Minna Jääskeläinen

Anni Nieminen

Reeta-Maria Pökkylä

Marjut Kauppinen

Annikki Liakka

Markku Heikinheimo

Tommi E Vaskivuo

Juha Klefström

M.D Juha S Tapanainen
email: juha.tapanainen@oulu.fi

Regulation of Cell death in Human Fetal and Adult Ovaries -Role of Bok and Bcl-X L

Keywords: Apoptosis, Bok, Bcl-X L, (Human), (Oocyte), (Granulosa cell)

Of eight million oocytes formed in fetal ovaries, only 400 are ovulated and the rest are degraded via apoptosis. Studies in rodents suggest an important role for Bok and Bcl-X L in ovarian apoptosis, but their expression patterns and roles in human ovaries are not known. Protein expression of Bok and Bcl-X L as well as the death pathway effectors TNF and caspase-3 were determined in an important collection of samples consisting of human fetal and adult ovaries. A penetrant expression of Bok, Bcl-X L , TNF and full length and cleaved caspase-3 were characterized in fetal ovaries, with specific patterns in oocytes and pre-granulosa/granulosa cells. Bok and Bcl-X L were detected also in adult ovaries. Lentiviral shRNA delivery demonstrated that loss of Bok markedly reduces vulnerability to apoptosis and, conversely, loss of Bcl-X L increases apoptosis in human granulosa tumour cell line. The results suggest important roles for Bok and Bcl-X L in human ovarian development, follicle maturation and apoptosis.

A c c e p t e d M a n u s c r i p t

Introduction

Apoptosis is a central mechanism regulating human ovarian development, follicle maturation and function from fetal to adult life. By mid-pregnancy nearly eight million oocytes are formed, but only around 400 of these will survive until ovulation during fertile life and most oocytes undergo atresia through apoptotic cell death [START_REF] Baker | A Quantitative and Cytological Study of Germ Cells in Human Ovaries[END_REF][START_REF] Vaskivuo | Survival of human ovarian follicles from fetal to adult life: apoptosis, apoptosisrelated proteins, and transcription factor GATA-4[END_REF]. This process has been proposed to serve in the selection of oocytes with best promises of producing offspring [START_REF] Krakauer | Mitochondria and germ-cell death[END_REF].

Ovarian apoptosis takes place mainly among either the oocytes or follicular granulosa cells and oocyte demise culminates in the destruction of the follicle, leading to follicular atresia. The destiny of an ovarian follicle might not depend on a single granulosa cell but rather on a threshold level of granulosa cells required for the wellbeing and survival of the follicle as whole. It is likely that oocyte cell death is the principal form of apoptosis during ovarian development and in resting follicles, while granulosa cell apoptosis dominates during fertile life and in growing follicles. However, both mechanisms are possible at any point of the ovarian life-span [START_REF] Vaskivuo | Survival of human ovarian follicles from fetal to adult life: apoptosis, apoptosisrelated proteins, and transcription factor GATA-4[END_REF][START_REF] Hsueh | Ovarian follicle atresia: a hormonally controlled apoptotic process[END_REF][START_REF] Rolaki | Novel trends in follicular development, atresia and corpus luteum regression: a role for apoptosis[END_REF].

Apoptotic signals can be processed through two main pathways: the cell extrinsic, and the cell intrinsic or mitochondria-associated pathway, with significant crosstalk and feedback occurring between them (Khosravi-Far and Esposti 2004). The most extensively characterized mediators of the cell extrinsic pathway are the soluble or membrane-bound death ligands: FAS ligand, tumour necrosis factor-α (TNF-α) and TNF-related apoptosisinducing ligand (TRAIL). The apoptotic process is initialized by these ligands binding to the TNF superfamily of death receptors on a cellular membrane [START_REF] Schultz | Apoptosis: programmed cell death at a molecular level[END_REF] and apoptotic signals are transmitted to the cell by amino acid tails of the receptors called "death domains" (DDs) (Zimmermann et al. 2001, Zimmermann andGreen 2001). The cell intrinsic apoptosis pathway, on the other hand, is operated by the Bcl-2 family of cytoplasmic and mitochondrial proteins [START_REF] Adams | The Bcl-2 protein family: arbiters of cell survival[END_REF]. The Bcl-2 family consists of both anti-(e.g. Bcl-X L , Bcl-2, Mcl-1) and proapoptotic (e.g. Bid, Bax, Bok, Bad) factors, and their apoptosisregulating effects are dependent on the balance of these competing family members [START_REF] Adams | The Bcl-2 protein family: arbiters of cell survival[END_REF]Cory 1998, Gross et al. 1999). Apoptosis is induced by proapoptotic members of the Bcl-2 family forming pores in the mitochondrial layer and changing the mitochondrial membrane potential, which allows apoptosis-mediating proteins, such as cytochrome-c, Smac (mitochondria-derived activator of caspases) and ICE (Interleukin-1beta-Converting Enzyme) to be released into the cytoplasm. Both apoptosis pathways ultimately end with activation of executioner caspase-3, followed by DNA degradation and apoptotic elimination of the cell.

Bok (Bcl-2-related ovarian killer) belongs to the group of channel-forming proapoptotic members of the Bcl-2 family [START_REF] Adams | The Bcl-2 protein family: arbiters of cell survival[END_REF] containing Bcl-2 homology (BH) domains 1, 2 and 3 but lacking the BH4 domain, which is typically present in antiapoptotic Bcl-2 family members [START_REF] Hsu | Bok is a pro-apoptotic Bcl-2 protein with restricted expression in reproductive tissues and heterodimerizes with selective anti-apoptotic Bcl-2 family members[END_REF]. In rodents Bok is expressed mainly in hormonally regulated reproductive tissues, particularly the ovary, uterus and testis. In adult rat ovary Bok mRNA has been detected in primary to antral follicles, where it is mainly localized to granulosa cells [START_REF] Hsu | Bok is a pro-apoptotic Bcl-2 protein with restricted expression in reproductive tissues and heterodimerizes with selective anti-apoptotic Bcl-2 family members[END_REF]. Bok has also been demonstrated to be expressed in adult human ovaries [START_REF] Gao | Membrane translocation and oligomerization of hBok are triggered in response to apoptotic stimuli and Bnip3[END_REF]. However, the exact expression pattern and role of Bok in human ovaries from fetal development to fertile life are not known.

The antiapoptotic Bcl-2 family member Bcl-X L contains four BH domains including BH4, vital for its apoptosispreventing effect [START_REF] Chao | BCL-2 family: regulators of cell death[END_REF]. Bcl-X L mRNA is expressed in rodent primordial germ cells and follicular granulosa cells [START_REF] Watanabe | Gene transfection of mouse primordial germ cells in vitro and analysis of their survival and growth control[END_REF][START_REF] Tilly | Expression of members of the bcl-2 gene family in the immature rat ovary: equine chorionic gonadotropin-mediated inhibition of granulosa cell apoptosis is associated with decreased bax and constitutive bcl-2 and bcl-xlong messenger ribonucleic acid levels[END_REF] and it has an important role in preventing ovarian cells from undergoing apoptosis. Bcl-X L hypomorphic mice show massive apoptotic loss of oocytes during fetal development and they have markedly decreased numbers of primordial and primary follicles and severely impaired fertility in adult life when compared with wild-type mice [START_REF] Rucker | Bcl-x and Bax regulate mouse primordial germ cell survival and apoptosis during embryogenesis[END_REF]. In humans, Bcl-X L mRNA is present in adult ovarian tissue and granulosa-lutein cells obtained from women undergoing fertility treatment [START_REF] Kugu | Analysis of apoptosis and expression of bcl-2 gene family members in the human and baboon ovary[END_REF]. However, the cellular localization and function of Bcl-X L in human fetal and adult ovaries have not yet been characterized.

Both the cell extrinsic and mitochondria-associated pathways are active in regulating ovarian apoptosis. However, in human ovaries, their roles and mechanisms are not well characterized. In the present study the expression patterns of two key apoptosis regulators, TNF and caspase-3, were evaluated in human ovaries during fetal development. In addition, protein expression of antiapoptotic Bcl-X L and proapoptotic Bok was studied in human fetal and adult ovarian tissues. For these studies we utilized biopsy and obduction material from fetuses and newborns collected systematically over several years at Oulu University Hospital. The possible regulatory roles of Bok and Bcl-X L in granulosa cell apoptosis were further evaluated by silencing their protein expression in a human tumour-derived granulosa cell line (KGN).

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Materials and methods

Tissue samples

Fetal and adult human ovarian tissues were collected from autopsy and biopsy samples at the Department of Pathology, Oulu University Hospital. Ovaries from 13 fetuses after spontaneous or therapeutic abortion and from 15 fetuses after intrauterine death followed by spontaneous or induced delivery or Caesarean section were collected. In addition, ovaries from 10 neonates who died as a result of perinatal asphyxia or infection within 15 min-7 days after birth were studied. Adult ovarian tissues were obtained from 11 pre-menopausal women aged 29-49 years undergoing ovariectomy because of endometriosis. The fetuses and neonates were stored until autopsy at + 4°C. The autopsy was performed as soon as possible during the next 24 hours after abortion or delivery. The removed ovaries of fetuses and neonates as well as the surgically removed adult ovarian tissue specimens were put immediately into 10% phosphate-buffered neutral formalin. The formalin fixation time for ovarian tissue of fetuses less than 22 weeks of gestational age and for the ovarian tissue samples of adults was 24 hours. The fixation time was 7 days for ovarian tissue removed from neonates and from fetuses older than 22 gestational weeks. After fixation the samples were routinely processed (tissue processor Leica ASP 300) and embedded in paraffin. Sections, 4 micrometers in thickness, were stained with hematoxylin and eosin. All fetuses and neonates with chromosomal abnormalities and samples with detectable autolysis were excluded from the study. The study was approved by the Ethics Committees of Oulu University Hospital and the University of Oulu. A permit to study human autopsy tissues and resection material was obtained from the Finnish National Authority for Medicolegal Affairs.

Immunohistochemistry

Immunohistochemical staining was performed following standard protocols. Briefly, tissue sections were deparaffinised in xylene and rehydrated through graded alcohols. The tissues were pre-treated in 10 mM sodium citrate (for TNF, Bcl-X L and caspase-3 immunohistochemistry) or in Tris-HCl (for Bok immunohistochemistry) in a microwave oven (800 W for 2 min and 300 W for 15 min). Endogenous peroxidase activity was blocked in 3% H 2 O 2 . Primary antibodies against human TNF (cat. no. sc-8301), Bok (cat. no. sc-11424), Bcl-X L (cat. no. sc-7122) or caspase-3 recognising both full length and cleaved caspase-3 (cat. no. sc-1226)(Santa Cruz Biotechnology, Santa Cruz, CA, USA) at concentrations of 1:100, 1:50, 1:100 and 1:100, respectively, were used. In addition, primary antibody against cleaved caspase-3 (cat.no. #9661, Cell Signaling Technology, Beverly, MA, USA) in a concentration of 1:100 was used. To visualize the bound antibodies, Vectastain elite ABC kits (Vector Laboratories, Burlingame, CA, USA) were used for TNF, Bcl-X L , caspase-3 and cleaved caspase-3 immunostainings. Bok was visualized by using an Envision plus Rabbit HRP system (Dako, Glostrup, Denmark). Colour reactions were brought about by using commercial diaminobenzidine tetrahydrochloride (DAB, DakoCytomation Ltd., Ely, UK) at 15 μL/mL and the samples were counterstained with haematoxylin. Peptide blocked antibody was used as negative control for Bcl-X L and Caspase-3 stainings following instructions of the manufacturer. Shortly, primary antibodies were combined to five-fold excess of specific blocking peptide (Cat nos. sc-7122P Bcl-X L blocking peptide and sc-1226P Caspase-3 blocking peptide) and incubated for 2 h in room temperature. The peptide blocked antibody was then used similarly to primary antibody in negative control samples. For Bok, TNF and cleaved caspase-3 antibody diluent (PBS for Bok and TNF and TBST/5% normal goat serum for cleaved caspase-3) was applied instead of primary antibody in negative control samples

Preparation of shBok-and shBcl-X L -silenced cell lines

The KGN cells were infected with lentiviral shRNA produced by Biomedicum Genomics (http://www.helsinki.fi/biomedicumgenomics/) and after 72 hours the cells were selected in hygromycin (100 ug/mL). Gateway pDSL_hpUGIH (AFCS) lentiviral vector was used for lentiviral production and expression of shRNA targeting the sequences against Bok at 5´-GACTGCAGGGAGATGTGCag-3´ and Bcl-x L at 5´-TCCATCTCCTTGTTGACACtt-3.

