Aurélien Bataille
email: aurelbataille@gmail.com

Pierre Galichon
email: pierre.galichon@aphp.fr

Morgane Wetzstein
email: morganewetzstein@yahoo.fr

David Legouis
email: davidlegouis@gmail.com

Sophie Va Ndermeersch

Eric Rondeau
email: eric.rondeau@aphp.fr

Alexandre Hertig
email: alexandre.hertig@aphp.fr

Affiliations

Sophie Vandermeersch
email: sophie.vandermeersch@upmc.fr

Prof Alexandre Hertig

Evaluation of the ability of bone marrow derived cells to engraft the kidney and promote renal tubular regeneration in mice following exposure to cisplatin Authors

Keywords: Acute Kidney Injury, Cisplatin, Bone Marrow Cells, Bone Marrow Transplantation, Stem cells

It has been suggested that bone marrow derived stem cells have the ability to engraft the kidney and improve the outcome of severe acute kidney injury in mice exposed to high doses of cisplatin, providing hope for cancer patients in whom irreversible renal damage occasionally occurs following the use of this highly effective anti-tumor drug. We tested the therapeutic potential of bone marrow derived cells injected during the acute phase (day 3 after cisplatin administration) of experimentally-induced acute kidney injury in C57Bl6/J mice, characterized by massive tubular necrosis, apoptosis, and a low proliferation capacity. We failed to show any benefit of bone marrow derived cells versus a regular homogenate of intact renal cells, or normal saline. Using cell tracers and flow cytometry, we demonstrated that bone marrow derived cells did indeed home to the bone marrow of the recipients but failed to settle in the kidney. Conversely, renal cells homed to injured kidneys. However, neither cell therapy protected the animals against cisplatin-induced death. We therefore question the short-term efficacy of bone marrow derived cells used to repair established injuries of the tubular epithelium.

Introduction

Platinum-based chemotherapy is widely used to treat solid cancers, such as testicular, bladder, cervical, and non-small cell lung cancers. [START_REF] Kelland | The resurgence of platinum-based cancer chemotherapy[END_REF] Cisplatin, the neutral cis-isomer of (PtII(NH 3 ) 2 Cl 2) , was approved by the USA Food and Drug Administration in 1978, and is still widely used today. Its antitumor efficacy involves covalent binding with the purine bases of DNA (resulting in what are known as platinum-DNA adducts); this in turn activates a DNA repair process leading to apoptosis and eventually cell death [START_REF] Kelland | The resurgence of platinum-based cancer chemotherapy[END_REF] . Platinum is extensively bound to proteins, and so few free cisplatin molecules are filtered through the glomerular barrier; in addition, the tubules do not reabsorb luminal cisplatin. Nevertheless, cisplatin may still be taken up from the basolateral side of the tubular cells by organic cation transporters (OCT). 2 OCT2 in particular is abundantly expressed by the S3 segment of the proximal tubules, which is located at the junction between the inner cortex and outer medulla. There, platination of DNA induces tubular cell death and may lead to acute kidney injury (AKI). Nephrotoxicity is one of the main safety issues regarding the use of cisplatin, and has led to an extensive search for less toxic analogues that retain its antitumor efficacy.

For the past decade, ischemia reperfusion injury (IRI) has been used worldwide as an experimental model of AKI. Recently, sophisticated genetically-engineered mice have been used to help to elucidate how injured tubular epithelium is repaired after IRI. It turns out that the kidney has no interstitial stem cells, and consequently the repair of its tubular epithelium depends entirely on the presence of epithelial cells that have survived the injury. [START_REF] Bonventre | Cellular pathophysiology of ischemic acute kidney injury[END_REF][START_REF] Humphreys | Intrinsic epithelial cells repair the kidney after injury[END_REF][START_REF] Humphreys | Repair of injured proximal tubule does not involve specialized progenitors[END_REF] It is interesting to note that unlike ischemic AKIwhich has similar effects on the tubules in the outer cortex, but typically recovers in two to three weekscisplatin-induced AKI has a very variable prognosis, and occasionally leads to a permanent loss of kidney function. [START_REF] Thadhani | Acute renal failure[END_REF] This suggests that the extent of the DNA damage that has occurred makes regeneration impossible or ineffective.

In cancer patients, kidney transplantation is hardly an option: immunosuppressors would facilitate tumor growth, and the shortage of organs for transplantation makes cancer-free patients a priority.

Repeated dialysis impairs quality of life, and survival is also compromised since many chemotherapies are contraindicated by persistent kidney failure. This makes the regeneration of native kidneys a question of life and death.

In the present study, we investigated the therapeutic interest of bone-marrow-derived stem cells (BMDC) during cisplatin-induced AKI. Our primary objective was to investigate the life-sparring benefit of BMDC injection at the acute phase of injury on the basis of three observations. First, genetically-intact, unsorted BMDC have been shown to repair genetically-induced glomerular diseases in mice by supplying the kidney with genetically intact cells, [START_REF] Prodromidi | Bone marrow-derived cells contribute to podocyte regeneration and amelioration of renal disease in a mouse model of Alport syndrome[END_REF][START_REF] Sugimoto | Bone-marrow-derived stem cells repair basement membrane collagen defects and reverse genetic kidney disease[END_REF] although this has been the subject of heated controversy. [START_REF] Gross | Stem cell therapy for Alport syndrome: the hope beyond the hype[END_REF] Second, in mice BMDC were also found to prevent or reduce cisplatin-induced AKI through a paracrine action. [START_REF] Imberti | Insulin-like growth factor-1 sustains stem cell mediated renal repair[END_REF][START_REF] Morigi | Mesenchymal stem cells are renotropic, helping to repair the kidney and improve function in acute renal failure[END_REF][START_REF] Morigi | Life-sparing effect of human cord blood-mesenchymal stem cells in experimental acute kidney injury[END_REF][START_REF] Morigi | Human bone marrow mesenchymal stem cells accelerate recovery of acute renal injury and prolong survival in mice[END_REF] Third, in the clinic, stem cells are regularly harvested from cancer patients before lethal chemotherapy, to allow the repopulation of bone marrow by autologous cells and promote patient survival. We therefore reasoned that the administration of genetically-intact BMDC (i.e. in BMDC that had not been exposed to cisplatin) would be one way to regenerate the tubular epithelium following massive damage by platinum adducts. It was crucial to confirm their ability to home to the kidney and to test their efficacy during the acute phase of AKI, in order to parallel the pathology timeline observed in human patients.

Materials and Methods

Ethics Statement

Animal care and the experimental procedures were approved by an independent Ethics committee for animal experimentation (Comité National de Réflexion Éthique sur l'Expérimentation Animale, numéro 5) under the number Ce5/2012/004.

Animals

Eight-week-old female wild-type mice (C57BL/6J background, from 16 to 21 g of total body weight) obtained from Jackson Laboratory ® and transgenic mice ubiquitously expressing green fluorescent protein (GFP) under the control of the promoter of β-actin [START_REF] Okabe | Green mice'as a source of ubiquitous green cells[END_REF] (C57BL/6-Tg (CAG-EGFP) C14-Y01-M131Osb) were maintained under standard conditions at the animal specific pathogen free facility located in the Research Building of Tenon Hospital; the mice were placed in 1284L ventilated boxes, with a 12/12 photoperiod, at a 20-24°C temperature and with 55 +/-10% relative humidity. Food and water were available ad libitum. Experimentation begun 1 week after animal arrival.

Cisplatin

Cisplatin (MYLAN®, 1 mg/ml) was further diluted in phosphate buffer saline (PBS) and administered as a single intraperitoneal injection containing a dose of cisplatin adjusted to allow for the bodyweight of the animal (doses of up to 20 mg/kg bodyweight were used to induce AKI, with an injected volume of 25 µl/g bodyweight).

Injection of the bone-marrow-derived cells

Briefly, the source animals for BMDC (whether wild type or GFP-transgenic) were sacrificed by cervical dislocation. Femurs, tibias, and humeri were isolated. After section of the epiphyses, a diaphyseal flush with PBS was performed. A cell suspension was obtained after passage through 35-micron filters. After ammonium lysis of the red blood cells using a lysis buffer and potassium chloride (ACK), a flow cytometric cell count was performed. Three days after the injection of cisplatin, each mouse received a retro-orbital injection of 1 million BMDC diluted in 200 µl of sterile PBS, under isoflurane anesthesia. Using flow cytometry, we found that 51% [49; 59] of this global population were CD45 negative (Figure 1); in comparison from 2 to 5.10 5 mesenchymal stem cells had been used to rescue mice from cisplatin induced AKI in previous studies. [START_REF] Imberti | Insulin-like growth factor-1 sustains stem cell mediated renal repair[END_REF][START_REF] Morigi | Mesenchymal stem cells are renotropic, helping to repair the kidney and improve function in acute renal failure[END_REF][START_REF] Morigi | Life-sparing effect of human cord blood-mesenchymal stem cells in experimental acute kidney injury[END_REF][START_REF] Morigi | Human bone marrow mesenchymal stem cells accelerate recovery of acute renal injury and prolong survival in mice[END_REF] It should be noted that the time between the flush and the orbital injection did not exceed an hour and a half. The BMDC were traced by detecting fluorescent GFP if the donor was GFP-transgenic, or detecting carboxyfluorescein succinimidyl ester (CFSE), after adding CFSE ex vivo (according to the Manufacturer's instructions) when wild-type BMDC were being used.

