P Chauveau
email: p.chauveau@gsi.de

K Hauschild

A Lopez-Martens

M Maccormick

E Minaya Ramirez

P G Thirolf

C Weber

Simulations of the novel double-Penning trap for MLLTRAP: Trapping, cooling and mass measurements

Keywords: Penning trap, In-trap decay spectroscopy, mass measurement

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Introduction

Investigating exotic nuclei far-off stability is necessary to validate or constrain many nuclear models operating in different regions of the chart of nuclei. It is a step towards understanding the structure of exotic nuclei and explaining complex astrophysical phenomena. The technological challenges of creating and studying these nuclei are being met in all major radioactive beam facilities in the world through the development of new beams and instruments. Of all the properties of a nucleus, its mass is one of the most fundamental ones, since the mass defect accounts for the sum of all nuclear interactions within. This makes mass measurement an essential (although incomplete) test for any predictive nuclear model. Electromagnetic traps have been the most successful devices used in mass separation and measurement, owing to long observation times and predictable particle trajectories. A fairly recent and thorough overview of traps and their use in experimental nuclear physics can be found in [START_REF] Eronen | Ion traps in nuclear physics-recent results and achievements[END_REF]. In particular, Penning traps have been known to measure the mass of radioactive nuclei with a precision down to 10 -8 -10 -9 [START_REF] Orford | Precision mass measurements of neutronrich neodymium and samarium isotopes and their role in understanding rare-earth peak formation[END_REF][START_REF] Karthein | Precision mass measurements using the Phase-Imaging Ion-Cyclotron-Resonance detection technique[END_REF][START_REF] Gulyuz | High precision determination of the β decay Q ec value of 11 C and implications on the tests of the standard model[END_REF][START_REF] Hakala | Precision mass measurements beyond 132 Sn: Anomalous behavior of odd-even staggering of binding energies[END_REF][START_REF] Bollen | Experiments with thermalized rare isotope beams from projectile fragmentation: A precision mass measurement of the superallowed β emitter 38 Ca[END_REF]. Many such setups are already in operation [START_REF] Ringle | Penning trap mass spectrometry of rare isotopes produced via projectile fragmentation at the lebit facility[END_REF][START_REF] Ramirez | Recent developments for high-precision mass measurements of the heaviest elements at shiptrap[END_REF][START_REF] Kreim | Recent exploits of the isoltrap mass spectrometer[END_REF][START_REF] Van Schelt | First results from the caribu facility: Mass measurements on the r-process path[END_REF][START_REF] Kolhinen | Recommissioning of jyfltrap at the new igisol-4 facility[END_REF][START_REF] Chaudhuri | Titan: an ion trap for accurate mass measurements of ms-half-life nuclides[END_REF][START_REF] Ketelaer | Mass measurements on stable nuclides in the rare-earth region with the penning-trap mass spectrometer triga-trap[END_REF] or under construction [START_REF] Ramirez | Conception of piperade: A high-capacity penning-trap mass separator for high isobaric contamination at desir[END_REF][START_REF] Mehlman | Status of the tamutrap facility and initial characterization of the rfq cooler/buncher[END_REF][START_REF] Schüssler | Recent developments at the high-precision mass spectrometer pentatrap[END_REF][START_REF] Huang | Status of lanzhou penning trap for accurate mass measurements[END_REF], showing both the need for measuring the ground-state properties of exotic nuclei and the success of the Penning trap in doing so. The review presented in [START_REF] Lunney | New mass measurements with trapped (radioactive) ions and related fundamental physics[END_REF] overviews recent ion traps and the masses they have allowed to measure.

As the most recently operational and upcoming facilities explore regions of the chart of nuclei further away from the valley of stability, the increasingly exotic nuclei produced are now always accompanied by large amounts of contaminants, complicating the study of the species of interest. Isobaric contaminants in particular are deleterious to trap-based mass measurements as they are hard to resolve and their own space charge can alter the trajectory of the ion of interest. For this reason most measurement Penning traps used in nuclear physics are preceded by a purification trap to clean the incoming ion bunch. While some systems use an independent magnet for the purification trap [START_REF] Orford | Precision mass measurements of neutronrich neodymium and samarium isotopes and their role in understanding rare-earth peak formation[END_REF][START_REF] Kreim | Recent exploits of the isoltrap mass spectrometer[END_REF], most second-generation setups have mounted both traps within the same magnet [START_REF] Ramirez | Recent developments for high-precision mass measurements of the heaviest elements at shiptrap[END_REF][START_REF] Kolhinen | Recommissioning of jyfltrap at the new igisol-4 facility[END_REF][START_REF] Ketelaer | Mass measurements on stable nuclides in the rare-earth region with the penning-trap mass spectrometer triga-trap[END_REF][START_REF] Ramirez | Conception of piperade: A high-capacity penning-trap mass separator for high isobaric contamination at desir[END_REF][START_REF] Huang | Status of lanzhou penning trap for accurate mass measurements[END_REF][START_REF] Kolhinen | Commissioning of the double penning trap system mlltrap[END_REF].

MLLTRAP was initially designed for high precision mass measurements of exotic nuclei. The setup uses a 7-T superconducting magnet and was built at the Maier-Leibnitz-Laboratory (MLL) of the Ludwig-Maximilians-University of Munich. It was commissioned off-line using a surface ionisation Rb ion source and proved capable of separating ions with a resolving power of 1.39 * 10 5 and measuring masses with a statistical precision of 2.9 * 10 -8 [START_REF] Kolhinen | Commissioning of the double penning trap system mlltrap[END_REF]. MLL-TRAP is currently installed at ALTO in Orsay, France, pending on-line commissioning [START_REF] Ramirez | New program for measuring masses of silver isotopes near the n=82 shell closure with mlltrap at alto[END_REF].

Complementary to mass measurements in traps, decay spectroscopy can provide direct insight into the nuclear structure of the daughter nuclei (nuclear level energy, spin, parity) or even the deep electronic structure of an atom. If the setup allows so, measuring the lifetime of some nuclear levels can bring additional information on the nuclear wavefunction. The combination of a Penning trap and particle/γ detectors perfectly befits decay spectroscopy: the Penning trap can be used either to clean the bunch from isobaric or isomeric contaminants and thus provide a purified sample to a post-trap decay station (trap-assisted decay spectroscopy), or to simply confine an ion bunch that then behaves like a point-like source of decay radiation in vacuum (in-trap decay spectroscopy). Of course a double Penning trap can be used for both by performing purification in the first trap and in-trap decay in the second trap.

An alternative double-trap assembly for MLLTRAP is being developed at CSNSM, Orsay, aiming to perform both in-trap decay spectroscopy of heavy α-particle emitters and mass measurements. In order to avoid confusion from here on, we will refer to this assembly as the second/novel tower and to the mass measurement double trap as the first tower. In the novel tower, the usual central ring of the second trap is replaced by a cubic arrangement of four silicon-strip detectors (SSD), and the operational bias of the detectors provides the trapping potential. Because of the strong magnetic field, conversion electrons are very efficiently guided outside the trap, while the comparatively heavy α particles can be detected by the in-trap SSD, allowing unperturbed detection of the α particles. When combined with a position-sensitive detector placed in the fringe field of the 7-T magnet to detect the electrons, this setup allows to implement the new DARING method [START_REF] Chauveau | 12 Application of in-trap spectroscopy to lifetime measurements with mlltrap[END_REF] to measure the lifetime of excited states populated in the α decay of exotic nuclei. This first-of-its-kind double-trap system has already been described by Weber et al. in [START_REF] Weber | Recent developments at mlltrap: Improving the system for mass measurements and in-trap observation of nuclear decays[END_REF][START_REF] Weber | Developments in penning trap (mass) spectrometry at mlltrap: Towards in-trap decay spectroscopy[END_REF][START_REF] Weber | Status of the mlltrap setup and future plans[END_REF], and recent simulations strongly support the feasibility of this lifetime measurement technique [START_REF] Chauveau | 12 Application of in-trap spectroscopy to lifetime measurements with mlltrap[END_REF]. Both assemblies will be commissioned at ALTO using existing or future beams. The neutron rich beams produced by photofission will allow to probe the mass surface near the magic numbers 50 and 82. ALTO currently lacks the necessary beams to test the second tower, although a fusion-evaporation target ion-source system is being studied to synthesise 196 Po (t 1/2 = 5.8s) in the framework of the TuLIP project (Target Ion Source For Short Lived Ion Production, ANR grant 18-CE31-0023). The magnet and its two towers will ultimately be installed at DESIR [START_REF] Blank | Perspectives for mass spectrometry at the desir facility of spiral2[END_REF], the low-energy experimental hall of the SPIRAL2 facility [26] at GANIL, Caen, France. There, MLLTRAP will receive beams from the existing SPIRAL facility as well as from the S3 spectrometer [START_REF] Déchery | The super separator spectrometer s3 and the associated detection systems: Sirius & leb-reglis3[END_REF], which will include very heavy and super-heavy elements as well as neutron-deficient nuclei at or near the N=Z line. This contribution describes the design of the novel tower and the simulations related to mass measurements with this assembly. Although this tower was not initially intended for mass measurements, we decided to design it with this objective in mind, as having an all-in-one system capable of decay spectroscopy, lifetime measurements and mass measurements would be an operational advantage. Simulations of the DARING technique completing those already covered in [START_REF] Chauveau | 12 Application of in-trap spectroscopy to lifetime measurements with mlltrap[END_REF] will be detailed in a forthcoming publication. The next section describes the geometry of the doubletrap and the features allowing for mass measurements. A brief introduction to Penning trap theory is then given in order to cover the basic equations used in this article. The following section details how the traps were optimised in order to enable mass measurements with the detector-trap. The last section covers the simulation of a typical mass measurement cycle in the second tower with a bunch of 100 ions, from its injection into the first trap to its ejection from the second trap.

