Samy Skander

Samy Skander Bahoura
email: samybahoura@yahoo.fr

An interior boundedness result for an elliptic equation

Keywords: C 0 weight, interior singularity, a priori estimate, maximum principle. MSC: 35J60, 35B44, 35B45, 35B50

An interior boundedness result for an elliptic equation

Introduction and Main Results

We set ∆ = ∂ 11 + ∂ 22 on open set Ω of R 2 with a smooth boundary.

We consider the following equation:

(P )        -∆u = 1 -log |x| 2d V e u in Ω ⊂ R 2 , u = 0 in ∂Ω.
Here:

0 ≤ V ≤ b, Ω 1 -log |x| 2d e u dx ≤ C, u ∈ W 1,1 0 (Ω),
and,

d = diam(Ω), 0 ∈ Ω
Equations of the previous type were studied by many authors, with or without the boundary condition, also for Riemannian surfaces, see [START_REF] Aubin | Some Nonlinear Problems in Riemannian Geometry[END_REF][START_REF] Bandle | Isoperimetric Inequalities and Applications[END_REF][START_REF] Bahoura | About Brezis Merle problem with Lipschitz condition[END_REF][START_REF] Bartolucci | sup+Cinf" inequality for Liouville-type equations with singular potentials[END_REF][START_REF] Bartolucci | sup+Cinf" inequality for the equation -∆u = V e u /|x| 2α[END_REF][START_REF] Bartolucci | A sup+inf inequality for Liouville type equations with weights[END_REF][START_REF] Bartolucci | A sup × inf-type inequality for conformal metrics on Riemann surfaces with conical singularities[END_REF][START_REF] Bartolucci | The Liouville equation with singular data: a concentration-compactness principle via a local representation formula[END_REF][START_REF] Boccardo | Nonlinear elliptic and parabolic equations involving measure data[END_REF][START_REF] Brezis | A sup+inf inequality for some nonlinear elliptic equations involving exponential nonlinearities[END_REF][START_REF] Brezis | Uniform estimates and Blow-up behavior for solutions of -∆u = V (x)e u in two dimension[END_REF][START_REF] Brezis | Semi-linear second-order elliptic equations in L1[END_REF][START_REF] Chen | A priori estimates for solutions to nonlinear elliptic equations[END_REF][START_REF] Chen | A sharp sup+inf inequality for a nonlinear elliptic equation in R 2[END_REF][START_REF] Dautray | Part 2, Laplace operator[END_REF][START_REF] Yy | Blow-up analysis for solutions of -∆u = V e u in dimension two[END_REF][START_REF] Yy | Harnack Type Inequality: the method of moving planes[END_REF][START_REF] Shafrir | A sup+inf inequality for the equation -∆u = V e u[END_REF][START_REF] Tarantello | A Harnack inequality for Liouville-type equation with Singular sources[END_REF], where one can find some existence and compactness results.

Among other results, we can see in [START_REF] Brezis | Uniform estimates and Blow-up behavior for solutions of -∆u = V (x)e u in two dimension[END_REF] the following important Theorem

Theorem A(Brezis-Merle [START_REF] Brezis | Uniform estimates and Blow-up behavior for solutions of -∆u = V (x)e u in two dimension[END_REF]).If (u i ) is a sequence of solutions of problem

(P ) with (V i ) satisfying 0 < a ≤ V i ≤ b < +∞ and without the term 1 -log |x| 2d
, then, for any compact subset K of Ω, it holds:

sup K u i ≤ c,
with c depending on a, b, K, Ω One can find in [START_REF] Brezis | Uniform estimates and Blow-up behavior for solutions of -∆u = V (x)e u in two dimension[END_REF] an interior estimate if we assume a = 0, but we need an assumption on the integral of e ui , namely, we have: Theorem B(Brezis-Merle [START_REF] Brezis | Uniform estimates and Blow-up behavior for solutions of -∆u = V (x)e u in two dimension[END_REF]).For (u i ) i and (V i ) i two sequences of functions relative to the problem (P ) without the term 1

-log |x| 2d
and with,

0 ≤ V i ≤ b < +∞ and Ω e ui dy ≤ C,
then for all compact set K of Ω it holds;

sup K u i ≤ c,
with c depending on b, C, K and Ω.

If we assume V with more regularity, we can have another type of estimates, a sup + inf type inequalities. It was proved by Shafrir see [START_REF] Shafrir | A sup+inf inequality for the equation -∆u = V e u[END_REF], that, if (u i ) i is a sequence of functions solutions of the previous equation without assumption on the boundary with V i satisfying 0 < a ≤ V i ≤ b < +∞, then we have a sup + inf inequality.

Here, we have:

Theorem For sequences (u i ) i and (V i ) i of the Problem (P ), for all compact subsets K of Ω we have:

||u i || L ∞ (K) ≤ c(b, C, K, Ω), Remark: Remark that we have a C 0 weight 1 -log |x| 2d
, the solutions are not C 2 , but if we add some assumptions on V i one can consider C 2 solutions and C 2 convergence of sequences. On can have the regularity C 2 of the solutions and the C 2 convergence of the solutions if we suppose for example V i ∈ C 0,ǫ , ǫ > 0 and for the convergence V i → V in the space C 0,ǫ , ǫ > 0. Indeed, one can reduce the problem to regularity and convergence of the Newtonian potential of a radial distribution f

(x) = f (|x|) = V i (0)e ui(0) -log |x| 2d
η(|x|), with η a cutoff function (η ≡ 1 in a neighborhood of 0 with compact support and radial), see for example the book of Dautray-Lions, chapter 2, Laplace operator.

By a duality theorem one can prove that (see [START_REF] Brezis | Semi-linear second-order elliptic equations in L1[END_REF]):

||∇u i || q ≤ C q , ∀ 1 ≤ q < 2.
If we add the assumption that

||∇V i || ∞ ≤ A,
then by a result of Chen-Li of "moving-plane" we have a compactness of (u i ) i near the boundary, see [START_REF] Chen | A priori estimates for solutions to nonlinear elliptic equations[END_REF].

We ask the following question about inequality of type sup + inf, as in the work of Tarantello, see [START_REF] Tarantello | A Harnack inequality for Liouville-type equation with Singular sources[END_REF] and Bartolucci-Tarantello, see [START_REF] Bartolucci | The Liouville equation with singular data: a concentration-compactness principle via a local representation formula[END_REF]:

Problems. 1) Consider the Problem (P ) without the boundary condition (without Dirichlet condition) and assume that:

0 < a ≤ V ≤ b < +∞, Does exists constants C 1 = C 1 (a, b, K, Ω), C 2 = C 2 (a, b, K, Ω) such that: sup K u + C 1 inf Ω u ≤ C 2 ,
for all solution u of (P ) ? 2) If we add the condition ||∇V || ∞ ≤ A, can we have a sharp inequality:

sup K u + inf Ω u ≤ c(a, b, A, K, Ω)?

Proof of the Theorem

We have:

u i ∈ W 1,1 0 (Ω), and 1
-log |x| 2d e ui ∈ L 1 (Ω).
Thus, by corollary 1 of Brezis and Merle we have:

e ui ∈ L k (Ω), ∀ k > 2.
Using the elliptic estimates and the Sobolev embedding, we have:

u i ∈ W 2,k (Ω) ∩ C 1,ǫ ( Ω).
By the maximum principle u i ≥ 0. Also, by a duality theorem or a result of Brezis-Strauss, we have:

||∇u i || q ≤ C q , 1 ≤ q < 2.
Since,

Ω 1 -log |x| 2d V i e ui dx ≤ C,
We have a convergence to a nonegative measure µ:

Ω 1 -log |x| 2d V i e ui φdx → Ω φdµ, ∀ φ ∈ C c (Ω).
Let's consider (by a variational method):

z i ∈ W 1,2 0 (B R (x 0 )), -∆z i = f i = 1 -log |x| 2d
V i e ui in B R (x 0 ), et z i = 0 on ∂B R (x 0 ).