Two control groups were added: one was injected at the same timepoint with the same volume (200 µl) of isotonic saline (NaCl 0.9%), and the other, injected with a homogenate of renal cells from similarly syngeneic mice that had not been exposed to cisplatin (thus genetically intact but a priori devoid of stem cell properties), both also under isoflurane anesthesia (Figure 2). To this end, after dermal ethanol asepsis, both kidneys were extracted, decapsulated, and stored in PBS under sterile conditions. A kidney cell suspension was obtained by passing the kidneys through a cell dissociator (04.1 Spleen protocol, gentleMACS ™, Miltenyi Biotec ® ), and filtering with a 35-micron filter. Here too, 200 µl of a solution containing 1 million cells was injected intravenously. The animals were syngeneic, and had not been subjected to irradiation before the injection of BMDC or renal cells.

Mice were randomly assessed by blocks of 5 animals for orbital injection of BMDC, renal cells or normal saline and the person in charge of the injection was blind from either group. Renal failure per se is not painful : animals presented activity slowdown and signs of dehydration but did not require analgesic support, as approved by the Ethics committee for animal experimentation. To evaluate the primary outcome, animals were daily checked for spontaneous death as a direct result of the intervention. Surviving animals were sacrificed on day 10 post AKI, for blood collection under ketamine/xylazine anesthesia, and kidney and bone marrow retrieval after cervical dislocation.

Histological analysis

For light microscopy, the renal tissue was fixed in alcohol-formalin-acetic acid, embedded in paraffin, and cut into 4-µm sections. The slides were stained with Masson's trichrome, periodic acid-Schiff and haematoxylin-eosin to assess tubular injury. Six random photographs were taken of each slide in non-overlapping cortical areas, at x400 magnification, using an Olympus© BX 51/DP70 microscope. The percentage of injured tubules was then scored semi-quantitatively (0: 0%, 1 < 10%, 2: 10-25%, 3: 26-75%, 4 > 76%), according to the presence of tubular dilation, the loss of the brush border, the presence of intra-luminal casts, and the loss of the epithelial border. For mice that survived for 10 days after the rescue injection of cells, a quantitative score was also used to look for subtle improvements: an 8x8 grid was superimposed over a representative picture of the renal cortex of each mouse. Fibrosis was quantified by Sirius Red staining under polarization contrast microscopy. In addition, immunohistochemistry was used to detect proliferating cells using the Ki-67 antibody from Abcam ® (dilution 1/10,000) revealed by a rabbit secondary antibody from Histofine ® and the DAKO ® AEC kit, and apoptotic cells were revealed using the TUNEL (TdTmediated X-dUTP nick end labeling) kit from Roche ® according to the Manufacturer's instructions.

Flow-cytometer analysis

The MACSQuant ® Analyzer (Miltenyi Biotec) was used. Flow cytometry was carried out at a distance from the sample. The kidneys were passed through a cell dissociator (04.1 Spleen protocol, gentleMACS ™, Miltenyi Biotec) and then filtered (35 microns). The bone marrow was simply filtered (35 microns). The cells were then stored at -20°C in a solution of PBS containing dimethyl sulfoxide (10%) and fetal calf serum (15%). EGFP fluorescence was searched for in the FITC channel (excitation by blue laser at 488 nm and detection through a 525/550 nm filter). Leukocytes were detected by an anti-CD45-VioBlue (Miltenyi Biotec). To note, red blood cells from EGFP transgenic mice are not expected to express EGFP. [START_REF] Okabe | Green mice'as a source of ubiquitous green cells[END_REF] For each marker, one million cells in 100 µL were incubated for 30 minutes in the presence of the antibody under saturating conditions (5μL), and then washed. Analysis was performed using FlowJo analysis software (Treestar Inc., version X.0.7). The analytic strategy involved including cell populations that were within the acceptable range of size and structure. Doublets were excluded by gating singlets after plotting the height vs the area of the forward scatter signal. Self-fluorescent events were excluded using a gating strategy on the VioGreen channel (excitation by a violet laser at 405 nm and detection through 525/550 nm filters) in order to optimize the specificity of GFP detection. [START_REF] Legouis | Ex vivo analysis of renal proximal tubular cells[END_REF]

Creatinin and urea analysis

Plasmatic creatinin and urea was measured using a Konelab automater (Thermo Fisher Scientific, Waltham, MA) with an enzymatic method (Konelab automater) and expressed in micro and millimoles per liter, rescpectively.

Real time PCR

RNA or genomic DNA (gDNA) were extracted from kidneys using TRI Reagent (Euromedex, Mundolsheim, France). After digestion with DNase 1, the RNA was reverse transcribed with the Maxima RT Kit (Fermentas). The quality of cDNA and gDNA was assessed by the ratio of the absorbances at 260 and 280 nm. Both were then amplified by PCR in a LightCycler 480 (Roche Diagnostics, Meylan, France) with SYBR Green (LightCycler 480 SYBR Green I Master; Roche Diagnostics) and specific primers for EGFP, IGF-1, β-glucuronidase (Gusb) and Actin b1 (Actb1) used as housekeeping genes (Table 1). EGFP primers were chosen on the basis of the Jackson Laboratory® genotyping procedure; those for Insulin Like Growth Factor-1 (IGF-1) and housekeeping genes were designed using the Universal Probe Library Roche website for operating under the following conditions: 95°C for 5 min, 45 cycles at 95°C for 20 s, 60°C for 15 s, and 72°C for 15 s (except for Actb1 PCR with gDNA: 30 s). Tissues from C57BL/6-Tg (CAG-EGFP) C14-Y01-M131Osb mice were used as positive controls.

Statistical analysis

Data are given as medians (with 25th and 75th percentiles) for the quantitative variables.

Comparisons were made using a Wilcoxon test, where appropriate. Survival was studied by Kaplan-Meier curves and log-rank tests were performed to compare groups. For comparison of quantitative variables between groups, a Kruskal-Wallis test was performed. All tests were two-sided and at a 0.05 significance level. Analyses were performed using the R.2.14.1 statistical package (R Development Core Team (2011). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0, URL http://www.Rproject.org/).

Results

Cisplatin induced a dose-dependent mortality in C57Bl/6J mice (Figure 3A). Three days after injection of the cisplatin, renal function was severely impaired (Figure 3B), due to extensive tubular necrosis (Figure 3C & 3D). Massive apoptosis was observed (Figure 3E), together with a low ability of the epithelium to proliferate (Figure 3F). A single injection of 17.5 mg/kg of cisplatin was finally chosen to test the ability of BMDC to rescue the mice at day 3 (i.e. during the acute phase of tubular injury).

Regarding the capacity of BMDC to prevent animal death after a lethal dose of cisplatin, 18/26, 13/26 and 16/25 animal died in the BMDC, renal cells and normal saline group, respectively. Survival curves show that both BMDC and renal cells failed to provide any significant benefit over saline (log-rank test p=0.369) (Figure 4). The kidneys of mice that survived for 10 days were all found to have similar tubular injury with some degree of regeneration (whether assessed by a semiquantitative injury score: median value  SEM for BMDC 30.5; renal cells: 10.3; saline 10.5, p=NS; or by a quantitative injury score: mean values of 25.28.0%, 8.02.7%, and 9.86.5%, respectively, p=NS) (Figure 5). No difference in renal functional parameters were found between groups (Figure 6) (p=0.949 for plasmatic creatinin and p=0.368 for plasmatic urea). No difference in interstitial fibrosis was found between groups (Figure 5) The therapeutic groups displayed similar apoptosis (massive in each group), and similar capacities to proliferate (almost absent); no increase in IGF-1 transcripts was observed in mice injected with BMDC (p=0.867) (Figure 7). No major adverse event modified the experimental protocol.

Considering the absence of therapeutic effect, we reasoned that either the cells failed to home to the kidney or that cells were ineffective in rescuing AKI despite effective kidney engraftment. Cell homing was therefore assessed at day 10 among the surviving mice in blood and bone marrow, and in the kidney using flow-cytometry (Table 2). In the blood, we detected positive cytometric events both in the BDMC and the renal cells groups, where the number of positive events exceeded those of the control group in all individuals.

Regarding the bone marrow, a significantly higher proportion of positive events were detected in the BMDC group compared to the renal cells group (p=0.006). The renal cells group showed a number of positive events equivalent to the negative control group. This result suggests a significant engraftment of BMDC in the recipients' marrow and in contrast the absence of renal cells homing to the marrow. Analyzing the results obtained from the cell suspension of dissociated kidneys, there was a significant disparity in the results. A positive signal was observed in one individual from the control group, perhaps due to the constitutive autofluorescence of renal cells. One individual from the renal cells group showed a high proportion of positive cells (Figure 8). The overall comparison of BMDC and RC groups, however, showed a significantly higher proportion of positive events in the renal cells group compared to the BMDC group (p = 0.012).

