Carmen Cifuentes-Diaz

Stefano Marullo

Stéphane Doly

Stephane Doly
email: stephane.doly@inserm.fr

Anatomical and ultrastructural study of PRAF2 expression in the mouse central nervous system

Keywords: PRAF2, JM4, CNS, GABA(B) receptor, synapse, cilium 10th Cerebellar lobule Io: inferior olive IOC: inferior olive subnucleus C IP: Interpeduncular nucleus LGP: lateral globus pallidus LH: lateral hypothalamic area LHb: lateral habenular nucleus LM: lateral mammillary nucleus LRt: lateral reticular nucleus M2: secondary motor cortex MdV: medullary reticular nucleus ventral part Med: medial fastigial cerebellar nucleus MePD: medial amygdaloid nucleus posterodorsal part MG: medial geniculate nucleus MHb: medial habenular nucleus median raphe nucleus MO: medial orbital cortex MVB: multivesicular bodies MVePC: medial vestibular nucleus parvicellular part Or: strata oriens PAG: Periaqueductal gray Par: parietal cortex PFl: paraflocculus Pir: Piriform cortex PMCo: posteromedial cortical amygdaloid nucleus Pn: pontine nuclei PRAF2: Prenylated Rab Acceptor Family, member 2 Prl: prelimbic cortex Pur: purkinje cells layer PVA: paraventricular thalamic nucleus Pyr: pyramidal cells Rad: stratum radiatum RER: rough endoplasmic reticulum Rt: reticular thalamic nucleus sm: stria medullaris thalamus SNC: substancia nigra compacta SNR: substantia nigra pars reticulate Sol

Prenylated Rab Acceptor Family, member 2 (PRAF2) is a four transmembrane domain protein of 19 kDa that is highly expressed in particular areas of mammalian brains. PRAF2 is mostly found in the endoplasmic reticulum (ER) of neurons where it plays the role of gatekeeper for the GB1 subunit of the GABA B receptor, preventing its progression in the biosynthetic pathway in the absence of hetero-dimerization with the GB2 subunit. However, PRAF2 can interact with several receptors and immunofluorescence studies indicate that PRAF2 distribution is larger than the ER, suggesting additional biological functions.

Here we conducted an immuno-cytochemical study of PRAF2 distribution in mouse central nervous system (CNS) at anatomical, cellular and ultra-structural levels. PRAF2 appears widely expressed in various regions of mature CNS, such as the olfactory bulbs, cerebral cortex, amygdala, hippocampus, ventral tegmental area and spinal cord. Consistent with its regulatory role of GABA B receptors, PRAF2 was particularly abundant in brain regions known to express GB1 subunits.

However, other brain areas where GB1 is expressed, such as basal ganglia, thalamus and hypothalamus, contain little or no PRAF2. In these areas GB1 subunits might reach the cell surface of neurons independently of GB2 to exert biological functions distinct from those of GABA B receptors, or be regulated by other gatekeepers. Electron microscopy studies confirmed the localization of PRAF2 in the ER, but identified previously unappreciated localizations, in mitochondria, primary cilia and sub-synaptic region. These data indicate additional modes of GABA B regulation in specific brain areas and new biological functions of PRAF2.

Introduction :

A group a structurally heterogeneous endoplasmic reticulum (ER)-or Golgi apparatusresident proteins, known as Yips (from Ypt-interacting proteins, Ypt being the yeast equivalent of mammalian Rab GTPases), are involved in the control of ER shape and of ER to Golgi trafficking in mammalian cells. Yips interact with and regulate the cell surface export of multi transmembrane domain cargo proteins, such as G protein coupled receptors (GPCRs) or aminoacid transporters (2007;[START_REF] Bjork | REEPs are membrane shaping adapter proteins that modulate specific g protein-coupled receptor trafficking by affecting ER cargo capacity[END_REF][START_REF] Doly | Gatekeepers controlling GPCR export and function Trends in[END_REF][START_REF] Pfeffer | Targeting Rab GTPases to distinct membrane compartments[END_REF]. Yips are classified in several families, including the 4-transmembrane domain PRAFs (Prenylated Rab Acceptor Family members), a group of 3 proteins of ≈19 kDa sharing a conserved prenylated Rab acceptor 1 (PRA1) motif that are enriched in the brain and implicated in cellular transport and vesicle trafficking [START_REF] Akiduki | Neural localization of addicsin in mouse brain[END_REF][START_REF] Fenster | Piccolo, a presynaptic zinc finger protein structurally related to bassoon[END_REF][START_REF] Inoue | Expression profile of addicsin/GTRAP3-18 mRNA in mouse brain[END_REF][START_REF] Koomoa | Expression profile of PRAF2 in the human brain and enrichment in synaptic vesicles[END_REF][START_REF] Lee | Human alpha-synuclein modulates vesicle trafficking through its interaction with prenylated Rab acceptor protein 1[END_REF]. PRAF1 (also known as PRA1, RABA1 and Yip3 in yeast) is a Golgi-resident protein, which activates the dissociation of prenylated Rabs from the GDP dissociation inhibitor GDI, thus facilitating their association with target Golgi membranes [START_REF] Hutt | PRA1 inhibits the extraction of membranebound rab GTPase by GDI1[END_REF]. PRAF3 (also known as JWA, PRA2, ARL6IP5, addicsin, GTRAP3-18, Yip6b) was reported to delay the ER exit of the Na + -dependent glutamate transporter Excitatory Amino-Acid Carrier 1 (EAAC1) [START_REF] Akiduki | Modulation of the neural glutamate transporter EAAC1 by the addicsininteracting protein ARL6IP1[END_REF][START_REF] Lin | Modulation of the neuronal glutamate transporter EAAC1 by the interacting protein[END_REF]. Finally, PRAF2 (also known as JM4 or Yip 6a) was found in a two-hybrid screen to interact with the carboxy-terminus of the chemokine receptor CCR5, a co-receptor of the type-1 human immunodeficiency virus [START_REF] Schweneker | JM4 is a four-transmembrane protein binding to the CCR5 receptor[END_REF].

For several years, no clear biological function was attributed to PRAF2, except its overexpression in multiple cancers [START_REF] Borsics | Subcellular distribution and expression of prenylated Rab acceptor 1 domain family, member 2 (PRAF2) in malignant glioma: Influence on cell survival and migration[END_REF][START_REF] Fo | Genomic organization, expression profile, and characterization of the new protein PRA1 domain family, member 2[END_REF][START_REF] Vento | Praf2 is a novel Bcl-xL/Bcl-2 interacting protein with the ability to modulate survival of cancer cells[END_REF][START_REF] Yco | PRAF2 stimulates cell proliferation and migration and predicts poor prognosis in neuroblastoma[END_REF]. Recently, PRAF2 was reported to interact with GB1, the ligand-binding subunit of the GABA B receptor [START_REF] Doly | Gatekeepers controlling GPCR export and function Trends in[END_REF]. GABA (gamma-amino butyric acid) is the principal inhibitory neuromediator of the central nervous system (CNS). Functional GABA B receptors are composed of two distinct GB1 and GB2 protomers, which are assembled within a hetero-dimer [START_REF] Kaupmann | GABA(B)-receptor subtypes assemble into functional heteromeric complexes[END_REF]. GB1 is retained within the ER in the absence of GB2 [START_REF] Benke | Mechanisms of GABAB receptor exocytosis, endocytosis, and degradation[END_REF]. PRAF2 behaves as a specific GB1 gatekeeper controlling the retention of this protomer and preventing its progression into the biosynthetic pathway, GB1 being released from PRAF2 upon competitive displacement by GB2 [START_REF] Doly | Gatekeepers controlling GPCR export and function Trends in[END_REF]. The local concentration of PRAF2, relative to that of GB1 and GB2, thus controls cell surface receptor density impacting on GABA B function in neurons.

Only partial data are available concerning PRAF2 distribution in the CNS [START_REF] Koomoa | Expression profile of PRAF2 in the human brain and enrichment in synaptic vesicles[END_REF]) and functional studies in vivo were exclusively performed in mice following modulation of PRAF2 concentration in the ventral tegmental area (VTA) [START_REF] Doly | Gatekeepers controlling GPCR export and function Trends in[END_REF].