Geometry of the trap

A precise description of the SSDs has already been given in [START_REF] Weber | Developments in penning trap (mass) spectrometry at mlltrap: Towards in-trap decay spectroscopy[END_REF] and a general description of the novel tower is featured in [START_REF] Chauveau | 12 Application of in-trap spectroscopy to lifetime measurements with mlltrap[END_REF]. Here, we give additional details on the design of the second trap. The middle panel of Fig. 1 shows the mechanical assembly of the second trap used at MLL for the tests of the SSD with an α-source. This assembly, however, did not yet allow for trapping. In this configuration the detectors are "plugged" into the copper electrodes using tenon joints. The new geometry is shown in the right panel of Fig. 1 and exhibits several features enabling mass measurements. Although it is clear that the cubic trap breaks the cylindrical symmetry usually found in precision Penning traps, it will be shown that this geometry does not prevent precision mass measurements with the ToF-ICR [START_REF] König | Quadrupole excitation of stored ion motion at the true cyclotron frequency[END_REF] or PI-ICR [START_REF] Eliseev | A phase-imaging technique for cyclotron-frequency measurements[END_REF] techniques.

In order to perform mass measurements or second-stage purification, the spectroscopic trap needs to have segmented electrodes for dipolar and quadrupolar excitation and a high-quality hyperbolic potential. The cubic layout of the trap conveniently provides the four segments required for the excitation. The oscillating potential, usually applied on the central electrode of the trap, will be applied on the flat correction electrodes (4 on Fig. 1). Since the support electrodes [START_REF] Bollen | Experiments with thermalized rare isotope beams from projectile fragmentation: A precision mass measurement of the superallowed β emitter 38 Ca[END_REF] in which the tenon joints are inserted are at the same potential as the correction electrodes, they have to be segmented as well. These support electrodes also fulfill the role of a shield, effectively closing the trap box from an electric point of view, in order to cancel any anharmonic contributions that can come from the support rods or cables. Instead of being located next to the side electrodes [START_REF] Ringle | Penning trap mass spectrometry of rare isotopes produced via projectile fragmentation at the lebit facility[END_REF], the support electrodes are wrapped around them, so as to keep the side electrodes close to the trap center. The axial length of these side electrodes has been optimised to reduce the higher order components of the trap's electric field. These changes have been supported by simulations detailed in the next sections. Overall a special attention was given to the shape of the electrodes to avoid direct line of sight between the trapped ions and the insulators so as to prevent them from charging.

Penning trap basics

Isobaric cleaning, in-trap decay spectroscopy and precision mass measurements all require to be able to trap ions in a confined space for extended periods of time. Earnshaw's theorem implies that a charged particle cannot be statically trapped by a purely electrostatic field. It allows, however, a particle to be dynamically trapped in a purely electrostatic field (Multi-Reflection device [START_REF] Wollnik | Time-of-flight mass spectrometers with multiply reflected ion trajectories[END_REF], Orbitrap [START_REF] Makarov | Electrostatic axially harmonic orbital trapping: a high-performance technique of mass analysis[END_REF]) in an oscillating electric field (Paul trap [START_REF] Paul | Electromagnetic traps for charged and neutral particles[END_REF]) or by a combination of electric and magnetic fields (Penning trap, storage ring). In a uniform, purely magnetic field B, a particle of charge q and mass m revolves perpendicularly to the field axis at the cyclotron frequency:

ω c = qB m (1)
In a Penning trap, a static harmonic electric field is superimposed on the magnetic field, ensuring axial and radial confinement, respectively. The perfect Penning trap is an especially elegant solution to Earnshaw's theorem: the electric field is static and harmonic in every direction and the stability of an ion inside the trap does not depend on its mass-over-charge ratio or its initial occupation of the phase space. As ω c (also dubbed the true cyclotron frequency) is inversely proportional to the mass, all mass measurement methods in a Penning trap revolve around measuring this frequency. Solving Poisson's equation in vacuum with the harmonicity condition (i.e. the potential depends on the spatial dimensions to the second order only) one finds:

V(x, y, z) -V(0, 0, 0) = V 0 4d 2 (2z 2 -x 2 -y 2 ) ( 2
)
Where d is the characteristic trap dimension calculated from the dimensions of the ring electrode and endcaps [START_REF] König | Quadrupole excitation of stored ion motion at the true cyclotron frequency[END_REF][START_REF] Brown | Geonium theory: Physics of a single electron or ion in a penning trap[END_REF], and V 0 is the potential difference between these electrodes. When using cylindrical or flat electrodes, the characteristic trap dimension does not match any mechanical length and must be calculated from the shape of the potential itself. The magnetic field is aligned with the z-axis. The motion of a charged particle in such a trap is a combination of three independent eigenmotions of frequencies:

ω z = qV 0 md 2 (3)
ω + = 1 2 ω c + ω 2 c -2ω 2 z (4) ω -= 1 2 ω c -ω 2 c -2ω 2 z (5)
The axial motion of frequency ω z is simply due to the harmonic electric potential and is of the order 50 kHz for very heavy ions, depending on the trapping potential. The two radial motions of frequency ω + and ω -are called reduced cyclotron motion and magnetron motion, respectively. The superposition of the electric field onto the magnetic field slightly modifies the pure cyclotron motion and thus its frequency, hence the name. However, ω + remains very close to ω c and is therefore almost perfectly linearly dependent on the mass ( 400 kHz at 250 amu). The slow magnetron motions originates from the E × B drift in an axially symmetric field and its frequency can be approximated to first order by ω -V 0 /2Bd 2 (i.e. 1 -5 kHz depending on the potential) and is therefore almost independent of the mass. Equations ( 4) and ( 5) yield

ω + + ω -= ω c (6)
and

ω 2 + + ω 2 -+ ω 2 z = ω 2 c ( 7
)
Eq. ( 6) implies that an excitation at the true cyclotron frequency can couple the two radial motions. This equality is, however, affected by imperfections in the electric field. Eq. ( 7) is generally used in the highest precision applications, as it is little sensitive to small trap imperfections [START_REF] Brown | Geonium theory: Physics of a single electron or ion in a penning trap[END_REF]. Indeed, in a real trap, the potential differs from the one given in Eq. ( 2). The true potential around the trap center can be conveniently expressed in spherical coordinates as:

V(r, θ, φ) = V 0 2 l,k C l,k r d l P k l (cosθ)cos(kφ) (8)
with P k l being the associated Legendre polynomial of degree l and order k with -l < k < l1 . From here on, we arbitrarily fix d = 10 mm and calculate an equivalent V 0 so that C 2,0 = 1. This allows to have comparable C l,k for traps with different geometries or voltage settings. In a perfect trap, the only non-zero coefficients are C 0,0 and C 2,0 and effectively, optimising a trap is equivalent to minimising or canceling all coefficients but these two. Imperfections of the electric and magnetic fields affect the eigenmotions and their frequency, thus possibly impairing the mass measurement capabilities of a trap. The precise effect of these imperfections on the different eigenfrequencies has already been described through a quantum mechanical approach [START_REF] Brown | Geonium theory: Physics of a single electron or ion in a penning trap[END_REF][START_REF] Bollen | The accuracy of heavyion mass measurements using time of flightion cyclotron resonance in a penning trap[END_REF] and a classical one [START_REF] Ketter | First-order perturbative calculation of the frequency-shifts caused by static cylindrically-symmetric electric and magnetic imperfections of a penning trap[END_REF].

One can notice that several of these coefficients are already cancelled owing to symmetries in the trap. Symmetry along the z-axis cancels the terms of odd l, while cylindrical symmetry guarantees that C l,k = 0 for all k 0. Thus in most cases, the study of trap imperfections is limited to C 4,0 and C 6,0 , higher order terms being neglected [START_REF] Eliseev | A phase-imaging technique for cyclotron-frequency measurements[END_REF][START_REF] Brown | Geonium theory: Physics of a single electron or ion in a penning trap[END_REF][START_REF] Bollen | The accuracy of heavyion mass measurements using time of flightion cyclotron resonance in a penning trap[END_REF][START_REF] Blaum | High-accuracy mass spectrometry with stored ions[END_REF][START_REF] Ramirez | An investigation of the accuracy of the pi-icr technique at shiptrap by a measurement of the mass difference between ¡sup¿132¡/sup¿xe and ¡sup¿131¡/sup¿xe[END_REF][START_REF] Nesterenko | Phaseimaging ion-cyclotron-resonance technique at the jyfltrap double penning trap mass spectrometer[END_REF]. Since in our case neither of the two traps from the novel tower are perfectly symmetric along the z-axis, the odd l coefficients will be discussed as well. In the second trap the cubic arrangement of the SSDs forces us to consider the k 0 coefficients, but the azimuthal π/2-periodicity imposes that k must be an integer multiple of 4.