These results are to be understood taking into account differences in the analysis and gating used for cytometry. Indeed, kidney cells emit significant autofluorescence which requires a specific analysis. However, we failed to detect any BMDC by either direct immunofluorescence of kidneys or by PCR amplification of the EGFP transcript, whether we used RNA or gDNA extracted from kidneys (whereas the transgene was clearly amplified using RNA and gDNA templates from transgenic EGFP+ tissues used as positive controls).

Discussion

Our study found no survival benefit following the use of genetically intact BMDC during the acute phase of cisplatin-induced AKI in mice, even though on four occasions an independent group has reported the contrary despite using similar amounts of stem cells, appropriate controls and a similarly severe model of AKI. [START_REF] Imberti | Insulin-like growth factor-1 sustains stem cell mediated renal repair[END_REF][START_REF] Morigi | Mesenchymal stem cells are renotropic, helping to repair the kidney and improve function in acute renal failure[END_REF][START_REF] Morigi | Life-sparing effect of human cord blood-mesenchymal stem cells in experimental acute kidney injury[END_REF][START_REF] Morigi | Human bone marrow mesenchymal stem cells accelerate recovery of acute renal injury and prolong survival in mice[END_REF] More precisely, mesenchymal stem cells (MSC) injected at day 1 were repeatedly found to protect mice against cisplatin-induced AKI (as opposed to hematopoietic stem cells, which had no therapeutic impact, [START_REF] Morigi | Mesenchymal stem cells are renotropic, helping to repair the kidney and improve function in acute renal failure[END_REF] whether of mouse [START_REF] Imberti | Insulin-like growth factor-1 sustains stem cell mediated renal repair[END_REF][START_REF] Morigi | Mesenchymal stem cells are renotropic, helping to repair the kidney and improve function in acute renal failure[END_REF] or human originthus both bone marrow [START_REF] Morigi | Human bone marrow mesenchymal stem cells accelerate recovery of acute renal injury and prolong survival in mice[END_REF] and cord blood [START_REF] Morigi | Life-sparing effect of human cord blood-mesenchymal stem cells in experimental acute kidney injury[END_REF] human MSC gave successful outcomes.

Our experimental design was different, though: we injected BMDC during the acute phase of the disease (day 3), which is the context that confronts physicians at the bedside when a cancer patient develops a severe AKI following platinum-based chemotherapy. The animal model of cisplatininduced AKI does not allow us to find out whether any benefit would be seen later on as dialysis is not an option in mice. The bulk of the mice did however survive for three days after the rescue cell injection, which was long enough for us to observe a difference in renal function, [START_REF] Morigi | Mesenchymal stem cells are renotropic, helping to repair the kidney and improve function in acute renal failure[END_REF] and even survival [START_REF] Morigi | Life-sparing effect of human cord blood-mesenchymal stem cells in experimental acute kidney injury[END_REF] in the experiments performed by Morigi and coworkers.

Apart from this difference, another difference should be pointed out. Morigi et al. used fluorescence technology (detection of the Y chromosome, or of a PKH-26 label) to trace stem cells and showed images of MSC localized in peritubular areas (and in a few cases inside tubules), in proportions from 0.5 to 3.4 per 10 5 renal cells. [START_REF] Imberti | Insulin-like growth factor-1 sustains stem cell mediated renal repair[END_REF][START_REF] Morigi | Life-sparing effect of human cord blood-mesenchymal stem cells in experimental acute kidney injury[END_REF] We failed to see any incorporation or even homing of BMDC in injured kidneys, even though we used highly sensitive techniques (flow cytometry and qRT-PCR) as well as two different fluorescent markers (GFP and CFSE), and of course a syngeneic background between donor cells and recipients.

With respect to the question of how MSC exerted their protective effect, it was initially argued that they might rapidly regenerate a damaged tubule through differentiation, [START_REF] Morigi | Mesenchymal stem cells are renotropic, helping to repair the kidney and improve function in acute renal failure[END_REF] yet very low levels of intratubular incorporation and tubular differentiation were actually found. MSC seem to act mainly through their trophic effect, being a source of renotropic growth factors such as IGF-11. [START_REF] Imberti | Insulin-like growth factor-1 sustains stem cell mediated renal repair[END_REF][START_REF] Morigi | Life-sparing effect of human cord blood-mesenchymal stem cells in experimental acute kidney injury[END_REF][START_REF] Morigi | Human bone marrow mesenchymal stem cells accelerate recovery of acute renal injury and prolong survival in mice[END_REF] The timepoint at which stem cells are injected to repair a tissue is undoubtedly critical. Under the experimental conditions that we used, BMDC did not affect survival at all, though, and we wonder to which extent this trophic effect is clinically relevant. We do not think that the severity of the model was an issue here, since we had a mean of 40% survival in each study group, while survival was null in the control group of the studies we are referring to.

A limitation of our study is that we used unsorted BMDC, and therefore a mixture of hematopoietic cells, mesenchymal stem cells, as well as lymphoid and myeloid progenitors. Although we are not aware that any of these components has any negative effect, we cannot exclude the possibility that one lineage could have canceled out the potential benefits afforded by MSC. However this seems unlikely, because two independent teams have reported that unsorted BMDC display a protective role in the mouse model of Alport-like glomerular disease, [START_REF] Prodromidi | Bone marrow-derived cells contribute to podocyte regeneration and amelioration of renal disease in a mouse model of Alport syndrome[END_REF][START_REF] Sugimoto | Bone-marrow-derived stem cells repair basement membrane collagen defects and reverse genetic kidney disease[END_REF] although once again, these data have given rise to controversy. [START_REF] Gross | Stem cell therapy for Alport syndrome: the hope beyond the hype[END_REF] In the context of organ injury, there is no evidence for the circulation of MSC in humans. [START_REF] Hoogduijn | No evidence for circulating mesenchymal stem cells in patients with organ injury[END_REF] Injection seems to be necessary to provide a protective effect. Our study questions the homing capacity of cells as we did not find BMDC tagged cells in the injured kidney. Lastly, it is noteworthy that EGFP+ renal cells were found to home in significant proportions to the injured kidneys and that this therapeutic group had the lowest histological injury scores. This finding supports the concept of kidney self-repair. Nevertheless, with respect to survival, which was our main outcome criteria, renal cells did not provide any significant protection.

In conclusion, our negative findings somewhat temper the hopes centered on cell therapy as a promising therapeutic option for cancer patients suffering from irreversible cisplatin-induced AKI.

They also reinforce the concept that the epithelium itself is the major source of tubular regeneration in the context of severe tubular injury. Will stem cells fulfill their promise for patients in whom the renal epithelial reservoir has been exhaustively damaged by a toxic drug? Clinical studies are in progress which we are justified in hoping will resolve the question (Clinical Trials NCT01275612). No difference in renal functional parameters were found between groups at day 10 in surviving animals (p=0.949 for plasmatic creatinin and p=0.368 for plasmatic urea).

Figure 1 .

 1 Figure 1. Flow cytometry analysis of bone-marrow, with a CD45 PerCP staining.

Figure 2 .

 2 Figure 2. Experimental protocol.To rescue mice from cisplatin-induced acute kidney injury, 10 6 BMDC were injected on day 3 post cisplatin injection. Two control groups were used: one received 10 6 renal cells and the other

Figure 3 .

 3 Figure 3. Lethality and severity of AKI following cisplatin injection.

Figure 4 .

 4 Figure 4. Kaplan-Meier curve of mouse survival after cell rescue therapy. Injection of 10 6 BMDC, 10 6 renal cells or of an equal volume of normal saline was performed

Figure 5 .

 5 Figure 5. Histology of kidneys from mice which survived for 10 days after the rescue cell injection,

Figure 6 .

 6 Figure 6. Renal functional parameters in surviving animals.

Figure 7 .

 7 Figure 7. IGF1 real-time PCR.

Figure 8 .

 8 Figure 8. Flow cytometry analysis of renal cells homing to injured kidneys.

F i g u r e 1 F i g u r e 2 F i g u r e 3 F i g u r e 4 F i g u r e 5

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Figure 7

 7 Figure 7

TABLE 1 .

 1 Primers used for qRT-PCR (mRNA strand sequences).

		forward	reverse
	EGFP	AAGTTCATCTGCACCACCG	TCCTTGAAGAAGATGGTGCG
	IGF-1	CTGCTTGCTCACCTTCACC	AGCCTGTGGGCTTGTTGA
	Gusb	CTCTGGTGGCCTTACCTGAT	CAGTTGTTGTCACCTTCACCTC
	Actb1 CTAAGGCCAACCGTGAAAAG	ACCAGAGGCATACAGGGACA

TABLE 2 .

 2 Detection of labeled cells in recipient surviving mice by flow cytometry. Results are expressed as medians [Q1; Q3]. (*: BMDC versus Renal Cells)

		Negative Control	BMDC	Renal Cells	p value*
	Blood	0.079 %	0.33 %	0.27 %	0.527
		[0.067 ; 0.142]	[0.27 ;0.42]	[0.24 ;0.375]
	Bone Marrow	0.015 %	0.049 %	0.01 %	0.006
		[0.015 ; 0.017]	[0.035 ;0.057]	[0.01 ;0.01]
	Kidney	0.110 %	0.041 %	0.220 %	0.012
		[0.080 ; 0.200]	[0.035 ; 0.061]	[0.205 ;0.330]

Acknowledgments

The authors thank Prof. Masaru Okabe for providing the C57BL/6-Tg (CAG-EGFP) C14-Y01-M131Osb strain, Prof. Selim Aractingi and Tatiana Ledent (INSERM UMRS 938) for their help in obtaining the GFP animals, Dr Laurent Mesnard for his excellent technical skills in animal handling, and Ms Caroline Martin and her team for animal care.