Western Blot analyses

Primary antibodies against human Bok (Cell Signaling Technology, Danvers, MA, USA, cat. no. 4521) and Bcl-X L (BD, Franklin Lakes, NJ, USA, cat. no. 610211) at a concentration of 1:1000 were used for detecting downregulation in KGN cells as described previously [START_REF] Nieminen | c-Myc primed mitochondria determine cellular sensitivity to TRAIL-induced apoptosis[END_REF]. Ovarian tissue samples were lysed in Precellys tube with ceramic beads in lysis buffer (10 mM Tris.HCl pH 7.4, 150 nM NaCl, 1 % Triton X-100, 1 mM EDTA, 1 mM EGTA, 0,5 % NP-40) with protease inhibitor coctail (Roche). Subsequently the samples were A c c e p t e d M a n u s c r i p t 5 homogenized in Precellys homogenizer (Bertin technologies) for 6500 rpm twice for 45 s and kept on ice for 30 min. Unbroken cells were removed by centrifugation at 13 000 rpm for 30 min at +4°C. Ovarian samples were analyzed in SDS-PAGE with primary antibodies against Bok (cat. no. sc-11424) and Bcl-X L (cat. no. sc-7122). Primary antibodies against B-tubulin (Abcam, Cambridge, MA, USA, cat. no. ab6046) and actin (cat. A4700, Sigma, St. Louis, MO, USA) were used as loading control.

The intensity of Bok and Bcl-X L blots in Western analyses were measured using Quantity One program. The results were adjusted to β-tubulin and compared to corresponding KGN control blots.

Cell culture

Human tumour-derived granulosa cells (KGN cells) [START_REF] Nishi | Establishment and characterization of a steroidogenic human granulosa-like tumor cell line, KGN, that expresses functional follicle-stimulating hormone receptor[END_REF]) and shBok-or shBcl-X L silenced KGN cells were cultured in DMEM/F-12 supplemented (10%) with fetal bovine serum (FBS). The cells were distributed in 96-well plates at approximately 20 000 cells/well and allowed to adhere overnight at 37 °C in an incubator. The cells were then treated with rTRAIL (Chemicon International Inc., Billerica, MA, USA) at 10, 25, or 50 ng/mL [START_REF] Jaaskelainen | TRAIL pathway components and their putative role in granulosa cell apoptosis in the human ovary[END_REF], TNF (R&D systems, Minneapolis, MN, USA, cat. no. 210-TA-010) at 10 or 100 ng/mL or 10 or 100 nM staurosporine (Sigma, St. Louis, MO, USA, cat. no. S5921) to induce apoptosis. Caspase activity was measured at 6 and 24 hours after treatment. All experiments were performed in triplicate and repeated at least three times.

Caspase Glo 3/7 activation assay

Caspase assays were performed by using Caspase Glo 3/7 activation assay kits (Promega Corporation, Madison, WI, USA) following the instructions of the manufacturer. Room temperature Caspase-Glo 3/7 substrate and buffer were mixed and fresh reagent was applied to the cells. Luminescence was analysed by means of a Labsystems Luminoskan RT reader (Labsystems, Helsinki, Finland) after 1 hour of incubation.

Apoptosis in situ 3´-end labelling

For TUNEL apoptosis detection assay the cells were distributed at approximately 50 000 cells/chamber on 8chamber slides. The cells were allowed to adhere overnight and were then treated with rTRAIL at 25 ng/mL, TNF at 100 ng/mL or 100 nM staurosporine. Apoptosis in situ 3´-end labelling was performed after 24 hours of incubation using an Apoptag ® Peroxidase In Situ Apoptosis Detection Kit (Millipore, Billerica, MA, USA, cat. no. S7100) following the instructions of the manufacturer. Briefly, the cells were washed with PBS and fixed with 1% paraformaldehyde in PBS for 10 minutes at room temperature and post-fixed and permeabilized in precooled ethanol/acetic acid (2:1) at -20 °C for 5 minutes. Endogenous peroxidase activity was blocked with 3% H 2 O 2 in PBS. DNA 3´-end-binding TdT enzyme was pipetted onto the samples and they were incubated under plastic cover slips at 37 °C for one hour. A colour reaction was achieved by using a Sigma Fast TM DAB peroxidase substrate tablet set (Sigma, St. Louis, MO, USA) and the samples were counterstained by brief incubation in haematoxylin.

Microscopy analysis and statistics

Immunohistochemical stainings were evaluated by two independent observers (TNF, Bok and Bcl-X L by M.J. and T.V.; caspase-3 and cleaved caspase-3 by M.J. and J.T.). For statistical analysis of apoptosis 3'-end labelling, positively labelled cells in shBok and shBcl-X L silenced cell lines were counted in ten visual fields and compared to KGN control cells. Apoptosis 3'-end labelling and caspase activation assay data were analysed by using SPSS 15.0 software (SPSS, Chicago, IL, USA). Student's t test (normally distributed groups) or the Mann-Whitney test (groups that were not normally distributed) were used to compare different treatment groups. A value of p < 0.05 was considered significant. * = p < 0.05, ** = p < 0.01 and *** = p < 0.001.

TNF, Bok, Bcl-X L and caspase-3 are expressed in human fetal ovaries

Tumour necrosis factor-α, Bok, Bcl-X L and caspase-3 were studied in human ovarian samples collected from fetuses/newborns from the 16th week onwards. These proteins were expressed in fetal ovaries at all gestational ages studied (Table 1, Fig. 1). TNF was expressed in pre-granulosa cells and oogonia of young ovaries (gestational age under 20 weeks) (Table 1, Fig. 1 a). In addition, at this age diffuse staining was detected on the cellular membranes and in the intercellular spaces. Later during development (gestational age 20 weeks onwards) oocyte cytoplasm was moderately stained, while granulosa cells of the developing follicles showed weak or moderate TNF expression (Table 1, Fig. 1 b-d).

The pro-apoptotic Bcl-2 family member Bok was expressed mainly in oocytes, but weak staining was also detected in granulosa cells of the developing follicles (Table 1, Fig. 1 e-h). Bok staining was observed in both cell cytoplasm and the nucleus (Table 1, Fig. 1 e-h).

Bcl-X L was expressed constantly in all fetal ovaries studied (Fig. 1 i-l). Before follicular formation, diffuse staining was observed in ovarian stroma and pre-granulosa cells (Table 1, Fig. 1 i). Later during fetal development Bcl-X L expression was mainly localized to the cell cytoplasm of oocytes and granulosa cells, oocyte expression being dominant (Table 1, Fig. 1 j-l).

Weak/moderate expression of caspase-3 protein was detected in human fetal ovaries at all gestational ages (Fig. 1 m-p). The staining was most profound in the ovarian cortex, where follicular structures were not yet formed. Weak/moderate expression could also be detected in oocytes and granulosa cells of small developing follicles (Table 1, Fig. 1 m-p). Caspase-3 was not expressed in secondary or small antral follicles in fetal ovaries. Cleaved caspase-3 was strongly and specifically expressed in fetal ovarian cells. In young ovaries (16-17 weeks) individual oogonias and pregranulosa cells outside the follicle structures were stained (Table 1, Fig. 1 q). After midpregnancy cleaved caspase-3 could be detected also in individual oocytes and granulosa cells of primordial follicles (Table 1, Fig 1 r-t).

Expression of Bok and Bcl-X L in adult human ovaries

In adult human ovaries Bok was strongly expressed in oocyte cytoplasm and nuclei of primordial, primary and secondary follicles (Table 2, Fig. 2 a-c). Granulosa cells expressed Bok at all follicular stages, but in primordial/primary follicles granulosa cell expression was weak (Fig. 2 a andb) and staining intensity was more profound in secondary and antral follicles (Fig. 2 c andd). Western analysis revealed a specific expression of 23kDa Bok in adult human ovary (Fig 3).

The anti-apoptotic protein Bcl-X L was detected in oocytes and granulosa cells of adult ovaries (Table 2, Fig. 2 gj). Oocyte expression was strong in primordial to secondary follicles (Fig. 2 g-i), and granulosa cells of primordial, primary, secondary and antral follicles expressed Bcl-X L moderately (Fig. 2 g-j). Western analysis revealed a specific expression of 26kDa Bcl-X L in adult human ovary (Fig. 3).

Bok operates as a proapoptotic factor in human tumour-derived granulosa cells

To study the possible effects of (proapoptotic) Bok in human granulosa cell apoptosis, shRNA-expressing constructs targeting Bok were lentivirally transduced into KGN cells. Transduction led to silencing effiency of >60% in Bok protein expression (Fig. 4 A). Bok-deficient KGN cells were subsequently treated with various apoptosis-inducing factors (TRAIL, TNF and staurosporine) and caspase-3/7-activation was measured at 6 and 24 hours of treatment. The results in Figure 4 B and C show that silencing Bok inhibits caspase-3/7 activation in different experimental conditions. No marked difference was observed in caspase activation of shBok-silenced and control KGN cells when incubated only in media for 6 or 24 hours (Fig. 4 B andC). Treatments with rTRAIL, TNF and staurosporine led to marked induction of caspase-3/7 activation and this induction was significantly lower in the shBok-silenced cells than in control KGN cells (Fig. 4 B andC). To confirm the results obtained from caspase activation assay, Bok-deficient cells were treated with media only, rTRAIL, TNF or staurosporine and apoptotic cells were recognized by TUNEL assay after 24 hours of treatment. At this time point considerably lower numbers of Bok-deficient cells were undergoing apoptosis in wells treated with TNF or staurosporine when compared with control KGN cells (Fig. 5 A a-d and e-h, respectively, Fig. 5 A c c e p t e d M a n u s c r i p t 7 B). A similar trend was also detected in shBok cells treated with media only or rTRAIL (Fig. 5 A a-d and e-h, respectively, Fig. 5 B).

Bcl-X L protects human tumour-derived granulosa cells from apoptosis

The shRNA construct targeting human Bcl-X L was lentivirally transduced into KGN cells to create a Bcl-X Ldeficient granulosa cell line. Immunoblotting showed >60% decrease in Bcl-X L protein expression in shBcl-X Lexpressing cells (Fig. 4 A). Bcl-X L -deficient cells were significantly more susceptible to apoptosis than control KGN cells (Fig. 4 B and C, Fig. 5). At 6 hours of incubation a marked increase in caspase activation was detected in Bcl-X L -deficient cells in wells treated with media only, TRAIL and TNF when compared with control KGN cells. At this time point Bcl-X L -deficient cells also tended to be more vulnerable to staurosporinemediated caspase activation, but this tendency did not reach statistical significance (Fig. 4 B; 8549 cpm vs. 6905 cpm, p = 0.257 with 10 nM staurosporine and 18079 cpm vs. 12903 cpm, p = 0.15 with 100 nM staurosporine). At 24 hours, however, staurosporine treatment also resulted in a significantly increased activation of caspases 3/7 in Bcl-X L -deficient cells (Fig. 4 C). Apoptosis in situ 3´-end labelling was applied to rTRAIL-, TNF-and staurosporine-treated shBcl-X L and control KGN cells to confirm the caspase assay results further. Apoptosis was measured after 24 hours of treatment and a markedly higher number of Bcl-X L -deficient cells undergoing apoptosis were observed when compared with similarly treated control KGN cells (Fig. 5 A i-l and e-h, respectively, Fig. 5 B). In the present study we elucidate the cellular expression patterns of TNF, Bok, Bcl-X L and caspase-3 in an important material consisting of human fetal ovaries at 16-40 weeks of gestation. In addition, novel data concerning the expression of Bok and Bcl-X L in adult human ovaries and their participation in granulosa cell apoptosis is presented.