Following the method shown in [START_REF] Brown | Geonium theory: Physics of a single electron or ion in a penning trap[END_REF][START_REF] Bollen | The accuracy of heavyion mass measurements using time of flightion cyclotron resonance in a penning trap[END_REF], one can calculate the shift in energy due to the terms of even l and deduce the resulting shifts in eigenfrequencies. In the second trap, it can be proven that the energy shift, and thus the frequency shift, due to the first k 0 terms C 4,4 and C 6,4 is zero. Therefore, we only need to consider the C l,0 coefficients, or simply C l . The impact of the term C 4 on the sum frequency is:

∆(ω + + ω -) C 4 = 3C 4 ω 2 z 4d 2 (ω + -ω -) [ρ 2 --ρ 2 + ] (9)
And the one of C 6 :

∆(ω + + ω -) C 6 = 30C 6 ω 2 z 16d 4 (ω + -ω -) [3z 2 (ρ 2 --ρ 2 + ) + (ρ 4 + -ρ 4 -)] (10)
Where ρ + and ρ -are the radii of the reduced cyclotron and magnetron motions, respectively. These equations show that the sum frequency will be equal to the true cyclotron frequency only when ρ + = ρ -. This happens only punctually during the conversion of a radial motion into another, but is generally not the case for any mass measurement procedure inside a Penning trap. Therefore all C l coefficients should be minimised to reduce the frequency shift between the measured sum frequency and the actual true cyclotron frequency, and thus allow for unbiased mass measurements. In the next section we describe how the potentials of both traps of the second tower were optimised.

Trap optimisation

We optimised the potentials of the different electrodes of both traps in order to enhance the quality of the electrostatic field. Practically, the first trap will be used for cooling and isobaric purification but not for mass measurement, which diminishes the interest of a precise potential optimisation. Indeed the mass resolution of the sideband cooling technique is typically a factor 50 larger than for ToF-ICR spectrometry for identical trapping times [START_REF] König | Quadrupole excitation of stored ion motion at the true cyclotron frequency[END_REF]. However, optimising the first trap is interesting for two main reasons:

• The mass measurement tower is composed of two identical cylindrical traps. Thus an optimisation of the first trap of the spectroscopy tower is valid for the second trap of the mass measurement tower and the calculated potentials could be used as a starting point for a manual optimisation.

• Simulated measurements of the cyclotron frequency in the first trap improve in accuracy after optimisation of the potentials (see further) and the frequency shift is consistent with the experimental mass precision measured during the offline tests [START_REF] Kolhinen | Commissioning of the double penning trap system mlltrap[END_REF]. This serves as a proof-of-principle for the optimisation and supports the performance expectation of the second trap.

Closed Open

Cylindrical trap Detector trap In the second trap, the axial lengths of the first two side electrodes were also optimised. From Eq. ( 2), we see that the quantity

H = V(x, y, z) -V(0, 0, 0) (x 2 + y 2 -2z 2 ) (11)
must be a constant in an ideal Penning trap. We thus chose to optimise the different potentials by minimising the goal function σ H / < H > over a certain volume near the trap center. This simple minimisation parameter allows quick and robust optimisation, though it does not give any direct insight on the mass measurement capabilities of a trap. Indeed σ H / < H > is a global parameter calculated over a volume and depends on the different C l,k coefficients. Yet, as seen before, each of these components has a different influence on the sum frequency ω + + ω -, therefore the frequency shift is correlated to σ H / < H > but cannot be derived from it. We thus decided to optimise the field with this parameter and check a posteriori the effect of this optimisation on the cyclotron frequency by simulation. Practically, H(x, y, z) was calculated at regularly spaced points in the trap using the potential array V built by the Poisson solver of SIMION 8.1 [START_REF]Simion charged particle optics simulation software[END_REF], and the goal function was minimised using the ROOT-implemented version of the MINUIT algorithm [START_REF] James | Minuit -a system for function minimization and analysis of the parameter errors and correlations[END_REF]. The potentials along the z-axis are shown in Fig. 2.

The coefficients C 1 to C 6 have been calculated from the potential array for both traps after optimisation and are reported in Table 1. We also included the results obtained with the potential set used in [START_REF] Kolhinen | Commissioning of the double penning trap system mlltrap[END_REF] for comparison (Non optimised or NO in the table). For the first trap, one can see that the optimisation decreased the even order coefficient and increased the odd ones. However, since odd components are very small by construction compared to even components, their impact is comparatively small. Also the first order parameter C 1 only slightly shifts (of the order of nanometers) the position of the potential center but does not impact the frequencies. In addition, it was shown in [START_REF] Brown | Geonium theory: Physics of a single electron or ion in a penning trap[END_REF] that the combination of first and third orders yields a frequency shift in the eigenfrequency ω z , which affects ω -and ω + but not the sum frequency. In the detector trap, the even order coefficients are comparable to those of the optimised first trap. The great difference in odd order terms between the two traps is due to the absence of a collimator on the exit side of the second trap, thus breaking the axial symmetry, while the first trap has collimators on both sides.

Figure 3 shows the simulated and theoretical shift in the frequencies of the radial motions. Simulations of the ion trajectories were done with SIMION and the fact that they mostly follow the theoretical trends demonstrates their reliability. The effect of the optimisation in the first trap is striking, as it almost cancels the frequency shifts. However, one can notice that the frequency shift in the second trap is much larger than in the first trap when both are optimised, while having comparable C l and even a smaller C 4 . This is due to the fact that the shifts are proportional not only to the C l coefficients, but also to the depth of the potential well, which is typically 5.4 times bigger in the second trap.

Although we chose to show the frequency shifts with the same axial amplitude in both traps, it should be noticed that it should be smaller in the second trap for the same trapping energy. Should the axial amplitude in the second trap be reduced, the corresponding frequency shifts would be reduced as well, though not uniformly for all ρ +/-.

With the Phase Imaging Ion Cyclotron Resonance technique (PI-ICR) [START_REF] Eliseev | Phase-imaging ion-cyclotron-resonance measurements for short-lived nuclides[END_REF], ions are excited to a quasi pure radial motion (either magnetron or reduced cyclotron) and then accumulate the phase from which the frequency of the corresponding motion can be deduced. If indeed ρ -can be neglected while measuring ω + and ρ + can be neglected while measuring ω -, then the theoretical frequency shifts are symmetric (as can be seen in Equations ( 9) and ( 10) and Figure 3) and the net effect on the sum frequency is 0. However, it was still important to minimise C 4 and C 6 as the ρ-dependency of the frequency could induce a smearing of the ion bunch after the phase accumulation and thus limit the precision of the mass measurement [START_REF] Eliseev | A phase-imaging technique for cyclotron-frequency measurements[END_REF].

It can be noticed in Figure 3 that the cyclotron frequency shift in the second trap follows nicely its theoretical lineshape, while the magnetron frequency shift steers away from it. In order to investigate this unexpected asymmetry we repeated the same simulations in SIMION, ignoring this time the potential calculated from the geometry and using instead a theoretical potential of our choice. This way, it was possible to artificially "turn on and off" the coefficients C 4 , C 6 , C 4,4 and C 6,4 to identify which was responsible for this effect. The additional frequency shift on the magnetron motion was observed to depend only on C 4,4 and to be proportional to C2 4,4 , which is quite remarkable since until now all calculated frequency shifts depended linearly on the C l . Thus this result does not contradict the previous statement that the expected frequency shifts due to non-cylindrical components should be 0, as this calculation was only considering linear dependencies on the C l coefficients 2 .

By summing the reduced cyclotron and magnetron frequency shifts, we can estimate that the systematic error in the estimation of the true cyclotron frequency is 5.3 * 10 -8 at a radius of 1 mm and 32 * 10 -8 at 2 mm. For comparison the systematic error in the first trap is 3.2 * 10 -8 at both radii, in both optimised and non-optimised configurations. Nevertheless, for small motion radii typically used in PI-ICR (< 1 mm), our cubic geometry is still comparable to a cylindrical Penning trap regarding the frequency shifts, the ρ-dependency of those shifts and the systematic error on the sum frequency.

The Time of Flight Ion Cyclotron Resonance technique (ToF-ICR) [START_REF] König | Quadrupole excitation of stored ion motion at the true cyclotron frequency[END_REF] raises different issues, as it does not feature a pure radial motion during most of the procedure. During a typical cycle of a ToF-ICR measurement, an initially pure magnetron motion is converted to a pure reduced cyclotron motion by a quadrupolar RF excitation. The motion conversion becomes resonant when the excitation frequency ν r f is close to the sum frequency. Because the

Δν -(Hz)

Figure 3: Simulated deviations of the magnetron (top) and reduced cyclotron (bottom) frequencies from the expected values in an ideal Penning trap as a function of the corresponding motion radius. Frequency deviations are shown for the non-optimised first trap (blue squares), optimised first trap (green crosses) and optimised second trap (yellow triangles). The magnetron (resp. reduced cyclotron) frequency has been obtained by simulating a trajectory with mixed magnetron (resp. cyclotron) and axial motions and measuring the accumulated phase of the radial motion over a 200 ms period. The amplitude of the axial motion was 1 mm in all cases. The curves of matching colour and trend are the theoretical frequency shifts calculated from Equations ( 9) and ( 10) and the C 4 and C 6 coefficients from Table 1. energy of the magnetron motion is negligible in comparison to the one of the reduced cyclotron motion in such electric and magnetic fields, the conversion resonance leads to an energy resonance that can eventually be measured by ToF. Without initial cyclotron motion, the two motion radii are related through:

ρ 2 -(t) = ρ 2 -(0) -ρ 2 + (t) (12)
Provided that the excitation potential is constant, the radii of both these motions follow two beating curves of opposite phase [START_REF] König | Quadrupole excitation of stored ion motion at the true cyclotron frequency[END_REF] and match each other only once per conversion cycle. This means that the frequency shifts expressed in Equations ( 9) and ( 10) cancel for a very short time and that the excitation is off-resonance during most of the motion conversion. However, for a complete conversion, ∆(ω + + ω -) C 4 /C 6 will be time-antisymmetric with respect to the point ρ + = ρ -and thus the average deviation at the resonance frequency due to ( 9) and (10) will be 0.