Right Running Head Bone marrow derived cells after cisplatin

Funding

This study was funded by a grant from the Fondation de l'Avenir, Paris, France (Project ET0-570), and one from Region Ile de France (CORDDIM). AB and MW are the recipients of a fellowship "Année recherche" from the Agence Régionale de Santé (from Ile de France and Amiens, France, respectively). AH is the recipient of an Interface contract with the French National Institute for Health and Medical Research (INSERM).

Declaration of Interest

The authors report no conflicts of interest. The authors alone are responsible for the content and writing of the paper.


Oldřich Ševeček
email: sevecek@fme.vutbr.cz

Michal Kotoul
email: kotoul@fme.vutbr.cz

Dominique Leguillon
email: dominique.leguillon@upmc.fr

Eric Martin
email: martin@lcts.u-bordeaux1.fr

Raul Bermejo
email: raul.bermejo@unileoben.ac.at

Modelling of edge crack formation and propagation in ceramic laminates using the stress-energy coupled criterion

Keywords: Edge crack, residual stresses, ceramic laminate, FE analysis, coupled criterion

The high compressive stresses in ceramic laminates utilized to enhance their fracture resistance may lead to the formation of edge cracks at the surface of the compressive layers. In this work, a 2D parametric numerical model is developed to assess the effect of residual stress and thickness of the compressive layers on the edge crack formation, by using a coupled stress-energy criterion. The results predict the existence of a lower bound, below which no edge crack occurs (i.e. obtaining crack-free laminates), and an upper bound, beyond which onset of the edge crack would lead to the complete delamination of the compressive layer.

Energy release rate as a function of edge crack length G inc (a) Incremental energy release rate as a function of edge crack length H Height of the specimen (characteristic size of the specimen) K Ic

Fracture toughness L Specimen length t 1, t (ATZ ) Thickness of the tensile layer t 2, t (AMZ ) Thickness of the compressive layer

Introduction

Ceramics have been used for many decades as structural components but, due to their inherent brittleness, they have mainly been utilized under compressive loading conditions. Nowadays, most of the new engineering designs need to withstand tensile stresses which imply potential limitations for ceramics due to their low fracture toughness and the sensitivity of ceramic material strength to the presence of defects [START_REF] Griffith | The Phenomena of Rupture and Flow in Solids Philosophical Transactions of the[END_REF][START_REF] Kingery | Introduction to ceramics[END_REF][START_REF] Danzer | A general strength distribution function for brittle materials[END_REF]. The brittle fracture of glasses and ceramics is a consequence of the material defects located either within the bulk or at the surface, resulting from the processing and/or machining procedures [START_REF] Morrell | Fractography of Brittle Materials[END_REF][START_REF] Danzer | Mechanical Failure of Advanced Ceramics: The Value of Fractography Key[END_REF]. Under external applied stress, the stress concentration associated with such defects is the common source of failure of ceramic components. If each defect is considered as a crack or a potential source for crack initiation, then the size and type of these defects obviously determine the mechanical strength of the material [START_REF] Lawn | Fracture of brittle solids[END_REF].

The distribution of defects of different sizes within a ceramic component yields a statistically variable strength which can be described by the Weibull theory [START_REF] Munz | Ceramics. Mechanical Properties, Failure Behaviour, Materials Selection[END_REF][START_REF] Danzer | Fracture of advanced ceramics[END_REF]. As a consequence of such a behaviour, there remains a (small) probability of failure even at very small applied loads (i.e., no lower threshold for strength). Since flaws are intrinsic to processing and in most cases unavoidable, the mechanical reliability of ceramic components is associated with such a flaw distribution. In order to reduce both the defect population and the defect size, many studies have been devoted in the past to improve ceramic processing [START_REF] Lange | Powder processing science and technology for increasing reliability[END_REF]. Another approach to increase strength has been to introduce compressive residual stresses at the surface. A successful example can be found in strengthened glass [START_REF] Green | Crack arrest and multiple cracking in glass through the use of designed residual stress profiles[END_REF] and more recently Gorilla® glass [START_REF] Qi | Design and preparation of high-performance alumina functional graded self-lubricated ceramic composites[END_REF]. However, a significant reduction of strength variability cannot be achieved with these approaches. In an attempt to reduce the level of uncertainty in mechanical strength and to overcome the lack of toughness of structural and functional ceramics, newer approaches have been developed in which knowledge about the energy release mechanisms has resulted in the creation of "flaw tolerant" materials (i.e. reducing strength variability), with improved fracture toughness [START_REF] Lange | Powder processing science and technology for increasing reliability[END_REF][START_REF] Green | Crack arrest and multiple cracking in glass through the use of designed residual stress profiles[END_REF][START_REF] Clegg | A Simple Way to Make Tough Ceramics[END_REF][START_REF] Marshall | Enhanced fracture toughness in layered microcomposites of Ce-ZrO 2 and Al 2 O 3[END_REF][START_REF] Chartier | Laminar ceramic composites[END_REF][START_REF] Cutler | Mechanical Behavior of Several Hybrid Ceramic-Matrix-Composite Laminates[END_REF][START_REF] Clegg | Design of Ceramic Laminates for Strucutral Applications[END_REF][START_REF] Rao | Laminar ceramics that exhibit a threshold strength[END_REF][START_REF] Mcmeeking | Optimal Threshold strength of laminar ceramics[END_REF][START_REF] Moon | R-Curve Behavior in Alumina-Zirconia Composites with Repeating Graded Layers[END_REF][START_REF] Orlovskaya | Robust design and manufacturing of ceramic laminates with controlled thermal residual stresses for enhanced toughness[END_REF][START_REF] Sglavo | Tailored Residual Stresses in High Reliability Alumina-Mullite Ceramic Laminates[END_REF][START_REF] Bueno | Layered materials with high strength and flaw tolerance based on alumina and aluminium titanate[END_REF][START_REF] Bermejo | Threshold strength evaluation on an Al 2 O 3 -ZrO 2 multilayered system[END_REF][START_REF] Tomaszewski | Multilayer ceramic composites with high failure resistance[END_REF][START_REF] Bermejo | Optimal strength and toughness of Al2O3-ZrO2 laminates designed with external or internal compressive layers[END_REF][START_REF] Bermejo | Processing optimisation and fracture behaviour of layered ceramic composites with highly compressive layers[END_REF][START_REF] Bermejo | Residual stresses, strength and toughness of laminates with different layer thickness ratios[END_REF].

Layered ceramic materials (also referred to as "ceramic laminates") are becoming one of the most promising areas of materials technology. They have been proposed as an alternative for the design of structural ceramics with improved fracture toughness, strength and mechanical reliability.

Among all, laminates designed with strong interfaces and compressive residual stresses have led to an increase in fracture energy, thermal shock resistance and, in some cases, a decrease in the sensitivity of the material strength to the different size of defects. The utilization of tailored compressive residual stresses acting as physical barriers to crack propagation has succeeded in many ceramic systems [START_REF] Rao | Laminar ceramics that exhibit a threshold strength[END_REF][START_REF] Bermejo | Threshold strength evaluation on an Al 2 O 3 -ZrO 2 multilayered system[END_REF][START_REF] Bermejo | Optimal strength and toughness of Al2O3-ZrO2 laminates designed with external or internal compressive layers[END_REF][START_REF] Lugovy | Crack Arrest in Si 3 N 4 -Based Layered Composites with Residual Stress[END_REF][START_REF] Lugovy | Apparent Fracture Toughness of Si 3 N 4 -Based Laminates with Residual Compressive or Tensile Stress in Surface Layers[END_REF][START_REF] Sglavo | Design and Production of Ceramic Laminates with High Mechanical Reliability[END_REF][START_REF] Bermejo | Fatigue behavior of alumina-zirconia multilayered ceramics[END_REF].

However, a limiting factor in the design of these multilayer systems is the fact that the beneficial compressive stresses in one type of layers have to be balanced by (potentially critical) tensile stresses in the counterpart layers. Therefore, the use of relatively high residual stresses to enhance the mechanical behaviour can lead to the onset of initial cracks in the layers, which may later propagate in service under external applied stresses, leading to failure of the component. Figure 1 illustrates typical surface cracks associated with residual stresses in planar ceramic-ceramic multilayer systems [START_REF] Lube | Mechanical Properties of Ceramic Laminates Key[END_REF]. Tunnelling cracks may appear at the free surface of the layers with tensile stresses, and are oriented perpendicular to the layer plane [START_REF] Ho | Tunneling cracks in constrained layers[END_REF][START_REF] Hillman | Cracking of Laminates Subjected to Biaxial Tensile Stresses[END_REF]. Another type of cracks are the socalled "edge cracks", which initiate from pre-existing flaws at the free surface of compressive layers, oriented parallel to the layer plane [START_REF] Ho | Surface Cracking in Layers Under Biaxial, Residual Compressive Stress[END_REF][START_REF] Bermejo | Residual stresses in Al2O3-ZrO2 multilayered ceramics: nature, evaluation and influence on the structural integrity[END_REF]. The third type is delamination, mainly occurring at the corner interface between adjacent layers.

