diet. It was previously shown that increased levels of liver triglycerides were only observed after 24 weeks of HFHS in mouse liver [START_REF] Burchfield | High dietary fat and sucrose results in an extensive and time-dependent deterioration in health of multiple physiological systems in mice[END_REF]. These observations support ours and confirm that the 12-week HFHS mice model is rather a model of diabetes than of liver steatosis, and that development of liver steatosis may require longer duration of HFHS diet at least in mouse [START_REF] Clapper | Diet-induced mouse model of fatty liver disease and nonalcoholic steatohepatitis reflecting clinical disease progression and methods of assessment[END_REF].

We have recently demonstrated that long-term intake of 9-PAHPA or 9-OAHPA with a control diet induced liver steatosis and fibrosis in some healthy mice [START_REF] Benlebna | Long-term high intake of 9-PAHPA or 9-OAHPA increases metabolism and insulin sensitivity but disrupts liver homeostasis in healthy mice[END_REF]. In the current study, the 9-PAHPA or 9-OAHPA intake seemed to increase liver steatosis, in some few mice fed the HFHS diet, as revealed by histological staining and visualization. However, this effect was not confirmed by biochemical analysis of lipid parameters and may rather result from smearing of lipid bodies in the slice from the edge of the liver lobe as this effect was not observed on whole liver. Moreover, minor fibrosis was observed with HFHS diet with no amplification by 9-PAHPA or 9-OAHPA intake, contrary to what was observed in the healthy mice fed the control diet. Indeed, the possible explanation for this difference if that in the present study the HFHS mice may have received a lower dose of 9-PAHPA or 9-OAHPA compared to the healthy mice fed the control diet in our previous study [START_REF] Benlebna | Long-term high intake of 9-PAHPA or 9-OAHPA increases metabolism and insulin sensitivity but disrupts liver homeostasis in healthy mice[END_REF]. This may be due a lower food intake from the HFHS diet and a lower distribution FAHFA in these obese mice because of their higher body weight compared to the control mice. All these results indicate that 9-PAHPA or 9-OAHPA intake may have no major effects on liver when given with a HFHS diet, in the contrary to what we previously observed with the healthy mice fed the diet [START_REF] Benlebna | Long-term high intake of 9-PAHPA or 9-OAHPA increases metabolism and insulin sensitivity but disrupts liver homeostasis in healthy mice[END_REF]. Yet, these results also indicate no beneficial impact of these FAHFAs on liver metabolism. Few studies have reported the impact of others on liver lipid metabolism. In particular, it was shown that chronic 5-PAHSA and 9-PAHSA treatment had no impact on liver triglyceride levels in HFD-fed mice, despite improved hepatic insulin sensitivity [START_REF] Zhou | PAHSAs enhance hepatic and systemic insulin sensitivity through direct and indirect mechanisms[END_REF] and that 5-PAHSA promoted fatty liver and inflammation in db/db mice, a type 2 diabetes mouse model characterized by extreme hyperglycemia [START_REF] Wang | High glucose concentration impairs 5-PAHSA activity by inhibiting AMP-activated protein kinase activation and promoting nuclear factor-kappa-B-mediated inflammation[END_REF].

Conclusion

In this study, we showed that long-term intake of 9-PAHPA or 9-OAHPA modulated basal metabolism and had insulin sensitizing effect in obesogenic diet-fed mice. Interestingly, unlike what was observed in our previous study [START_REF] Benlebna | Long-term high intake of 9-PAHPA or 9-OAHPA increases metabolism and insulin sensitivity but disrupts liver homeostasis in healthy mice[END_REF] on healthy control diet-fed mice supplemented with 9-OAHPA or 9-PAHPA, these FAHFAs had no major adverse effect on liver metabolism and homeostasis. Both 9-PAHPA and 9-OAHPA were given with the HFHS diet in initially non-obese animals to investigate their effect during the development of obesity and glucose/lipid metabolism perturbation. It would be interesting to explore their insulin-sensitizing effect in nutritionally or genetically animal models, where obese/insulin-resistance was already installed before 9-PAHPA and 9-OAHPA treatment.

Fig. 2

 2 Fig. 2 Mice characteristics. a Body weight, lean and fat mass, plasma leptin and IL6, and circulating lipids, b oxygen consumption (VO2), c carbon dioxide consumption (VCO2) and d respiratory exchange ratio (RER) in mice. Results were expressed as means ± SD, n = 8-10 animals per group. HFHS diet vs. control diet was tested by a student t test; *p < 0.05 for HFHS vs. control diet. Inside the three HFHS diets, the effects of FAHFA intake was tested by a one-way ANOVA test,

Fig. 3

 3 Fig. 3 Glucose and insulin parameters. a insulin tolerance test (ITT), b Glucose tolerance test (OGTT), c glycemia in fasted state and insulinemia in fasted or fed state (30 min glucose injection), HOMA index and plasma total GLP-1 level and d liver protein expression of markers of glucose metabolism. Results were expressed as means ± SD, n = 8-10 animals per group. HFHS diet vs. control diet was tested by a student t test; *p < 0.05 for HFHS vs. control diet.