Changes of PRAF2 concentration were documented during embryonic neuronal growth in culture [START_REF] Doly | Gatekeepers controlling GPCR export and function Trends in[END_REF], in human nervous system cancers [START_REF] Borsics | Subcellular distribution and expression of prenylated Rab acceptor 1 domain family, member 2 (PRAF2) in malignant glioma: Influence on cell survival and migration[END_REF][START_REF] Geerts | Expression of prenylated Rab acceptor 1 domain family, member 2 (PRAF2) in neuroblastoma: correlation with clinical features, cellular localization, and cerulenin-mediated apoptosis regulation[END_REF][START_REF] Vento | Praf2 is a novel Bcl-xL/Bcl-2 interacting protein with the ability to modulate survival of cancer cells[END_REF][START_REF] Yco | PRAF2 stimulates cell proliferation and migration and predicts poor prognosis in neuroblastoma[END_REF] or in case of chronic alcohol intake [START_REF] Enoch | A factor analysis of global GABAergic gene expression in human brain identifies specificity in response to chronic alcohol and cocaine exposure[END_REF]. Because of the prominent regulatory effects of PRAF2 on GABA B function and the multiple roles of this receptor in the CNS, a precise analysis of PRAF2 distribution relative to that of GABA B subunits is of major interest. In addition, in confocal immunofluorescence microscopy studies, PRAF2 was predominantly found colocalized with ER markers, whereas fractionation studies reported its presence in synaptic vesicles preparations from rat brain [START_REF] Koomoa | Expression profile of PRAF2 in the human brain and enrichment in synaptic vesicles[END_REF]. Electron microscopy (EM) studies are thus necessary to determine the precise subcellular distribution of PRAF2 and appreciate potential additional functions other than that of ER gatekeeper.

Methods:

Animals. Wild type 129S2 mice (8-10 week old) used in these experiments were in a 129S2/SvPas (129S2) background (Charles River, France). Mice were maintained on a 12 light / 12 dark schedule (lights on at 8:00 am), and housed in groups of 3 to 5, in agreement with the institutional guidelines for use of animals and their care, in compliance with national and international laws and policies (Council directives no. 87-848, October 19, 1987, "Ministère de l'Agriculture et de la Forêt, Service Vétérinaire de la Santé et de la Protection Animale", agreement N° 75-974 to M.D., 75-976 to M.B.E).

Cell Culture. Human Embryonic Kidney 293 (HEK-293) cells were maintained in Dulbecco's modified Eagle's medium at 37°C in 5% CO2-enriched humidified atmosphere.

Media were supplemented with 10% fetal bovine serum (FBS) and 1% Penicillin-

Streptomycin.

Plasmids and transfections. PRAF2, PRAF3 and PRAF1 cDNAs were amplified by reverse PCR from mouse brain total RNA preparations and subcloned in frame into the pEGFP-N1 vector (Clontech). HEK-293 cells were transfected using GeneJuice Transfection Reagent (Novagen) according to manufacturer instructions.

Antibodies, Peptide. The following monoclonal antibodies (mAb) or polyclonal antibodies were used for immunofluorescence labeling and electron microscopy: PRAF2 antibody (ARP American Research Products, Massachusetts, USA, JM4/PRAF2, #L166), an affinity-purified rabbit polyclonal antiserum raised against amino acid residues 165-178 of PRAF2. This sequence does not produce any significant alignments with the other PRAF members or with unrelated proteins (Protein Blast NCBI); monoclonal anti-rabbit IgG (H+L) coupled to Alexa-594 (Invitrogen, France); F(ab')2 fragment of goat-anti-rabbit IgG (H&L, Aurion, France); polyclonal biotinylated anti-rabbit IgG (Vector, Burlingame, CA). A synthetic peptide, corresponding to amino acids 165-178 of Human PRAF2 (ARP American Research Products, Massachusetts, USA, JM4/PRAF2, #L166 BS1195P) was used as PRAF2 antibody blocking peptide. The immunizing peptide at a 5:1 ratio of peptide to antibody protein (w/w) was preincubated two hours in PBS with the PRAF2 antibody. Tissue preparation. Twenty-five mice under pentobarbital anesthesia (60 mg/kg) were perfused intracardially with 10 ml of 0.9% NaCl, containing 0.1% sodium nitrite followed by 50 ml of 4% paraformaldehyde in 0.1 M sodium phosphate buffer (PB), pH 7.4. Brains and spinal cords were dissected fixed overnight in the same fixative at 4°C. Transversal sections (50-µm thick) were made using a vibratome.

Light microscopy.

Immunocytochemistry was performed on free-floating sections. Sections were pre-incubated for 30 min at room temperature in 0.02 M PB, pH 7.4, containing 0.9% NaCl (PBS) and 3% bovine serum albumin (PBS-BSA), then incubated for 12 h at room temperature with rabbit anti-PRAF2 antibodies (1/500 dilution). For light-microscopy experiments, pre-incubation and incubation baths were supplemented with 0.2% Triton X-100. After extensive washing in PBS-BSA, sections were incubated for 1 h with the antirabbit IgG (H+L) antibody coupled to Alexa-594 (Invitrogen, France, 1/500 dilution).

Sections were then washed in PBS, transferred onto glass slides, and mounted in Mowiol (Sigma, France).

Electron microscopy with peroxidase staining. Immunocytochemistry was performed on free-floating sections. Sections were pre-incubated for 30 min at room temperature in PBS-BSA and then incubated for 12 h at room temperature with anti-PRAF2 antibodies (1/500 dilution). After extensive washing in PBS-BSA, sections were incubated for 1 h with the biotinylated anti-rabbit IgG (Vector, Burlingame, CA, 1/200 dilution). Sections were then washed in PBS and incubated for 1 h with the avidin-biotinylated-peroxidase complex (Vector) diluted (1/200) in PBS. After a 10-min wash in 0.05 M Tris-HCl, pH7.4, sections were incubated in the same buffer supplemented with 0.03% (w/v) 3,3-diaminobenzidine (Sigma, France) and 0.01% (v/v) hydrogen peroxide. The reaction proceeded at room temperature under light microscope control and was stopped after 5-10 min of incubation by washing in Tris buffer. Sections were incubated in 2.5% glutaraldehyde in PB, rinsed with the same buffer and incubated for 1 h with 2% osmium tetroxide in PB. They were dehydrated in a series of ethanol and flat embedded in epoxy resin (EPON 812 Polysciences). After polymerization, blocks were cut at 70 nm thickness, picked up in 200 mesh cupper grids and observed directly, without staining, under electron microscope.

Electron microscopy with immuno-gold staining. Mice were perfused transcardially with a solution containing 4% paraformaldehyde and 0.1% glutaraldehyde in 0.1 M PB, pH 7.4.

After perfusion, brains were removed from the skulls, and immersed in the same fixative for 12 h at 4°C. Tissue blocks were washed in 0.1 M PB and sectioned (vibratome) into coronal sections of 50 µm. Sections were cryo-protected in 20% sucrose in 0.1M PB, freeze-thawed in isopentane and liquid nitrogen. Samples were post-fixed in 2.5 % glutaraldehyde in 0.1 M PB for 20 min, washed and incubated with 2% osmium tetroxide in PB for 20 min. Samples were dehydrated in a series of ethanol and flat embedded in epoxy resin (EPON 812 Polysciences).

After polymerization, blocks were cut at 70 nm thickness using an ultramicrotome (Ultracut E Leica) with a diamond knife, picked up on formvar-coated 200 mesh nickel grids. For etching resin and remove osmium, sections were treated with saturated aqueous sodium periodate (NaIO 4) . They were then immunostained as described [START_REF] Slot | Cryosectioning and immunolabeling[END_REF], by indirect immunolabeling with protein gold as immunomarker. Protein A-gold probes (20 nm) were obtained from CMC Utrecht (Netherlands). After immunolabeling, the sections were double stained with uranyl acetate and lead citrate. Control immuno-stainings were performed, in which the primary antibody was omitted. Under these conditions, no selective labeling was observed. Electron microscopic images of the tissue were obtained using a digital camera (Gatan Orius) interfaced with a transmission electron microscope (Philips CM100).

Immunofluorescence analysis. Confocal microscopy and image analysis were performed at the Institut du Fer-à-Moulin Imaging Facility. Sequential labeled images from each region of interest were obtained using laser-scanning confocal microscopy (Olympus Fluoview). To assess the overall level of immunoreactivity in a specific brain area, the optical density of the area was measured with image-J: 100µm diameter circles were acquired for each regions of interest, the acquisition of at least two circles (up to 20 circles for the largest areas) being used to assess the level of immunoreactivity in a specific zone. Immunoreactivity was scored as negative (-), very low (+), low (++), moderate (+++), dense (++++), depending of the mean OD value obtain for each nucleus. Brain structures were defined according to the mouse brain atlas in stereotaxic coordinates from Keith B. J. Franklin and George Paxinos (second edition).