Figure 1. Schematic of surface cracks in ceramic laminates designed with tensile (t) and compressive (c) residual stresses [START_REF] Lube | Mechanical Properties of Ceramic Laminates Key[END_REF].

Experimental observations have shown that edge cracking may be associated not only with the magnitude of internal compressive stresses but also with the thickness of the compressive layer [START_REF] Bermejo | Processing optimisation and fracture behaviour of layered ceramic composites with highly compressive layers[END_REF]. Some authors have speculated that this phenomenon may be related to crack bifurcation observed in some laminates with relatively high compressive residual stresses [START_REF] Hbaieb | Crack bifurcation in laminar ceramics having large compressive stress[END_REF][START_REF] Chen | Numerical analysis on special cracking phenomena of residual compressive inter-layers in ceramic laminates[END_REF]. In a recent work, the present authors have applied a stress-energy criterion to set the conditions for edge cracking formation and extension within a particular laminate [START_REF] Leguillon | Edge cracking due to a compressive residual stress in ceramic laminates[END_REF]. However, an understanding of the parameters related to the onset and extension of such edge cracks in the compressive layers is still lacking.

In this work, a 2D parametric finite element (FE) model is developed to predict the onset and propagation of edge cracks in ceramic laminates. The FE model utilizes the stress-energy coupled criterion (CC) [START_REF] Leguillon | Strength or toughness? A criterion for crack onset at a notch[END_REF], which combines the necessary stress and energy conditions for the onset of the edge/tunnelling cracks. Several geometries are examined, and the effect of the compressive residual stresses and thickness of the compressive layers on the formation and propagation of edge cracks in ceramic laminates is analysed.

Experimental observations

The ceramic laminate being examined consists of 9 alternated layers combining two ceramic materials: (i) alumina with 5% tetragonal zirconia, named as ATZ, (ii) alumina with 30% monoclinic zirconia, referred to as AMZ [START_REF] Bermejo | Processing optimisation and fracture behaviour of layered ceramic composites with highly compressive layers[END_REF]. Figure 2 shows a schematic of a prismatic bending bar with approx. sizes of (LxBxH) 45mm x 4mm x 3mm. Due to the different thermal strains during cooling down from the sintering temperature, elastic strains are generated in the ATZ and AMZ layers, which lead to internal (in-plane) residual stresses. In this particular case, the ATZ layers develop tensile stresses and the AMZ layers are subjected to compressive stresses. For more details on the estimation of residual stresses, references [START_REF] Bermejo | Processing optimisation and fracture behaviour of layered ceramic composites with highly compressive layers[END_REF][START_REF] Bermejo | Residual stresses in Al2O3-ZrO2 multilayered ceramics: nature, evaluation and influence on the structural integrity[END_REF] can be read.

In Fig. 2, an edge crack along the centre of the AMZ layer can clearly be seen. This is due to the tensile stress component generated at the free surface, having its maximum value at the edge, and decreasing quickly along the z direction into the material (see [START_REF] Ho | Surface Cracking in Layers Under Biaxial, Residual Compressive Stress[END_REF] for more details). The most relevant properties of both materials were determined in monolithic samples, and are listed in Table 1 [17].

Table 1. Material properties of the layers of the ceramic laminate [START_REF] Rao | Laminar ceramics that exhibit a threshold strength[END_REF] Material general, the decrease of E with temperature is associated with an increase in . Thus, both effects may be counterbalanced. This temperature dependence has not been taken into account in our study for the sake of simplicity, but it is foreseen to include it in further calculations to obtain more accurate results.

E [GPa]  [-]  x10 6 [K -1 ]  c [MPa] K Ic [MPa.m 1/2 ] G c [J/m 2 ] ATZ 39010 0.22 9.80.2 422±30 3.20.1 252 AMZ 28010 0.22 80.2 90±20 2.60.1 232
The critical tensile stress  c (i.e. bending strength) and energy release rate G c (derived from fracture toughness measurements) were measured at room temperature. The strength of brittle materials as those studied here may change with temperature if (i) the critical defect size changes with temperature and/or (ii) if the K Ic varies with temperature. The size of critical defects might change with temperature if (for instance) phenomena such as subcritical crack growth is considered.

In our case, simulation of the cooling down process from sintering is done, and thus this may be ruled out. What could change with temperature is the K Ic of the material due to, for instance, changes in the microstructure. This might occur at higher temperatures (e.g. above 1400°C) but not below the temperature considered in this study. Same argument explained above applies also to the critical energy release rate G c (based on K Ic ). No significant change in K Ic for the temperature range studied here is thus expected.

Numerical modelling of the edge cracking

FE model

The FE model for this study has been designed as a fully parametric model, which enables automatic creation of any arbitrary laminate configuration with different volume ratios of particular material components (leading to different levels of residual stresses) or different thicknesses of the AMZ layer. Based on the real geometry of specimens, the considered model consists of nine layers composed by alternating ATZ and AMZ materials. The height and width of the laminate is fixed for all simulations to be H=3mm and B=4mm, respectively. The thickness of the inner AMZ layers, i.e. t 2 , is varied in the interval (30-350m), and the thicknesses of the ATZ layers, i.e. t 1 , is correspondingly adjusted to reach the total thickness of 3mm. The material properties for the ATZ and AMZ layers needed for the numerical simulation are listed in Table 1.

To simulate (i) the nucleation and (ii) the propagation of the edge crack and its dependency on the layer thickness and level of residual stress inside the layer, a 2D FE model of the laminate crosssection is createdsee Figure 3. Quadratic PLANE183 elements with generalized plane strain option are used to correctly capture the thermoelastic stress state in the laminate. FE software ANSYS 15.0 is used for this purpose. The thickness of the inner AMZ layer is set to values between 30m and 350m; the prospective length (depth) of the edge crack into the AMZ layer is set to be within the interval 0m to 400m. In each simulation, an edge crack is introduced within each AMZ layer and for every thickness of the AMZ layer. In the first step, when the edge crack length is equal to 0m (no edge crack) the stresses  yy along the prospective crack path and potential energy W(0) of the uncracked body are calculated and stored for further post-processing.

In next simulations, the prospective edge crack of a given length is introduced in the model and the actual potential energy of the cracked body (for each crack length) W(a) is calculated again and used later for the calculation of the incremental energy release rate G inc (a) and the energy release rate (ERR) G(a) at the crack tip as follows:

  ( ) (0) ( ) / ( ) ( ) /     inc G a W W a a G a dW a da . ( 1
)
For verification purposes, the ERR G(a) at the crack tip is also numerically calculated using ANSYS, utilizing the implemented CINT function (employing J-integral). It leads to values very close to those provided by the energy approach based on Eq. ( 1). The advantage of the energy approach is that we can directly calculate the incremental ERR G inc (a) as well as the ERR at the crack tip G(a). If the contour integral method is to be used, more care about the used mesh is necessary, and a recalculation of G(a) to G inc (a) has also to be made in the post-processing. It should be pointed out that, although two edge cracks (in AMZ layers) are present in the 1/4 FE model, results of G(a), G inc (a) and  yy are the same for both these cracks (if a symmetric and periodic laminate is considered). Therefore, in the following, post-processing of only one crack (placed in the bottom AMZ layer) is taken into account. In order to determine the suitable conditions for the onset of the edge crack, the coupled stress-energy criterion is employed. A small description of the method is given below; for more details please see [START_REF] Leguillon | Strength or toughness? A criterion for crack onset at a notch[END_REF][START_REF] Martin | Energetic conditions for interfacial failure in the vicinity of a matrix crack in brittle matrix composites[END_REF].

Coupled stress energy criterion (CC)

The coupled (stress-energy) criterion (CC) states that a crack originates if two conditions (i.e. stress and energy conditions) are simultaneously fulfillednamely G inc (a)≥G c (AMZ) and  yy ≥ c (AMZ) . The first condition states that there should be enough energy available to create a crack, and the second condition stipulates that the tensile stress should be higher than the material tensile strength all along the new presumed crack path. The CC [START_REF] Leguillon | Strength or toughness? A criterion for crack onset at a notch[END_REF][START_REF] Martin | Energetic conditions for interfacial failure in the vicinity of a matrix crack in brittle matrix composites[END_REF] allows us avoiding any assumption on the existence of flaws able to trigger cracking, as is commonly used [START_REF] Hbaieb | Crack bifurcation in laminar ceramics having large compressive stress[END_REF][START_REF] Chen | Numerical analysis on special cracking phenomena of residual compressive inter-layers in ceramic laminates[END_REF]. In addition, there is no adjustable parameter in the CC, whereas the flaw size must be selected when using other methods in order to fit with the experimental measures. This choice is somewhat arbitrary, because it does not rely on micrographic observations. Moreover, the approach that considers a flaw size analyses the early stage of the edge cracking, and assumes a further crack growth in depth and along the specimen faces (i.e. channelling) to reach the observable state (see Fig. 2). In the case of the CC, we make the assumption that the crack almost simultaneously appears all around the specimen and then grows in depth.