We simulated with SIMION the motion conversion of a single ion with an initially pure magnetron motion in both traps. Figure 4 (top) shows the well known energy vs frequency resonance for the optimised first trap and fitted by the theoretical curve from [START_REF] König | Quadrupole excitation of stored ion motion at the true cyclotron frequency[END_REF]. If the excitation frequency is different from the unperturbed cyclotron frequency, the motion conversion will always be incomplete, and the average magnetron radius will be larger to the average reduced cyclotron radius. Thus, although the central peak of the resonance will be almost unperturbed, the side peaks will be shifted in frequency in the same direction. This distortion is barely visible on the resonance itself, but its effect is much clearer on the fit residues shown in the bottom panel of Figure 4. The residues in all three cases (non-optimised and optimised first trap, optimised second trap) are close to 0 at the resonance frequency and the shift of the side peaks makes the residues antisymmetric. When using the unoptimised set of potentials in the first trap, the distortion of the resonance induces a shift in the estimation of the cyclotron frequency of 2.4 * 10 -7 , while with optimised potentials, it drops to 2.0 * 10 -8 . Because the trapped ions actually have a continuous distribution in z-amplitude and initial ρ -, these shifts are responsible for resonance broadenings and systematic uncertainties of the same order. Thus the frequency shift in the first trap can be rightfully compared to the mass uncertainty of 2.9 * 10 -8 and the accuracy of 3.6 * 10 -8 obtained during the commissioning of the measurement tower [START_REF] Kolhinen | Commissioning of the double penning trap system mlltrap[END_REF].

The shift in the estimation of the cyclotron frequency in the cubic trap is 8.6 * 10 -8 . Once again, the larger error mostly results from the fact that the potential well in the detector-trap is much deeper than in the first trap. The residues and the systematic error would be lower if the ions had a smaller axial amplitude in the second trap. The inaccuracy difference could also be partially due to the difference in the C 4/6 factors, which is a consequence of the suboptimal aspect ratio of the second trap (i.e. the ratio of the width of the trap to its length) imposed by the size of the detectors.

In any case, it should be noticed that the reduced performances of the second trap are not caused by its cubic nature, since the average energy shift from the azimuthal components of the field over a turn of cyclotron/magnetron motion is 0, as is the resulting frequency shift. Thus the mass measurement capabilities of our detector trap seem mostly limited by the octupolar and dodecapolar components of the electric field and the depth of the potential well. This conclusion remains valid for any trap geometry featuring square-shaped electrodes. In our case the geometry of the silicon box and the potentials to be applied are constrained by the α-decay spectroscopy requirements.

Bunch Manipulation

In order to obtain more realistic expectations of the trap's performances, we simulated the flight path of a bunch of 100 ions through both the preparation and measurement traps. In the first trap the ions where exited by a dipolar pulse of 20 ms of amplitude 200 mV at the magnetron frequency, followed by a quadrupolar excitation of amplitude 45 mV for 250 ms at the cyclotron frequency. As the magnetron motion is slowly converted into reduced cyclotron motion, the latter is continuously dampened by helium buffer gas with a pressure of 10 -4 mbar. The ion-gas interaction was simulated by a simple viscous damping model. The centering of the bunch is illustrated in Figure 5. The centered bunch was then transferred to the second trap and submitted to a ToF-ICR excitation pattern. A 10 ms dipolar magnetron excitation of 420 mV was followed by a 250 ms quadrupolar cyclotron excitation of 300 mV. The energy resonance for the complete ion bunch is shown in Figure 6. The measured frequency is shifted from the true cyclotron frequency by 10(10) mHz, i.e. a relative shift of 23(23) * 10 -9 at mass A = 250, confirming the quality of the field. The results are better with a realistic bunch than with a single pure-motion ion as considered in the previous section. This can be explained by the fact that the simulated transfer of the ion bunch from the first trap to the second leaves the ions with an axial amplitude below 0.5 mm. It is possible that the electric field imperfections in the real trap will turn out to be larger than what has been estimated, since our model does not account for misalignments or the possible charging of the small fraction of the PCB surface not covered by any electrode (see Fig. 1), though in the latter case, small plate-electrodes could be inserted to shield the insulating parts. However, our simulations show that this geometry itself is at least compatible with mass measurements with an uncertainty of a few 10 -8 .

Conclusion and perspectives

In this paper we have described the goals and layout of a new double-trap assembly initially designed for in-trap decay spectroscopy and explored the possibility of using the same apparatus for precision mass measurements. The geometry and potentials of the novel trap have been adjusted to allow for dipolar and quadrupolar excitations required by the ToF-ICR and PI-ICR techniques. Simulations of the first trap with realistic bunches are consistent with the theory and simulations of the second trap support the feasibility of mass measurement with an uncertainty down to 23(23) * 10 -9 . Should the second trap of the novel tower be able to reach such precision, it could be used for mass measurements of exotic nuclei, wether they are α-emitters or not, and could provide valuable inputs in different regions of the chart of nuclides.

Mass measurements in the VHE and SHE regions allow to probe the evolution of shell structure and onset of deformation, and could be performed "simultaneously" with α-decay spectroscopy. Indeed, since an α-decaying ion is lost for mass measurement anyway, it does not matter wether its decay product is detected or not.

If the novel trap is limited to a precision of 10 -7 it could still measure masses of astrophysical interest, in particular those relevant to the paths of the rapid capture processes responsible for the abundances of elements heavier than iron. The first assembly will already measure masses of neutron-rich nuclei produced at ALTO, especially in the silver chain [START_REF] Ramirez | New program for measuring masses of silver isotopes near the n=82 shell closure with mlltrap at alto[END_REF], and the second assembly could be tested for mass measurement as well. In DESIR, the S3-beams will provide many mass measurement opportunities along the rp-process line. Finally, mass measurements in the 10 -7 -10 -8 precision range could be used as inputs or discrimination tests for the many nuclear interaction models that describe the exotic regions of the chart of nuclei to be covered by ALTO and S3.

Figure 1 :

 1 Figure 1: Left, PCB-mounted silicon detector with (1) silicons strips, (2) guard ring, (3) contact pads and (4) gold-plated sections used as correction electrodes. Center, mechanical assembly used at MLL to test the silicon detectors inside the magnet, showing (5) customized PEEK connectors. Right, CAD view of the designed trap structure, featuring (6) segmented support electrodes and (7) side electrodes.

Figure 2 :

 2 Figure 2: Top, SIMION view of the two-trap system. The potential maps of each trap have been superimposed and exhibit the expected hyperbolic equipotentials. Bottom, potential along the beam axis. The potential depth of the second trap results from the optimisation after imposing a 100 V difference between the silicon strips and the guard rings.

Figure 4 : 2 (

 42 Figure 4: Top, kinetic energy of an ion after simulated quadrupolar excitation as a function of the detuning (first trap with optimised potentials). The shape of the resonance is remarkably well fitted by the theoretical curve sin 2 (ω B T r f )/ω 2 B with ω B = 1 2 (ω r f -ω c ) 2 + k 2 0 . : parameters used for the simulation are z(0) = 2 mm, ρ -(0) = 1.18 mm, A/Q = 250, V r f = 25 mV and T r f = 102.4 ms. Bottom, fit residues of the resonances in a non-optimised first trap (blue squares), an optimised first trap (green crosses) and an optimised second trap (yellow triangles).

Figure 5 :

 5 Figure 5: Bunch of 100 ions before (black) and after (green) cooling in the first trap.

Figure 6 :

 6 Figure 6: Energy distribution of the ion bunch as a function of the detuning frequency. The resonance is fitted with a reduced χ 2 of 1.3, owing to the trap imperfections.

Table 1 :

 1 Comparison of the C l coefficients and the optimisation goal function σ H /H for non-optimised (NO) and optimised (O) sets of potentials for both traps.

		First Trap	Second Trap
		NO	O	O
	σ H /H	9.84 10 -3	1.56 10 -3	4.17 10 -3
	C 1	1.09 10 -7	3.02 10 -7	7.77 10 -6
	C 2	1.0	1.0	1.0
	C 3	4.10 10 -8	1.14 10 -7	1.23 10 -4
	C 4	-1.01 10 -2	1.07 10 -3	8.82 10 -4
	C 5	4.75 10 -9	1.31 10 -8	1.33 10 -5
	C 6	-6.78 10 -3 -5.61 10 -3	-9.38 10 -3

The order of the associated Legendre polynomials is almost always referred to as "m" in the literature. We chose to use "k" here instead to avoid confusion with the mass.