Results:

The specificity of PRAF2 antibodies was assessed in immunohistochemistry and western blot assays (Fig. 1). Confirming the specificity of the PRAF2 antibody, immunostaining was abolished by preabsorption of the antibody with the blocking peptide on mouse brain slices (Fig. 1A). The antibody was characterized further by immunoblotting after sodium dodecyl sulfate-polyacrylamide gel electrophoresis (SDS-PAGE) on total HEK cells membrane preparations, transfected with PRAF1-V5, PRAF2-V5 or PRAF3-V5 constructs (Fig. 1B). In stringent SDS-containing lysis buffer, the PRAF2 antibody recognized a ≈17-kDa molecular species (arrow), consistent with the expected molecular weight of endogenous PRAF2 and a ≈21-kDa molecular species (arrowhead), consistent with the expected molecular weight of PRAF2-V5 (Fig. 1B, upper panel). In HEK cells transfected with PRAF1-V5 or PRAF3-V5 constructs, the PRAF2 antibody only recognize the endogenous PRAF2 (Fig. 1B, upper panel). The peptide--blocked PRAF2 antibody did not recognize PRAF2 or PRAF2--V5, confirming the specificity of this antibody (Fig. 1B, middle panel). As expected, the V5 epitope-directed antibody only recognized PRAF1-V5, PRAF2-V5 and PRAF3-V5 (Fig. 1B, lower panel). Moreover, in a series of immunoblot experiments on rat hippocampal neurons, the signal associated with the anti-PRAF2 antibody was markedly inhibited in extracts from neurons transfected with a PRAF2-specific siRNA compared to control neurons [START_REF] Doly | Gatekeepers controlling GPCR export and function Trends in[END_REF].

Immunohistochemical experiments were then performed, to investigate the distribution of PRAF2, on coronal sections at various levels of the rostrocaudal axis of mouse CNS. The general expression pattern of PRAF2, previously described in the human brain [START_REF] Koomoa | Expression profile of PRAF2 in the human brain and enrichment in synaptic vesicles[END_REF]) was confirmed in mice. PRAF2 was strongly expressed in Purkinje cells and less expressed in molecular and granular layers of mouse cerebellum. In the cerebral cortex and hippocampus, PRAF2 protein was also detected in neurons, but not in non-neuronal cells. A detailed description of PRAF2 expression is provided below and summarized in Table 1 where the relative labeling intensities of cell body and neuropil immunoreactivity were analyzed: labeling was scored as negative (-), very low (+), low (++), moderate (+++), dense (++++) or very dense (+++++).

Main olfactory bulb

In olfactory bulbs, strong PRAF2 immunoreactivity was present in the mitral cell layer, contrasting with the sparse labeling of neuronal cell bodies in the external plexiformis glomerular, internal plexiformis and granule layers (Fig. 2A). PRAF2 is also expressed in the anterior olfactory nucleus (Fig. 2B), but not in the accessory olfactory bulb (not shown).

Cerebral cortex and Basal ganglia

In the cerebral cortex, PRAF2 immunoreactivity was mainly detected in layers II and V (Fig. 2,3). Only scattered cell body immunostaining were observed in the other laminae, with the exception of an intense band of cell body staining in the deepest part of lamina VI (Fig. 3C).

Strong immunolabeling was present in the piriform cortex, compared to other cortical regions (Fig. 3A,C). No immunolabeling was found in basal ganglia such as the nucleus accumbens the globus pallidus and the caudate-putamen (Fig. 3), either in neuronal cell bodies or neuropili (Fig. 3B), contrasting with a strong, almost exclusively cellular, labeling in the endopiriform nucleus (Fig. 3C).

Hippocampus, Amygdala and habenula

In the hippocampus, PRAF2 immunoreactivity was found in the pyramidal layer of the CA1-3 field and in the granular layer of the dentate gyrus (Fig. 4A,B,C). Scattered immunoreactivity was present in the hilus of the dentate gyrus, the strata oriens and radiatum of the CA1-3 field (Fig. 4C). Among the various sub-nuclei of the amygdala, the highest intensity of PRAF2 labeling was found in the basomedial, medial and lateral amygdaloid nuclei (Fig. 4B). Dense labeling was observed in the medial habenula but only scattered neuronal cell body staining was found in the other nuclei, including the lateral habenula nucleus (Fig. 4B).

Thalamus

Surprisingly, only some sub-nuclei of the thalamus were labeled with the anti-PRAF2 antibody, despite the fact that this area expresses high levels of the GB1 subunit [START_REF] Bowery | GABAA and GABAB receptor site distribution in the rat central nervous system[END_REF][START_REF] Calver | The expression of GABA(B1) and GABA(B2) receptor subunits in the cNS differs from that in peripheral tissues[END_REF][START_REF] Charles | Distribution of a GABAB-like receptor protein in the rat central nervous system[END_REF][START_REF] Charles | Comparative immunohistochemical localisation of GABA(B1a), GABA(B1b) and GABA(B2) subunits in rat brain, spinal cord and dorsal root ganglion[END_REF][START_REF] Margeta-Mitrovic | Immunohistochemical localization of GABA(B) receptors in the rat central nervous system[END_REF][START_REF] Ulrich | Functional mapping of GABA(B)-receptor subtypes in the thalamus[END_REF]). Among the thalamic nuclei, we found the highest immunoreactivity in the anterodorsal and the reticular nuclei (Fig. 4A,B); a moderate level of immunostaining was present in the paratenial laterodorsal and paraventricular nuclei (Fig. 3 and4A,B).

Interestingly, at higher magnification, the labeling pattern of the cell bodies was different between the anterodorsal thalamic nucleus and the pyramidal layer of the hippocampus: an intense punctate immunoreactivity in the former contrasted with a diffuse staining in the latter (Fig. 4A,B).

Midbrain

In the midbrain, the most noticeable labeling was found in the ventral tegmental area and in the substantia nigra pars compacta. Only a weak staining was present in the colliculus, or the periaqueductal gray and oculomotor nuclei (Fig. 5,6). In the ventral tegmental area, some neuronal cell bodies exhibited the same punctate pattern of PRAF2 expression, as in the anterodorsal thalamic nucleus (Fig. 5D).

Pons and Cerebellum

Intense PRAF2 immunoreactivity was found in pontine nuclei, locus coeruleus and pontine raphe nuclei (Fig. 6A,B). In the cerebellum, PRAF2 immunoreactivity was weak in the granule cell layer, the molecular layer and undetectable in white matter-rich areas. Most labeled cell bodies were concentrated in the Purkinje cells layer (Fig. 6B).

Medulla oblongata

Intense cellular staining could be observed in the midline raphe nuclei (Fig. 6A). Some nuclei of the medulla oblongata, such as cochlear, facial, external cuneate, spinal trigeminal, lateral reticular and cuneate nuclei contained highly immunoreactive cell bodies (Fig. 6B,C,D,E and Fig. 7). Scattered cell body immunoreactivity was present in the ambiguus and the gigantocellular reticular nuclei, whereas diffuse staining of neuropili was found in the solitary tract nucleus, the area postrema, and the inferior olive subnucleus. Intense punctate immunoreactivity could be observed in cell bodies of the medulla (Fig. 7A).

Spinal cord

In the spinal cord, the most intense PRAF2 immunoreactivity was observed in the ventral horn at all spinal levels (Fig. 8). In lamina VIII-IX, the cell bodies of presumably large motoneurons were intensely stained, whereas in round smaller-size neurons, presumably interneurons, the staining was much weaker. Some immunoreactive neurons were also distributed around the central canal of lamina X at all spinal levels. Labeling in the dorsal horn was more diffuse and could not be easily attributed to any cell compartment.

Subcellular distributions

The localization of PRAF2 at the subcellular level was then investigated by electron microscopy in the VTA. In these experiments PRAF2 immunoreactivity appeared under the form of either electron-dense amorphous DAB reaction products or gold particles.

PRAF2 was present in axon terminals, identified by the presence of synaptic vesicles (Fig. 9 black star). Both gold particles and DAB products were found at the edge of synaptic vesicles (black arrows) or in mitochondria (m) present in the terminals (Fig. 9A,B,H,I). PRAF2 immunoreactivity was also present in the postsynaptic region of axo-somatic (arrow head in Fig. 9A,B,G) or axo-dendritic contacts (arrow head in Fig. 9D,F,G). Both asymmetric (Fig. 9A,B,D,F,G) and symmetric (Fig. 9C,E) synapses (arrow head) were stained, suggesting that PRAF2 is expressed in excitatory and inhibitory synapses, respectively.