Application to ceramic laminates

In order to illustrate the application of the stress-energy criterion to describe the edge cracking in laminates, a sample layered architecture is chosen (depicted in Fig. 3) considering a thickness of t 2 =150m for the AMZ layers. Since the ATZ and AMZ are strongly bonded (with strong interfaces), a tensile and compressive (in-plane) stress field is originated in the ATZ and AMZ layers, respectively, during cooling down from the sintering reference temperature. In this study, the reference temperature under which stresses develop is chosen as 1300 °C -see Ref. [START_REF] Green | Residual stresses in alumina-zirconia laminates[END_REF], which may be a low bound for this type of ceramic laminates [START_REF] Chlup | On the determination of the stress-free temperature for alumina-zirconia multilayer structures[END_REF]. The magnitude of residual stresses in the layers is increasing during this process as a function of the different temperature increment, T, reaching a maximum at room temperature. For the sake of simplicity, we discuss some examples for different selected T, i.e. for different magnitude of compressive stresses.

According to the numerical modelling, implementing the stress-energy CC, the relationship between G inc (a) and G c (AMZ) , as well as between  yy and  c (AMZ) , can be computed, as a function of

2 (AMZ) (AMZ) 2 (AMZ) res , Ic c K t C σ   (2)
where K Ic is the fracture toughness of the compressive layer,  res is the in-plane compressive residual stress, and C is a constant as estimated by the above authors to be equal to 0.34 (see [START_REF] Ho | Surface Cracking in Layers Under Biaxial, Residual Compressive Stress[END_REF] and [START_REF] Chen | Numerical analysis on special cracking phenomena of residual compressive inter-layers in ceramic laminates[END_REF] for more details). By implementing the CC approach to the solution of the edge cracking problem and fitting Eq. ( 2), we obtain a very similar result for C constantnamely C=0.32. For comparison purposes, the dependence of the critical layer thickness on the level of residual stress  res (AMZ) , as is predicted by Eq. ( 2), is represented in Figure 6 by the black thick dotted line. One can see a very good agreement of this relation with predictions made by the coupled stress-energy criterion, especially in the region of residual stresses 700MPa to 350MPa. Nevertheless, for residual stresses higher than 350MPa, Eq. ( 2) may no longer be valid, and thus predictions made by the CC approach should be taken into account. [m]

Conclusions

This work presents a novel approach to predict the onset and propagation of surface cracks (namely edge cracks) in ceramic laminates, associated with the residual stresses developed after cooling down from the sintering step. A full parametric 2D finite element model has been developed to simulate the initiation and propagation of the edge crack in the compressive layers. The conditions for crack initiation/propagation are assessed using a stress-energy coupled criterion. The analysis only requires the values of the elastic modulus and Poisson's ratio of the layers, the coefficient of thermal expansion, and the toughness and tensile strength of the compressive layer. There is no adjustable parameter, and there is no need to assume the presence of surface defects to initiate fracture. It is further found that, for a given thickness of the compressive layer, no edge crack is to initiate for relatively low internal (in-plane) compressive residual stress in the layer. For higher stress values, edge crack may initiate and grow in a stable manner. Finally, for relatively higher stress values, the formation of edge cracks is followed by the fracture (delamination) of the entire layer in an unstable fashion. Additional work is needed to validate the obtained results on different real specimens with various thicknesses and levels of residual stresses, aiming to provide guidelines for the fabrication of layered ceramics with controlled surface cracks.

Appendix

In every case where dissimilar materials are sealed together through a relative strong interface and subsequently undergo differential dimensional change, stresses arise between the materials [START_REF] Oël | Stress Distribution in Multiphase Systems: I, Composites with Planar Interfaces[END_REF].

Hence, a particular challenge in the processing of ceramic laminates is to understand the nature of these residual stresses, especially if they have to be used to enhance their mechanical properties. In ceramic laminates, residual stresses can be due to different factors: (i) different CTEs, (ii) phase transformations and/or (iii) chemical reactions. For ideal elastic materials, neglecting the influence of the external surfaces (where stresses may relax) and considering the laminate as an infinite plane plate (i.e. zero net bending moment), the stress field can be determined analytically [START_REF] Chartier | Laminar ceramic composites[END_REF][START_REF] Oël | Stress Distribution in Multiphase Systems: I, Composites with Planar Interfaces[END_REF][START_REF] Green | Residual stresses in alumina-zirconia laminates[END_REF]. In each layer, a homogeneous and biaxial residual stress state exists far from the free edges. The stress magnitude in each layer, i , res  , can be defined as follows:

i i i i i i i E T E              1 ) ( 1 , res (A.1)
where , ii E  and i  are material properties of the i th layer (i.e. Young's modulus, Poisson's ratio and coefficient of thermal expansion, respectively).

(

) ii T   
    is the mismatch strain of the i th layer, where the coefficient  is given as a weighted averaged expansion coefficient of the laminate: [START_REF] Qi | Design and preparation of high-performance alumina functional graded self-lubricated ceramic composites[END_REF] 11

NN i i i i i ii ii E t E t        (A.2)
with i t being the thickness of the i th layer and N the number of layers. Note that the reference temperature T ref is, in practice, not easy to determine. For typical alumina-based or silicon-based ceramics, this stress-free empirical temperature is generally between 1200 °C and the sintering temperature (approx. 1500 °C), depending on the components, compositions, etc. [START_REF] Chlup | On the determination of the stress-free temperature for alumina-zirconia multilayer structures[END_REF][START_REF] Cai | Constrained Densification of Alumina/Zirconia Hybrid Laminates, I: Experimental Observations of Processing Defects[END_REF][START_REF] Cai | Constrained Densification of Alumina/Zirconia Hybrid Laminates, II: Viscoelastic Stress Computation[END_REF].

A particular simple laminate case is that using only two types of layer materials (A and B). In such a case, Eq. (A.2) can be written in the form [START_REF] Sglavo | Design and Production of Ceramic Laminates with High Mechanical Reliability[END_REF]:

A B A B A A B B A B A, B, A, B, 1 1 1 1 A B A B 1 1 1 1 n n n n i i i i i i i i E E E E t t t t                                      (A.3)
According to Eq. ( 11), the magnitude of the residual stresses depends on the ratio between the total thickness of the layers of type A (i. release rates for arbitrary level of residual stress in the AMZ layer help to save a lot of computational time necessary for performing such a parametric study.

Figure 2 .

 2 Figure 2. Experimental observation of the edge crack phenomenon in a compressive AMZ layer, and stress redistribution at the free surface of the thin compressive layer.

Figure 3 .

 3 Figure 3. Schematic of the fully parametric FE model, developed to study the propagation of edge cracks in the compressive AMZ layers.

Figure 6 .

 6 Figure 6. Depths of the edge cracks in m against residual compressive stress in the AMZ layer and thickness of the compressive layer. The numbers in white boxes inside the plot denote the final edge crack depth in m for certain combination of  res (AMZ) and t (AMZ) .

.

  e. A A,i Tt   ) and B (i.e. B B,i Tt   ). The ratio of total thickness of the layer materials equals their volume ratio: B A B A // T T V V  . Thus the magnitude of the left-hand side of Eqs. (A.5) correspond to values which would be calculated in the same way in a laminate with the level of residual stress (AMZ) res ' Such recalculations of stresses and energy

Acknowledgements

The work has been supported by the NETME Centre established thanks to a financial support of the European Regional Development Fund under the Operational Program Research and Development for Innovation. The presented results have been obtained within NETME CENTRE PLUS (LO1202) project co-funded by the Czech Ministry of Education, Youth and Sports within the support program National Sustainability Program I.

A financial support of the Czech Science foundation under the project no. 14-11234S is also gratefully acknowledged.

the (potential) edge crack length, a, for different temperature increments, T. Accordingly, the formation and propagation of an edge crack during cooling down from the reference temperature can be estimated. Figures 4a, 4b and4c show the normalized incremental energy release rate G inc (a)/G c (AMZ) , the normalized energy release rate G(a)/G c (AMZ) and the normalized tensile stress If the difference between reference and investigated temperature is relatively low (e.g. T=-730°C), the magnitude of compressive residual stresses remains moderate low (in this particular case  res (AMZ) =-400MPa). As a result, no edge crack is initiated (see Figure 4a), because either the energy or the stress criteria are not fulfilled at any point (i.e. G inc (a)≤G c (AMZ) and  yy < c ).

In the particular situation that the specimen is cooled down with T=-788°C, corresponding to a value of residual stresses  res (AMZ) =-432MPa, both criteria are simultaneously fulfilled for the first time (namely G inc =G c (AMZ) and  yy = c ), and the edge crack is originated with a sudden jump from zero length to length a 1 = 59m, as is depicted in Figure 4b).