By a duality theorem:

z i ∈ W 1,q 0 (B R ), ||∇z i || q ≤ C q . By the maximum principle, u i ≥ z i in B R (x 0 ). 1 -log |x| 2d e zi ≤ 1 -log |x| 2d e ui ≤ C. (4)
On the other hand, z i → z a.e. (uniformly on compact sets of B R (x 0 )-{x 0 }) with z solution of :

-∆z = µ in B R (x 0 ), et z = 0 on ∂B R (x 0 ).
Also, we have up to a subsequence, z i → z in W 1,q 0 (B R (x 0 )), 1 ≤ q < 2 weakly, and thus z ∈ W 1,q 0 (B R (x 0 )). Then by Fatou lemma:

1 -log |x| 2d e z ≤ C. (5)
As x 0 ∈ S is not regular point we have µ({x 0 }) ≥ 4π, which imply that, µ ≥ 4πδ x0 and by the maximum principle in W 1,1 0 (B R (x 0 )) (obtainded by Kato's inequality)

z(x) ≥ 2 log 1 |x -x 0 | + O(1) if x → x 0 .
Because,

z 1 ≡ 2 log 1 |x -x 0 | + 2 log R ∈ W 1,s 0 (B R (x 0 )), 1 ≤ s < 2.
Thus,

1 -log |x| 2d e z ≥ C -|x -x 0 | 2 log |x| 2d
, C > 0.

Both in the cases x 0 = 0 and x 0 = 0 we have:

We set S the following set: S = {x ∈ Ω, ∃ (x i ) ∈ Ω, x i → x, u i (x i ) → +∞}. We say that x 0 is a regular point of µ if there function ψ ∈ C c (Ω), 0 ≤ ψ ≤ 1, with ψ = 1 in a neighborhood of x 0 such that:

We can deduce that a point x 0 is non-regular if and only if µ(x 0 ) ≥ 4π.

A consequence of this fact is that if x 0 is a regular point then:

We deduce (2) from corollary 4 of Brezis-Merle paper, because we have by the Gagliardo-Nirenberg-Sobolev inequality:

We denote by Σ the set of non-regular points.

Step 1: S = Σ. We have S ⊂ Σ. Let's consider x 0 ∈ Σ. Then we have:

Suppose contrary that:

For R small enough, which imply (1) for a function ψ and x 0 will be regular, contradiction. Then we have (3). We choose R 0 > 0 small such that B R0 (x 0 ) contain only x 0 as non -regular point. Σ. Let's x i ∈ B R (x 0 ) scuh that:

We have x i → x 0 . Else, there exists x i k → x = x 0 and x ∈ Σ, i.e. x is a regular point. It is impossible because we would have [START_REF] Bandle | Isoperimetric Inequalities and Applications[END_REF].

Since the measure is finite, if there are blow-up points, or non-regular points, S = Σ is finite.

Step 2: Σ = {∅}. Now: suppose contrary that there exists a non-regular point x 0 . We choose a radius R > 0 such that B R (x 0 ) contain only x 0 as non-regular point. Thus outside Σ we have local unfirorm boundedness of u i , also in C 1 norm. Also, we have weak *-convergence of V i to V ≥ 0 with V ≤ b.


Andong Wang

Amlan Das

Olivier Utéza

David Grojo
email: david.grojo@univ-amu.fr

Refractive index engineering inside silicon by infrared laser pulses of different pulse durations in the picosecond regime

We report on the refractive index engineering inside silicon bulk by picosecond infrared lasers. Different responses are observed depending on the pulse durations. This represents a critical step for prototyping 3D silicon photonics microdevices.

Introduction

One of the challenges in silicon photonics is to extend the architectures of the microdevices from 2D to 3D. Infrared laser can penetrate inside bulk silicon, therefore offering a promising tool for 3D refractive index engineering and silicon photonics devices prototyping. Of all the laser parameters, the pulse duration was found to have a great impact on the laser modification. Recently, successful modification inside the silicon were reported by using nanosecond laser pulses [START_REF] Tokel | In-chip microstructures and photonic devices fabricated by nonlinear laser lithography deep inside silicon[END_REF][START_REF] Chambonneau | Writing waveguides inside monolithic crystalline silicon with nanosecond laser pulses[END_REF][START_REF] Verburg | Two-photon-induced internal modification of silicon by erbium-doped fiber laser[END_REF][START_REF] Yu | Internal modification of intrinsic and doped silicon using infrared nanosecond laser[END_REF]. Despite the easy success of modification by nanosecond laser, the types of modification are very limited, and the written waveguides exhibit high losses. Femtosecond lasers was found to be very difficult for bulk modification due to nonlinear propagation and ionization effects. The success of modification deep inside silicon was not achieved until we recently introduced the solid-immersion focusing [START_REF] Chanal | Crossing the threshold of ultrafast laser writing in bulk silicon[END_REF], but the flexibility is limited due to the contact nature of solid-immersion focusing. Picosecond laser is accompanied with less nonlinear effects compared to femtosecond laser, while offering more possibilities of modification types compared with nanosecond laser. However, the modification of silicon using picosecond laser with different pulse durations remains poorly investigated. In this work, picosecond laser with different pulse durations were used for modification inside the silicon.

Results and discussion

The experimental setup used in this research is shown in Fig. 1. The laser source (Pharos, Light-conversion) generates infrared laser pulses at 1030 nm central wavelength. The wavelength of the laser pulses is converted to 1550 nm by using an optical parametric amplifier and the pulse duration is measured at 174 fs. The energy is controlled by the combination of a half-wave plate and a broadband polarized beam splitter (PBS). Then the beam is injected in a stretcher arrangement consisting of two Littrow gratings (Thorlabs) to introduce negative group velocity dispersion to the original laser pulses. The incident angle is 10 ° away from the Littrow angle. The pulse duration of the laser pulses can be tuned by changing the distance between the gratings. The pulse duration is checked by using a long-range auto-correlator implemented next to the irradiation setup. Afterwards, the pulses are focused 300 μm inside the Si samples by Micro-objective lens (N.A. 0.85, Olympus LCPLN-IR 100x), which has a correction collar to compensate the spherical aberration induced by the pre-foci silicon material. The Si samples are 1 mm thick intrinsic silicon crystals with 100(±5°) orientation. They are prepared by cleaving a wafer (Siltronix). After irradiation, the phase change of the samples will be measured by an infrared phase microscopy [START_REF] Li | Quantitative-phase microscopy of nanosecond laser-induced micro-modifications inside silicon[END_REF] (as shown in Fig. 1(b)). Before irradiation experiments, the pulse durations of different grating distance were measured, as shown in Fig. 2(a). The experimental results fitted very well with theoretical predicts based on the dispersion theory. Then, the stretched laser with different pulse durations were used for irradiation. For each different pulse duration, totally 10 different energy levels from 10% to 100% were used. The incident pulse energy before the pulse stretcher setup was kept the same. At each spot, 1000 pulses were used for modification, with the laser repetition rate of 1 kHz. The modification inside the silicon varies with different pulse duration is shown in Fig. 2(b). When the pulse duration decreases, the area of the modification tends to become smaller, and the energy range of modification also becomes smaller. Fig. 2(c) shows the map of fabrication results under different pulse duration and threshold. In Zone A, the pulse energy doesn't exceed the damage threshold so that no modification is obtained; Zone B represents the combinations of pulse duration and pulse energy which may lead to modification; in Zone C, the pulse energy is very high, but no modification occurred. The existence of Zone C implies that, at some pulse durations, high incident pulse energy doesn't guarantee higher absorbed energy by the material and higher modification possibilities. This interesting phenomenon proves the high nonlinearity in the laser propagation inside the bulk silicon.