In the cytoplasm, gold particles or DAB products were principally associated with rough endoplasmic reticulum (RER). Among the other cellular organelles, which appear to contain PRAF2 after immunoperoxidase or immunogold staining, there are mitochondria, the cis-Golgi apparatus, nuclei, lysosomes and primary cilia.

In the RER, labeling was mainly found in cisternae, at the cytosolic interface, either under the form of single gold particles, or as aggregates (Fig. 9A,E and Fig. 10D). In smooth endoplasmic reticulum, lacking attached ribosomes, labeling was mostly found at the membrane. PRAF2 also appeared associated with tubulo-vesicular structures.

In mitochondria, the labeling was on both membranes, each of them being well stained by DAB; the immunostaining of the inner membrane extended to the cristae (Fig. 9B,C,D). Gold particles were observed in the internal cristae and also associated with the external membrane (Fig. 9I). In the Golgi apparatus gold particles or DAB products were associated with both cisternae and vesicles: particles were more frequently present in cisternae neighboring RER elements (likely the cis-Golgi) (Fig. 10E,F). In nuclei, the immunoperoxidase staining was observed at the level of the nuclear envelope, with a strong labeling of the nuclear pores (Fig. 11A), the heterochromatin, nucleoli and Cajal bodies (Fig. 11B). Immunostaining was present in both leaflets of the nuclear membrane, which is in continuation with the RE. Gold particles were visible in the nucleoplasm associated to heterochromatin and in nucleoli. In lysosomes immunogold labeling was found in dense matrix or located at the cytosolic side of the lysosomal membrane (Fig. 11C).

Discussion:

Consistent with its function of GB1 gatekeeper [START_REF] Doly | Gatekeepers controlling GPCR export and function Trends in[END_REF], PRAF2 was present in brain areas expressing the GABA B , including the cortex, the hippocampus, the VTA and raphe nuclei [START_REF] Charles | Distribution of a GABAB-like receptor protein in the rat central nervous system[END_REF][START_REF] Charles | Comparative immunohistochemical localisation of GABA(B1a), GABA(B1b) and GABA(B2) subunits in rat brain, spinal cord and dorsal root ganglion[END_REF][START_REF] Fritschy | Independent maturation of the GABA(B) receptor subunits GABA(B1) and GABA(B2) during postnatal development in rodent brain[END_REF][START_REF] Kulik | Subcellular localization of metabotropic GABA(B) receptor subunits GABA(B1a/b) and GABA(B2) in the rat hippocampus[END_REF][START_REF] Margeta-Mitrovic | Immunohistochemical localization of GABA(B) receptors in the rat central nervous system[END_REF]). PRAF2 expression perfectly matched the distribution of GB1 in these areas. It is likely that in the zones that also express the GB2 subunit [START_REF] Charles | Comparative immunohistochemical localisation of GABA(B1a), GABA(B1b) and GABA(B2) subunits in rat brain, spinal cord and dorsal root ganglion[END_REF][START_REF] Clark | Distribution of the GABA(B) receptor subunit gb2 in rat CNS[END_REF][START_REF] Kulik | Subcellular localization of metabotropic GABA(B) receptor subunits GABA(B1a/b) and GABA(B2) in the rat hippocampus[END_REF], the actual concentration of cell surface GABA B is controlled by the relative amount of PRAF2 and GB2. Consistent with our previous observation that moderate changes of PRAF2 expression in the VTA induce hyperactivity in mice [START_REF] Doly | Gatekeepers controlling GPCR export and function Trends in[END_REF], the unbalanced expression of these proteins would perturb GABA B receptivity and potentially produce pathological effects. For example, PRAF2 appears to be expressed, as the GABA B , in the pyramidal and granular layers of the hippocampus (Margeta-Mitrovic et al. 1999), a brain area involved in the processing of drug reinforcement behaviors.

Preclinical studies have implicated GABA B receptors in the rewarding effects of drugs of abuse and GABA B agonists can decrease alcohol withdrawal symptoms in humans and rats [START_REF] Colombo | Role of GABA(B) receptor in alcohol dependence: reducing effect of baclofen on alcohol intake and alcohol motivational properties in rats and amelioration of alcohol withdrawal syndrome and alcohol craving in human alcoholics[END_REF][START_REF] Maccioni | Role of the GABA(B) receptor in alcohol-seeking and drinking behavior[END_REF]. Moreover, a recent transcriptomic study in postmortem hippocampi found a significant reduction of PRAF2 transcripts in alcoholic patients compared to controls [START_REF] Enoch | A factor analysis of global GABAergic gene expression in human brain identifies specificity in response to chronic alcohol and cocaine exposure[END_REF], and previous studies demonstrated that PRAF2 controls GABA B function in primary hippocampal neurons [START_REF] Doly | Gatekeepers controlling GPCR export and function Trends in[END_REF].

Overall, these findings suggest that PRAF2 regulates GABA B function in these areas and might participate in GABA B -dependent neurological disorders.

In other brain areas PRAF2 expression did not matched perfectly that of GB1. For example, in the spinal cord only motoneurons of the ventral horn were strongly labeled with PRAF2 antibody, whereas the expression of GB1 and GB2 subunits was well documented in both the dorsal and the ventral horn [START_REF] Charles | Comparative immunohistochemical localisation of GABA(B1a), GABA(B1b) and GABA(B2) subunits in rat brain, spinal cord and dorsal root ganglion[END_REF][START_REF] Margeta-Mitrovic | Immunohistochemical localization of GABA(B) receptors in the rat central nervous system[END_REF], suggesting that GABA B function in the dorsal horn is not controlled by PRAF2.

The absence of detectable PRAF2 expression in basal ganglia (caudate putamen, globus palidus, nucleus accumbens) or hypothalamic neurons is particularly appealing, since these brain areas also express small amounts of GB2 subunits comparatively to GB1 [START_REF] Burman | GABAB receptor subunits, R1 and R2, in brainstem catecholamine and serotonin neurons[END_REF][START_REF] Calver | The expression of GABA(B1) and GABA(B2) receptor subunits in the cNS differs from that in peripheral tissues[END_REF][START_REF] Clark | Distribution of the GABA(B) receptor subunit gb2 in rat CNS[END_REF][START_REF] Durkin | An in situ hybridization study of the distribution of the GABA(B2) protein mRNA in the rat CNS Brain[END_REF][START_REF] Ng | Differential expression of GABA(B)R1 and GABA(B)R2 receptor immunoreactivity in neurochemically identified neurons of the rat neostriatum[END_REF].

Interestingly, despite low GB2 expression, physiological functions attributable to GB1 were documented in these nuclei [START_REF] Chen | GABAergic neurotransmission in globus pallidus and its involvement in neurologic disorders Sheng[END_REF][START_REF] Va | GABA(B) receptors in neuroendocrine regulation[END_REF]. Previous studies showed that reconstituted cell systems or neurons lacking the GB2 subunit could nevertheless express functional, although often atypical, GB1-containing GABA receptors [START_REF] Baloucoune | GABAB receptor subunit GB1 at the cell surface independently activates ERK1/2 through IGF-1R transactivation[END_REF][START_REF] Gassmann | Redistribution of GABAB(1) protein and atypical GABAB responses in GABAB(2)deficient mice[END_REF][START_REF] Kaupmann | Expression cloning of GABA(B) receptors uncovers similarity to metabotropic glutamate receptors[END_REF][START_REF] Richer | GABA-B(1) receptors are coupled to the ERK1/2 MAP kinase pathway in the absence of GABA-B(2) subunits[END_REF]. In these situations, the unbalanced expression of GB1 over that of PRAF2 may overload the PRAF2-mediated ER retention, thereby allowing a fraction of GB1 to reach the cell surface despite the absence of GB2 and somehow couple to G-proteins. In this context, the atypical responses elicited by GB1 activation [START_REF] Gassmann | Redistribution of GABAB(1) protein and atypical GABAB responses in GABAB(2)deficient mice[END_REF]) might proceed via alternative coupling of GB1 homodimers or from the heterodimerization of GB1 with other GPCRs co-expressed in the same neurons.