In the case that the specimen is reaching the room temperature, i.e. T=-1280°C, the residual compressive stress inside the AMZ layers reaches its maximum value of -700MPa. The corresponding stress and energy curves are illustrated in Figure 4c. According to the referred figure, once the crack is nucleated, it propagates through the AMZ layer provided that the ERR at the crack tip G(a) be larger than G c (AMZ) . The final crack length after the cooling down process is thus determined by point 3 in Figure 4c, reaching a value of a 3 =166m in this case.

A consequence derived from these diagrams is that increments on T, associated with increments of residual stress in the compressive layers, may yield the condition where the curve of G(a) becomes higher than G c (AMZ) at all points along the possible edge crack path. In such a case, the edge crack would propagate through the entire AMZ layer, leading to the delamination of the laminate.

Results and discussion

The influence of the AMZ layer thickness and magnitude of residual stress inside this layer on the formation and propagation of the edge crack is investigated using the FE model and applying the CC. Different laminate configurations are computed, where the thickness of the AMZ layer is varied in the interval 30 to 350m and the thicknesses of the ATZ layers correspondingly adjusted to reach a total thickness of 3mm. The magnitude of residual stress in the AMZ layers is considered between -200MPa and -800MPa for each laminate configuration. We caution the reader that, since the total height of the laminate is kept constant for this study, each configuration results in different volume ratios between ATZ and AMZ materials, and therefore different magnitude of residual stresses (upon the same T), see Appendix for more details. In order to enable a comparative study of edge crack formation and propagation in laminates with different layer thicknesses at a given level of residual stress, a corresponding T (inducing that level of residual stress) has to be first calculated for each laminate configuration.

After selecting a given residual stress level, a set of simulations is performed by introducing an edge crack with a length between 0m (no edge crack) and 400m (with a step of 1m), enabling the estimation of G, G inc and  yy (along the prospective crack path) as a function of the edge crack length a. These quantities are calculated through a FE analysis only for one specific temperature increment, i.e. T=100°C, and then (due to the linear elastic character of the solution) recalculated to arbitrary level of residual stress in the AMZ layer (for more information see the Appendix).

For illustrative purposes, we consider now the magnitude of residual stress in the AMZ layer to be  res (AMZ) =-200MPa. The normalized ERR and tangential stress  yy ahead of the crack tip are plotted together in Figure 5a. This plot clearly shows that no edge cracking is possible, because both the energy and stress conditions are not fulfilled for any potential edge crack length (i.e. the conditions  yy ≥ c and G inc (a)≥G c (AMZ) are not simultaneously fulfilled for the range of edge crack length).

If the level of compressive stress is increased up to a value of  res (AMZ) =300MPa, as is shown in Figure 5b, it can clearly be observed that, for AMZ layers equal or thicker than 222m, edge cracking is predicted, because both conditions  yy ≥ c and G inc (a)≥G c (AMZ) are simultaneously fulfilled (see Point 1 in Fig. 5b). The predicted initial length of the edge crack corresponds to ≈ 85µm. Once the edge crack is created, it propagates as long as the ERR at the crack tip remains higher than the fracture energy of the material, i.e. G(a) ≥G c (AMZ) . Again for layer thicknesses lower than 222m, no edge cracking is predicted. On the other hand, when the AMZ layer is thicker or equal to ≈ 307µm, the edge crack propagates through the entire plane of the AMZ layer since G(a)≥G c (AMZ) all along the crack path (G(a) is equal to G c (AMZ) only at the point 2 in Fig. 5b).

Beyond that critical thickness, the edge crack would propagate through the entire AMZ layer, yielding total delamination of the laminate.

Further increasing the compressive stress level up to  res (AMZ) =500MPa decreases the critical thickness required for edge crack formation to 85m (see Fig. 5c). In addition, as a consequence of such high compressive stresses, another critical thickness results (i.e. 204 µm in Fig. 5c), where the G(a) curve becomes higher than or equal to G c (AMZ) at all points, along the possible edge crack path, and total fracture of the laminate is predicted. Figure 6 shows the combined effect of residual stress  res (AMZ) and AMZ layer thickness t (AMZ) on the final edge crack length, as is predicted by the parametric studies, where  res (AMZ) is varied between -200MPa and -800MPa and t (AMZ) between 30µm and 350µm. The corresponding curves allow estimating the final edge crack depth (indicated in m in the curve) for corresponding values of  res (AMZ) and t (AMZ) . One can thus easily retrieve from this plot the critical combinations of both parameters, which may lead to edge cracking. If their combination lays in the light grey area, i.e. at the bottom of the graph, no edge cracking is expected. If the pair ( res (AMZ) and t (AMZ) ) lays in the central part of the graph, edge cracking is expected to occur and propagate into the AMZ layer a certain depth, as is prescribed by the number at the corresponding curve. Finally, the top dark grey area of the plot reveals the "undesired" combination of  res (AMZ) and t (AMZ) , which would lead to the total breakage of the AMZ layer (the energy release rate at the tip of the edge crack is higher than G c all along the prospective edge crack pathin the whole mid-plane of the AMZ layer).

The critical thickness of the AMZ layer leading to the edge cracking, i.e. t c (AMZ) , can also be described using the equation derived (in a similar form) by Ho and Hillman in [START_REF] Ho | Surface Cracking in Layers Under Biaxial, Residual Compressive Stress[END_REF] and employed also in [START_REF] Chen | Numerical analysis on special cracking phenomena of residual compressive inter-layers in ceramic laminates[END_REF]:

In order to study the influence of the AMZ layer thickness and magnitude of residual stress inside this layer on the formation and propagation of the edge crack, different laminate configurations have been calculated, where the thickness of the AMZ layer has been varied in the interval (30-350m) and the thicknesses of the ATZ layers correspondingly tailored to reach a total thickness of 3mm. Since the total thickness of the laminate is kept constant, the change of the AMZ layer thickness modifies the volume ratio between materials, and thus the magnitude of residual stress in the AMZ layers, as is inferred from Eq. (A.3).

Note:

The solved problem is considered as linear elastic. Therefore, solution of just one arbitrary residual stress state (given by arbitrary T) in a laminate of specific volume ratio (AMZ layer thickness) is sufficient. One can afterwards recalculate the results of  yy , G(a), and G inc (a) along the crack path, to values corresponding to arbitrary residual stress state (AMZ) res '  lying in the investigated interval 800 MPa to 200 MPa. The multiplication factor for this conversion: (i) in the case of stress recalculation, it is equal to the ratio of residual stress in the AMZ layer for given T (calculated for instance by Eq. (A.1) or using FEM) to the desired level of residual stress in the above mentioned investigated interval; (ii) in the case of energy release rate recalculations, it is the factor from (i) considered in the second power as follows:


Jean-François Flot
email: jfflot@mnhn.fr

Hélène Magalon

Corinne Cruaud

Arnaud Couloux

Simon Tillier

Patterns of genetic structure among Hawaiian corals of the genus Pocillopora yield clusters of individuals that are compatible with morphology

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

Patterns of genetic structure among Hawaiian corals of the genus Pocillopora yield clusters of individuals that

are compatible with morphology.

Introduction

Delimitation and identification of coral species is rendered difficult by intra-and interpopulational morphological variations that are often similar in range to, or even greater than, differences between currently recognized species [START_REF] Veron | Corals in Space and Time: The Biogeography & Evolution of the Scleractinia[END_REF]. Indeed, coral colonies are known to display phenotypic plasticity in response to "light, sedimentation, current and water agitation, temperature, depth, salinity, emersion, physical damage, predation, intra-and interspecific competition, association with other organisms, disease, substrate topography" [START_REF] Randall | Some problems in reef coral taxonomy[END_REF], and even gravity [START_REF] Meroz | The effect of gravity on coral morphology[END_REF]. Moreover, crossings between morphologically different corals currently considered as distinct species have been demonstrated to bring out intermediate morphologies that add to the general confusion [START_REF] Vollmer | Hybridization and the evolution of reef coral diversity[END_REF].

Since it is not subject to ecophenotypic variation, the DNA of an organism is commonly used as a source of information to tell intraspecific genetic diversity and phenotypic plasticity from interspecific differences. DNA sequence markers are well suited for this purpose as they generally cross-amplify over a wide range of species, genera and families: the mitochondrial cox1 gene, in particular, can be amplified consistently from most living creatures by using universal primers [START_REF] Folmer | DNA primers for amplification of mitochondrial cytochrome c oxidase subunit I from diverse metazoan invertebrates[END_REF] and has been proposed as a reference marker for the 'barcoding of life' [START_REF] Hebert | Biological identifications through DNA barcodes[END_REF]. The nuclear, ribosomal internal transcribed spacers (ITS) are also widely used [START_REF] Àlvarez | Ribosomal ITS sequences and plant phylogenetic inference[END_REF]: their presence in several hundred copies per genome makes them easy to amplify, whereas concerted evolution [START_REF] Liao | Concerted evolution: molecular mechanism and biological implications[END_REF][START_REF] Dover | Molecular drive: a cohesive mode of species evolution[END_REF] usually results in the presence of a single dominant ITS type per individual, with little intraspecific variation [START_REF] Hillis | Ribosomal DNA: molecular evolution and phylogenetic inference[END_REF]. More recently, exon-primed, intron-crossing (EPIC) PCR amplification of gene introns [START_REF] Palumbi | Contrasting population structure from nuclear intron sequences and mtDNA of humpback whales[END_REF][START_REF] Bierne | Screening for intron-length polymorphisms in penaeid shrimps using exon-primed intron-crossing (EPIC)-PCR[END_REF][START_REF] Jarman | Oligonucleotide primers for PCR amplification of coelomate introns[END_REF] was proposed as a way to assess variation at several independent nuclear loci.