In[START_REF] Ketter | First-order perturbative calculation of the frequency-shifts caused by static cylindrically-symmetric electric and magnetic imperfections of a penning trap[END_REF] for example, these have been called "first order frequency shifts", but we avoid this term here to avoid confusion with the order k of the Legendre polynomial.

Acknowledgements

This work was supported by CNRS and the P2IO LabEx (ANR-10-LABX-0038) in the framework "Investissements d'Avenir" (ANR-11-IDEX-0003-01) managed by the Agence Nationale de la Recherche (ANR, France).


Olivier Dumortier

Gaia Fabris

Didier Pisani

Virginie Casamento

Nadine Gautier

Charlotte Hinault

Patricia Lebrun

Christophe Duranton

Michel Tauc

Stéphane Dalle

F Pisani

Stephane Dalle

Julie Kerr-Conte

François Pattou

Marc Prentki

Emmanuel Van Obberghen
email: emmanuel.van-obberghen@unice.fr

microRNA-375 regulates glucose metabolism-related signaling for insulin secretion

Keywords: diabetes, glucose metabolism, insulin secretion, microRNAs, pancreatic islets GSIS, Glucose-stimulated insulin secretion, KIC, alpha-ketoisocaproate, KRBH, Krebs-Ringer Bicarbonate-Hepes buffer, Ldh, lactate dehydrogenase, LP diet, low protein diet, Mdh1, malate dehydrogenase 1, Mpc, mitochondrial pyruvate carrier, miR, microRNA, miR-375, microRNA-375, Pc, pyruvate carboxylase, Pdh, pyruvate dehydrogenase, Pdk, pyruvate dehydrogenase kinase

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Introduction

The main beta cell mission consists in its ability to secrete insulin for maintenance of organismal glucose homeostasis. This hallmark requires expression of a set of genes (allowed genes) and the concomitant repression of others (disallowed genes) [START_REF] Pullen | When less is more: the forbidden fruits of gene repression in the adult betacell[END_REF][START_REF] Quintens | Why expression of some genes is disallowed in beta-cells[END_REF]. Indeed, beta cells have a dedicated metabolism comprised of a tightly regulated chain of elements from glucose sensors to a specialized exocytosis machinery.

Glucose metabolism in beta cells linked to insulin secretion has several exclusive features. First, glucose transport is not limiting for its metabolism, and it results in a rapid equilibrium between intracellular and extracellular glucose at all glycemic levels. The second particular trait is that glycolysis is initiated by glucokinase having a high Km for glucose associated to an elevated Vmax, and being devoid of feedback control [START_REF] Prentki | Metabolic signaling in fuel-induced insulin secretion[END_REF]. As beta cells express low levels of plasma membrane monocarboxylate transporters, little or no monocarboxylates, including lactate, enter the cells. Further, the low lactate dehydrogenase (LDH) activity of the beta cells accounts for the fact that a major fraction of the glucose entering the beta cells is oxidized by the mitochondria [START_REF] Delghingaro-Augusto | Islet beta cell failure in the 60% pancreatectomised obese hyperlipidaemic Zucker fatty rat: severe dysfunction with altered glycerolipid metabolism without steatosis or a falling beta cell mass[END_REF][START_REF] Schuit | Metabolic fate of glucose in purified islet cells. Glucose-regulated anaplerosis in beta cells[END_REF]). These distinctive beta cell properties must be maintained to achieve efficient oxidative phosphorylation, lipid metabolism and signaling [START_REF] Prentki | Metabolic signaling in fuel-induced insulin secretion[END_REF], thus making optimal glucose sensing possible. It is thought that beta cell dysfunction in type 2 diabetes could result from a reduced expression of key genes, triggering the loss of beta cell identity and hence promoting dedifferentiation [START_REF] Delghingaro-Augusto | Islet beta cell failure in the 60% pancreatectomised obese hyperlipidaemic Zucker fatty rat: severe dysfunction with altered glycerolipid metabolism without steatosis or a falling beta cell mass[END_REF]Talchai, et al. 2012;Weir, et al. 2001). Importantly, grounds have been gleaned in favor of beta cell dedifferentiation in human type 2 diabetes. Indeed, dedifferentiated cells account for almost 40% of the beta cells in type 2 diabetes patients compared to 8% in controls [START_REF] Cinti | Evidence of beta-Cell Dedifferentiation in Human Type 2 Diabetes[END_REF]). Thus, it appears that the maintenance of beta cell identity throughout life is crucial for glucose homeostasis and organismal physiology.

The biological importance of microRNAs is substantiated by the diverse and profound phenotypic consequences occurring upon changes in their expression. These modifications are associated with physiological modulations, but also with perturbed development and pathological situations. Thus, microRNAs have emerged as major modulators of gene expression in many biological programs including organ development and metabolism [START_REF] Dumortier | MicroRNAs and Metabolism Crosstalk in Energy Homeostasis[END_REF].

One of the most relevant and widely explored microRNAs in beta cells is miR-375 [START_REF] Dumortier | Shaping and preserving beta-cell identity with microRNAs[END_REF][START_REF] Guay | MicroRNAs and the functional beta cell mass: For better or worse[END_REF][START_REF] Martinez-Sanchez | MiRNAs in beta-Cell Development, Identity, and Disease[END_REF], which is preferentially expressed in islets and is the most abundant microRNA in adult beta cells [START_REF] Poy | A pancreatic islet-specific microRNA regulates insulin secretion[END_REF]).

We and others demonstrated that this microRNA is a chief regulator of beta cell mass and functions through incompletely understood mechanisms [START_REF] Dumortier | Maternal protein restriction leads to pancreatic failure in offspring: role of misexpressed microRNA-375[END_REF][START_REF] El Ouaamari | miR-375 targets 3'-phosphoinositide-dependent protein kinase-1 and regulates glucose-induced biological responses in pancreatic beta-cells[END_REF][START_REF] Latreille | miR-375 gene dosage in pancreatic beta-cells: implications for regulation of beta-cell mass and biomarker development[END_REF][START_REF] Poy | miR-375 maintains normal pancreatic alpha-and beta-cell mass[END_REF]). In addition, several studies have found that miR-375 expression is upregulated in islets from type 2 diabetics [START_REF] Bloomston | MicroRNA expression patterns to differentiate pancreatic adenocarcinoma from normal pancreas and chronic pancreatitis[END_REF][START_REF] He | A Systematic Study of Dysregulated MicroRNA in Type 2 Diabetes Mellitus[END_REF]Zhao, et al. 2010). Similarly, we observed in a murine model of predisposition to type 2 diabetes following a low protein diet (LP) during pregnancy, that miR-375 expression is increased in the endocrine pancreas of the progeny [START_REF] Dumortier | Maternal protein restriction leads to pancreatic failure in offspring: role of misexpressed microRNA-375[END_REF]. This is accompanied by a reduction in both glucose-stimulated insulin secretion (GSIS) and beta cell proliferation.

Anti-miR-induced normalization of miR-375 expression levels in the islets of LP descendants partially restored insulin secretion and cell proliferation to levels of control animals. However, it should be noted that no consensus exists on the differential expression of miR-375 in the healthy versus the type 2 diabetic condition as reported by other studies in humans [START_REF] Ofori | Elevated miR-130a/miR130b/miR-152 expression reduces intracellular ATP levels in the pancreatic beta cell[END_REF][START_REF] Seyhan | Pancreasenriched miRNAs are altered in the circulation of subjects with diabetes: a pilot cross-sectional study[END_REF] or animals [START_REF] Esguerra | Differential glucose-regulation of microRNAs in pancreatic islets of non-obese type 2 diabetes model Goto-Kakizaki rat[END_REF], in which no increased miR-375 expression was observed in the disease situation. This missing general agreement could be due, at least in part, to the pronounced heterogeneity of type 2 diabetes concerning the underlying pathophysiology, epigenetic/genetic landscape, disease progession and degree of metabolic perturbations.

While it is generally accepted that miR-375 is essential for the development of the endocrine pancreas [START_REF] Avnit-Sagi | The promoter of the pri-miR-375 gene directs expression selectively to the endocrine pancreas[END_REF][START_REF] Joglekar | Expression of islet-specific microRNAs during human pancreatic development[END_REF][START_REF] Kloosterman | Targeted inhibition of miRNA maturation with morpholinos reveals a role for miR-375 in pancreatic islet development[END_REF], facts in favor of additional roles are appearing. Indeed, evidence is being built highlighting an association between low miR-375 levels and beta cell dedifferentiation [START_REF] Nathan | MiR-375 promotes redifferentiation of adult human beta cells expanded in vitro[END_REF]. Further, it has been recently found in vitro that miR-375 overexpression is sufficient to generate insulinproducing cells from pluripotent stem cells or from human mesenchymal stem cells (Shaer, et al. 2014a;Shaer, et al. 2014b). Taken together the striking features of miR-375 action in beta cells, i.e. inhibition of GSIS and promotion of beta cell differentiation, reveal at first glance a potentially discordant image. Beta cell differentiation is a complex multistep process finely orchestrated by numerous transcription factors.The ultimate beta cell maturation step is thought to occur around weaning.