Strong PRAF2 expression was found in some brain areas expressing no or low levels of GB1, such as cuneate, gracile and lateral reticular nuclei, suggesting that PRAF2 might control the export of other GPCRs or other types of plasma membrane proteins in the CNS. Although, GABA B receptors are the prototypical model of intracellularly-retained GPCRs with regulated cell-surface export, several other GPCRs undergo similar regulated trafficking from ER or Golgi stores [START_REF] Achour | An escort for G Protein Coupled Receptors to find their path: implication for regulation of receptor density at the cell surface[END_REF]. In particular, PRAF2 was reported to interact with the chemokine receptor CCR5 [START_REF] Schweneker | JM4 is a four-transmembrane protein binding to the CCR5 receptor[END_REF]) and preliminary Bioluminescence Resonance Energy Transfer (BRET) and co-IP experiments indicated that PRAF2 can associate with other chemokine receptors, such as CCR2 and CCR7, and with 5-HT2 serotoninergic receptors (unpublished data).

Previous fluorescence microscopy studies indicated that PRAF2 was mostly co-localized with ER markers [START_REF] Doly | Gatekeepers controlling GPCR export and function Trends in[END_REF]. However, in hippocampal neurons, a fraction of PRAF2 was consistently found co-localized with a cis-Golgi marker and additional protein did not colocalize with either marker. The electron microscopy study confirmed the presence of PRAF2 in additional organelles or structures. Some PRAF2 was expressed in presynaptic vesicles and in the postsynaptic density. This finding is reminiscent of previous studies on PRAF1 and PRAF3, showing that both proteins were also located in the synaptic area and could interact with specific synaptic proteins, such as VAMP2, synaptophysin, synuclein and piccolo [START_REF] Akiduki | Neural localization of addicsin in mouse brain[END_REF][START_REF] Fenster | Piccolo, a presynaptic zinc finger protein structurally related to bassoon[END_REF][START_REF] Lee | Human alpha-synuclein modulates vesicle trafficking through its interaction with prenylated Rab acceptor protein 1[END_REF][START_REF] Martincic | Isolation and characterization of a dual prenylated Rab and VAMP2 receptor[END_REF]. Moreover, PRAF2 was found in synaptic vesicles preparations from rat brain [START_REF] Koomoa | Expression profile of PRAF2 in the human brain and enrichment in synaptic vesicles[END_REF].

Altogether, these observations suggest that PRAF2 might play a role in the regulation of the synaptic function through the control of the vesicular trafficking or docking of GPCRs or other membrane-associated proteins. Although not investigated so far, PRAF2 might regulate the plasma membrane translocation of some specific Rab protein in the presynaptic (Rab3/5) or postsynaptic (Rab8/5) area [START_REF] Ng | Rab GTPases and their roles in brain neurons and glia[END_REF]. Some PRAF2 labeling was present at the nuclear membrane, nuclear pores and nucleoli, consistent with the presence of PRAF2 in nuclei and perinuclear regions of neuroblastoma cells and in the nuclear fraction of U-87 malignant glioma cells [START_REF] Borsics | Subcellular distribution and expression of prenylated Rab acceptor 1 domain family, member 2 (PRAF2) in malignant glioma: Influence on cell survival and migration[END_REF][START_REF] Geerts | Expression of prenylated Rab acceptor 1 domain family, member 2 (PRAF2) in neuroblastoma: correlation with clinical features, cellular localization, and cerulenin-mediated apoptosis regulation[END_REF]). To date, there is no evidence for a nuclear function of PRAF2. However, Yip3p, the yeast homologue of PRAF1 was reported to interact with RTN1p reticulon [START_REF] Geng | Saccharomyces cerevisiae Rab-GDI displacement factor ortholog Yip3p forms distinct complexes with the Ypt1 Rab GTPase and the reticulon Rtn1p[END_REF], whereas PRAF2 interacts with RTN4, also known as the neurite outgrowth inhibitor Nogo [START_REF] Vento | Praf2 is a novel Bcl-xL/Bcl-2 interacting protein with the ability to modulate survival of cancer cells[END_REF]. Reticulons are membrane-associated proteins involved in cell trafficking, inhibition of axonal growth, and apoptosis [START_REF] Chiurchiu | The role of reticulons in neurodegenerative diseases[END_REF][START_REF] Yang | The reticulons: a family of proteins with diverse functions[END_REF]. Interestingly, RTN4A also localizes to subdomains of the nuclear envelope and its inhibition by anti-RTN4A antibodies limits nuclear envelope assembly [START_REF] Kiseleva | Reticulon 4a/NogoA locates to regions of high membrane curvature and may have a role in nuclear envelope growth[END_REF]). PRAF2/RTN4 interaction might thus play a role in nuclear envelope maintenance or in the localization of protein partners in this compartment.

The localization of PRAF2 in the mitochondria of midbrain neurons is consistent with the observation that PRAF2 and PRAF3 can interact with both Bcl-2 and Bcl-xL [START_REF] Vento | Praf2 is a novel Bcl-xL/Bcl-2 interacting protein with the ability to modulate survival of cancer cells[END_REF]. Whereas Bcl-2, is predominantly localized in the ER, Bcl-xL is mainly a mitochondrial outer membrane protein [START_REF] Kaufmann | Characterization of the signal that directs Bcl-x(L), but not Bcl-2, to the mitochondrial outer membrane[END_REF]. PRAF2 overexpression induces the translocation and the aggregation of Bax in mitochondria, increasing caspase activity and cell death. As a pro-survival member of the Bcl-2 familly, Bcl-xL plays a unique role in the general resistance to cytotoxic agents. In neurons, it also stimulates synapse formation, increases mitochondrial fission and fusion and modulates exchange of metabolites across the outer mitochondrial membrane [START_REF] Berman | Bcl-x L increases mitochondrial fission, fusion, and biomass in neurons[END_REF][START_REF] Li | Bcl-xL induces Drp1-dependent synapse formation in cultured hippocampal neurons[END_REF][START_REF] Vander Heiden | Bcl-xL promotes the open configuration of the voltage-dependent anion channel and metabolite passage through the outer mitochondrial membrane[END_REF]. Pro-apoptotic Bcl-2 family members, such as Bax, regulate programmed cell death in neurons [START_REF] Krajewski | Immunohistochemical determination of in vivo distribution of Bax, a dominant inhibitor of Bcl-2[END_REF][START_REF] Oltvai | Bcl-2 heterodimerizes in vivo with a conserved homolog, Bax, that accelerates programmed cell death[END_REF]. Bax and Bcl-xL are expressed in midbrain dopaminergic neurons and were implicated in trauma response and Parkinson disease [START_REF] Anderton | Co-regulation of survival of motor neuron and Bcl-xL expression: implications for neuroprotection in spinal muscular atrophy[END_REF][START_REF] Horowitz | BAX proteinimmunoreactivity in midbrain neurons of Parkinson's disease patients[END_REF][START_REF] Shim | Enhanced in vitro midbrain dopamine neuron differentiation, dopaminergic function, neurite outgrowth, and 1-methyl-4-phenylpyridium resistance in mouse embryonic stem cells overexpressing Bcl-XL[END_REF][START_REF] Van Der Heide | The BCL2 code to dopaminergic development and Parkinson's disease[END_REF][START_REF] Vila | Targeting programmed cell death in neurodegenerative diseases[END_REF]. PRAF2 might control Bcl-xl and Bax localization in the RE or mitochondria of midbrain neurons, the impaired sorting of these proteins potentially leading to neurodegeneration or neural death after brain injury. PRAF2-dependent perturbation of the pro and anti-apoptotic equilibrium, trough BAX and Bcl-xL relocation, might play a role in cancer genesis or progression [START_REF] Borsics | Subcellular distribution and expression of prenylated Rab acceptor 1 domain family, member 2 (PRAF2) in malignant glioma: Influence on cell survival and migration[END_REF][START_REF] Fo | Genomic organization, expression profile, and characterization of the new protein PRA1 domain family, member 2[END_REF][START_REF] Geerts | Expression of prenylated Rab acceptor 1 domain family, member 2 (PRAF2) in neuroblastoma: correlation with clinical features, cellular localization, and cerulenin-mediated apoptosis regulation[END_REF][START_REF] Vento | Praf2 is a novel Bcl-xL/Bcl-2 interacting protein with the ability to modulate survival of cancer cells[END_REF][START_REF] Yco | PRAF2 stimulates cell proliferation and migration and predicts poor prognosis in neuroblastoma[END_REF].

A previously non-documented specific localization of PRAF2 is the primary cilium.