Conclusion

Modifications inside silicon by different durations in picosecond range were investigated, which shows that the energy range when modifications occur are highly related to the pulse duration. The pulse duration may also influence the refractive index changes, which needs further characterization by the infrared phase microscopy. This research can offer more understanding for the optimization of pulse duration for the refractive index engineering by infrared laser.

Fig. 1 (

 1 Fig. 1 (a) The schematic of the experimental setup for silicon modification with stretched pulse; (b) The schematic of the phase microscopy for detection of the phase change.

Fig. 2 (

 2 Fig. 2 (a) Experimental measurement and theoretical predictions of pulse width changes v.s. the grating distance; (b) The modification results of different pulse duration and energy level; (c) The map of fabrication results under different pulse duration and pulse energy.

Acknowledgement

This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (Grant Agreement No. 724480).


Agnès O Martin

Marie-Noëlle Mathieu

Claude Chevillard

Nathalie C Guérineau
email: guerinea@u469.montp.inserm.fr

Drs O Manzoni

P Chavis

P Mollard

U Gerber

M Passama

A Carrette

Gap junctions mediate electrical signaling and ensuing cytosolic Ca 2+ increases between chromaffin cells in adrenal slices: a role in catecholamine release

Keywords: electrical propagation, gap junction coupling, rat adrenal slices, chromaffin cells, real-time confocal microscopy, catecholamine release, nicotinic stimulation

In adrenal chromaffin cells, a rise in cytosolic calcium concentration ([Ca 2+ ]i) is a key event in the triggering of catecholamine exocytosis upon splanchnic nerve activation. Action potentialor nicotine-induced [Ca 2+ ]i transients are well described in individual chromaffin cells, but whether they remain spatially confined to the stimulated cell or propagate to adjacent cells is not yet known. To address this issue, the spatio-temporal organization of electrical and associated Ca 2+ events between chromaffin cells was investigated using the patch-clamp technique and real-time confocal imaging in rat acute adrenal slices. Spontaneous or electrically evoked action potential-driven [Ca 2+ ]i transients were simultaneously detected in neighboring cells. This was likely due to gap junction-mediated electrotonic communication, as shown by i) the bi-directional reflection of voltage changes monitored between cell pairs, ii) Lucifer yellow (LY) diffusion between cells exhibiting spontaneous synchronized [Ca 2+ ]i transients and iii) the reduction of LY diffusion using the uncoupling agent carbenoxolone. Furthermore, transcripts encoding two connexins (Cx36 and Cx43) were found in single chromaffin cells. This gap junctional coupling was activated upon a synaptic-like application of nicotine that mediated synchronous multicellular [Ca 2+ ]i increases. In addition, nicotinic stimulation of a single cell triggered catecholamine release in coupled cells, as shown by amperometric detection of secretory events. Functional coupling between chromaffin cells in situ may represent an efficient complement to synaptic transmission to amplify catecholamine release after synaptic stimulation of a single excited chromaffin cell.

INTRODUCTION

In adrenal tissue, the physiological stimulus for catecholamine secretion from chromaffin cells is the synaptic release of acetylcholine, which increases membrane excitability leading to cytosolic Ca 2+ elevations (reviewed by [START_REF] Douglas | Stimulus-secretion coupling: the concept and clues from chromaffin and other cells[END_REF][START_REF] Kidokoro | Chromaffin cell action potentials and their possible role in adrenaline secretion from rat adrenal medulla[END_REF][START_REF] Wakade | Studies on secretion of catecholamines evoked by acetylcholine or transmural stimulation of the rat adrenal gland[END_REF]. To date, the relationships between electrical activity, [Ca 2+ ]i increases and exocytosis underlying stimulation-secretion coupling have been mainly studied at the single cell level, either in dissociated chromaffin cells in culture or more recently in chromaffin cells in situ using acute slice preparations [START_REF] Voets | Mechanisms underlying phasic and sustained secretion in chromaffin cells from mouse adrenal slices[END_REF][START_REF] Albillos | R-type Ca 2+ channels are coupled to the rapid component of secretion in mouse adrenal slice chromaffin cells[END_REF][START_REF] Voets | Dissection of three Ca 2+ -dependent steps leading to secretion in chromaffin cells from mouse adrenal slices[END_REF]. Due to the anatomical organization of chromaffin cells into discrete cell complexes within the medulla [START_REF] Hillarp | Functional organization of the peripheral autonomic innervation[END_REF], it is, however, of physiological interest to characterize stimulussecretion coupling at the cell cluster level. It is currently proposed that each cluster functions as an independent unit to release catecholamines upon activation of the splanchnic nerve [START_REF] Iijima | Synaptic activation of rat adrenal medulla examined with a large photodiode array in combination with a voltage-sensitive dye[END_REF]. But whether each chromaffin cell exocytoses in an autonomous manner upon co-activation of its own synaptic inputs [START_REF] Coupland | Electron microscopic observations on the structure of the rat adrenal medulla. I. The ultra-structure and organization of chromaffin cells in the normal adrenal medulla[END_REF] and/or whether chromaffin cells may also communicate between themselves to spatially and temporally harmonize their intracellular transduction signals remains an open question. As reported by Kidokoro's group, the spreading of electrical activity between chromaffin cells induced by transmural stimulation of the splanchnic nerve would be mostly dependent on nerve fiber activity rather than cell-to-cell coupling, leading to simultaneous excitation of all the chromaffin cells belonging to the same cluster [START_REF] Kajiwara | Functional organization of chromaffin cells and cholinergic synaptic transmission in rat adrenal medulla[END_REF]. However, fast cell-to-cell communication mechanisms such as gap junction-mediated coupling may also be involved in the generation of simultaneous co-activation in adjoining chromaffin cells. Propagation of action potentials between chromaffin cells via electronic coupling was previously postulated to amplify the secretory signal to ensure massive release of catecholamines in the intact gland [START_REF] Ceña | Pharmacological dissection of receptor-associated and voltage-sensitive ionic channels involved in catecholamine release[END_REF]. More recently, a junctional pathway coupling chromaffin cells in situ has been reported to potentially underlie the simultaneous firing of a cell cluster [START_REF] Moser | Low-conductance intercellular coupling between mouse chromaffin cells in situ[END_REF].

In the present study, we addressed the issue of the involvement of gap junctions between chromaffin cells and their role in catecholamine release. We therefore investigated the spatio-temporal organization of both electrical activity and ensuing [Ca 2+ ]i increases between chromaffin cells in rat adrenal acute slices upon single cell electrical or cholinergic stimulation. We showed that [Ca 2+ ]i increases induced in response to spontaneous or evoked action potentials or to iontophoretic application of nicotine can be concomitantly observed in several chromaffin cells adjoining the stimulated one. This is likely to involve a gap junctionmediated pathway. Moreover, single cell stimulation led to spike-like secretory events resulting from catecholamine exocytosis in neighboring coupled cells. We propose here an additional mechanism mediating catecholamine secretion that might occur preferentially during episodes of low synaptic activity when only few chromaffin cells are synaptically stimulated.