It consists in the acquisition of glucose stimulus-secretion coupling which depends on the occurrence of glucose metabolism dedicated to insulin secretion [START_REF] Stolovich-Rain | Weaning triggers a maturation step of pancreatic beta cells[END_REF].

As glucose metabolism governs insulin secretion and is inherent to mature beta cells we posit here that the miR-375 effects on beta cell function could be due to glucose metabolism alterations.

Materials and methods

Reagents

Culture media and buffer solutions were from Gibco (ThermoFisher Scientific, Gometz le Châtel, France), FBS and trypsin from Invitrogen (Cergy Pontoise, France). Other reagents were from Sigma-Aldrich Chimie (Saint-Quentin Fallavier, France).

Human islets

Islets were provided by the Islets for Research distribution program through the European Consortium for Islet Transplantation under the supervision of the Juvenile Diabetes Research Foundation (31-2012-783). Human pancreases were harvested from 5 adult brain-dead individuals (males=2, females=3; age, mean ± SEM: 44.0±10.0 years; BMI, 21.0±1.0 kg/m 2 ; HbA1c, 36±1 mmol/mol (5.4±0.1%)) in agreement with French regulations and Lille University Ethical Committee. Experiments used islets with >90% viability and >80% purity (endocrine versus exocrine tissue).

Animals and diets

All procedures followed ARRIVE guidelines, were conducted in accordance with EU directives for animal experiments (2010/63/EU) and were approved by the French Research Ministry (MESR 00500.02). Three month-old Wistar rats (Janvier; Le Genest Saint Isle, France) were kept under conventional conditions, with free access to water and food. Nulliparous female rats (200-250 g) were mated with male rats and used at day 21 of gestation.

Islet isolation

3 month-old rat islets were obtained after density gradient centrifugation in histopaque-1077 (Sigma) as previously described [START_REF] Dumortier | Impairment of rat fetal beta-cell development by maternal exposure to dexamethasone during different time-windows[END_REF]. Hand-picked islets were cultured in RPMI-1640 medium supplemented with FBS (10%, v/v) and antibiotics. Neoformed fetal rat islets were obtained as described [START_REF] Dumortier | Impairment of rat fetal beta-cell development by maternal exposure to dexamethasone during different time-windows[END_REF].

Culture and transfection of dissociated islet cells

Rat or human islets were dissociated by trypsinization, and seeded at a density of 25×10 3 cells/cm 2 in dishes coated with 804G-ECM [START_REF] Dumortier | Maternal protein restriction leads to pancreatic failure in offspring: role of misexpressed microRNA-375[END_REF][START_REF] Parnaud | Signaling pathways implicated in the stimulation of beta-cell proliferation by extracellular matrix[END_REF]

RNA extraction and RT-qPCR

RNAs were isolated using TRIzol reagent (Invitrogen) according to the manufacturer's instructions and RNA quality was tested by UV spectrophotometry on a NanoDrop 1000 device (Thermo Fisher Scientific).

For miRNA analysis, 10 ng of total RNA was reverse transcribed using Universal cDNA synthesis kit (Exiqon). qPCR reactions were prepared using SYBR Green master mix, Universal RT (Exiqon) and microRNA LNA PCR primers (Exiqon) according to the manufacturer's manual. qPCR and data evaluation were performed using StepOnePlus apparatus and associated software (Applied Biosystem, ThermoFisher). Data were analyzed using Ct method with U6 and 5S (control primers set from Exiqon ref. YP00203906 and YP00203907) as endogenous controls and "miR-CTL group" as control condition.

For mRNA analysis, 1 μg of RNA was reverse-transcribed into cDNA using M-MLV-RT and analyzed using SYBR Green (Applied Biosystem, ThermoFisher) and a StepOnePlus apparatus and associated software (Applied Biosystem, ThermoFisher). Data were analyzed using Ct method with Cyclophilin A as housekeeping and "miR-CTL group" as control condition.

The primers sequences are displayed in Table 1.

Lactate determination

Lactate concentration was determined by ionic chromatography using a Dionex DX600 device equipped with an ion Pac AS11 column (ThermoFisher). Sequential anion elution including lactate was obtained at 1 ml/min by a KOH gradient generated by the EG40 eluent generator according to the manufacturer's instructions.

Insulin secretion

All experiments were performed using Krebs-Ringer Bicarbonate-Hepes buffer (KRBH) containing 3 mmol/l glucose and 0.1% BSA (w/v). Dissociated islet cells were pre-incubated for 1h at 37 °C before incubation in fresh medium containing secretagogues. After 1h, media and cell homogenates obtained by sonification were analyzed for insulin content using a rat insulin ELISA kit (Mercodia AB, Uppsala, Sweden). To eliminate variations due to differences in cell number, insulin secretion was expressed as the percentage of the cellular insulin content, which is referred to as fractional insulin release.

Glucose uptake

Islet cells were preincubated for 45 min at 37°C in 3 mmol/l glucose KRBH and then 10 min in KRBH containing 20 mmol/l glucose and 0.5 uCi of [ 3 H] deoxyglucose (Amersham Pharmacia Biotech, Uppsala, Sweden). Glucose incorporation was stopped on ice and cells were lysed using NaOH 0.2N and neutralized with HCl 0.2N. Radioactivity was measured and the total protein amount recorded using BCA method. Results are expressed in cpm/mg protein/min.

Mitochondrial metabolism

For metabolic analysis, dissociated cells were seeded in a 24 multi-well plate (Seahorse, Agilent, Santa Clara, CA, USA) and cultured/transfected as described above. The oxygen consumption rate (OCR) was determined using an XF24 Extracellular Flux Seahorse Analyzer (Agilent). Rotenone and antimycin-A (2 µmol/l each) were used to inhibit mitochondrial respiration and oligomycin A (1.2 µmol/l) to inhibit ATP synthase.

Statistical analysis

Data are presented as mean ± SEM. Statistical analyses were performed using InStat3 software (Graphpad, San Diego, CA, USA). Paired two-tailed Student's t tests were used to compare differences between samples from paired experiments. Differences between all other datasets were analyzed by one-way ANOVA with Student-Newman-Keuls post-hoc test. p-values <0.05 were considered significant.

Results

miR-375 overexpression in islet cells impairs insulin secretion and the Ca2+ rise induced by glucose but not by KCl

We investigated the miR-375 impact on beta cell function by comparing dissociated primary adult rat islet cells transfected with miR-375 or control microRNA (CTL). Double-stranded RNA oligonucleotides corresponding to mature miR-375-3p or control microRNA were first tested in a dose-response experiment from 50 to 200 nmol/l and compared to the untransfected condition (Fig. 1a-c). Augmenting the amount of transfected miR-375 resulted in an increased miR-375 level in the cell (Fig. 1a) and in a decreased insulin secretion in response to 20 mmol/l glucose (Fig. 1b), without affecting the insulin cell content (Fig. 1c). Note that under our experimental conditions 100 nM control oligonucleotide are not deleterious for beta cell function and insulin secretion as these are the same compared to the untransfected condition.

Therefore, we choose to use transfection with 100 nmol/l of miR-375 which resulted in an approximately 25-fold increase in miR-375 level and a reduced GSIS by approximately 50% at all glucose concentrations (Fig. 2a).

To evaluate whether this could be attributed to altered exocytosis, we measured insulin secretion at low glucose (3 mmol/l) in the presence of depolarizing KCl concentrations. High miR-375 levels did not modify insulin secretion at the KCl concentrations tested (Fig. 2b).

Further, the glucose-induced cytosolic Ca 2+ rise was almost abolished, whereas that caused by KCl was preserved (Fig. 2c). Together the data are compatible with the view that miR-375 interferes with GSIS by altering beta cell metabolism and metabolic signaling for secretion rather than by hampering late steps in regulation of the exocytosis apparatus.

miR-375 impacts glucose-stimulated respiration

To investigate whether the dampened insulinotropic action of glucose could be due to a miR-375-induced inhibition of glucose uptake, we compared glucose transport using 3 H-2deoxyglucose in adult rat primary islet cells transfected with control microRNA or with miR-375. As shown (Fig. 2d), no difference in 2-deoxyglucose uptake was observed at 20 mmol/l glucose. To decrypt miR-375 effects on intermediate metabolism, O2 consumption in response to glucose was evaluated. It was profoundly reduced by miR-375 (Fig. 2e-g) to a similar extent as the GSIS inhibition. Moreover, miR-375 transfected cells must synthesize less ATP in response to glucose as they consume less oxygen (Fig. 2f) with an equivalent coupling to ATP synthesis (Fig. 2g).