However this finding is consistent with the result of a genomic screen aimed at identifying ciliogenesis modulators [START_REF] Kim | Functional genomic screen for modulators of ciliogenesis and cilium length[END_REF]. In this study siRNA-induced PRAF2 knockdown was reported to facilitate ciliogenesis and primary cilium extension. Interestingly, all PRAF members might participate in ciliogenesis regulation: PRAF1 was identified in a proteomic analysis of the cilium complex [START_REF] Liu | The proteome of the mouse photoreceptor sensory cilium complex[END_REF]); PRAF3 interacts with the Arf-like GTPase ARL6, which is implicated in the regulation of ciliary transport and recruitment of the BBS (Bardet-Biedl Syndrome) complex, a group of proteins involved in genetic ciliopathies [START_REF] Fan | Mutations in a member of the Ras superfamily of small GTP-binding proteins causes Bardet-Biedl syndrome[END_REF]). The molecular mechanisms of PRAF2-dependent regulation of ciliogenesis and cilium extension have not been investigated so far but might involve the capacity of PRAF2 to regulate GPCRs. Indeed, primary cilia are enriched in some GPCRs, such as the somatostatin receptor 3 (Sstr3) [START_REF] Handel | Selective targeting of somatostatin receptor 3 to neuronal cilia[END_REF], the serotonin receptor 6 (5-HT6r) [START_REF] Brailov | Localization of 5-HT(6) receptors at the plasma membrane of neuronal cilia in the rat brain[END_REF], the melanin-concentrating hormone receptor 1 (Mchr1) (Berbari et al. 2008a) and the dopamine receptor 1 (D1r) [START_REF] Domire | Dopamine receptor 1 localizes to neuronal cilia in a dynamic process that requires the Bardet-Biedl syndrome proteins[END_REF]. Interestingly, BBS proteins are required for Sstr3 and Mchr1 localization in cilia (Berbari et al. 2008b) and impaired GPCR targeting to cilia can cause learning and memory defects or hyperphagia-induced obesity (Berbari et al. 2008b;[START_REF] Davenport | Disruption of intraflagellar transport in adult mice leads to obesity and slow-onset cystic kidney disease[END_REF][START_REF] Einstein | Somatostatin signaling in neuronal cilia is critical for object recognition memory[END_REF]. In conclusion, PRAF2 might play either direct or indirect role, via its interacting partners, in the relocalization or trafficking of GPCRs to primary cilia.

In summary, PRAF2 appeared widely distributed in various regions of the CNS, from the olfactory bulbs to the spinal cord. PRAF2 expression was particularly dense in brain regions previously shown to contain the GB1 subunit of the GABA B receptor but other areas exist where GB1 and PRAF2 expression do not overlap. These finding suggest that GABA B function is not exclusively controlled by PRAF2 and, on the other hand, that PRAF2 might control the export of other membrane-associated proteins in the CNS. At the subcellular level, several other organelles contain PRAF2 in addition to the RE anticipating additional functions that remain to be elucidated.

Fig. 1 :Fig. 2 :

 12 Figure Legends:

Fig. 3 :

 3 Fig.3: Lack of PRAF2 immunoreactivity in the nucleus accumbens and caudate-

Fig. 4 :

 4 Fig.4: Distribution of PRAF2 immunoreactivity in the anterodorsal thalamic nucleus

Fig. 5 :

 5 Fig.5 : Distribution of PRAF2 immunoreactivity in the lateral mammillary nuclei (A),

Fig. 6 :

 6 Fig.6 : Distribution of PRAF2 immunoreactivity in the periaqueductal gray, dorsal and

Fig. 7 :

 7 Fig.7 : Distribution of PRAF2 immunoreactivity in the cuneate nucleus (A), lateral

Fig. 8 :Fig. 9 :

 89 Fig.8 : Distribution of PRAF2 immunoreactivity in the cervical (C2-C6), thoracic (T1),

  Figure9

Table 1 :

 1 Distribution of PRAF2 in the Mouse Central Nervous System Intensity of PRAF2: +++++, very strong; ++++, strong; +++, moderate; ++, low; +, very low; -, absente

Acknowledgments :

This work was supported by grants from the Ligue Contre le Cancer, comité de l'Oise to SD; from the PIC (projets inter-équipes) to SD ; from the French Agency for AIDS Research (ANRS-09) and the Fondation pour la Recherche Médicale (Equipe FRM-2012) to SM; SM team is member of the 'Who-am-I' research consortium.

Conflict of Interest:

The authors declare that they have no conflict of interest.

Main olfactory bulb

Thalamus


B Ravelo
email: ravelo@esigelec.fr

F Vurpillot
email: francois.vurpillot@univ-rouen.fr

A K Jastrzebski

Asymmetrical PCB Interconnect Tree Modelling with Coupling Effect

Keywords: Behavioral model, asymmetrical tree, signal integrity, interconnect network, SIMO/SISO-transform. I

The paper describes integrity analysis of the signal propagating on asymmetrical tree with coupling from neighboring lines. Theoretical principle illustrating the modelling methodology and the developed routine algorithm is mathematically established. The developed model was applied to 2:1 asymmetrical microstrip tree with neighboring single lines at 10-to-100µm distance. Frequency-and time-domain analyses were conducted to check the coupling influence onto the signal distribution tree due to the substrate dielectric dispersion using broadband model. Examples of applications from DC to 10GHz were investigated to evaluate the influence of the coupling on the asymmetrical tree responses. It was shown that ringing effects and distorted signals were occurring from the two tree branch outputs. Furthermore, time-domain analyses were performed with 8-bits high speed input signal data with 0.5 Gbps rate. It was found that the signal quality was degraded and the amplitude of the shared signals was slightly affected by the coupling.

INTRODUCTION

Signal and power integrity (SPI) and electromagnetic compatibility (EMC) phenomena become crucial when operating frequency, processing speed and integration density of digital electronic systems (DRAM, MPU, DIMM packages, etc. …) are increased [START_REF]International Technology Roadmap for Semiconductors Update Overview[END_REF][START_REF] Beyene | Design and Analysis of High-Speed Links[END_REF][START_REF] Cases | Main Memory Design for SPI Engineers[END_REF]. Design and fabrication engineers have to respect required compliances notably in the interconnection networks such as memory buses (DDR4, GDDR5, XDR, IO2, HBM), front side bus (quick path interconnect, hypertransport), cable (USB, HADMI, FireWire Cat X), Ethernet (XAUI, XFI, CEI-6GLR, SONNET), etc. [START_REF] Cases | Main Memory Design for SPI Engineers[END_REF]. Fig. 1 illustrates an example of complex signal distribution interconnect tree [START_REF] Averill | Chip Integration Methodology for the IBM S/390 G5 and G6 Custom Microprocessors[END_REF]. Such a structure in the modern high speed memory system is challenging on the SPI and EMC constraints effects on interconnect lines (ILs) due to channel attenuation, crosstalk, reflection, delay and distortion [START_REF] Zhu | High-Speed Clock Network Sizing Optimization Based on Distributed RC and Lossy RLC Interconnect Models[END_REF][START_REF] Deutsch | When are Transmission-Line Effects Important for On-Chip Interconnection[END_REF]. So, prediction methods were developed based on various IL based approaches, such as RC-and RLC-models [START_REF] Buckwalter | Predicting Microwave Digital Signal Integrity[END_REF][START_REF] Ravelo | Investigation of Reduced Models of Capacitive Loaded Interconnects for the High-Speed SI Applications[END_REF].

More generally, different models of interconnect tree topologies were developed [START_REF] Ravelo | Modelling of symmetrical distributed clock RC H-tree[END_REF][START_REF] Restle | Designing the Best Clock Distribution Network[END_REF][START_REF] Hungwen | A Tree-Topology Multiplexer for Multiphase Clock System[END_REF][START_REF] Rakuljic | Tree-Structured DEM DACs with Arbitrary Numbers of Levels[END_REF]. But those models are not valid for structures presenting asymmetrical behavior, such as comb-tree depicted in Fig. 2. However, analytical model including the unbalanced interconnect tree was recently proposed in [START_REF] Eudes | Distributed Model of Two-Level Asymmetrical PCB Interconnect Tree[END_REF]. Firstly, the model assumed that the IL can be described by an RLCG equivalent circuit with frequency varying per unit length parameters (R u (f), L u (f), C u (f) and G u (f)) by denoting f the frequency variable. Secondly, the circuit equivalent approach was used with the single input multiple output (SIMO) structure transformed into single input single output system (SISO) [START_REF] Eudes | Distributed Model of Two-Level Asymmetrical PCB Interconnect Tree[END_REF]. The analytical operations were handled with ABCD-to-Z matrix transform (to generate the IL impedance matrix), Z-to-Y matrix transform (to extract the equivalent parallel lines), and Y-to-ABCD matrix transform (to find the equivalent transfer parameters) [START_REF] Cho | Mixed-Mode ABCD Parameters: Theory and Application to Signal Integrity Analysis of PCB-Level Differential Interconnects[END_REF][START_REF] Frickey | Conversions Between S, Z, Y, h, ABCD and T Parameters which are Valid for Complex Source and Load Impedances[END_REF]. The output responses across different paths from the single input N in to any output N m (m={1,…,8}) were mathematically formulated via the voltage transfer functions:

H m =V m /V in . ( 1
)
Figure 2. Example of 8:1 comb or asymmetrical interconnect tree.