MATERIALS AND METHODS

Adrenal slice preparation. Acute adrenal slices were prepared according to the technique previously described by [START_REF] Barbara | Quantal release at a neuronal nicotinic synapse from rat adrenal gland[END_REF]. Briefly, the adrenal glands were removed from 12-16 week-old Wistar female rats that had been killed by decapitation after cervical dislocation. After keeping the glands in ice-cold saline for 2 min, a gland was glued onto an agarose cube and transferred to the stage of a vibratome (Microslicer ® , DTK-1000, D.S.K, Dosaka EM CO. LTD, Kyoto, Japan). Slices of 250 µm thickness were then cut with a razor blade and transferred to a storage chamber maintained at 32°C, containing Ringer's saline (in mM): 125 NaCl, 2,5 KCl, 2 CaCl 2 , 1 MgCl 2 , 1,25 NaH 2 PO 4 , 26 NaHCO 3 , 12 glucose and buffered to pH 7.4. The saline was continuously bubbled with carbogen (95% O 2 / 5% C0 2 ). As reported for the anterior pituitary [START_REF] Guérineau | Synchronized spontaneous Ca 2+ transients in acute anterior pituitary slices[END_REF], acute adrenal slices were suitable for patch-clamp recording and Ca 2+ signal imaging immediately after cutting.

To obtain optical and/or electrophysiological recordings, slices were then transferred to a recording chamber attached to the stage of an upright microscope fitted with differential interference contrast optics (Axioskop FS, Zeiss, Le Pecq, France) and continuously superfused with Ringer's saline at 30°C.

Confocal imaging of cytosolic calcium. Ca 2+ changes were routinely monitored with a real-time (30-480 frames/s) confocal laser scanning microscope equipped with an Ar/Kr laser (Odyssey XL with InterVision 1.5.1 software, Noran Instruments Inc., Middleton, WI). Cells were viewed with a 63x 0.9 NA achroplan water immersion objective (Zeiss). The largest detection slit (100 µm) of the confocal microscope was used for [Ca 2+ ]i measurements, giving bright images with a 3.1 µm axial resolution. Slices were loaded with the Ca 2+ -sensitive fluorescent probe Oregon Green 488 BAPTA-1 by intermittent exposure to 15 µM Oregon Green 488 BAPTA-1 acetoxymethyl ester (Molecular Probes, Eugene, OR) for 20-30 min at 32°C, delivered onto a cell field with a blunt pipette [START_REF] Bonnefont | Rhythmic bursts of calcium transients in acute anterior pituitary slices[END_REF]. Oregon Green 488 BAPTA-1 was excited through a 488 nm-band-pass-filter and the emitted fluorescence was collected through a 515 nm-barrier filter. To follow the time course of Oregon Green 488 BAPTA-1 emission changes, the bright-over-time tool of the software package was applied to live images (120 images/s with averaging 4 frames). Because Oregon Green 488 BAPTA-1 is a single-wavelength dye, its emission is a function of both intracellular Ca 2+ and dye concentrations. [Ca 2+ ]i changes were expressed as the F/Fmin ratio where Fmin was the minimum fluorescence intensity measured during the recording [START_REF] Mollard | Activation of nicotinic receptors triggers exocytosis from bovine chromaffin cells in the absence of membrane depolarization[END_REF]. No detectable difference was noted between slices used just after cutting or after several hours (up to 8 hours) in the storage chamber. Acquired data and images were then processed for analysis with Igor Pro 3.16 (Wavemetrics Inc., Lake Oswego, OR), NIH Image 1.6.0 and Adobe Photoshop 5.0.2 software.

Electrophysiology.

All experiments were performed in the whole-cell configuration of the patch-clamp technique [START_REF] Hamill | Improved patch-clamp techniques for high-resolution current recording from cells and cell-free membrane patches[END_REF]. Patch pipettes were pulled to a resistance of 4-8 MΩ from borosilicate glass (1.5 mm outer diameter, 1.17 mm inner diameter) and filled with the following internal solution (in mM): 140 potassium-gluconate, 2 MgCl 2 , 1.1 EGTA, 5 HEPES, that was titrated to pH 7.2 with KOH. The membrane potential of a single chromaffin cell or cell pairs was recorded under current-clamp conditions using an EPC-9 dual patch-clamp amplifier (HEKA Electronik, Lambrecht/Pfalz, Germany) and filtered at 3 kHz. Intercellular junctional currents were monitored under dual voltage-clamp conditions [START_REF] Neyton | Single-channel currents of an intercellular junction[END_REF] using a modified intrapipette solution (in mM: 140 Cs +gluconate, 2 ATP, 2 MgCl 2 , 1.1 EGTA, 5 HEPES) and filtered off-line with a Kaiser low-pass filter (Igor Filter Design Laboratory software, version 3.1, Wavemetrics Inc.). For combined experiments in which membrane potential was simultaneously recorded with Ca 2+ events, Oregon Green 488 BAPTA-1 in free acid form (10 µM) was directly added to the internal pipette solution. In some experiments, membrane potential was recorded in the perforated patch-clamp configuration using amphotericin B (0.5 mg/ml in the standard intrapipette solution), as described [START_REF] Albillos | R-type Ca 2+ channels are coupled to the rapid component of secretion in mouse adrenal slice chromaffin cells[END_REF]. Cells with an access resistance >50 MΩ were discarded. Signals were acquired and analyzed using Pulse + PulseFit software (version 8.5, HEKA Electronik) on a G4 Macintosh computer.

Dye transfer. The fluorescent dye Lucifer yellow (Lucifer yellow-CH, LY, 1 mM) was introduced into cells using sharp microelectrodes or via passive diffusion through the patch pipette. In this case, the cells were patched for few minutes before image acquisition. Dye transfer between co-active coupled cells was visualized with confocal microscopy using the 488 nm-centered wavelength of the laser beam.

Single cell RT-PCR. Single cell RT-PCR was carried out as previously described [START_REF] Lambolez | AMPA receptor subunits expressed by single Purkinje cells[END_REF]. Patch pipettes were filled with 10 µl autoclaved internal K + -gluconate solution. After breaking the patch, cell contents were collected by applying negative pressure to the patch pipette. The pipette's content was expelled into an Eppendorf microtube containing 20 U ribonuclease (RNase) inhibitor (Roche, Meylan, France). The tube was then immediately frozen in liquid nitrogen and kept at -80°C until processed. The sample was denatured at 70°C for 5 min in the presence of 25 µM hexamers and reverse transcription (RT) was performed in 20 µl RT buffer containing: 200 U MMLV reverse transcriptase (Life Technologies, Cergy Pontoise, France), 20 U RNase inhibitor, 10 mM dithiothreitol and 0.6 mM of each dNTP (Roche), for 3 h at 37°C. The reaction was stopped by heating at 95°C for 5 min. Due to the high amounts of dopamine β-hydroxylase (DβH) in chromaffin cells, a single PCR was sufficient to detect the messengers. However, the amplification of mRNA encoding connexins (Cxs) required a nested PCR. PCRs were carried out using a T-gradient thermal cycler (Biometra, Göttingen, Germany). All PCR amplifications were achieved using 5 to 8 µl of RT product or first PCR product in 20 µl of PCR buffer containing 1.5 mM MgCl 2 , 0.2 mM dNTP, 1 µM of each primer and 1U DyNAzyme EXT polymerase (Finnzymes, Expoo, Finland). For the first PCR, the initial melt at 95°C (5 min) was followed by 35 cycles (92°C (1 min), 64°C (1 min) and 72°C (2 min) and final extension at 72°C (7 min). For the unique DβH PCR and the nested Cx PCR, the protocol used was the following: after the initial melt at 95°C (2 min), 10 cycles were performed: 94°C (10 s), 64°C