Reduced endogenous miR-375 levels in adult rat primary islet cells increases glucose metabolism and insulin secretion

To confirm the repressive miR-375 action on insulin secretion, we decreased the endogenous miR-375 level with its antisens. miR-375 reduction in adult rat primary islet cells increased GSIS with no impact on insulin content (Fig. 3a-b). Remarkably, the diminished miR-375 level augmented glucose-induced O2 consumption (Fig. 3c-d). Together, our gain and loss of function approach identifies miR-375 as a robust insulin secretion modulator which impacts glucoseinduced mitochondrial metabolism.

miR-375 does not affect the action of a fuel stimulus enhancing mitochondrial metabolism independently of glycolysis

To further explore miR-375 action on cell metabolism, we used α-ketoisocaproate (KIC), which induces insulin release by directly augmenting the tricarboxylic acid (TCA) cycle intermediate -ketoglutarate, and also via acetyl-CoA and acetoacetate production. As illustrated in Fig. 4a, KIC stimulated insulin secretion in a dose-dependent manner comparably in control and miR-375 overexpressing islet cells. Further, mitochondrial metabolism remained unaltered in miR-375-transfected islets in response to KIC, as reflected by O2 consumption determinations (Fig. 4b-c).

miR-375 modifies pyruvate metabolism

The above results suggest that miR-375 could perturb insulin secretion by interfering with the production of glycolysis metabolites, in particular the last one in the pathway, pyruvate. To examine if miR-375 controls pyruvate mitochondrial metabolism we tested the effect of high pyruvate (50 mmol/l) concentrations on insulin secretion and O2 consumption. We used an elevated concentration of pyruvate, as it is not an efficacious secretagogue because the plasma membrane monocarboxylate transporter-1 is poorly expressed in adult islets [START_REF] Pullen | Overexpression of monocarboxylate transporter-1 (SLC16A1) in mouse pancreatic beta-cells leads to relative hyperinsulinism during exercise[END_REF]. While pyruvate induced insulin secretion in control islets, its insulinotropic effect in miR-375 transfected islets was diminished (Fig. 4d) to a similar extent as GSIS (Fig. 1a).

Forced miR-375 expression also reduced O2 consumption in response to pyruvate (Fig. 4e). In differentiated beta cells, pyruvate is slightly reduced to lactate and hence most of the glucosederived pyruvate is metabolized in the mitochondria via pyruvate dehydrogenase and anaplerotic reactions [START_REF] Ainscow | Acute overexpression of lactate dehydrogenase-A perturbs beta-cell mitochondrial metabolism and insulin secretion[END_REF]. However, islet cells overexpressing miR-375 showed a 2-fold increase in lactate release into the medium (Fig. 4f). This suggests that enhanced miR-375 expression partially redirects pyruvate metabolism from mitochondrial oxidation to anaerobic glycolysis and lactate production.

Forced miR-375 expression in human islet cells reduces insulin secretion in response to glucose but not to KCl or to KIC

Next we addressed in human beta cells the role of miR-375 as regulator of glucose metabolism and GSIS. We measured insulin secretion in islets from 5 non-diabetic donors transfected or not with miR-375. An approximately 12-fold increased miR-375 level 72 h post transfection (Fig. 5a) markedly reduced GSIS, without affecting the insulinotropic action of KIC or KCl (Fig. 5b). Hence, the miR-375 overexpression data on human islet cells reproduce the results obtained with adult rat islet cells in terms of insulin secretion in response to glucose, KIC and KCl.

Forced miR-375 expression in adult rat primary islets and human islet cells causes deregulation of genes involved in specialized beta cell metabolism

To explore the molecular underpinnings of the action of miR-375 on insulin secretion we looked at the gene expression of key actors of mitochondrial metabolism. As shown in Fig. 6a, in rat islets overexpressing miR-375 mitochondrial pyruvate carrier-1 and -2 expression was not affected by miR-375 suggesting that pyruvate's uptake into the mitochondria is unaltered. Once in the mitochondria, pyruvate enters the TCA cycle after its decarboxylation to acetyl CoA by the PDH complex or after its carboxylation to oxaloacetate by pyruvate carboxylase (PC).

Interestingly, in miR-375 overexpressing cells, the mRNA level of Pdk4 (pyruvate dehydrogenase kinase-4) was increased, while that of Pc was decreased (Fig. 6a). Together our data support the notion that miR-375 reduces pyruvate oxidation and its conversion via carboxylation into intermediates for the TCA cycle. Further, the mRNA encoding cytosolic malate dehydrogenase1 (Mdh1), a component of the malate-aspartate shuttle that transfers reducing equivalents to the mitochondria and the pyruvate-citrate cycle, was downregulated (Fig. 6a). Reduced Mdh1 transcript levels suggest diminished mitochondrial energy metabolism and cataplerotic signals in response to glucose, that will decrease insulin secretion. Of note, in human islets overexpressing miR-375, similarly to rat islets, Pc and Mdh1 expressions were downregulated, while Pdk4 mRNA was upregulated (Fig. 6b).

Reduced miR-375 expression is associated with in vitro glucose responsiveness and maturation of fetal rat beta cells

We next explored the possibility that miR-375 could be involved in beta cell metabolic maturation for GSIS and thus interfere with the acquisition of glucose-responsiveness in the transition from fetal to neonatal beta cells. We took advantage of the finding that functional maturation of glucose stimulus-secretion coupling of fetal rat islets can be accelerated in vitro by glucose (Sjoholm, et al. 2000a, b). Thus, we measured the expression of miR-375 in untreated fetal islets compared with fetal islets after in vitro maturation by glucose (neonatal islets). As illustrated in Fig. 7a, untreated fetal islets did not respond to 20 mmol/l glucose, but they released insulin when stimulated with KIC. However, after in vitro maturation, they secreted insulin appropriately in response to high glucose (Fig. 7b). Remarkably, lower glucose responsiveness of insulin release by untreated fetal beta cells was associated with high miR-375 expression compared to neonatal islets (Fig. 7c). Collectively, these results suggest that repression of miR-375 expression participates to the acquisition of glucose stimulus-secretion coupling.

Discussion

Since their discovery, several microRNAs have been implicated in the development and function of beta cells [START_REF] Dumortier | Shaping and preserving beta-cell identity with microRNAs[END_REF][START_REF] Guay | MicroRNAs and the functional beta cell mass: For better or worse[END_REF]. Amongst these, miR-375 stands out as it is highly expressed and regulates not only beta cell development and proliferation, but also its function [START_REF] El Ouaamari | miR-375 targets 3'-phosphoinositide-dependent protein kinase-1 and regulates glucose-induced biological responses in pancreatic beta-cells[END_REF][START_REF] Jafarian | The Generation of Insulin Producing Cells from Human Mesenchymal Stem Cells by MiR-375 and Anti-MiR-9[END_REF][START_REF] Kloosterman | Targeted inhibition of miRNA maturation with morpholinos reveals a role for miR-375 in pancreatic islet development[END_REF][START_REF] Nathan | MiR-375 promotes redifferentiation of adult human beta cells expanded in vitro[END_REF][START_REF] Poy | A pancreatic islet-specific microRNA regulates insulin secretion[END_REF][START_REF] Poy | miR-375 maintains normal pancreatic alpha-and beta-cell mass[END_REF]. However, while it is accepted that miR-375 is essential for endocrine pancreas development [START_REF] Avnit-Sagi | The promoter of the pri-miR-375 gene directs expression selectively to the endocrine pancreas[END_REF][START_REF] Joglekar | Expression of islet-specific microRNAs during human pancreatic development[END_REF][START_REF] Kloosterman | Targeted inhibition of miRNA maturation with morpholinos reveals a role for miR-375 in pancreatic islet development[END_REF]), its inhibitory action on insulin secretion reveals its multiple facets in beta cell physiology. Thus, deciphering miR-375 precise functions and mode of action is of considerable interest. To this end, using primary rat and human islets, we delved into the miR-375 effects on glucose metabolism, that governs insulin secretion and modulates beta cell characteristics. Overall our data support the view that miR-375 inhibits GSIS by modifying the expression of a series of genes tightly linked to metabolic signaling for GSIS , including Pc, Pdk4 and Mdh1. In silico analysis, using microRNA target prediction software, did not propose their mRNAs as potential miR-375 targets. Thus, we can assume that miR-375, by targeting one or several undefined transcripts upstream of these key metabolic enzymes may regulate beta cell function linked to insulin secretion induced by glucose.

Insulin secretion in immature beta cells is characterized by a poor responsiveness to glucose but a mature-like sensitivity to amino acids [START_REF] Bliss | Glucose-induced insulin release in islets of young rats: time-dependent potentiation and effects of 2-bromostearate[END_REF][START_REF] Hellerstrom | Functional maturation and proliferation of fetal pancreatic beta-cells[END_REF]. In addition, immature islets consume more oxygen at low glucose compared with mature islets but their ability to increase oxygen consumption in response to high glucose is considerably lesser compared with mature islets. This clearly suggests that beta cell maturation is associated with profound metabolic changes [START_REF] Stolovich-Rain | Weaning triggers a maturation step of pancreatic beta cells[END_REF]. Transcriptomic analyses to determine the basis of poor glucose responsiveness of neonatal beta cells, compared with adult beta cells, revealed that many genes are differentially expressed, including those encoding enzymes of mitochondrial shuttles, Pc and carnitine palmitoyl-transferase 2 [START_REF] Jermendy | Rat neonatal beta cells lack the specialised metabolic phenotype of mature beta cells[END_REF]). In addition, Ldh was significantly elevated in neonatal beta cells, which is particularly interesting as efficient Ldh expression would divert pyruvate away from the mitochondria towards lactate production. This scenario is compatible with the idea that metabolic specialization of adult beta cells for generating ATP and additional anaplerosisderived metabolic coupling factors from aerobic glycolysis is deficient in immature neonatal beta cells [START_REF] Jermendy | Rat neonatal beta cells lack the specialised metabolic phenotype of mature beta cells[END_REF]). However, glucose exposure of immature beta cells fosters their metabolic maturation. Indeed, nutrient shifts at weaning, induced by replacement of fatenriched maternal milk with a carbohydrate-rich diet, drive postnatal beta cell maturation via islet-specific microRNAs [START_REF] Jacovetti | Postnatal beta-cell maturation is associated with islet-specific microRNA changes induced by nutrient shifts at weaning[END_REF]. While in the latter report no alterations in miR-375 expression were observed, the entirely different developmental stages examined and experimental conditions used in our study very likely account for the divergence in microRNA expression. It is well known that fetal rat islets cultured with 11 mmol/l glucose acquired nearadult levels of insulin secretion in response to high glucose [START_REF] Freinkel | Differential effects of age versus glycemic stimulation on the maturation of insulin stimulus-secretion coupling during culture of fetal rat islets[END_REF]). Here we confirmed this and further demonstrated such decreased miR-375 expression in fetal rat islets matured in 11 mmol/l glucose. By contrast, forced miR-375 expression in mature rat and human beta cells resulted in mirror effects on GSIS. Further, we found that upon miR-375 overexpression mature beta cells display enhanced lactate production.