We found that TNF was widely expressed in the developing ovary, with most of the follicles showing positive staining. Although TNF has an apoptosis-regulating role in developing mammalian ovaries [START_REF] Marcinkiewicz | The involvement of tumor necrosis factor-alpha (TNF) as an intraovarian regulator of oocyte apoptosis in the neonatal rat[END_REF], it also has many non-apoptotic functions [START_REF] Terranova | Potential roles of tumor necrosis factor-alpha in follicular development, ovulation, and the life span of the corpus luteum[END_REF]) that may explain its wide expression pattern in healthy follicles. In rat ovaries, expression of TNF has been detected only after the formation of primordial follicles [START_REF] Marcinkiewicz | Oocytic tumor necrosis factor alpha: localization in the neonatal ovary and throughout follicular development in the adult rat[END_REF], while in humans it was observed not only in the intercellular space and cellular membranes, but also in immature oocytes and pre-granulosa cells before follicular development. These findings may reflect species-specific developmental differences between humans and rats. In a previous study on human ovarian tissue, TNF was found to be expressed in oocytes of all follicular stages, but only maturing antral follicles showed expression in granulosa cells [START_REF] Kondo | Immunohistochemical evidence for the presence of tumor necrosis factor-alpha in the infant and adult human ovary[END_REF]. The present results extend these findings by demonstrating weak/moderate TNF staining in follicular granulosa cells and moderate or strong expression in oocytes of small developing follicles.

In the present study we found that caspase-3 is expressed in ovarian tissue throughout gestation indicating the potency of fetal ovarian cells to undergo caspase-3 mediated apoptosis. In addition, primary antibody against cleaved caspase-3 was used to detect the cells undergoing apoptosis. Cleaved caspase-3 was strongly present in fetal ovarian pregranulosa cells and oogonias outside the follicle structures but in older fetuses (after midgestation) also in individual oocytes and granulosa cells of primordial/primary follicles. Many of the positively labelled cells had features of the apoptotic morphology: shrunken cytoplasm, chromatin condensation and apoptotic body formation. These results are in agreement with an earlier study on human fetal ovaries before the 20th week of gestation [START_REF] Fulton | Germ cell proliferation and apoptosis in the developing human ovary[END_REF]. Furthermore, a high number of cleaved caspase-3 labeled cells were detected at midgestation which coincides with the high rate of oocyte apoptosis observed in earlier studies [START_REF] Vaskivuo | Survival of human ovarian follicles from fetal to adult life: apoptosis, apoptosisrelated proteins, and transcription factor GATA-4[END_REF][START_REF] Baker | A Quantitative and Cytological Study of Germ Cells in Human Ovaries[END_REF]).

In addition to participating in apoptotic processes, active caspase-3 may have non-apoptotic functions in the developing ovary. It has previously been shown to have a role in controlling cell cycle, cell differentiation and migration for instance in T-lymphocytes, platelets, nervous tissue and ovarian cancer cells [START_REF] Rosado | Early caspase-3 activation independent of apoptosis is required for cellular function[END_REF][START_REF] Gulyaeva | Non-apoptotic functions of caspase-3 in nervous tissue[END_REF][START_REF] Zhao | Caspase-3-dependent activation of calcium-independent phospholipase A2 enhances cell migration in non-apoptotic ovarian cancer cells[END_REF]. Furthermore, studies in caspase-3 knockout mice have demonstrated that these animals are smaller and born at lower frequency which may be a result of disturbed development or reduced cell number caused by non-apoptotic or apoptotic mechanisms [START_REF] Matikainen | Caspase-3 gene knockout defines cell lineage specificity for programmed cell death signaling in the ovary[END_REF][START_REF] Los | Caspases: more than just killers?[END_REF]. The exact role of caspase-3 in ovarian apoptosis is, however, somewhat unclear, since caspase-3 deficiency has not been shown to affect oocyte death or the size of the follicle pool in prenatal or postnatal mouse ovaries [START_REF] Matikainen | Caspase-3 gene knockout defines cell lineage specificity for programmed cell death signaling in the ovary[END_REF][START_REF] Los | Caspases: more than just killers?[END_REF]).

In concordance with earlier observations in rat [START_REF] Hsu | Bok is a pro-apoptotic Bcl-2 protein with restricted expression in reproductive tissues and heterodimerizes with selective anti-apoptotic Bcl-2 family members[END_REF]) and human [START_REF] Gao | Membrane translocation and oligomerization of hBok are triggered in response to apoptotic stimuli and Bnip3[END_REF]) the expression of Bok was detected in granulosa cells and oocytes of human fetal and adultovaries and it was localized to both cell cytoplasm and nucleus. Nuclear localization of Bok has previously been identified in cells derived from human breast, ovarian and pancreatic cancer tissues [START_REF] Bartholomeusz | Nuclear translocation of the pro-apoptotic Bcl-2 family member Bok induces apoptosis[END_REF]. In contrast to other Bcl-2 family members, Bok has a unique nuclear export signal enabling it to transfer into the nucleus, which has been suggested to be required for the apoptosis-inducing effect of Bok [START_REF] Bartholomeusz | Nuclear translocation of the pro-apoptotic Bcl-2 family member Bok induces apoptosis[END_REF]). The localization pattern of Bok in the present study and the results of previous studies [START_REF] Hsu | Bok is a pro-apoptotic Bcl-2 protein with restricted expression in reproductive tissues and heterodimerizes with selective anti-apoptotic Bcl-2 family members[END_REF][START_REF] Bartholomeusz | Nuclear translocation of the pro-apoptotic Bcl-2 family member Bok induces apoptosis[END_REF] suggest that follicular cells with distinct nuclear staining may have a greater susceptibility to apoptosis than cells expressing Bok only in the cytoplasm.

The protein expression of Bok and Bcl-X L was silenced in KGN cells by means of a lentivirus-based system that has been successfully used in studying apoptosis-regulating genes in cells of an origin other than the ovary [START_REF] Nieminen | c-Myc primed mitochondria determine cellular sensitivity to TRAIL-induced apoptosis[END_REF]). The present results demonstrated that down-regulation of Bok had a marked protective effect on granulosa cells in experimental conditions that differentially activated the cell extrinsic and intrinsic pathways. These important in vitro observations in human ovarian cells are in line with previous studies in rodents showing the proapoptotic role of Bok in female reproductive tissues [START_REF] Hsu | Bok is a pro-apoptotic Bcl-2 protein with restricted expression in reproductive tissues and heterodimerizes with selective anti-apoptotic Bcl-2 family members[END_REF][START_REF] Hsu | A splicing variant of the Bcl-2 member Bok with a truncated BH3 domain induces apoptosis but does not dimerize with antiapoptotic Bcl-2 proteins in vitro[END_REF].

A c c e p t e d M a n u s c r i p t

In accordance with the results of previous studies on mammalian and avian ovaries [START_REF] Watanabe | Gene transfection of mouse primordial germ cells in vitro and analysis of their survival and growth control[END_REF][START_REF] Tilly | Expression of members of the bcl-2 gene family in the immature rat ovary: equine chorionic gonadotropin-mediated inhibition of granulosa cell apoptosis is associated with decreased bax and constitutive bcl-2 and bcl-xlong messenger ribonucleic acid levels[END_REF][START_REF] Johnson | Susceptibility of avian ovarian granulosa cells to apoptosis is dependent upon stage of follicle development and is related to endogenous levels of bcl-xlong gene expression[END_REF], Bcl-X L was widely expressed in human oocytes and granulosa cells. Silencing of Bcl-X L had a significant apoptosis-enhancing effect in response to various apoptotic stimuli in KGN cells, indicating that human granulosa cell sensitivity to apoptotic signals coming from outside the cell are dependent on the expression level of Bcl-X L . The wide expression pattern of Bcl-X L in human ovaries during fetal and adult life, and a marked contribution of its expression level to human granulosa tumour cell survival, suggests that Bcl-X L has an active role in protecting human ovarian cells from apoptosis, as earlier demonstrated in rodents [START_REF] Rucker | Bcl-x and Bax regulate mouse primordial germ cell survival and apoptosis during embryogenesis[END_REF].

The origin and nature of KGN cells have to be taken into consideration when interpreting results obtained from in vitro experiments, since the expression patterns of Bcl-2 family members and the susceptibility to apoptosis of ovarian cancer cells may differ from those in normal ovary [START_REF] Marone | bcl-2, bax, bcl-XL, and bcl-XS expression in normal and neoplastic ovarian tissues[END_REF]). However, KGN cells have many functions of normal cells such as hormone responsiveness and a similar pattern of Fas-mediated apoptosis as demonstrated in normal human granulosa cells [START_REF] Nishi | Establishment and characterization of a steroidogenic human granulosa-like tumor cell line, KGN, that expresses functional follicle-stimulating hormone receptor[END_REF]. Thus, we believe that the KGN cell line is a good experimental model for studying the regulation of apoptosis in human granulosa cells.

The highest rate of oocyte apoptosis in humans is detected at midgestation [START_REF] Vaskivuo | Survival of human ovarian follicles from fetal to adult life: apoptosis, apoptosisrelated proteins, and transcription factor GATA-4[END_REF][START_REF] Baker | A Quantitative and Cytological Study of Germ Cells in Human Ovaries[END_REF] when the expression of apoptosis regulating proteins TNF, Bok, Bcl-X L , caspase-3 and cleaved caspase-3 was significant. This suggests that these factors may be involved in the regulation of fetal ovarian development and apoptosis. Furthermore, the expression of Bok and Bcl-X L in follicular cells of adult human ovaries and the markedly changed apoptosis rate in Bok-and Bcl-X L -deficient KGN cells suggests that these two factors play a role in the survival and death of ovarian follicles. In the young ovaries (16-17 weeks) the most intensive TNF staining was detected in small non-follicular cells. More diffuse staining was also observed in the intercellular space (a). Later in fetal development, TNF localizes preferentially to oocyte cytoplasm, but weak/moderate staining was also detected in granulosa cells (b-d).

Bok was strongly expressed in oocytes in all fetal ovaries studied. Staining was localized to the cell cytoplasm and nucleus (e-h). Staining intensity in different follicles varied from negative to strong. The expression of Bok in fetal granulosa cells was weak or negligible (e-h). Before follicular formation Bcl-X L was detected in stroma and pre-follicular cells of the developing ovary (i).

Later, strong or moderate Bcl-X L protein expression was detected in follicular cells. Expression was strong in follicle-encapsulated oocytes and weak/moderate in granulosa cells (j-l).

Caspase-3 staining was limited mainly to extra-follicular cells located in the cortex area of the ovary (m-p).