for DβH or 57°C for Cxs (30 s), 72°C (45 s) followed by 40 identical cycles with 5 s increments added to each cycle to an extension time (72°C) and a final extension at 72°C (7 min). For each experiment, a blank (without mRNA) and a positive control (total adrenal mRNA) were prepared. PCR products were submitted to electrophoresis on 2% agarose gel in Tris Borate EDTA buffer containing ethidium bromide for visualization. The primer sequences for specific amplifications of DβH [START_REF] Melia | Detection and regulation of tyrosine hydroxylase mRNA in catecholaminergic terminal fields: possible axonal compartmentalization[END_REF], Cx36 and Cx43 (Oligo 4.0 software) were summarized in table 1. Pairs of primers contained an intronic sequence in order to discriminate cDNA amplification product versus genomic DNA amplification product. Note that for DβH and Cx36, the presence of an intronic sequence was inferred from the human and mouse sequences as rat cDNAs were not available.

Real-time amperometric measurements of catecholamine release. Nicotine-driven catecholamine exocytosis from chromaffin cells was monitored by the electrochemical detection of secretory events [START_REF] Chow | Delay in vesicle fusion revealed by electrochemical monitoring of single secretory events in adrenal chromaffin cells[END_REF]. To perform single cell studies, carbon fibers with a 10 µm diameter tip and 50 µm length (WPI, Herts, United Kingdom) were chosen as previously reported [START_REF] Barbara | An adrenal slice preparation for the study of chromaffin cells and their cholinergic innervation[END_REF]. The tip of the electrode was gently pressed against the cell surface. Amperometric currents were measured at a constant voltage of 800 mV with an EPC-9 patch-clamp amplifier and were analyzed and filtered using Igor Pro + Igor Filter Design Laboratory (Kaiser low-pass filter) software.

Test substances. In order to mimick a focal and brief stimulation, nicotine (nicotine chloride, 200 mM) was iontophoretically applied onto the cell of interest using a sharp microelectrode (100 MΩ if filled with acetate buffer), the tip of which was positioned near the cell. The concentration reported is that in the microelectrode. Nicotine was prepared from a stock solution in an acetate buffer (pH 4). At this pH value, nicotine was negatively charged and, consequently, could be delivered from the microelectrode upon application of outward current pulses (50 nA intensity, 1 ms duration). Tetrodotoxin/cadmium-containing solution was pressure-ejected from an extracellular micropipette positioned in the vicinity of recorded cells. Nicotine, cadmium chloride, tetrodotoxin (TTX) Lucifer yellow (LY) and the gap junction blocker carbenoxolone were purchased from Sigma.

Statistics. Numerical data are expressed as the mean ± SEM. Student's t test (paired or unpaired) was used to compare means. Percentages were compared using a contingency table and the chi-square test. Differences with p<0.001 were considered significant.

RESULTS

Propagation of action potential-induced [Ca 2+ ]i transients between neighboring chromaffin cells.

Intercellular Ca 2+ rises triggered by action potentials in a given chromaffin cell were imaged while simultaneously monitoring associated [Ca 2+ ]i changes in neighboring cells. As illustrated in figure 1A, a 50 ms duration depolarizing current evoking a doublet of action potentials induced a simultaneous [Ca 2+ ]i rise in the stimulated cell (cell 1) and in an adjacent cell (cell 2). The [Ca 2+ ]i of other neighboring cells in the same optical plane remained at basal levels. The kinetics of both action potential-induced and propagated [Ca 2+ ]i transients were not significantly different (time to peak: 160 ± 20 ms, n = 12 versus 150 ± 20 ms, n = 12, p>0.001). But the amplitude of the Ca 2+ response in the unstepped cell was usually smaller than in the stimulated cell. The delay between the onset of both Ca 2+ signals was very short (39.8 ± 9.4 ms, n = 12), leading to a speed of propagation of about 500 µm/s (based on a 20 µm distance between cell centers and the acquisition sample time). To determine whether the extent of propagation (one cell in the example shown in figure 1) depended on the amplitude of the [Ca 2+ ]i rise in the stimulated cell, the depolarizing step duration was increased to 500 ms (figure 1B). A burst of thirteen action potentials induced a larger [Ca 2+ ]i increase, but did not modify the number of responsive cells (n = 9 cell fields). Such a simultaneous [Ca 2+ ]i increase between adjacent chromaffin cells (up to 3 cells in the same optical plane) upon depolarization-evoked action potentials was observed in 39.5% of recorded cell fields (n = 15 out of 38).

We then investigated whether simultaneous [Ca 2+ ]i rises also occurred spontaneously

Evidence for a gap junction-mediated electrical coupling

What are the mechanisms involved in the simultaneous [Ca 2+ ]i rises occurring in neighboring chromaffin cells? Two cell-to-cell communication pathways (gap junctions or local release of compounds acting on neighboring cells) could explain this propagation. Two observations i) the rapid speed of propagation between two cells (500 µm/s) and ii) the similar kinetics of both action potential-induced and propagated [Ca 2+ ]i transients (see figure 1), suggesting that action potentials are conducted to adjacent cells, support the hypothesis of junctional communication. To further confirm gap junctional coupling between chromaffin cells, the membrane potential of cell pairs was recorded in the whole-cell configuration with the dual patch-clamp technique (figure 3). The passive biophysical membrane properties of chromaffin cells in slices were: i) resting membrane potential (-68 ± 1 mV, n = 172), input resistance (0.82 ± 0.04 GΩ, range = 0.13-3 GΩ, n = 172) and capacitance (11.64 ± 0.40 pF, n = 28).

These results are in agreement with those reported by other groups [START_REF] Barbara | Quantal release at a neuronal nicotinic synapse from rat adrenal gland[END_REF][START_REF] Barbara | An adrenal slice preparation for the study of chromaffin cells and their cholinergic innervation[END_REF][START_REF] Kajiwara | Functional organization of chromaffin cells and cholinergic synaptic transmission in rat adrenal medulla[END_REF]. The fact that many chromaffin cells had a low membrane input resistance (≤ 500 MΩ in 32% of cells) was consistent with the idea that chromaffin cells could be coupled. In 40% of cell pairs (n = 68), the voltage changes in response to hyperpolarizing/depolarizing current injected in the stimulated cell were reflected in the unstepped cell (figure 3A andB) and vice-versa (data not shown). However, among the cell pairs, the response transmitted to the unstepped cell displayed variable amplitudes. In 75% of coupled pairs, the action potential was distorted leading only to small depolarizations (figure 3A), whereas in the remaining pairs, the action potential was transmitted (figure 3B).