At variance with previous reports using MIN-6 insulinoma cells or primary mice -cells [START_REF] Latreille | miR-375 gene dosage in pancreatic beta-cells: implications for regulation of beta-cell mass and biomarker development[END_REF][START_REF] Poy | A pancreatic islet-specific microRNA regulates insulin secretion[END_REF][START_REF] Poy | miR-375 maintains normal pancreatic alpha-and beta-cell mass[END_REF]), overexpression of miR-375 has no impact on insulin exocytosis in dissociated islet cells from rat or human origin. Indeed, in islets from both species, KCl-induced insulin secretion was preserved upon overexpression of miR-375.

The reason for this discrepancy is unclear, but one possible explanation could be different animal species. Previously, when studied in the MIN-6 line, miR-375 has been implicated in limiting insulin exocytosis by downregulating myotrophin (Mtpn) transcripts [START_REF] Poy | A pancreatic islet-specific microRNA regulates insulin secretion[END_REF]).

However, we were unable to reproduce this MTPN decrease in dissociated primary rat islet cells transfected with miR-375 (not shown). Others confirmed our findings, showing that MTPN mRNA did not change following miR-375 overexpression in a cell line from rat origin (INS-1 832/13) [START_REF] Salunkhe | Modulation of microRNA-375 expression alters voltage-gated Na(+) channel properties and exocytosis in insulin-secreting cells[END_REF] or in human -cells [START_REF] Nathan | MiR-375 promotes redifferentiation of adult human beta cells expanded in vitro[END_REF]. In fact, the implication of MTPN in the inhibition of insulin secretion observed with miR-375 has been derived from studies using for the greater part the MIN-6 cell line. As the miRNA profile of this cell-line differs from that seen in primary -cells (LaPierre and Stoffel 2017), caution should be exerted in extrapolating the MTPN implication to more physiological -cell systems.

Together our findings strongly support the view that robust miR-375 expression in human or rat -cells favors an immature metabolic phenotype with low glucose-responsiveness rather than impacting on the exocytosis machinery per se.

Recently, the concept emerged that the reduction in beta cell mass in type 2 diabetes could reflect a loss/fading of their crucial attributes rather than increased apoptosis [START_REF] Brereton | beta-Cell dysfunction in diabetes: a crisis of identity?[END_REF][START_REF] Jeffery | beta-cell differentiation status in type 2 diabetes[END_REF]Talchai et al. 2012). Considering the increased miR-375 expression in islets from animals and humans with type 2 diabetes demonstrated in several studies [START_REF] Bloomston | MicroRNA expression patterns to differentiate pancreatic adenocarcinoma from normal pancreas and chronic pancreatitis[END_REF][START_REF] He | A Systematic Study of Dysregulated MicroRNA in Type 2 Diabetes Mellitus[END_REF][START_REF] Poy | miR-375 maintains normal pancreatic alpha-and beta-cell mass[END_REF]Tattikota, et al. 2014;Zhao et al. 2010) , and the current study showing that miR-375 overexpression results in reduced GSIS in human and rat islets, miR-375 appears to be a likely contributor to the fading of essential characteristics of beta cells in type 2 diabetes pathogenesis.

Conclusion

This study enhances our understanding of the diverse roles whereby miR-375 modulates beta cell function. First, we report that miR-375 modulates key beta cell metabolic pathways specifically for GSIS, but not in response to other secretagogues (fuel and non-fuel stimuli).

Second, our work, by focusing on metabolism, unearths a novel mode of action of this microRNA. Third, it provides a plausible mechanism to explain how miR-375 modulates GSIS by redirecting glucose carbons from mitochondrial metabolism to lactate formation, and thus inhibiting glucose-induced ATP generation and the production of additional anaplerosisderived regulatory metabolites. Finally, our findings uncover relevant links between epigenetic regulators, key beta cell traits and type 2 diabetes pathogenesis. Considering that the beta cell demise is a most challenging conundrum in the diabetes field, understanding the safeguarding of beta cell fundamental properties will be of major importance for leveraging strategies to preserve it in pathophysiological conditions.

  Talchai C, Xuan S, Lin HV, Sussel L & Accili D 2012 Pancreatic beta cell dedifferentiation as a mechanism of diabetic beta cell failure. Cell 150 1223-1234. Tattikota SG, Rathjen T, McAnulty SJ, Wessels HH, Akerman I, van de Bunt M, Hausser J, Esguerra JL, Musahl A, Pandey AK, et al. 2014 Argonaute2 mediates compensatory expansion of the pancreatic beta cell. Cell Metab 19 122-134. Theys N, Ahn MT, Bouckenooghe T, Reusens B & Remacle C 2011 Maternal malnutrition programs pancreatic islet mitochondrial dysfunction in the adult offspring. J Nutr Biochem 22 985-994. Weir GC, Laybutt DR, Kaneto H, Bonner-Weir S & Sharma A 2001 Beta-cell adaptation and decompensation during the progression of diabetes. Diabetes 50 Suppl 1 S154-159. Zhao H, Guan J, Lee HM, Sui Y, He L, Siu JJ, Tse PP, Tong PC, Lai FM & Chan JC 2010 Up-regulated pancreatic tissue microRNA-375 associates with human type 2 diabetes through beta-cell deficit and islet amyloid deposition. Pancreas 39 843-846.

Figure 1 .

 1 Figure legends.

Figure 2 .

 2 Figure 2. Forced miR-375 expression in adult rat primary pancreatic islet cells impairs

Figure 3 .

 3 Figure 3. Reduced miR-375 expression in adult rat primary pancreatic islet cells increases

Figure 4 .

 4 Figure 4. Forced miR-375 expression in adult rat primary pancreatic islet cells impairs

Figure 5 .

 5 Figure 5. Effect of miR-375 on insulin secretion in human islet cells. (a) miR-375 expression

Figure 6 .

 6 Figure 6. Forced miR-375 expression in adult rat and human islet cells alters the

Figure 7 .

 7 Figure 7. The repression of miR-375 expression is required for the acquisition of the

  Figure 1.

  Figure 2.

Table 1 : Sequences used for mRNA and miRNA qPCR analysis. Human oligonucleotide sequences for qPCR analysis name Reverse primer Forward primer

 1

	Cyclophilin A	CAGTCTTGGCAGTGCAGAT	ACACGCCATAATGGCACTGG
	MDH1	AGGGCACAGTCTTGCAGTTC	GCAGCTGGTCAAATTGCATA
	PC	TGCCTGTCCACCAGGAACTC	GCGACTCTGTGAAACTCGCTAA
	PDK4	TGGCAAGCCGTAACCAAAAC	ATGGATAATTCCCGGAATGCT
	Rat oligonucleotide sequences for qPCR analysis
	name	Reverse primer	Forward primer
	Cyclophilin A	CAGTCTTGGCAGTGCAGAT	ACACGCCATAATGGCACTGG
	LDHA	GCGGTGATAATGACCAGCTT	ATGAGCTTGCCCTTGTTGAT
	MDH1	TCACGTTGGCTTTCAGTAGG	CTGATGGAGCTGCAAGACTG
	MPC1	AGCTGAGCGACTTCGTTTGT	AGATTATCAGTGGGCGGATG
	MPC2	GATCCGAAACAGCTGAGAGG	TGCTGGATTAGCTGACATGG
	PC	AGCCCCTTCCCAATACTCAC	CTCCCACTGCACATCCATAC
	PDK1	CAGCTGTGTAAAACCGGGTA	GGATCACCCCTTCTTTGTGA
	PDK2	GGTCAGGAAGCAGGTTGATCT	ACATCGAGCACTTCAGCAAG
	PDK4	TGGATTGGTTGGCCTGGA	TCGCCAGAATTAAAGCTCACAC
	miRNA

oligonucleotide sequences for qPCR analysis name oligonucleotide sequence target

	hsa-miR-375 and
	5'UUUGUUCGUUCGGCUCGCGUGA
	rno-miR-375-3p

Acknowledgements. The authors thank the IRCAN animal housing facility, genomics core and cytometry core (Cytomed).