Weak/moderate staining could also be detected in follicular oocytes and granulosa cells (n, o). Cleaved caspase-3 was strongly and specifically detected in individual oogonias and pregranulosa cells before primordial follicle assembly (q). After midgestation cleaved caspase-3 was also present in some follicular oocytes and granulosa cells (r-t). Controls: negative controls using peptide blocked antibody (Bcl-X L and Caspase-3) or antibody diluent instead of primary antibody (TNF, Bok and cleaved caspase-3). * = Oocyte, arrows indicate granulosa cells. Scale bar 100 μm. Bok was strongly present in the oocytes of primordial/primary (a and b) and secondary (c) follicles. Bok staining in the granulosa cells of small primary follicles was weak (a and b), but in secondary follicles (c) it was moderate and in antral follicles (d) strong granulosa cell staining was observed. Bok expression was localized to cell cytoplasm and the nucleus (a-c). Bcl-X L was strongly expressed in oocytes at all follicular stages (g-i). Granulosa cells were also moderately stained (g-j). Bcl-X L staining was mainly localized to the cell cytoplasm. Controls: negative controls using peptide blocked antibody (Bcl-X L ) or PBS instead of primary antibody (Bok)primordial/primary follicles (e and k) and antral follicles (k and l). * = Oocyte, arrows indicate granulosa cells. Scale bar 100 μm. Protein expression of Bok and Bcl-X L was detected by immunoblotting. Both proteins were present in control KGN cells and lentiviral shBok-and shBcl-X L delivery resulted in >60% silencing efficiency in Bok and Bcl-X L protein expressions (A). The cells were treated with rTRAIL at 10, 25 or 50 ng/mL, TNF at 10 or 100 ng/mL and 10 or 100 nM staurosporine (STS). Apoptosis induction was measured by caspase-3/7 activation assay after 6 (B) and 24 (C) hours of treatment and the results compared with that in similarly treated control KGN cells. Significantly decreased caspase-3/7 activation was detected in Bok-deficient KGN cells response to treatment with rTRAIL, TNF and STS when compared with control KGN cells. This difference was detected at both time points (B and C). Increased caspase-3/7 activation was observed in shBcl-X L -expressing cells in all treatment groups, even in wells treated with media only. This elevated caspase activation was observed at 6 hours (B) and it remained so at 24 hours (C) of treatment. The results are shown as arithmetic means + SD. All experiments were performed in triplicate, and repeated at least three times (n = 3-5). * = p < 0.05, ** = p < 0.01 and *** = p < 0.001. The cells were cultured in media only (a, e and i), rTRAIL at 25 ng/mL (b, f and j), TNF at 100 ng/mL (c, g and k) or 100 nM staurosporine (STS) (d, h and l) and apoptosis in situ 3´-end labelling was performed after 24 hours of treatment. In all treatment groups fewer apoptotic granulosa tumor cells were detected in Bok-deficient cultures (A: a-d, B) although the difference was not statistically significant in media only or TRAIL treated cells.

A c c e p t e d M a n u s c r i p

  cell apoptosis are essential mechanisms for the regulation of ovarian development and follicle maturation. The exact roles of the apoptosis-regulating factors in human ovarian cell death are, however, still largely unknown.

Figure 1 .

 1 Figure legends Figure 1. Protein expression of TNF, Bok, Bcl-X L and caspase-3 in human fetal ovaries.

Figure 2 .

 2 Figure 2. Protein expression of Bok and Bcl-X L in adult human ovaries.

Figure 3 .

 3 Figure 3. Western analyses in adult human ovary.Western analyses revealed a specific expression of 26 kDa Bcl-X L and 23kDa Bok in adult human ovary.

Figure 4 .

 4 Figure 4. Protein expression and caspase activation assays in shBok-and shBcl-X L -deficient and control KGN cells.

Figure 5 .

 5 Figure 5. Apoptosis in situ 3´-end labelling in Bok-and Bcl-X L -deficient and control KGN cells.

  Figure 1

  Figure 4

Figure 5

 5 Figure 5

Table 1 .

 1 Summary of TNF, Bok, Bcl-X L and caspase-3 protein expression in human fetal ovaries.

	Protein	Stroma	Oocytes	Granulosa cells	Cytoplasm	Nucleus
	TNF	Diffuse staining	Moderate to	Strong or moderate	Strong	Negative
		in stroma and	strong expression	staining in extra-	staining
		intercellular space	in extra-follicular	follicular cells of
		before follicle	cells of young	young ovaries.
		formation	ovaries. Moderate	Weak to moderate
			staining in	expression in
			oocytes	granulosa cells
	Bok	Negative	Moderate or	Weak or negligible	Strong	Strong
			strong expression	expression in	staining	staining
				follicular granulosa
				cells
	Bcl-X L	Diffuse staining	Moderate or	Weak to moderate	Strong	Negative
		before follicle	strong expression	expression	staining
		formation
	Caspase-3	Weak staining	Expressed mainly	Expressed mainly in	Strong	Staining
			in extra-follicular	extra-follicular cells	staining	detected in
			cells on ovarian	located on ovarian		some cells
			cortex.	cortex.
			Weak/moderate	Weak/moderate
			staining detected	staining in follicular
			also in	granulosa cells.
			primordial/primar
			y follicles
	Cleaved	Negative	Expressed in	Expressed in	Strong	Strong
	caspase-3		oogonias and	pregranulosa cells	staining	staining
			individual	and individual
			oocytes inside the	follicular granulosa
			primordial follicle	cells.
			structures.

Table 2 .

 2 Summary of Bok and Bcl-X L expression in human adult ovaries.

	Protein	Stroma	Oocytes	Granulosa cells	Cytoplasm	Nucleus
	Bok	Weak	Strongly	Weak expression	Strong staining Strong staining
		staining	expressed in	in primordial and
			oocytes in	primary follicles.
			primordial to	Staining increased
			antral follicles	to moderate or
				strong in
				secondary and
				antral follicles
	Bcl-X L	Weak	Strong expression	Moderate	Strong staining Negative
		staining	at all follicular	expression at all
			stages	follicular stages

Acknowledgements

We thank Drs. Nishi and Yanase for providing the KGN cell line. We also thank Taru Jokinen for her skilful laboratory assistance and paediatric pathologist Riitta Herva for providing the fetal tissue samples. In addition, special thanks go to Nick Bolton for revising the language. The project was supported financially by grants from the Academy of Finland (MH, JST), the Sigrid Jusélius Foundation (MH, JST), The Finnish Cancer Foundation (MH) and Oulu University Hospital (JST).


C Klever

K Seemann

M Stüber

S Ulrich

H Brunken

A Ludwig

H Leiste

Epitaxially stabilised TiN/(Ti,Fe,Co)N multilayer thin films in pseudo-fcc crystal structure by sequential magnetron sputter deposition

Multilayer thin films were grown by non-reactive sequential magnetron sputter deposition from ceramic TiN and metallic FeCo targets addressing a combination of wear resistance and sensoric functionality. Coatings with bilayer period values ranging from 449 nm down to 2.6 nm were grown with the total amount of either material maintained constant. The multilayer thin films were post-annealed ex-situ at 600 C for 60 min in vacuum.

X-ray diffraction results imply the multilayer thin films to undergo significant changes in its crystalline structure when the bilayer period is decreased. By using high resolution transmission electron microscopy as well as selected area electron diffraction it is shown that in case of multilayer thin films with bilayer periods of several ten nanometers and higher FeCo layers and TiN layers in their respective common CsCl and NaCl type crystal structures alternate. In contrast, in the multilayer thin films with bilayer periods of only a few nanometers, grain growth across the interfaces between the individual layers takes place and a strongly textured microstructure is formed which features columns in pseudo-fcc crystal structure grown in heteroeptaxial growth mode.

It is suggested that the experimental findings imply the latter multilayer thin films to be alternately composed of TiN layers and (Ti,Fe,Co)N solid solution layers which have been formed by solid state reaction during the deposition process. As the consequence, epitaxially stabilised columnar grains in strongly textured pseudo-fcc structure are formed. This structure is preserved after the annealing procedure which qualifies these coatings for use in applications where temperatures of up to 600 C are reached.

Introduction

Wear protection coatings produced by physical vapour deposition (PVD) are used in many engineering applications since the early 1980ies. Soon after the first commercial application of single layer hard coatings for enhanced wear protection it was recognised that appropriately selected thin film materials can be combined as a multilayer system, leading to coating properties and performances significantly exceeding those of either constituent. Since then, the systematic selection of material combinations, the specific design of the multilayer architecture (e. g. individual layer thickness, interface constitution), the understanding of growth conditions, and the correlation between microstructure and properties are subject to intensive research in the field of multilayer wear resistant thin films [START_REF] Yashar | Nanometer scale multilayered hard coatings[END_REF][START_REF] Eh Hovsepian | Recent progress in large scale manufacturing of multilayer/superlattice hard coatings[END_REF][START_REF] Mayrhofer | Microstructural design of hard coatings[END_REF][START_REF] Stueber | Concepts for the design of advanced nanoscale PVD multilayer protective thin films[END_REF]. Beyond the approach of improving the coating performance with respect to their passive functionality, studies were published focussing on the design of films which would be able to adapt their actual functionality in response to external influences as, for instance, environmental changes or mechanical load. A particular example for this type of coatings are the so-called "chameleon coatings" [START_REF] Voevodin | Supertough wear-resistant coatings with "chameleon" surface adaptation[END_REF][START_REF] Voevodin | Nanocomposite tribological coatings with "chameleon" surface adaptation[END_REF][START_REF] Baker | Preparation of Al 2 O 3 /DLC/Au/MoS 2 chameleon coatings for space and ambient environments[END_REF]. However, in-situ condition monitoring is-in general-not possible. There are hence some studies available presenting coating concepts addressing the integration of sensoric functionality into passive functional coatings. For instance, results on protective and thermal barrier coatings with integrated photoluminiscent phases were reported [START_REF] Muratore | Smart tribological coatings with wear sensing capability[END_REF][START_REF] Steenbakker | Sensor thermal barrier coatings: Remote in situ condition monitoring of EB-PVD coatings at elevated temperatures[END_REF].

In the context of the combination of passive and active functionality with the focus on use in sensor applications, we had recently published an article on the integration of a magnetic sensor phase into the standard wear resistance material TiN [START_REF] Klever | Multifunctional FeCo/TiN multilayer thin films with combined magnetic and protective properties[END_REF]. It had been shown that the growth of multilayer thin films by alternate deposition of TiN and FeCo layers, using non-reactive sequential magnetron sputter deposition followed by an ex-situ annealing procedure under vacuum conditions (60 min, 600 C, static magnetic field with ñ 0 H = 50 mT), is an appropriate technique to fabricate coatings which simultaneously can provide protective and sensoric properties (the latter through the ferromagnetic properties of FeCo). It had in particular been found that by decreasing the bilayer period down to only a few nanometers important macroscopic physical properties (nanoindentation hardness, ferromagnetic softness, response to an external electromagnetic HF-field) can be improved significantly. Concerning the structure of the multilayer thin films, Low-angle X-ray diffraction (LA-XRD) and Auger electron spectroscopy (AES) depth profiles had clearly indicated that the layered structure of all films have remained unchanged after the annealing procedure [START_REF] Klever | Multifunctional FeCo/TiN multilayer thin films with combined magnetic and protective properties[END_REF].

This article presents a detailed microstructural analysis of these multilayer coatings. X-ray diffraction (XRD) spectra of the films in the as-deposited and the annealed state were recorded and analysed. In addition, cross-sectional transmission electron microscopy (XTEM and HRTEM) images as well as selected area electron diffraction (SAED) patterns of multilayer thin films representative for each small and high bilayer periods were recorded and evaluated. The results are discussed and a model is proposed for the specific multilayer thin film microstructure evolved at small bilayer periods as well as its formation.