978-1-4799-3226-9/14/$31.00 © 2014 IEEE

That modeling method was applied to perfectly isolated asymmetrical tree structure. However, for systems using high density PCBs, the interconnections can be significantly localized and can create unintentional EM coupling or crosstalk effects [START_REF] Chanodia | Effects of Crosstalk Noise on H-tree Clock Distribution Networks[END_REF][START_REF] Chanodia | Effects of Parameter Variations and Crosstalk on H-Tree Clock Distribution Networks[END_REF]. This paper addresses that case, with modelling methodology enabling to predict crosstalk on asymmetrical tree. The model developed herein is the synergy of the tree topology presented in [START_REF] Eudes | Distributed Model of Two-Level Asymmetrical PCB Interconnect Tree[END_REF] and the coupling model in [START_REF] Eudes | Fast Estimation of High-Speed Signal Integrity for Coupled PCB Interconnects[END_REF].

II. METHODOLOGY WITH CIRCUIT TRANSFORM

Throughout this paper, we will focus on asymmetrical 2:1 tree topology, similar to that proposed in [START_REF] Eudes | Distributed Model of Two-Level Asymmetrical PCB Interconnect Tree[END_REF], with single input and two-outputs. Then, a neighboring line is placed in the proximity of the tree network branches in order to investigate the coupling effect.

We shall assume that the transmission lines (TL) constituting the tree are characterized by their characteristic impedance Z c , physical length d, phase constant γ, and electrical length :

d ⋅ = γ θ . ( 2
)

A. Topology of Asymmetrical 2:1 Tree Interconnect Understudy

The building blocks of the theoretical presented SI process are fundamentally constituted by the implementation of the equivalent circuit theory. Fig. 3(a) represents the circuit configuration of the 2:1 asymmetrical tree. The single input with internal impedance Z s is excited by v in . The asymmetrical tree outputs are loaded by impedances Z L1 and Z L2 , and the branches are essentially comprised of pieces of input lines TL 0 (connected between nodes N in and N 0 ) and output lines TL 1 (between N 0 and output node N 1 ) in parallel with output lines TL 21 cascaded with TL 22 (between N 0 and N 2 ). We will compare this isolated circuit tree with the tree shown in Fig. 3(b) containing neighboring line TL c placed in proximity of TL 21 . We propose to replace TL 21 by cascaded pieces of lines TL 21 ', TL 21 '' and TL 21 ''', with the length of TL 21 '' the same as TL c here denoted as d c . As described in [START_REF] Eudes | Fast Estimation of High-Speed Signal Integrity for Coupled PCB Interconnects[END_REF], the overall coupled line impedance and admittance matrices are denoted:

Z s TL 0 TL 1 N in N 0 N 1 N 2 V in TL 22 Z L1 Z L2 TL 21 V 1 V 2 Z s TL 0 TL 1 N in N 0 N 1 N 2 V in TL 22 Z L1 Z L2 Z L3 Z L4 TL 21 ' TL 21 " TL 21 '" TL c V 1 V 2 (a)
[ ] [ ] [ ] ) ( ) ( ) ( ω ω ω ω L j R Z + = , (3)
and

[ ] [ ] [ ] ) ( ) ( ) ( ω ω ω ω C j G Y + = , (4)
respectively (j is the complex number 1 and ω is the radian frequency). The even-and odd-mode impedances and electrical angles of coupled branches TL 21 "-TL c are denoted

( ) (ω e Z , ) (ω o Z
) and (

c e e d ⋅ = ) ( ) ( ω γ ω θ , c o o d ⋅ = ) ( ) ( ω γ ω θ ). The ABCD matrix [T N2N0 ] of equivalent to N 0 N 2 is determined by the relation: [ ] [ ][ ][ ][ ] ) ( ) ' ' ' ( ) ' ' ( ) ' ( 22 21 21 21 0 2 TL T TL T TL T TL T T N N ⋅ ⋅ ⋅ = , (5)
where the elementary line ABCD matrices are written as:

[ ] ( ) ( ) ( ) ( ) 22 , 21 cosh / sinh sinh cosh ) ( = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⋅ = m m c m m c m m m m Z Z TL T θ θ θ θ , (6)
The ABCD matrix of the coupled lines (TL 21 "-TL c ≡TL 21c ) is analytically defined as:

[ ] [ ] [ ] [ ] [ ] { } 2 , 1 , 1 21 ) ' ' ( = - ⋅ ⋅ ⋅ ⋅ = l k x c Y Z eig T Y Z eig TL T , (7)
where the four elements of the matrix [ ]

x T are: [ ] [ ] ( ) ( ) [ ] ( ) ( ) [ ] ( ) ( ) ⎪ ⎪ ⎪ ⎩ ⎪ ⎪ ⎪ ⎨ ⎧ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = = o o e e x o o e e x o e x x Z Z T Z Z T T T / sinh 0 0 / sinh ) 1 , 2 ( sinh 0 0 sinh ) 2 , 1 ( cosh 0 0 cosh ) θ θ θ . ( 8
)
Next, we shall apply SIMO/SISO transform for the transfer function extraction along electrical paths N in N m (m={1,2}).

B. Asymmetrical Input-Output Path Equivalent SISO Circuit

Thanks to the TL and circuit theory, we establish the electrical circuit corresponding to path link from input N in and each tree outputs N 1,2 . After classical electrical transforms, we generate the SISO equivalent circuits of 2:1 tree shown in Figs. [START_REF] Averill | Chip Integration Methodology for the IBM S/390 G5 and G6 Custom Microprocessors[END_REF] and Figs. 5 for the electrical paths N in N 1 and N in N 2 , respectively.

We can see that the reduced circuits have parallel impedances Z in,m (m=1,2) expressed with the classical relation between impedance-and ABCD-matrices. After inclusion of the parallel impedances with the coupling effects, the asymmetrical tree transfer functions as defined in (1) are mathematically established for m={1,2}: By combining all the previous analytical elements of each piece of line defined before, we have the associated ABCD matrix for each output branch written as: To check the validity of this behavioral model, examples of applications were considered and analyzed using numerical calculations with Matlab. III. APPLICATIONS A microstrip interconnect tree was considered as the numerical proof of concept of the model developed in the previous section. The frequency-and time-domain analyses were also performed for the circuit.

[ ] ) 1 , 1 ( ) ( 1 in m m N TLN T H = . ( 9
)
Z s TL 0 TL 1 N in N 0 N 1 V in Z L1 Z in2 ' V 1 Z s TL 0 TL 1 N in N 0 N 1 V in Z L1 Z in2 V 1 (a) (b)
Z s TL 0 N in N 0 N 2 V in TL 22 Z in1 Z L2 TL 21 V 2 Z s TL 0 N in N 0 N 2 V in TL 22 Z in1 Z L2 TL 21c V 2
[ ] [ ] [ ] ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⋅ ⋅ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⋅ ⋅ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = 0 / 1 1 1 ) ( 0 / 1 1 1 ) ( 0 1 1 ) ( 1 1 1 2 0 L in s N N Z TL T Z TL T Z TL T in . ( 10
) [ ] [ ] [ ] [ ][ ] ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⋅ ⋅ ⋅ ⋅ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⋅ ⋅ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = 0 / 1 1 1 ) ' ' ' ( ) " ( ) ' ( 0 / 1 1 1 ) ( 0 1 1 ) (

A. Substrate Permittivitty Broadband Model

The model presented in this paper can be advantageously extended to structure including broadband frequency influences. As the test application, the interconnect tree circuit substrate was defined with Svesson-Djordjevic model proposed in [START_REF] Svensson | Time Domain Modeling of Lossy Interconnects[END_REF][START_REF] Djordjevic | Wideband Frequency-Domain Characterization of FR-4 and Time-Domain Causality[END_REF], as shown below:

⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + + ⋅ + = ω π ω π ε ω ε j f j f a j H L r rf 2 2 ln ) ( , (12)
with

⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + + - = 0 0 ln / ) tan( jf f jf f j a H L r δ ε , (13) 4

B. Description of Asymmetrical Circuit for Numerical Test

We designed an arbitrary chosen physical lengths (width and lengths) 2:1 distribution tree network as an IL under test. The structure was intentionally folded in order to show the EM coupling between the interconnect branch lines. Then, lumped loads inspired from realistic PCBs were considered to find out the feasibility of the method with different load parameters. Fig. 6 shows schematic layout illustrating the configuration of the 2:1 asymmetrical interconnect tree considered here as the application example. This structure is comprised of the microstrip interconnect tree driven by the numerical source v in with internal impedance Z s =25Ω and loaded by capacitors 10pF which form impedances Z L1 and Z L2 . The electrical paths N in N 1 and N in N 2 are set with physical lengths of 2.5mm and 9mm, respectively. The coupled perturbation line has physical length of 7.5mm and is loaded by Z L3 =25Ω and Z L4 corresponding to 10pF capacitor.