Consequently, the coupling ratio exhibited a wide distribution range from 0.03 to 0.95 (mean 0.34 ± 0.10, n = 14 coupled pairs, figure 3C). It is interesting to note that the coupling ratio value for a given cell pair remained constant independent of the amplitude or polarity of the current step. In accordance with gap junction-driven electrical coupling, junctional currents were recorded in 61% (8 out of 13) of Cs + -loaded chromaffin cell pairs. Cell pairs were voltage clamped at -80 mV and voltage steps were delivered from this potential with command pulses of both polarities to cell 1. The resulting junctional currents (Ij) recorded in the unstepped cell appeared to remain constant for the duration of the step (figure 3D, inset).

The amplitude of Ij was then plotted as a function of the transjunctional potential (figure 3D).

The I/V curve displayed a linear relationship within the transjunctional membrane potential range of -80 to +100 mV. The curve used to fit the data was derived from a linear regression, given a macroscopic conductance of about 3 nS.

Further support for the presence of functional gap junctions in chromaffin cells was obtained in experiments to detect mRNA encoding connexins in randomly chosen cells. We focused on two connexins, Cx43 described in numerous endocrine/neuroendocrine tissues [START_REF] Meda | Differential expression of gap junction connexins in endocrine and exocrine glands[END_REF] and Cx36, a recently cloned connexin preferentially expressed in cell types of neural origin [START_REF] Condorelli | Cloning of a new gap junction gene (Cx36) highly expressed in mammalian brain neurons[END_REF] such as chromaffin cells. All samples were first assessed for the expression of dopamine β-hydroxylase to confirm that harvested cells were indeed chromaffin cells. Due to the low expression level of mRNA encoding Cxs in single cells, the nested PCR procedure was required. The detection of Cx43 mRNA in 50% of harvested cortical cells was used as a control (n = 10), since rat cortical cells in the zona fasciculata and the zona reticularis are highly coupled by Cx43-containing gap junctions [START_REF] Murray | Characterization of gap junction expression in the adrenal gland[END_REF]. Under the same experimental conditions, 20.6% and 25% of DβHpositive cells expressed at least Cx43 or Cx36 mRNA, respectively (n = 34 and 16). In some chromaffin cells (3/16), both Cx36 and Cx43 transcripts were found (figure 4). Although PCR experiments were done on different chromaffin cells than those recorded from, this result suggests that Cx36 and/or Cx43 may functionally and dynamically connect chromaffin cells in situ.

To further confirm the presence of functional gap junctions, chromaffin cells were impaled with a microelectrode filled with Lucifer yellow (LY), a fluorescent tracer able to pass through gap junctions. LY diffusion was observed only between cells exhibiting synchronous [Ca 2+ ]i transients (figure 5A, n = 4 cell fields). LY never diffused between non synchronized cells (n = 8 cell fields, data not shown). When LY was randomly injected into cells that were not Ca 2+ imaged, the tracer diffused from the impaled cell to neighboring cells (up to 3) in 32.8% of the clusters impaled (n = 64). This percentage was not significantly different to that found for electrically coupled cells (40%, see figure 3) and cells in which action potentials triggered simultaneous [Ca 2+ ]i transients (39.5%, see figure 1) (p>0.001). To assess the involvement of functional gap junctions in intercellular coupling, the fluorescent tracer was then injected in chromaffin cells chosen at random in the presence of bath-applied carbenoxolone (100 µM), a decoupling agent [START_REF] Ishimatsu | Synchronous activity in locus coeruleus results from dendritic interactions in pericoerulear regions[END_REF]. Under these experimental conditions, the probability of observing an intercellular coupling (seen by LY diffusion) significantly decreased (0.06 versus 0.31 in control conditions, n = 46, p<0.001, figure 5B). Current polarity inversion (n = 10) or application of nicotine-free saline (n = 8) never induced [Ca 2+ ]i changes in either stimulated or adjacent cells. Extracellular diffusion of nicotine could reasonably be ruled out since i) a [Ca 2+ ]i increase was not observed in all cells belonging to the same cluster, while all these cells were sensitive to pressure ejection of nicotine, ii) in some experiments, only the stimulated cell exhibited a [Ca 2+ ]i rise, iii) the iontophoretic flux of nicotine was oriented in the opposite direction of the perifusion stream and iv) saline was continuously ejected in the vicinity of the recorded cell field through a blunt macropipette, thus reinforcing the perifusion stream. The propagated signal between chromaffin cells reliably persisted upon repetitive applications of nicotine, indicating that the intercellular mechanism underlying the propagation did not desensitize during the recording time (data not shown).

Involvement of gap junction-mediated coupling upon nicotinic stimulation

The functional implication of gap junctions in nicotine-induced signal propagation was further demonstrated by the blocking effect of carbenoxolone. Bath-application of carbenoxolone (100 µM, 15 min before nicotine iontophoresis) specifically suppressed the [Ca 2+ ]i rises in coupled cells, without dramatically altering the Ca 2+ response in the stimulated cell (figure 6A, middle and right traces). In separate experiments, we checked that carbenoxolone, per se, did not alter i) the percentage of spontaneously active cells (44.3 ± 5.2% versus 44.6 ± 5.5% before and during carbenoxolone application, respectively, n = 17 cell clusters, p>0.001, paired t-test) and ii) the amplitude (0.49 ± 0.03 ∆F/Fmin versus 0.51 ± 0.03, p>0.001, n = 41) and the duration (29.4 ± 1.4 s versus 26.1 ± 1.3, p>0.001, n = 41) of the nicotine-activated Ca 2+ response. The effect of carbenoxolone was only partly (~50% recovery) reversible after a 10-20 min washout (figure 6B).

Catecholamine secretion triggered upon electrical and nicotinic stimulation in gap junction-coupled cells

Because an increase in [Ca 2+ ]i is a prerequisite for exocytosis in chromaffin cells, we investigated the physiological relevance of action potential-and nicotine-triggered Ca 2+ increases in coupled cells. To address this question, catecholamine exocytosis was monitored using the amperometric constant-voltage method (+800 mV) in cells neighboring the stimulated one. In 12.5% of cell clusters, a burst of action potentials induced catecholamine release from the stimulated cell as previously reported [START_REF] Moser | Rapid exocytosis in single chromaffin cells recorded from mouse adrenal slices[END_REF] and, more interestingly, also from non-stepped neighboring cells (perforated patch-clamp, n = 16, figure 7). This percentage is similar to that found for highly coupled cell pairs (10%, see figure 3), in which unattenuated propagation of action potentials occurred.

Similarly, an iontophoretic application of nicotine (1 ms) triggered spike-like secretory events in non-stimulated cells in which [Ca 2+ ]i previously was shown to increase (figure 8, cell 2, n = 8 out of 11). The delay between nicotinic stimulation and the first secretory event was 1.04 ± 0.36 s (n = 8, range from 0.02 to 3.1 s). Catecholamine exocytosis was never detected in noncoupled cells (figure 8, cell 3). This result is in agreement with our data showing a that nicotine-driven Ca 2+ signal was not observed in all the cells neighboring the stimulated cell (data not shown). Taken together, these results suggest that gap junction signaling activated by nicotine represents a functional mechanism leading to catecholamine secretion.

DISCUSSION

Based on anatomical data [START_REF] Carmichael | Morphology and innervation of the adrenal medulla[END_REF][START_REF] Tomlinson | The innervation of the adrenal gland. IV. Innervation of the rat adrenal medulla from birth to old age. A description and quantitative morphometric biochemical study of the innervation of the chromaffin cells and adrenal medullary neurons in Wistar rats[END_REF], the currently proposed concept for chromaffin cell secretion considers each cell as an independent functional unit releasing catecholamines upon activation of its synaptic inputs [START_REF] Iijima | Synaptic activation of rat adrenal medulla examined with a large photodiode array in combination with a voltage-sensitive dye[END_REF]. Nevertheless, we describe here an additional mechanism involving gap junctionmediated coupling between chromaffin cells in rat adrenal slices. This cell-to-cell communication pathway underlies the propagation of electrical signal leading to simultaneous multicellular [Ca 2+ ]i increases, thereby triggering catecholamine exocytosis.