Experimental details

Multilayer thin films were deposited by non-reactive sequential magnetron sputtering in a Leybold Z550 laboratory device by using FeCo and TiN targets (both with 99.9 % nominal purity and 150 mm diameter). Thermally oxidised Si substrates (10 × 10 mm 2 surface area) were placed 50 mm below the target center on a rotatable substrate holder and kept at floating potential during all processes. The base pressure in the chamber was < 1 × 10 -6 mbar. After sputter cleaning of targets and substrates (for a more detailed description see [START_REF] Klever | Multifunctional FeCo/TiN multilayer thin films with combined magnetic and protective properties[END_REF]), the films were deposited at 0.2 Pa working gas pressure in a Ar atmosphere (99.9999 % purity): The plasmas under both targets were run simultaneously during the film growth process; the TiN target was supplied with 700 W DC power whereas the FeCo target was supplied with 250 W HF power for the deposition of all multilayer thin films. The resulting cathode voltage (target self-bias) was -564 V and -1440 V, respectively. The substrates were moved in stopand-go-mode between both targets, starting and stopping with TiN for each multilayer thin film. The time of interruption of substrate rotation, respectively the duration of deposition in front of the target without substrate movement, was equal below each target in order to keep the thickness ratio of the individual layers constant (neglecting deviations between the deposition rate profiles alongside the target diameters). The thickness ratio of the individual layers can hence be estimated by using the respective deposition rates (D TiN ∼ 0.93 nm s -1 , D FeCo ∼ 0.33 nm s -1 , ascertained by means of contact profilometry). The holding time was reduced from 807 s to 0 s (the latter corresponding to the continuous rotation of the substrate holder). Accordingly, the number of bilayers was increased from n = 1 to n = 390 such that all films were grown with a nominal total thickness of 1 ñm. In addition, TiN and FeCo single layer films with 1 ñm thickness were grown using the same deposition conditions as a reference. All multilayer thin films were post-annealed ex-situ at 600 C for 60 min in vacuum (p < 1 × 10 -8 mbar) subsequent to the deposition.

The microstructure of the multilayer thin films was analysed before and after annealing by using X-ray diffraction in Bragg-Brentano geometry (XRD). Low-angle X-ray diffraction (LA-XRD) was used in order to determine the bilayer periods lower than 10 nm. Cu K α radiation was used.

Cross-sections of representative films were prepared for TEM analysis both in the as-deposited state and after annealing by focused ion beam cutting (FEI Quanta 3D 200i). XTEM and HRTEM images, as well as SAED patterns, were recorded from the multilayer thin film cross-sections at 200 kV using a Tecnai F20 instrument.

Results

In figure 1, XRD patterns of the as-deposited multilayer thin films with different bilayer periods are shown. The bilayer periods higher than 10 nm were determined by using the deposition rates and the deposition time, the other values had been determined experimentally by means of Low-angle X-ray diffraction (LA-XRD). The diffraction patterns of 1 ñm thick TiN and FeCo single layers grown at identical conditions are shown as a reference. The full width at half maximum (FWHM) values of the TiN(200) and the TiN(111) peaks are comparatively large indicating the TiN single layer to be nanocrystalline. In particular, no amorphous regions are obtained in any of the TiN films in all cases. A dependency of the multilayer thin films' microstructure on the bilayer period can be observed: The diffraction pattern obtained from the film with Λ = 449 nm exhibits the (111) and (200) reflections of TiN in the NaCl tape crystal structure as well as the (110) reflection of FeCo in the CsCl type crystal structure which are the stable phases of the respective binary material at standard conditions [START_REF] Sourmail | Near equiatomic FeCo alloys: Constitution, mechanical and magnetic properties[END_REF]. When the bilayer period is reduced to values below 449 nm the FeCo(110) reflection vanishes which indicates a decrease in the grain size in the FeCo phase. Down to the bilayer period of 5.5 nm the early disappearance of the TiN(111) reflection as well as a significant increase in the FWHM of the TiN(200) reflection imply the presence of smaller grains as a consequence of the reiterated interruption of the individual layer growth. In the diffraction patterns for multilayer thin films with bilayer periods of 4.3 nm and lower a striking change in the XRD patterns is observed: In the pattern of the multilayer thin film with Λ = 4.3 nm, the TiN(200) reflection is splitted into a double-peak structure. In the multilayer thin film with the bilayer period of 2.6 nm the same phenomenon is observed with an even more increased distance between the two reflections.

In figure 2 a representative cross-sectional HRTEM image from the as-deposited multilayer thin film with a bilayer period of 87 nm is shown. The darker region on the left hand side is the FeCo layer which is covered by a TiN layer. Both films are polycrystalline and several grains obtaining distinct orientations can be observed. Both layers are separated by a predominantly incoherent interface region characterised by a high degree of lattice distortions. As is verified by the SAED pattern (shown in the inset), both TiN and FeCo are polycrystalline in its respective equilibrium crystal structure (NaCl and CsCl type, respectively), as all diffraction rings can unambiguously allocated to the respective phase (which is explicitely shown for the five innermost diffraction rings). This result complements the findings from the the corresponding XRD pattern, the TiN(111) and the FeCo(110) peaks are not resolved in, anymore, due to the comparatively small average grain size.

The XTEM image shown in figure 3 confirms that even the multilayer thin film with the smallest bilayer period of Λ = 2.6 nm exhibits a multilayer structure, as was also been shown for the annealed film and had been supported by XRR and AES depth profiles which had been shown in an earlier publication [START_REF] Klever | Multifunctional FeCo/TiN multilayer thin films with combined magnetic and protective properties[END_REF]. A representative section of an HRTEM image taken from the very same film as in figure 3 is shown in figure 4. In the detail shown, two distinct grains can be discerned which vary in the lattice orientation with respect to the electron beam direction. While the individual layers cannot be discerned due to the particular contrast conditions, pseudo-epitaxial growth along the growth direction can be well identified. The grain boundary between the columnar grains shown is partially coherent. In particular, the (HR)TEM images confirm that the film has grown in columnar growth mode with the lattice planes being continued across the layer interfaces. The lattice distances were determined by measuring the distance along a number of lattice planes. The values yielded are identical to those expected for TiN in NaCl type crystal structure. Based on this matter on fact the FFT insets are indexed in order to facilitate a comparison with the according SAED patterns later on.

The XRD patterns of the annealed multilayer thin films are shown in figure 5. In the multilayer thin films with bilayer periods ≥ 5.5 nm a decrease in the FWHMs compared to the corresponding as-deposited state pattern implies a grain size increase during the annealing procedure both in the FeCo and the TiN phase. In the films with Λ < 5.5 nm, the "peak splitting" phenomenon is likewise present after annealing albeit the reflections are shifted with respect to their previous positions. In figure 6, the SAED pattern of the multilayer thin film with the smallest bilayer period of Λ = 2.6 nm after annealing is shown. During the recording of the SAED pattern, the electron optics was adjusted such that the complete film thickness was used for diffraction processes. The sole appearance of diffraction spots without any additional ring patterns as well as the axial symmetry of the spot pattern imply the predominance of regions with pronounced texture. The SAED spots are schematically depicted in the inset in the figure : The location of all diffraction spots can be consistently indexed in terms of the superposition of diffraction patterns of a crystal in pseudo-fcc structure in consideration of distinct zone axises (ZA's). With the convention of [002] being the growth direction, the diffraction spots can be indexed as shown in figure 6: • Spots originated by diffraction with [010] being the ZA depicted by the black filled bulls, • spots originated by diffraction with [110] being the ZA depicted by the bluerimmed, empty bulls, • spots originated by diffraction with [210] being the ZA depicted by the red-rimmed squares, • spots originated by diffraction with [310] being the ZA depicted by the green filled squares.

Proceeding the above systematics, all appearing diffraction spots can be indexed. There are explicitely no diffraction spots present indicative for crystalline regions in pseudo-bcc (or CsCl) crystal structure. The superlattice reflections visible at the lowest order spots with [110] being the ZA corrobate the finding that a well defined multilayer structure with bilayers of equal bilayer period is maintained after annealing. At the other diffraction spots, the multilayer reflections are not visible or considerably blurry which might be caused by the respective beam orientation. The double peak structure of the (200) reflection in the XRD pattern is not identifiable in the SAED pattern since the (200) spot is represented in maximum intensity on the negative.

Discussion

The passing of the TiN(200) reflection into a double peak structure in the XRD patterns when the bilayer periods are decreased implies significant microstructural changes in the multilayer thin films examined. By analysing HRTEM images and SAED patterns it is demonstrated that for small bilayer periods the multilayer thin films are predominantly grown in columnar growth mode beyond all layer interfaces with the distinct columns being nanostabilised due to pseudo-epitaxial growth in pseudo-fcc crystal structure. This behaviour is in contrast to the film growth mode for higher bilayer periods at which TiN and FeCo layers in its regular stable NaCl and CsCl type crystal structure, respectively, alternate as expected.

It is known that Fe x Co 1-x can be stabilised in (pseudo-)fcc crystal structure at room temperature under appropriate conditions (choice of substrate, growth conditions, film thickness). These observations were frequently made at distinct dimensionalities as pseudomorphically grown single layer films [START_REF] Winkelmann | Perpendicular magnetic anisotropy induced by tetragonal distortion of FeCo alloy films grown on Pd(001)[END_REF][START_REF] Yildiz | Strong perpendicular anisotropy in Fe 1-x Cox alloy films epitaxially grown on mismatching Pd(001), Ir(001), and Rh(001) substrates[END_REF], multilayer thin films [START_REF] Graff | Atomic level mixing induced by Kr irradiation of FeCo/Cu multilayers[END_REF] as well as nanocrystalline films [START_REF] Liu | FeCoSiN film with ordered FeCo nanoparticles embedded in a Si-rich matrix[END_REF]. However, the lattice constants of equiatomic (pseudo-)fcc FeCo (a FeCo = 0.354 nm [START_REF] Sourmail | Near equiatomic FeCo alloys: Constitution, mechanical and magnetic properties[END_REF]) and TiN (a TiN = 0.424 nm [16]) would yield a relative lattice mismatch of ((a TiN -a FeCo )/a TiN = 0.165). Due to this considerable lattice mismatch pseudomorphic growth of (pseudo-)fcc FeCo layers onto TiN in NaCl type crystal structure is not expected to be possible.

By using PVD techniques thin films are grown far from thermodynamical equilibrium. As a consequence, films can be grown in crystal structures which differ from the predictions in the according (equilibrium) phase diagrams. As a prominent example, nonstoichiometric TiN 1-x films can be grown with x reaching considerable (positive and negative) values while otherwise maintaining its structure which at standard conditions is not predicted by the according phase diagram [START_REF] Schmid | Optical and electronic properties of sputtered TiNx thin films[END_REF]. Both the phase diagrams of the Fe-N system [START_REF] Predel | Fe-N (Iron-Nitrogen), volume 5e: Dy-Er-Fr-Mo of SpringerMaterials -The Landolt-Börnstein Database[END_REF] and of the Co-N system [START_REF] Predel | Cobalt-Nitrogen), volume 5e: Dy-Er-Fr-Mo of SpringerMaterials -The Landolt-Börnstein Database[END_REF] predict the existence of nitrogen-poor phases in (pseudo-)fcc crystal structure. Both the TiN and the FeCo layers were observed to not consist any amorphous regions or porosity such that interdiffusion caused by any of these facts can be excluded. Given a sufficient kinetic energy of the impinging atoms during the deposition process, the formation of a complex nitride formed from Ti, Fe, and Co should hence be possible. As a similar example, the growth of single layer (Ti,Fe)N films with ∼ 13 % of Ti atoms being replaced by Fe atoms within a pseudo-fcc crystal structure was reported by Kirsten et al [START_REF] Kirsten | Mössbauer investigations of (Ti,Fe)N hard coatings[END_REF]. However, the films prepared by Kirsten et al were grown in a one-step process by reactive magnetron sputter deposition from a Ti metal target equipped with Fe metal pins rather than non-reactive sequential deposition from two distinct sources.