FFig. 4

 4 Fig. 4 Liver morphology and steatosis investigation. a Liver weight after 12 weeks of diet, b hepatic lipid content measured on tissue homogenate by enzymatic methods, c Oil red O staining of liver, pictures are representative from each group, d liver gene expression of key players in de novo lipogenesis, e liver β-HAD activity and f protein expression of key players in de novo lipogenesis. Results were expressed as means ± SD, n = 9-10 animals per group. HFHS diet vs. control diet was tested by a student t test; *p < 0.05 for HFHS vs control diet. Inside the three HFHS diets, the effects of

Fig. 5

 5 Fig. 5 Liver fibrosis investigation. a Sirius Red staining of liver, pictures are representative from each group (magnification × 10). b % of fibrosis and c plasma ALT activity. d Gene expression of liver fibrosis markers and e liver inflammation markers by qPCR. f Protein expression of TNF-α and IL-6 by western blot and representative pictures from each group. Results were expressed as means ± SD, n = 9-10 animals per group. HFHS diet vs. control diet was tested by a student t test; *p < 0.05 for HFHS vs. control diet. Inside the three HFHS

Fig. 6

 6 Fig. 6 Mitochondrial activity and hepatic oxidative stress parameters. a Mitochondrial respiratory chain activities. b Citrate synthase activity. c SOD, MnSOD, Catalase and GPx activities. d TBARS and -SH values. e GSH and GSSG values. f Phytoprostanes, Isoprostanes and Neuroprostanes values.Results were expressed as means ± SD, n = 10 animals per group. HFHS diet vs. control diet was tested by a student t test; *p < 0.05 for HFHS vs. control diet. Inside the three HFHS diets, the effects of FAHFA intake was tested by a one-way ANOVA test, followed up by a Fisher's Least Significant Difference test. The means not sharing the same letter significantly differ. The limit of statistical significance was set at p < 0.05. CI complex I, CII complex

  Fig.[START_REF] Yore | Discovery of a class of endogenous mammalian lipids with anti-diabetic and anti-inflammatory effects[END_REF] Gene expression of markers of thermogenic fat cells in epididymal WAT by qPCR. Results were expressed as means ± SD, n = 9-10 animals per group. HFHS diet vs. control diet was tested by a student t test; * p < 0.05 for HFHS vs control diet. Inside the three HFHS diets, the effects of FAHFA intake was tested by a one-

7

  Gene expression of markers of thermogenic fat cells in epididymal WAT by qPCR. Results were expressed as means ± SD, n = 9-10 animals per group. HFHS diet vs. control diet was tested by a student t test; * p < 0.05 for HFHS vs control diet. Inside the three HFHS diets, the effects of FAHFA intake was tested by a one-way ANOVA test, followed up by a Fisher's Least Significant Difference test. The means not sharing the same letter significantly differ.

	The limit of statistical significance was set at p< 0.05. UCP1 uncou-
	pling protein 1, CIDEA Cell death activator CIDE-A, PRDM16 PR
	domain-containing 16

Acknowledgements

The authors thank Biocampus for animal staff from Metamus DMEM facility which belongs to RAM, Montpellier animal facilities network, for technical support and expertise for metabolism phenotyping, and for RHEM Facility for histology/immunohistology experiments. We acknowledge SIRIC Montpellier Cancer (Grant INCa_Inserm_DGOS_12553) to RHEM, and Metamontp platform supported by the European fund for the regional development of Occitanie (FEDER). The authors express their deep acknowledgements to Guillaume Reversat, Amandine Rocher and Camille Oger for their technical aid in the isoprostanoid analysis, Charlene Couturier for the WAT qPCR analysis and Annabelle Tavernier for the GLP-1 analysis.

Author contribution Author contributions were as follows: study design (CC, FC, CF-C), FAHFAs synthesis (LB, MB), data collection (MB, BB, LP, JG, GF, CV, SG, OK), statistical analysis (CC, MB, FC, CF-C), data interpretation (MB, CC, FC, FB, SG, OK, TD, LB, CF-C), manuscript preparation (MB, CC, OK, LB, FC, CF-C), literature search (MB, CC, FC, CF-C) and funds collection (CC, OK, FC, CF-C). All the authors have read and approved the final version of this manuscript.

Funding Melha Benlebna thanks the Algerian Ministry of Higher Education and Scientific Research for the financial support of her PhD program. The authors also acknowledge the financial support of the French Lipid Nutrition Group, and the Czech Science Foundation (20-00317S). The authors are also grateful for the National Research Institute for Agriculture, Food and Environment (INRAE), in particular the Human Nutrition Department (Alim-H department) for their financial support.

Compliance with ethical standards

Conflict of interest The authors confirm that this article content has no conflict of interest.