Fast activation of simultaneous [Ca 2+ ]i increases in adjoining chromaffin cells: the hallmark of electrotonic coupling via gap junctions

We show for the first time that the triggering of action potentials or the nicotinic stimulation of a single chromaffin cell results in simultaneous [Ca 2+ ]i increases in adjoining cells due to the propagation of a depolarizing voltage wave. As a general rule, excitable cells use distinct but not mutually exclusive pathways to communicate amongst themselves, i.e. synaptic transmission, gap junctions and paracrine secretion. Based on our experimental results, gap junctions are likely to represent the anatomical correlate of the functional coupling observed here. At least four observations support this proposal: i) bidirectional propagation of membrane depolarization between two cells, ii) junctional current recorded in cell pairs, iii) diffusion of LY between simultaneously active cells and iv) reduction of signal propagation by the uncoupling agent carbenoxolone upon nicotinic stimulation. Nevertheless, chromaffin cell granules are known to contain various compounds co-stored and co-released with catecholamines, such as ATP [START_REF] Rojas | Real-time measurements of acetylcholine-induced release of ATP from bovine medullary chromaffin cells[END_REF] that could act locally on neighboring cells.

Because of the slow velocity of ATP diffusion in the extracellular space (~40 µm/s, [START_REF] Guthrie | ATP released from astrocytes mediates glial calcium waves[END_REF], paracrine secretion of ATP is unlikely to be involved in the concomitant [Ca 2+ ]i rises that we observed between chromaffin cells (speed of propagation of ~500 µm/s). A gap junction-mediated pathway usually ensures both electrotonic and metabolic communication between coupled cells, each of which is associated with distinct speeds of propagation.

Although we cannot definitively rule out metabolic coupling (i.e. simple diffusion of second messengers), the speed of the propagation wave between coupled cells (~500 µm/s) strongly suggests the involvement of electrotonic coupling. In this way, the depolarization wave occurring either spontaneously or upon stimulation rapidly propagates into the clusters of coupled chromaffin cells.

Functional electrical coupling mediated by gap junctions between rat chromaffin cells has not been demonstrated previously. Based on electrophysiological properties, the idea that chromaffin cells may be electrically coupled in situ has been hypothetized for various species, including rats [START_REF] Ishikawa | Influences of extracellular calcium and potassium concentrations on adrenalin release and membrane potential in the perfused adrenal medulla of the rat[END_REF], mouse [START_REF] Nassar-Gentina | Electrical activity in chromaffin cells of intact mouse adrenal gland[END_REF][START_REF] Moser | Low-conductance intercellular coupling between mouse chromaffin cells in situ[END_REF] and guinea pigs [START_REF] Holman | Synaptic transmission from splanchnic nerves to the adrenal medulla of guinea-pigs[END_REF]. In addition, the presence of gap junctions has been reported in the rat adrenal medulla [START_REF] Meda | Differential expression of gap junction connexins in endocrine and exocrine glands[END_REF]. Strengthening these findings, our dual patch-clamp recordings clearly show that gap junctions between chromaffin cells are functional and underlie the bi-directional transfer of voltage changes between coupled cells.

In most cases, the amplitude of the voltage response induced in the unstepped cell was not sufficient to trigger action potentials, indicating weak coupling, as reported in mouse adrenal slices [START_REF] Moser | Low-conductance intercellular coupling between mouse chromaffin cells in situ[END_REF]. In the remaining cell pairs, coupling strength was high enough to transmit action potentials. The distortion of the transmitted voltage signal compared to the original signal indicates significant low-pass filtering of the voltage response, as described in neurons [START_REF] Venance | Connexin expression in electrically coupled postnatal rat brain neurons[END_REF]. Several proposals can explain such filtering: i) the presence of a few open gap junctions at the cell surface [START_REF] Moser | Low-conductance intercellular coupling between mouse chromaffin cells in situ[END_REF], ii) the expression of distinct connexin types with different unitary conductances and iii) the expression of connexins with a low voltage sensitivity.

Our data on the connexins involved in the junctional communication between chromaffin cells are in agreement with previous reports showing that Cx43-or Cx36containing gap junctions are expressed beween neuroendocrine/endocrine [START_REF] Meda | Differential expression of gap junction connexins in endocrine and exocrine glands[END_REF][START_REF] Munari-Silem | Gap junction-mediated cell-to-cell communication in endocrine glands[END_REF][START_REF] Belluardo | Expression of connexin36 in the adult and developping rat brain[END_REF][START_REF] Serre-Beinier | Cx36 preferentially connects beta-cells whithin pancreatic islets[END_REF]. Two of our results indicate that Cx36 and Cx43 are present in chromaffin cells. First, the messengers encoding these two connexins were detected in single chromaffin cells. Second, experiments showing LY diffusion are in agreement with the possible involvement of Cx36 and/or Cx43, as both are dye-permeable [START_REF] Veenstra | Size and selectivity of gap junction channels formed from different connexins[END_REF][START_REF] Srinivas | Functional properties of channels formed by the neuronal gap junction protein connexin36[END_REF]. Assuming a unitary conductance of 61 pS and 10 pS for Cx43 and Cx36 respectively [START_REF] Valiunas | Conductances and selective permeability of connexin 43 gap junction channels examined in neonatal rat heart cells[END_REF][START_REF] Srinivas | Functional properties of channels formed by the neuronal gap junction protein connexin36[END_REF], the estimation of the junctional conductance in a rat chromaffin cell pair (3 nS maximum) would correspond to about 50 and 300 open Cx43-and Cx36-built channels, adequate numbers to support significant voltage propagation when compared to only 7-10 open channels present between mouse chromaffin cells, leading to a too low junctional conductance to support spreading of electrical activity [START_REF] Moser | Low-conductance intercellular coupling between mouse chromaffin cells in situ[END_REF].

As shown by our results, ~50% (depending on the technique used) of chromaffin cells in situ are functionally coupled via gap junctions to at least one apposing cell located in the same optical plane. To better assess the extent of coupling, a three-dimensional approach would be necessary. On the other hand, the dynamic aspects of coupling (occurrence of spontaneous coupling/decoupling) requiring long-lasting recordings merits further investigation.

Nevertheless, in our view, intercellular signaling mediated through gap junctions most likely contributes to the mechanisms of communication within the adrenal medulla. The electrotonic coupling that we describe represents only one aspect of the role for gap junctions between chromaffin cells. As gap junctions are permeable to numerous low-molecular weight compounds, they are likely to subserve metabolic coupling thereby propagating biological messages encoding different cell functions. With respect to the strength of the coupling, an unresolved issue raised by our findings is the functional consequences of strong and weak electrotonic coupling. Although [Ca 2+ ]i changes were not simultaneously monitored during dual patch-clamp experiments, one could assume that strong and weak coupling are associated with the degree of the [Ca 2+ ]i rise in the coupled cells. The propagation of action potentials triggers a Ca 2+ signal that is sufficient to stimulate catecholamine exocytosis. In weakly coupled cell pairs, the depolarizations occurring near resting potential might also generate [Ca 2+ ]i elevations, as reported for other endocrine cells [START_REF] Mollard | Cytosolic Ca 2+ of excitable pituitary cells at resting potentials is controlled by steady-state Ca 2+ currents sensitive to dihydropyridines[END_REF] and might control Ca 2+ -dependent cell functions other than exocytosis.