The formation of a complex nitride is the process proposed to take place in our deposition process due to the high target self bias voltage at the FeCo target and the comparatively low working gas pressure. The structural reordering process necessary for the evolution of the multilayer thin film structure presented in this study for small bilayer periods is more probable to take place during the deposition step below the FeCo target rather than that below the TiN target due to several reasons: First, the target bias voltage at the FeCo target has been considerably higher than that at the TiN target. Second, the higher mass of Fe and Co atoms compared to that of Ti and N atoms is expected to result in a higher momentum transfer during the Fe and Co particle impact on the substrate surface than during the Ti and N particle impact. The microstructure observed for small bilayer periods is thus suggested to be a consequence of collision-induced atomic mixing caused by momentum transfer subsequent to the arrival of the Fe and Co atoms at the previously deposited TiN layer.

According to the above considerations, the following structure formation model is proposed for the multilayer thin films grown with sufficiently small bilayer period:

• A (nearly) stoichiometric TiN film is grown.

• Fe and Co particles impinge. Their kinetic energy is sufficiently high in order to be built into the TiN lattice. Under the condition that the FeCo layer thickness t FeCo remains smaller than a critical thickness t crit , an understoichiometric (Ti,Fe,Co)N solid solution with the maintained pseudo-fcc crystal structure is formed. • The successional (nearly) stoichiometric TiN film is grown on top of the solid solution (Ti,Fe,Co)N layer. Due to t < t crit the epitaxial stabilisation of the solid solution layer in an fcc pseudo-structure is energetically favourable.

The formation of this TiN/(Ti,Fe,Co)N multilayer thin film in pseudo-fcc crystal structure is expected to evolve under the given experimental conditions and in the case that the nominal FeCo layer thickness t FeCo is smaller than a critical value t FeCo,crit . The expected and the resulting multilayer structures are illustrated in figure 7. It is expected that diffusion of N atoms takes place due to the now present concentration gradient resulting in the formation of understoichiometric TiN with in turn changed lattice parameters. We suggest that the lattice distances of the two distinct materials in combination with diffraction effects due to the artificial superlattice structure, as described by Fullerton et al [START_REF] E E Fullerton | Structural refinement of superlattices from x-ray diffraction[END_REF], are the reasons for the distinct changes in the XRD patterns.

Conclusions

In the multilayer thin films investigated, a distinct change in the XRD patterns when the bilayer periods were low suggessted substantial changes in the films' microstructure. With complementary TEM experiments, the following conclusions were drawn for the multilayer thin films with small bilayer periods:

(i) As a result of appropriate multilayer thin film architecture as well as growth conditions a high volume fraction of ferromagnetic Fe and Co atoms was inserted into an fcc TiN lattice by sequential magnetron sputter deposition. A multilayer structure evolves even for bilayer periods as small as 2.6 nm. The distinct layers grow in a pseudo-epitaxial relationship which results in the formation of columnar grains. (ii) A (Ti,Fe,Co)N solid solution in a pseudo-fcc crystal structure is suggested to be formed as a consequence of collision induced atomic mixing and subsequent nanostabilisation.

(iii) The microstructure of the multilayer thin films is thermally stable against annealing for 60 min at 600 C.

The film deposition processes presented in this paper were shown to allow for the insertion of a large fraction of FeCo into an fcc crystal structure. From a technical point of view the film architecture deposited is considered to be appropriate for applications for which combined mechanical and soft magnetic properties at high temperatures (up to 600 C) are important.

Figure 1 .

 1 Figure 1. XRD patterns of the as-deposited multilayer thin films with different bilayer periods. The spectra of ∼ 1 ñm thick FeCo and TiN single layer films grown at identical deposition conditions as the multilayer thin films are shown for comparison. The dotted lines indicate the positions of the (111) and (200) reflections of TiN in NaCl type crystal structure and the (110) reflection of FeCo in CsCl type crystal structure. Substrate peaks are designated by 's'.

Figure 2 .

 2 Figure 2. HRTEM image taken from the as-deposited multilayer thin film with a bilayer period of 87 nm. The growth direction is indicated by the arrow. The interface region is adumbrated by the lines. In the inset the SAED pattern with diffraction along virtually the whole specimen cross-section is shown. The indexes of the five innermost rings are indicated; continuous rings are assigned to TiN in NaCl type structure, the dotted rings are assigned to FeCo in CsCl type structure.

Figure 3 .

 3 Figure 3. XTEM image taken from the as-deposited multilayer thin film with a bilayer period of 2.6 nm. The growth direction is indicated by the arrow.

Figure 4 .

 4 Figure 4. HRTEM image taken from the as-deposited multilayer thin film with a bilayer period of 2.6 nm. Two distinct grains can be discerned in this section. The grain boundary region is adumbrated by the dotted lines. The respective FFT images of both grains are shown in the insets in order to facilitate the allocation to the respective diffraction patterns. The growth direction of the multilayer thin film is indicated by the arrow.

Figure 5 .

 5 Figure 5. XRD patterns of the annealed multilayer thin films with different bilayer periods. The dotted lines indicate the positions of the (111) and (200) reflections of TiN in NaCl type crystal structure and the (110) reflection of FeCo in CsCl type crystal structure. Substrate peaks are designated by 's'.

Figure 6 .

 6 Figure 6. SAED pattern of the multilayer thin film with a bilayer period of 2.6 nm subsequent to 60 min annealing in vacuum at 600 C. The diffraction spots are schematically shown in the inset and indexed as explained in the text.

Figure 7 .

 7 Figure 7. Illustration of the expected (left) and the resulting multilayer structure as proposed (right).

Acknowledgements

The authors are grateful for funding by the DFG within the framework of the priority program SPP 1299 'HAUT'.


Stefano Viaggiu
email: viaggiu@axp.mat.uniroma2.it

An inhomogeneous universe with thick shells and without cosmological constant

Keywords: numbers: 98.80.-k, 98.80.Jk, 95.36.+x, 04.20.-q

An inhomogeneous universe with thick shells and without a cosmological constant

Introduction

Supernovae type Ia (SNIa) observations of the past decade seem to indicate an accelerating universe ( [1,2,3]). In the standard approach with the Friedmann-Lemaître models (FRLW), an accelerating universe invokes the presence of a large amount of the so called dark energy. In the FRLW picture, this dark energy is given by the cosmological constant. The dark energy 1 Confidential: not for distribution. Submitted to IOP Publishing for peer review 6 May 2010 represents a puzzle and perhaps the biggest problem in modern cosmology. In fact, a direct detection of a cosmological constant is still lacking. In the last decade, many attempts have been made (see [4]- [24] and references therein) to obtain physically sensible inhomogeneous models. Some authors (see for example [16,17,20,21,22,23,24]) showed that inhomogeneities can generate an accelerating universe by using Lemaître-Tolman-Bondi (LTB) metrics (see [25,26,27]), but several conditions must be imposed (see [4]) in order to build regular physically viable models. In particular, in [21,22] it is shown that LTB metrics can mimic the distance-redshift relation of the FRLW models at least at the third order in a series expansion with respect to the redshift near the center where the observer is located. More generally, in the LTB solutions, apparent acceleration in the redshift-distance relation seen by a central observer can be shown to coexist with a volume average deceleration on a spacelike hypersurface (see [28]). The assumption of spherical symmetry is (obviously) not in agreement with the Copernican principle. In any case, a spherical symmetry can be justified as the outcome of a smoothing out with respect to the angles: the metric so obtained becomes spherical. An accelerating universe can also be built by averaging inhomogeneities (see [4,5,6,7,8,9,10,11,12,13,14,15]) by means of the techniques depicted in [8,10,11]. The approaches dealing by averaging on spatial domains are different with respect to the ones dealing with exact spherical solutions. First of all, averaged cosmologies retain Copernican principle, although in a generalized statistical sense. Further, the exact spherically symmetric models try to describe apparent acceleration by means of a large amount of inhomogeneities. Conversely, the "Copernican" cosmologist introduce inhomogeneities without special symmetries and then try to understand the modifications to the average evolution from backreaction. For a review of inhomogeneous cosmological models see [START_REF] Krasinski | Inhomogeneous Cosmological Models[END_REF][START_REF] Plebanski | An Introduction to General Relativity and Cosmology[END_REF]. In particular, we study the idea developed in Wiltshire's papers [13,14,15]. There, the dimming of the distant galaxies is interpreted as a "mirage" effect by means of a "Copernican" statistical model. This effect is due to the different rate of clocks located in averaged not expanding galaxies, where the metric is spatially flat, with respect to clocks in voids where the spatial curvature is negative. To a negative spatial curvature can be associated a positive quasilocal energy. This gravitational energy is non-local, according to the strong equivalence principle. In this picture the universe is composed by a cosmic web of regions evolving asymptotically like an Einstein-de Sitter universe (our local universe) "matched" with local voids evolving like a Milne universe. The matching conditions are imposed with a uniform Hubble flow by equating the radial null sections of the cosmic web. Although this matching is reasonable, it cannot be enough to define a geometry. In this context, inspired by Wiltshire's idea, we introduce clock effects, but with an exact spherically symmetric model and without introducing backreaction. In this way we can build a geometry with a non-uniform time flow by imposing the usual matching conditions required by general relativity, which are missing in [13,14,15]. To mimic Wiltshire's idea, our model is built with a central zone up to a small redshift z 1 (< 100/h M pc) made of a flat Friedmann metric, where at the center is located the observer. In practice, the inhomogeneities can be taken into account by glueing together different homogeneous portions of universe (see for example [24]). It should be noticed that cosmological models with only two metrics can be exhaustively found in [START_REF] Alexander | [END_REF]. By means of a thick shell of anisotropic matter, the flat zone can be smoothly matched with an hyperbolic Friedmann metric up to the zone where dimming galaxies are observed [START_REF] Riess | [END_REF]. Finally, we stress that the hyperbolic metric can be smoothly matched to an hyperbolic LTB solution on a comoving boundary surface, according to WMAP data [33]. Actually, we could choose the flat Friedmann one (without cosmological constant!), but WMAP predicts a flat metric only at early times, while at later epochs a negatively curved metric is more appropriate. Our solution is exact and no approximations have been made, thus providing a general framework to analyze the effects of a possible non-uniform time flow. In this context, we show that, after a formal Taylor expansion of the distance-redshift relation near the center at z = 0, a negative deceleration parameter is only compatible with a non-uniform Hubble flow within a non-uniform time flow. The physical content of the thick shell is studied together with the energy conditions. Finally, it is conjectured that a non-vanishing heat flow term in the energy-momentum tensor of the thick shell can explain the possibly non-uniform time flow. In section 2 we introduce the metrics of our model. In section 3 the junction conditions are discussed. In section 4 the matter content of the thick shell is studied. In section 5 the case of a uniform time flow is analyzed, while in section 6 the case of a uniform Hubble flow is presented. Section 7 is devoted to the study of the general case. Finally, section 8 collects some final remarks and conclusions.