Investigation on the comparison between the responses of the 2:1 interconnect tree without and with the perturbation coupling line was performed by plotting the outputs (v 1 ,v 2 ) and (v c1 ,v c2 ) respectively.

Z s V in (t) Z L1 V 1 (t) Z L2 V 2 (t) Z L4 Z L3 d 1 d

C. Frequency Analysis Results

As aforementioned, the start point of the modelling was the extraction of the frequency dependent broadband RLCG(f) per unit lengths parameters of each branch of the tree. Then, by following the methodology suggested in Section II, the frequency dependent ABCD-and Z-matrices were calculated with Matlab. By using expressions ( 9), ( 10) and ( 11), we establish the transfer function corresponding to the electrical path N in N 1,2 without the coupling line, represented by:

H 1,2 (jω)=V 1,2 (jω)/V in (jω). ( 14
)
Then, it is compared with that one with the coupling line defined as:

H c1,2 (jω)=V c1,2 (jω)/V in (jω). ( 15
)
Figs. 7 display the frequency responses (magnitudes labelled in left side and phases labelled in right side) corresponding to these expression applied to the structure understudy which is presented in Fig. 6. The response from the asymmetrical PCB tree without and with coupling effects are respectively plotted in solid and dashed lines. The classical behaviors of low pass structures are occurred for the both tree outputs. Moreover, a significant resonance effect occurs at about 0.61GHz along the path N in N 1 . This is due to the stub effect from the other branch of the tree. As we can see, due to the crosstalk between the coupled branches of the tree the coupled responses are influenced noticeably above 5GHz.

The introduced calculation results are performed very fast on a typical modern computer running Matlab and are of the order of about hundred milliseconds.

H d B H cdB φ φ c H 1 (f) (d B ) φ (H 1 ) (°) F re q ue n c y (G H z ) 0 2 4 6 8 1 0 H 2 (f) (d B ) φ (H 2 ) (°) H dB H cdB φ φ c - 2

D. Matrix Impedance Analyses

The frequency analysis of the previous transfer functions can be additionally completed with further investigation the behavior of the asymmetrical tree network impedances [ ] Z . To do this, we realized the comparison between the transfer impedances Z N3Nin and Z N4Nin respectively corresponding to the electrical paths N in N 3 and N in N 4 . Fig. 8 displays the obtained coupling impedances up to 10GHz. It can be stated that Z N3Nin presents in one hand transmission zero frequencies at about 0.17GHz, 3.27GHz and 9.37GHz. In the other hand, Z N4Nin transmission zero frequency is occurred at about 2GHz. However, the coupling level is lowered at about 0.90GHz, 5.43GHz and 8.06GHz for Z N3Nin . These coupling impedances explain the degradation which can change the behavior of the signal propagating along the perturbed interconnect line. This finding can be pointed out with the reflection input access impedance Z NkNk and transfer impedance Z NkNin with the output index k={1,2}. The differences between the own impedances Z NkNk (plotted in solid lines) and disturbed by coupling impedances Z cNkNk (plotted in dashed lines) are highlighted by Figs. 9 and 10.

More illustrative insight on the EMC effect on the distributed SI through the tree understudy can be achieved with the time-domain analysis. This approach constitutes the main object of the next paragraph.

E. Time-Domain Analysis Results

During the numerical test for this time-domain investigation, a high speed digital signal represented by eight bits input data "01001000" was assumed as input. The data bits signal was assumed to be trapezoidal with 0.5Gbps rate and 150ps rise and fall times.

The signal plots displayed in Figs. 11 presented the timedomain computed results with the asymmetrical tree understudy. The input signal is traced in solid bold blue line. Moreover, the asymmetrical tree outputs without and with the coupled perturbations are shown as solid red and dashed green lines, respectively.

The results highlight the influence of the parasitic coupling on the asymmetrical interconnect distribution tree. We can see that due to the asymmetrical behavior of the two input branches, the outputs are completely different from each other. It can be stressed that the data SI was significantly degraded with considerable distortion. Moreover, the propagation delays are of about 0.22ns for the electrical path N in N 1 and 0.5ns for the path N in N 2 . A reflection effect is also observed on the path N in N 1 which is related to the resonance effect, as seen in Fig. 7(a) introduced in the previous paragraph. T im e (n s ) T im e (n s )

V in V 1 V c1 0 4 8 1
0 4 8 1 2 1 6 V in V 2 V c2
Figure 11. Eight bits data responses of the 2:1 asymmetrical tree presented in Fig. 6 without (solid lines) and with (dashed lines) coupling.

F. Discussion

The developed modelling method confirms the influence of EM coupling caused by the perturbation line on the asymmetrical tree network. The model offers the possibility to predict fastly the tree frequency responses by taking into account the dispersive effects on the substrate materials. Various techniques on analyses based on the transfer functions, matrix impedances and time-domain responses show the electrical behaviors of the 2:1 tree. For the effectiveness analysis, the model was implemented into Matlab. In conclusion, for the considered here example:

□ The output signal shapes are quite well preserved because the bandwidth of the input data is lower than 6GHz.

□ The time-delay between the two responses is lower than 200ps.

□ The slight variation of the output transient voltage amplitudes of about 10% were found when placing the coupling perturbation at 100µm of the tree.

IV. CONCLUDING REMARKS

The investigation was performed of the high speed SI of an asymmetrical 2:1 tree distribution network perturbed by a coupled length of a transmission line. Analytical behavioral model of the network was developed using ABCD, Z and Y matrices. The model can include the broadband dispersion effect of relative permittivity as proposed by Svesson-Djordjevic in [START_REF] Svensson | Time Domain Modeling of Lossy Interconnects[END_REF][START_REF] Djordjevic | Wideband Frequency-Domain Characterization of FR-4 and Time-Domain Causality[END_REF]. The model was implemented in Matlab programming language and is computationally very efficient.

The proposed model was verified on the example of a microstrip asymmetrical tree with parasitic coupled line operating at a high data rate of 0.5 Gbps. Both frequency-and time-domain analyses were performed. It was found that the signal integrity of the asymmetrical microstrip tree with parasitic coupling degraded significantly under the test conditions.

The proposed model is beneficial in terms of flexibility, simplicity and computational speed. It can be useful for the design and manufacture engineers for assessing the degradation of sharing high-speed signals in asymmetric tree. Application areas include miniaturized microelectronic interconnect systems and packaging structures. The prediction of the high density interconnect effects will allow to optimize the packaging structures and also probably to establish a post processing technique for the signal degradation compensation. ACKNOWLEDGMENT

Figure 1 .

 1 Figure 1. Electronic boards with complex interconnect tree network [4].

Figure 3 .

 3 Figure 3. (a) 2:1 comb tree topology and (b) comb tree topology including coupling line TLc.

Figure 4 .

 4 Figure 4. Equivalent SISO circuits for extracting the output V1.

Figure 5 .

 5 Figure 5. Equivalent SISO circuits for extracting the output V2.

Figure 7 .

 7 Figure 7. Frequency responses of the 2:1 asymmetrical tree presented in Fig.6without (solid lines) and with (dashed lines) coupling influences.

Figure 8 .

 8 Figure 8. Magnitude of coupling impedances between the main input access Nin and the perturbation line N3N4.

FFigure 9 .Figure 10 .

 910 Figure 9. Magnitude of the transfer impedance of the structure under study without (solid lines) and with (dashed lines) coupling influences.

Proc. of the 2014 International Symposium on Electromagnetic Compatibility (EMC Europe 2014), Gothenburg, Sweden,September 1-4, 2014

Acknowledgement is made to European Union and Upper Normandy region in France for the support of this research through the ERDF and European Programme INTERREG IVA France (Channel) -England by co-funding project No 5700 entitled "HD indOor coMmunication tErminal with flexible Substrate (HOMES)".