Physiological relevance of gap junctions in the adrenal medulla: complementing synaptic transmission to drive catecholamine exocytosis?

In endocrine glands in which secretagogues are delivered from the blood circulation, it is well known that gap junctions (mainly composed of Cx43) are required to ensure fast synchronized hormone release [START_REF] Meda | The role of gap junction membrane channels in secretion and hormonal action[END_REF][START_REF] Munari-Silem | Gap junction-mediated cell-to-cell communication in endocrine glands[END_REF]. Although the synaptic boutons present on each chromaffin cell [START_REF] Carmichael | Morphology and innervation of the adrenal medulla[END_REF] themselves represent an efficient process to induce fast release of catecholamines, the gap junction-delineated route is also used for chromaffin cell exocytosis. The fact that simultaneous [Ca 2+ ]i rises can occur spontaneously suggests that a spatio-temporal code between gap-junction coupled cells [START_REF] Guérineau | Synchronized spontaneous Ca 2+ transients in acute anterior pituitary slices[END_REF] coordinates basal exocytosis at the cell cluster level. During neurotransmission, the involvement of gap junctions in nicotine-induced multicellular [Ca 2+ ]i rises and subsequent exocytosis suggests that in vivo direct chromaffin cell-to-cell interactions would be an important determinant in the regulation of secretory cell activity by acetylcholine. Although we show that gap junctions mainly ensure electrotonic coupling leading to exocytosis, we cannot rule out a role in other cell functions such as metabolic coupling, which would allow for the diffusion of chemical messengers (Ins(1,4,5)P 3 , ATP…) between chromaffin cells.

Our study also raises the interesting issue that chromaffin cells are under the dual control of the splanchnic nerve (hitherto described as the major regulator of secretion) and of adjacent cells. We propose that within these anatomically well described cell complexes [START_REF] Hillarp | Functional organization of the peripheral autonomic innervation[END_REF], both mechanisms might occur to activate catecholamine release depending on the catecholamine needs and/or the activation state of the synaptic pathway. Under basal conditions corresponding to low frequency discharge of the splanchnic nerve, few synaptic boutons are stimulated and the propagation of the secretory events between gap junctioncoupled cells may be sufficient to release catecholamines. In contrast, during stressful situations, the massive catecholamine secretion suddenly required might be mediated mostly by the synaptic pathway activated by sustained discharges of the splanchnic nerve, as reported earlier [START_REF] Kajiwara | Functional organization of chromaffin cells and cholinergic synaptic transmission in rat adrenal medulla[END_REF]. In particular physiological/pathological conditions, the functional state of synaptic transmission (presence of non-functional synapses as immature synapses, silent synapses…) may also represent an intrinsic determinant requiring gap junctions, as an efficient aid to synapses leading chromaffin cells to exocytose catecholamines. In addition to this direct secretory role, the propagation of electrical activity and associated Ca 2+ rises upon activation of cholinergic nicotinic receptors might also stimulate other Ca 2+ -dependent cell activities (such as secretory vesicle trafficking, gene expression…) in order to sensitize chromaffins cells to exocytosis upon subsequent synaptic activation.

Figure legends

  between adjacent cells. As shown by time-lapse optical sequences of Oregon Green 488 BAPTA-1-loaded cells, about 16% of chromaffin cells displaying spontaneous [Ca 2+ ]i transients fired in synchrony with at least one neighboring cell (figure 2A, n = 195 cells from 4 different experiments). These spontaneously co-active chromaffin cells co-existed with asynchronous cells. Within a cluster, the synchronized cells were spatially confined (up to 4 cells in the same confocal plane). [Ca 2+ ]i transients of co-active cells displayed similar kinetics (time to peak: 290 ± 65 ms versus 290 ± 61 ms for cell 1 and cell 2, n = 10 cell pairs, p>0.001, paired t-test). When [Ca 2+ ]i transients were imaged for longer periods (> 10 min), sequences of spontaneous synchronization/desynchronization were observed (data not shown). Synchronous and asynchronous [Ca 2+ ]i transients probably resulted from spontaneous action potentials, since they were reversibly abolished in the presence of TTX (0.5 µM) + Cd 2+ (0.5 mM), blockers of voltage-activated Na + and Ca 2+ channels, respectively, (figure 2B, n = 22/29), TTX alone or Cd 2+ alone (n = 11/20 and 31/37, respectively, data not shown). Taken together, these results indicate that in situ, either spontaneous or electrically evoked action potential-linked [Ca 2+ ]i transients are not confined to the initially stimulated cells, but are transmitted to other chromaffin cells, indicating information transfer between adjoining cells.

  Does the gap junction-driven response occur under physiological cholinergic stimulation? To mimick the in vivo release of transmitters into the synaptic cleft, the cholinergic secretagogue nicotine was iontophoretically applied onto a single chromaffin cell via a sharp microelectrode, leading to focal stimulation of a single cell. Subsequent multicellular [Ca 2+ ]i changes were simultaneously imaged with real-time confocal microscopy. A 1 ms nicotinic application induced a transient [Ca 2+ ]i rise in the stimulated cell as expected, but more interestingly, [Ca 2+ ]i simultaneously increased in several adjacent cells (figure 6A, left traces).

Figure 1 :

 1 Figure 1: Propagation of action potential-induced [Ca 2+ ]i transients between chromaffin

Figure 2 :

 2 Figure 2: Synchronized spontaneous [Ca 2+ ]i transients between chromaffin cells

Figure 3 :

 3 Figure 3: Electrical coupling between chromaffin cell pairs

Figure 4 :

 4 Figure 4: Expression of Cx36 and Cx43 mRNA in a single chromaffin cell

Figure 5 :

 5 Figure 5: Lucifer yellow diffusion between spontaneously synchronized chromaffin cells

Figure 6 :

 6 Figure 6: Blocking effect of carbenoxolone on nicotine-induced simultaneous [Ca 2+ ]i

Figure 7 :

 7 Figure 7: Action potential-induced catecholamine release in coupled chromaffin cells.

  FIGURE 1

Table 1 :

 1 Primer sequences used for the specific amplication of dopamine β-hydroxylase, connexin 43 and connexin 36 in single cells.

			Primer sequence Sense (5'-3')	Primer sequence Antisense (5'-3')	Predicted
					product size
	DßH	1st PCR	AGTGCCGTGGATGATGGCTTCC CAGCACTATTCTATGGAAGGGGGTC	438 bp
	Cx43 1st PCR	AACTTTGGCGGCGGCTTCAC	CAGGAAGGCCACCTCGAAGACAG	560 bp
		nested PCR	TGGAGGGAAGGTGTGGCTG	TGAAGAGGATGCTGATGATGTAGG	425 bp
	Cx36 1st PCR	ACAGCGATGGGGGAATGGAC	CACTTGGATGATGTAGAAGCGGG	615 bp
		nested PCR	TCCTGTTGACTGTGGTGGTG	ACTTCTTATCTTCTCGCTTGCTC	360 bp

for critical readingfor their excellent technical assistance. This work was supported by grants from Institut National de la Santé et de la

current deflections, action potentials were effective in stimulating catecholamine release in both the stepped cell and in the neighboring cell.