The model

All the astrophysical observations agree with the assumption that our "near" local universe is rather inhomogeneous. Nevertheless, at sufficiently large scales (∼ 100/h M pc) the inhomogeneities can be averaged to obtain a statistically homogeneous universe. In any case, from the perturbations of the primordial inflation, a model with an overdense density surrounded by voids seems to be the most probable. Hence, we can build an inhomogeneous universe by glueing together different homogeneous volumes. As a consequence, the central region, with the observer located at the center, is provided by a flat Friedmann metric

ds 2 B = -dt 2 B + a 2 B (t B )(dη 2 B + η 2 B dΩ 2 ), a B (t B ) = a Bi t B t Bi 2 3 , (1)
where in (1) we have assumed a dust model and a Bi , t Bi are initial values. With (1), the Hubble flow H B is given by

H B = 1 a B da B dt B = 2 3t B . (2)
The zone where the dimming galaxies are observed (z ≤ 1.7) is modeled with an hyperbolic Friedmann metric with negative spatial curvature and a common centre with (1). In appropriate coordinates, the metric can be put in the form

ds 2 F = -dt 2 + a(t) 2 [dη 2 F + sinh 2 η F dΩ 2 ], (3)
H i t = Ω i 2(1 -Ω i ) 3 2 (sinh ξ -ξ) , a(t) = a i Ω i 2(1 -Ω i ) (cosh ξ -1) , a(t) 2 H 2 (1 -Ω) = 1,
where Ω i is an initial density parameter, H i an initial Hubble constant and a i an initial expansion factor to be specified. An observer in the portion of universe given by (3) measures the observables by means of the comoving time t. With respect to this time, an observer in (3) measures an Hubble flow with a time dependent Hubble constant H given by

H = 1 a da dt = 2H i sinh ξ Ω i (cosh ξ -1) 2 1 -Ω i 3 2 . ( 4
)
The only way to smoothly match the metrics (1) and ( 3) is by means of a thick shell living in the region z ∈ [z 1 , z 2 ]. Without loss of generality, we can choose the metric of the thick shell mimic the expression of a LTB metric

ds 2 thick = -e G(τ,η) dτ 2 + R 2 ,η (τ, η) f 2 (η) dη 2 + R 2 (τ, η)dΩ 2 , (5)
where e G(τ,η) denotes the lapse function. Furthermore, to achieve agreement with WMAP data [33], the universe beyond the dimming zone could be modeled with an hyperbolic LTB spacetime (see [25,26,27])

ds 2 = -dτ 2 + R2 ,η (τ , η) f 2 (η) dη 2 + R2 (τ , η)dΩ 2 , f 2 (η) > 1. (6)
In fact, WMAP forces us to conclude that at early epochs the LTB metric must approach a flat one and, as a result, we must impose the condition that the density parameter Ω m approaches unity at early times (recombination era), i.e. Ω m (τ rec ) → 1. According to [34], at later epochs the metric could as well be taken to have a negative spatial curvature.

Matching conditions

First of all, it should be noticed that the matching of the Friedmann metrics of this paper can be obtained only by taking a thick shell. We perform the matching along comoving surfaces (the boundary of the thick shell) given by

η B = η B(1) , η = η (1) , η = η (2) , η F = η F (2) , (7)
where the subscripts (1) -(2) denote the boundaries of the shell. For the thick shell, the continuity of the first and the second fundamental form [START_REF] Darmois | Les Equations de la Gravitation Einstenienne[END_REF][START_REF] Israel | [END_REF] leads to

dt B dτ (1) = e G(τ,η (1) ) 2 , dt dτ (2) = e G(τ,η (2) ) 2 , (8)
R(τ, η (1) ) = η B(1) a B (t B ), R(τ, η (2) ) = a(t) sinh η F (2) , (9)
f (η (1) ) = 1, f (η (2) ) = cosh η F (2) , (10)
G ,η (τ, η (1) ) = G ,η (τ, η (2) ) = 0. ( 11
)
Together with equations ( 8)-( 11), we have the "gauge" condition

dt dt B = J(ξ), H(ξ) = α(ξ)H B (t B ). ( 12
)
The function J(α(ξ)) depends upon the chosen function α. With condition (11), the heat flow is vanishing at the boundaries of the thick shell (see the next section). To integrate the system ( 8)- (11), we can fix an expression for G satisfying equation (11) and the relations t = t(τ, η), t B = t B (τ, η) that satisfy equation (8). In this way, thanks to the equations ( 9), the behaviour of R(τ, η) is fixed at the boundaries ( 1) -(2), and, as a result, we have the freedom to choose R(τ, η) inside the shell and so also the function f with the conditions (10).

For a smooth matching between ( 3) and ( 6) on a comoving boundary surface

η F = η F (3) , η = η(3) we have τ = t, (13) R(τ , η(3) ) = a(t) sinh η F (3) , (14) f(η (3) ) = cosh η F (3) , (15)
It should be noticed that there exist a relationship between the metrics ( 5) and (6). First of all, at the recombination era (early epochs) we have:

τ rec τrec , G(τ rec , η) 0, R(τ rec , η) R(τ rec , η). (16)
Furthermore, thanks to the matching conditions ( 8) and ( 13), we have (remember that η (2) is a constant)

e G(τ,η (2) ) dτ 2 = g(τ )dτ 2 = dτ 2 , (17)
Finally, without loss of generality, we could also set η = η in ( 5) and (6).

Since the matching conditions have been discussed, we can give the formal expressions for the angular distance d A and the distance luminosity d L where [START_REF] Ellis | Relativistic cosmology[END_REF][START_REF] Etherington | [END_REF][START_REF] Penrose | General Relativistic Energy flux and Elementary Optics[END_REF]). In fact, thanks to the conditions ( 8)-( 11) and ( 13)-( 15), we obtain (see [24])

d L = d A (1 + z) 2 (see
d A = a B (t B )η B , z≤ z 1 , (18)
d A = R(τ, η), z∈ [z 1 , z 2 ], d A = a(t) sinh η F , z ∈ [z 2 , z 3 ], d A = R(τ , η), z≥ z 3 ,
where, z 3 (> 1.7) represents the "starting point" of the LTB metric. For our purposes, we are interested in the patch of universe where the dimming galaxies are observed, i.e. the third of equations (18).

Energy-momentum tensor for the thick shell

In this section we study the metric (5). The most general energy-momentum tensor T ab compatible with it is

T ab = EV a V b + P ⊥ [W a W b + L a L b ] + +P η S a S b + K [V a S b + S a V b ] , (19)
with

V a = -e G 2 , 0, 0, 0 , (20)
W a = [0, 0, R, 0] , L a = [0, 0, 0, R sin θ] , S a = 0, R ,η f , 0, 0 , (21)
where E is the energy-density, P η the radial pressure, P ⊥ the tangential pressure, K being the "heat flow term" or radial energy flux. In particular, Einstein's equations for K give

K = - fR ,τ G ,η RR ,η e G 2 . (22)
The regularity conditions require that (R ,η , R ,τ , R, f) = 0. Hence, from equation (22), it follows that K = 0 if and only if G ,η = 0. Therefore, a non trivial lapse function is only compatible with a non-vanishing energy flux.

If we take the most general expression for a spherically symmetric metric that is

ds 2 = -e G(τ,η) dτ 2 + A 2 ,η (τ, η) f 2 (η) dη 2 + B 2 (τ, η)dΩ 2 , (23)
the energy flux for ( 23) is vanishing if and only if

G ,η = 2(ln B ,τ ) ,η -2(ln A ,τ ) ,η B ,η B ,τ . (24)
To the best of our knowledge, the only non-static metric with a non-barotropic equation of state satisfying the equation ( 24) is the Stephani metric [START_REF] Stephani | [END_REF]. Remember that a time dependent spherical matter cannot have a barotropic equation of state (E = E(P )) within a finite radius [41]. It is a simple matter to see that the spherically symmetric Stephani space-time cannot satisfy the matching conditions ( 8)- (11). As a result, a link between the heat flow and a non-trivial lapse function can be conjectured, at least for spherically symmetric space-times. Should this argument be correct, we would have a possible physical mechanism to generate clock effects.

In what follows, starting from the conditions ( 8)- (11), we analyze the possibility to build a physically reasonable anisotropic thick shell. For simplicity, we study the case G = 0 (t = t B ). Hence, the matching conditions ( 9)-( 10) can be fullfilled by taking, for example

R = η t 2 3 Y 2 + a(t)η Ỹ 2 , (25)
f (η) = Y 2 + 1 + η 2 2 Ỹ 2 , (26)
Y = 1 - (η -η 1 ) 2 (η 2 -η 1 ) 2 , Ỹ = Y = 1 - (η 2 -η) 2 (η 2 -η 1 ) 2 ,
where, without lost of generality, we have taken (only for this section!):

a Bi (t rec ) = 1, t Bi = t rec = 1, η = sinh η F , η B = η, (27)
and η 1 , η 2 denote the location of the comoving shell. Furthermore, we have set in (27) the scale of times to be the unity at the recombination era. Regularity conditions impose that R > 0, R ,η > 0. By performing, after fixing the time, a Taylor expansion near the boundaries of the thick shell, we have

E(t, η η 1 ) = 4 3t 2 + o(1), (28)
E(t, η η 2 ) = 3a ,t -1 a 2 + o(1) 2 t 2 + o(1), P η (t, η η 1 ) = s(η -η 1 ) 2 + o(1), P η (t, η η 2 ) = 2 η 2 (η 2 -η) a 2 + o(1) P ⊥ (t, η η 1 ) = sη 1 (η -η 1 ) + o(1), P ⊥ (t, η η 2 ) = - 2a ,t,t a + a 2 ,t a 2 - 1 t 2 + o(1) s = 4t -8 3 9η 2 1 (η 2 -η 1 ) 2 [t 4 3 (18 1 + η 2 2 -9) + 4aη 2 1 - -18η 2 1 t 2 a ,t,t -12η 2 1 ta ,t ],
where the symbol on the right hand side means that the expression is evaluated for t >> 1. From the equations (28), although the tangential pressure can have a negative value near η = η 2 , the energy conditions follow near the boundaries of the thick shell. This means that physically reasonable thick shells can be built with our matching conditions. It should be stressed again that the junction conditions ( 8)-( 11) only fix the behaviour on the boundaries ( 1) -(2). In the next three sections we apply the technology developed above to physically interesting situations.

Case with G = 0

First of all, we must integrate along the past null cone inward. Generally, we have there an equation given by

dT = - A(T, η) f (η) dη, ( 29
)
where t B = τ = t = T . Following Célérier (see [21,22]), we obtain for the redshift z

dT dz = - A(T (η), η) (1 + z)A ,T (T (η), η) . ( 30
)
We are interested in the determination of the distance-redshift formula for the dimming galaxies. Therefore, from the third of equations ( 18), we get

d L = (1 + z) 2 a(t) sinh η F . (31)
Obviously, we must solve equation [START_REF] Plebanski | An Introduction to General Relativity and Cosmology[END_REF] in the three regions (hyperbolic Friedmann, thick shell and flat Friedmann) up to an observer located at

z = 0. For z ∈ [z 2 , z], (A(T (η), η) = a(T ), f(η) = 1) we have 1 + z 1 + z 2 = a(T 2 ) a(T ) . ( 32
) For z ∈ [z 1 , z 2 ], we have (A(T (η), η) = R ,η ) ln 1 + z 2 1 + z 1 = - T 2 T 1 R ,η,T R ,η dT = γ(T 2 , T 1 ). ( 33
)
From ( 33) we get

1 + z 2 1 + z 1 = e γ , ( 34
)
where γ > 0 and physical plausibility requires that e γ is of the order of unity (≥ 1).

For the time flow, we read

t = t B = T = Ω 0 2H 0 (1 -Ω 0 ) 3 2 (sinh ξ -ξ) . (35)
Finally, thanks to [START_REF] Darmois | Les Equations de la Gravitation Einstenienne[END_REF], for z ≤ z 1 we obtain (A(T (η), η) = a B (T ), f(η) = 1)

1 + z 1 = a B (T 0 ) a B (T 1 ) = sinh ξ 0 -ξ 0 sinh ξ 1 -ξ 1 2 3 , ( 36
)
with the subscript "0" denoting the actual time at z = 0. By multiplying equations ( 32)-( 36), we get

1 + z = e γ a(T 2 ) a(T ) a B (T 0 ) a B (T 1 ) . ( 37
)
For η F along the past null cone we have

η F = ξ 0 -ξ , ξ ≤ ξ 0 . ( 38
)
As a result, since Ω(ξ) = 2 1+cosh ξ , equation ( 37) becomes

1 + z = 2F (1 + z 1 ) (1 -Ω 1 ) Ω 1 (cosh ξ -1) , (39)
where "1" refers to the time T 1 (or ξ 1 ) and

F = e γ (cosh ξ 2 -1) (cosh ξ 1 -1) . (40)
Physical plausibility requires that F be of order of unity. Thanks to (3) and ( 39), the formula (31) becomes

d L = Ω 0 (1 + z)(1 + z 1 ) H 0 (1 -Ω 0 ) 3 2 F (1 -Ω 1 ) Ω 1 sinh(ξ 0 -ξ). (41)
Equations ( 39) and ( 41) hold for z ≥ z 2 and obviously the junction conditions only imply the continuity of d L and not its analyticity when crossing the boundaries of the model. This obviously applies to any inhomogeneous model built by matching two or more metrics (as for example in [13,15,24]). Nevertheless, to make contact with the astrophysical data at intermediate redshifts, a central observer can formally expand expression (41) in a Taylor series in the range

z 1 << 1, z 2 -z 1 << 1 (Ω 0 Ω 1 , F 1
). To the first order in z we formally obtain

d L = z H obs + o(z), (42)
H obs = H 0 (1 -Ω 0 ) 3 2 Ω 1 F (1 -Ω 1 )(1 + z 1 )Ω 0 P , P = F (1 -Ω 1 )(1 + z ), = -Ω 1 [F (1 + z 1 ) -1] + F (1 + z 1 ).
Therefore, in our inhomogeneous universe, after writing the correct matching conditions, a central observer extrapolates an effective Hubble flow given by (42). It is worth noticing that, in the limit F = 1, Ω 1 → Ω 0 , z 1 = 0, = 1, in which the full space-time is composed only with the hyperbolic Friedmann metric, we have H obs → H 0 , a correct result. Furthermore, the inequality H obs = H 0 in a general inhomogeneous universe is compatible with the fact that in such space-times we have not a unique definition of an observed Hubble flow (see [42]): a direct way is to infer its value by a formal Taylor expansion (if this is possible) near the observer. The extrapolated central deceleration parameter q 0 is given by

q 0 = -H obs d 2 dz 2 (d L (z = 0)) + 1. (43)
Note that, from equation (36), we could express Ω 1 as a function of z 1 , ξ 0 , although this is not necessary for our purposes. The equation (43), thanks to (41), gives

q 0 = Ω 1 2 . ( 44
)
From equation ( 42) we must have > 0 (H obs > 0) and therefore q 0 ≥ 0 , for all times T and no "formal" acceleration is perceived by the central observer by considering the distance-redshift function. At early times (ξ 0) we have q → 1 2 and q → 0 + asymptotically (for ξ 1 → ∞).

Uniform Hubble flow

The case of a uniform Hubble flow has been studied in [13,15] in the context of the Buchert equations with backreaction ( [8]). In [13,15] the overdensity evolves asymptotically as an Einstein-de Sitter space-time, while the underdensity as a Milne universe. As a result, our model can be considered as representing the far future limit (t → ∞) of [13,15], where backreaction is asymptotically vanishing. With the uniform Hubble gauge we have

H = H B , α = 1, J(ξ) = dt dt B = 3 2 (1 + cosh ξ) (2 + cosh ξ) . ( 45
)
The calculations are similar to the ones of the last section. However, the central observer measures the redshift with respect to its proper time t B . As a result, along the past null cone we have

dt B = - a J(ξ) dη F → η F = ξ 0 -ξ 1 + z 1 + z 2 = J(ξ) J(ξ 2 ) a(ξ 2 ) a(ξ) . (46)
Instead of the equation ( 33) we read

1 + z 2 1 + z 1 = e γ J(ξ 2 ) J(ξ 1 ) (1 + z 2 ) (1 + z 1 ) , (47)
(1 + z 2 ) (1 + z 1 ) = - τ 2 τ 1 e G 2 R ,η R ,η e G 2 ,τ dτ, (48)
z 1 , z 2 being the redshifts measured by a comoving observer with time τ . The approximation ( ) in (47) has been given as an example and is valid when ξ 2 ξ 1 . It does not enter in the calculations of this section. The expression [START_REF] Alexander | [END_REF] becomes

d L = (1 + z) 2 a(t) J(ξ) sinh(ξ 0 -ξ). (49)
Concerning the relation between t B and t we get

t B = Ω 0 3H 0 (1 -Ω 0 ) 3 2 (cosh ξ -1) 3 2
(1 + cosh ξ)

1 2 . ( 50
)
Instead of the equation ( 36) we have

1 + z 1 = t B0 t B1 2 3 . ( 51
)
if the clock effects depicted in this paper (and in [13,15]) there exist in the real universe, the actual data at intermediate redshifts are in agreement with a non-uniform Hubble flow.

Conclusions

We built a model for the universe without dark energy, by means of an exact spherically symmetric solution taking into account the observed inhomogeneous universe. The main purpose of this paper is to show how the non-uniform time flow depicted in [13,15] can be obtained within an exact solution of Einstein's equations by imposing the correct matching conditions required by general relativity. In this sense, since the backreaction is absent in our model, our approach is different from Wiltshire's, where the backreaction is analyzed in a statistical ("Copernican") model within the Buchert formalism.

The model is composed of three regions, a central flat Friedmann metric, an hyperbolic Friedmann zone and eventually a bulk LTB hyperbolic metric, according to WMAP. Within our exact solution , it is shown that, after a "formal" Taylor expansion of the distance-redshift relation near the observer and by imposing the correct matching conditions, a uniform Hubble "gauge" (present in [13,15]) does not lead to an "apparent" acceleration as extrapolated from the redshift-distance relation. In a purely spherically symmetric universe, such an acceleration can only be obtained with a nonuniform Hubble flow. Furthermore, in our model we have a parameter (A in the paper) at our disposal that permits us to obtain a large amount of "apparent" acceleration which is consistent with the other parameters of the model (for example the thickness z 2 -z 1 << 1). Furthermore, in the presentation given in [13,15] the physical mechanism that can generate a non-uniform time flow is not yet clear. In fact it is always possible to build an inhomogeneous universe with a global cosmic time by means, for example, of LTB metrics. An exact formulation requires that the junction conditions are fulfilled only by means of a thick shell. We have shown a possible link between a non-uniform time flow and a radial energy flux present in the energy-momentum tensor of the thick shell. Hence, this "heat flow" term can give a possible physical explanation for the clock effects depicted in [13,15] (if they exist!). The introduction of thick shells can be useful to explore exact models obtained by glueing different Friedmann metrics. An anisotropic thick shell is certainly an unusual choice, but this alleviates the drawbacks of a whole universe filled with an exotic dark energy. It should be noticed that the radial flux energy vanishes on the boundaries of the thick shell. In fact the radial symmetry inhibits a "heat flow" between the flat central Friedmann metric and the "dimming" hyperbolic Friedmann one. A more realistic model could be obtained by relaxing the spherical symmetry and susbstituing the Friedmann metrics with more general ones, admitting a non-vanishing energy flux. Unfortunately, at the present day such metrics are not at our disposal. In any case, our calculations can suggest an improvement of the Wiltshire's model. In fact, Wiltshire's paper neglects the shear, but this encodes fundamental informations related to the variation of non-local gravitational energy, which is a fundamental ingredient in [13,15]. As it is well know, it is not a simple task to relate the shear to physical observable quantities (see [34]). To this purpose, Wiltshire's model could be amended by taking (< θ >) fi = 0, (< σ 2 >) fi = 0, (63)

(< θ >) s = 3H s , (< σ 2 >) s = 0, ( 64
) (< θ >) v > 0, (< σ 2 >) v = 0, (65)
where, following the notation of [13], "fi" stands for "finite-infinity" and "v" for "voids", H s is the averaged Hubble parameter for the thick shell. Hence, as suggested by the matching conditions, a third scale between "fi" and "v" with a non-vanishing shear is introducted: this is the scale at which variations in the flux energy are appreciable. Finally, note that the dark energy appears in two "phase transitions" for the universe: the formation of the big structures and the end of it. Hence, since cosmic strings and superstrings in the context of the M-theory are supposed to have acted during the inflation epoch to give (in principle) observable effects a later times, a link between them and the thick structures depicted in this paper can be suggested (see [43]).

After defining e γ = F (cosh ξ 1 -1) (cosh ξ 2 -1)

(2 + cosh ξ 1 ) (2 + cosh ξ 2 )

(1 + cosh ξ 2 ) (1 + cosh ξ 1 ) ,

and with the same technique of the last section, we obtain cosh ξ = -

Performing a formal Taylor expansion of (55) at z = 0, we again get an effective observed H obs , and by means of equation (43) we can obtain the central deceleration parameter. In any case, we always have q = 1 2 at early times. Furthermore, the extrapolated parameter q 0 remains positive and approaches zero as follows:

As a result, in presence of a uniform Hubble flow q 0 goes to zero more rapidly than in the case G = 0 (see equation ( 44)), albeit always from positive values. In practice, we recover the results of [14], but imposing the correct matching conditions.

The general case

In the general case H = α H B . Hence, the relation between t B and t becomes

(1 + cosh ξ)

For the lapse factor J(ξ), we obtain

To explore the case with a non-uniform Hubble flow with G = 0 we can take

The case with A = 1 has been studied in the section above. The calculations are similar to the ones of the section 6 and after posing

we get

The expressions for H obs and q 0 are rather cumbersome. However, some general remarks can be done on the behaviour of the extrapolated central deceleration parameter q 0 at different values of the parameter A. First of all, ∀A ∈ (0, ∞), q 0 (ξ = 0) = 1 2 . Furthermore, ∀A ∈ [1, ∞), the parameter q 0 is always positive and asymptotically q 0 (ξ → ∞) → 0 + . Conversely, ∀A ∈ (0, 1), the parameter q 0 becomes negative at some value of B, and after an absolute minimum, reaches 0 -asymptotically but from negative values. As an example, for A = 1 2 , q 0 = 0 for B 0 5.3 and for B 10 we have q 0min -0.075. For A = 1 3 , q 0 = 0 for B 0 4.2 with q 0min -0.16 at B 8. For A = 1 5 , q 0 = 0 for B 0 3.6 with q 0min -0.31 at B 6. For A = 1 9 , q 0 = 0 for B 0 3.2 and q 0min -0.51 at B 5. In any case, ∀A ∈ (0, 1) it is always possible to have, from the equation (62), reasonable values for F ( 1, with z 2 -z 1 << 1) and Ω 0 compatible with an apparent acceleration at some later time calculated by means of the equation [START_REF] Israel | [END_REF], provided that B > B 0 . The inequality B > B 0 imposes a constraint on Ω 1 Ω 0 . As an example, for F = 1.1, z 1 = 0.01 and A = 1 2 we have an accelerated universe if and only if Ω 1 Ω 0 < 0.24, while for A = 1 2 and F (1 + z 1 ) = 1, z 1 << 1, we have Ω 1 Ω 0 < 0.22. Further, for A = 1 9 , F = 1.1, z 1 = 0.01 we have formal acceleration when Ω 1 Ω 0 < 0.25. It is also possible to mimic for A ≤ 1 9 a value for q 0 compatible with the actual observations. Furthermore, note that the models with A ∈ (0, 1) represent the case with α(ξ) < 1., i.e. H B > H(this can be see by noticing that the equation (57) has, in the limit ξ >> 1, the tracker solution α = A). As a result, the clock effects depicted in this paper can mimic a model with a large underdensity surrounded by an overdensity (see [24]). Concluding,