Coral biodiversity, however, has proved difficult to study using molecular sequence markers. Cnidarian mitochondrial DNA seems to evolve very slowly [START_REF] Shearer | Slow mitochondrial DNA sequence evolution in the Anthozoa (Cnidaria)[END_REF][START_REF] Hellberg | No variation and low synonymous substitution rates in coral mtDNA despite high nuclear variation[END_REF], and cox1 sequences typically display little to no variability among congeneric corals [START_REF] Ridgway | Testing the applicability of molecular genetic markers to population analyses of scleractinian corals[END_REF][START_REF] Fukami | Analysis of complete mitochondrial DNA sequences of three members of the Montastraea annularis coral species complex (Cnidaria, Anthozoa, Scleractinia)[END_REF], whereas in Acropora the presence of silenced, mutation-prone ITS pseudogenes [START_REF] Márquez | Pseudogenes contribute to the extreme diversity of nuclear ribosomal DNA in the hard coral Acropora[END_REF] as well as of ancestrally shared lineages [START_REF] Vollmer | Testing the utility of internally transcribed spacer sequences in coral phylogenetics[END_REF] has cast doubt on the utility of ribosomal DNA for coral species delimitation. As for EPIC-PCR, its application to corals has been limited until now to Acropora [START_REF] Vollmer | Hybridization and the evolution of reef coral diversity[END_REF][START_REF] Van Oppen | The evolutionary history of the coral genus Acropora (Scleractinia, Cnidaria) based on a mitochondrial and a nuclear marker: reticulation, incomplete lineage sorting, or morphological convergence?[END_REF][START_REF] Van Oppen | Examination of species boundaries in the Acropora cervicornis group (Scleractinia, Cnidaria) using nuclear DNA sequence analyses[END_REF] and Montipora [START_REF] Van Oppen | Patterns of evolution in the scleractinian coral genus Montipora (Acroporidae)[END_REF] and has yet to provide the basis for a taxonomic revision of these genera.

In the discussion surrounding scleractinian coral species delimitation, corals of the genus Pocillopora are of special interest due to their spectacular, supposedly intraspecific morphological variations [START_REF] Veron | Corals of the World[END_REF]. Species boundaries in this group are poorly understood, and the resulting taxonomic uncertainties undermine the numerous physiological and ecological studies conducted on these keystone organisms. Previous attempts to develop variable molecular sequence markers in this group have been largely unsuccessful [START_REF] Ridgway | Testing the applicability of molecular genetic markers to population analyses of scleractinian corals[END_REF][START_REF] Ridgway | Allozyme electrophoresis still represents a powerful technique in the management of coral reefs[END_REF][START_REF] Conception | Noncoding mitochondrial loci for corals[END_REF], except for the second internal transcribed spacer (ITS2) [START_REF] Flot | Molecular phylogeny and systematics of the scleractinian coral genus Pocillopora in Hawaii[END_REF][START_REF] Chen | Secondary structure and phylogenetic utility of the ribosomal internal transcribed spacer 2 (ITS2) in scleractinian corals[END_REF]. The present article reports the development of five other variable sequence markers in Pocillopora: two regions identified as the most variable in the mitochondrial genome of Pocillopora (the putative D-loop and an open reading frame of unknown function) [START_REF] Flot | The mitochondrial genome of Pocillopora (Cnidaria: Scleractinia) contains two variable regions: The putative D-loop and a novel ORF of unknown function[END_REF], and three nuclear EPIC markers (an intron of calmodulin, an intron of elongation factor-1α and an intron of the nuclear gene encoding the β subunit of the mitochondrial ATP synthase). All six markers (including ITS2) were then tested on a set of Hawaiian coral samples attributed to five different morphospecies in order to assess their utilities and draw guidelines for future studies. or intermediary morphologies are rarely observed. To avoid mistaking small P. eydouxi colonies for P. meandrina, only large colonies of P. eydouxi were sampled. Genomic DNA was purified directly from fresh samples using the Wizard Genomic DNA Extraction kit (Promega). As these coral DNA extracts also contained DNA from zooxanthellae and possibly bacteria, coral-specific primers (Table 2) were defined with the help of Primer3 [START_REF] Rozen | Primer3 on the WWW for general users and for biologist programmers[END_REF] based on alignments of coral, human, bacterial and dinoflagellate sequences (whenever available) obtained from GenBank. Each marker was amplified in 25-µl PCR amplification products obtained from nuclear markers frequently contained more than a single sequence type (Table 1). Mixed sequences were disentangled by direct phase extraction [START_REF] Flot | Phase determination from direct sequencing of length-variable DNA regions[END_REF] with the help of Champuru v1.0 [START_REF] Flot | Champuru 1.0: a computer software for unraveling mixtures of two DNA sequences of unequal lengths[END_REF], (available online at http://134.157. 186.185/champuru) when they differed in length, by interindividual comparison [START_REF] Clark | Inference of haplotypes from PCR-amplified samples of diploid populations[END_REF] when they had identical lengths, and by resequencing using haplotype-specific internal primers [START_REF] Rudi | Direct haplotypespecific DNA sequencing[END_REF][START_REF] Hare | The accuracy of heterozygous base calling from diploid sequence and resolution of haplotypes using allele-specific sequencing[END_REF] whenever the two previous methods yielded ambiguous or uncertain results.

Materials and methods

Thirty

P. damicornis KB 1 1 1 2 2 1 2 - - 1 1 1 2 2 2 3 - - 1 1 2 4 3 3 4 - - 1 1 1 4 2 3 5 - - 1 1 2 3 2 3 6 - - 1 1 3 2 2 2 7 - - 1 1 2 3 5 2 8 - - 1 1 2 2 1 2 9 - - 1 1 1 2 2 1 10 - - 1 1 1 2 2 2 11 - - 1 1 2 2 2 1 12 - - 1 1 2 2 1 2 13 - - 1 1 2 3 2 2 14 - - 1 1 2 2 2 1 15 - - 1 1 2 2 2 2 16 - - 1 1 1 2 1 2 17 P. meandrina - 1 1 2 2 1 2 18 - - 1 1 2 2 2 2 19 - - 1 1 2 2 3 2 20 - - 1 1 2 2 3 2 21 - - 1 1 2 2 3 2 22 - - 1 1 2 2 2 2 23 - - 1 1
All sequences obtained in this study were deposited in GenBank (accession numbers EU374225-EU374581). For each marker, sequences were imported into MEGA3 [START_REF] Kumar | MEGA3: Integrated software for Molecular Evolutionary Genetics Analysis and sequence alignment[END_REF] and aligned by eye without difficulty. Sequences alignments were converted into the Roehl format using DnaSP [START_REF] Rozas | DNA polymorphism analyses by the coalescent and other methods[END_REF], and haplotype networks were constructed using the median-joining algorithm [START_REF] Bandelt | Median-joining networks for inferring intraspecific phylogenies[END_REF] implemented in Network 4.1 (available online at http://www.fluxus-engineering.com/).

For mitochondrial DNA, clusters of haplotypes were delimited somewhat arbitrarily by grouping together haplotypes separated by a single mutation step. A different method was used for the nuclear markers: in order to detect clusters of haplotypes corresponding to clusters of individuals, connections between haplotypes found co-occurring in a coral colony were added as curves on the median-joining networks. This is analogous to the proposal by Doyle [START_REF] Doyle | The irrelevance of allele tree topologies for species delimitation, and a non-topological alternative[END_REF] to consider a group of individuals sharing a common pool of alleles as a 'field for recombination' [START_REF] Carson | The species as a field for recombination[END_REF] (FFR), i.e., a species-level population unit; with the difference that, in the present case, not all co-occurring haplotypes of a given marker may have the potential to recombine, since it is unclear whether they are orthologous or paralogous sequences (which is also the reason why we call them haplotypes, and not alleles). In the graphical representation introduced here, clusters of haplotypes that correspond to clusters of individuals stand out as having a single connection to the rest of the network: each such cluster of individuals comprises one or several FFRs, but FFRs can be found that are not part of any cluster (see figures).

Results and discussion

Mitochondrial markers yield clusters of individuals that are compatible with morphology

As expected for mitochondrial markers in the absence of recombination, haplotype networks obtained for the open reading frame and for the putative control region are congruent and only the network resulting from the concatenation of both markers is presented here (Fig. 1). A total of seven haplotypes are detected: a single haplotype specific of P. molokensis, two closely related haplotypes (separated by a single mutation) specific of P. ligulata, two closely related haplotypes (separated by a single mutation) for corals of the P. eydouxi and P. meandrina morphotypes and two not-so-closely related haplotypes (separated by 8 mutations) for corals of the P. damicornis morphotype.

P. molokensis and P. ligulata corals fall in two distinct clusters, whereas a single cluster comprises all individuals of the P. meandrina and P. eydouxi morphotypes. Small colonies of P. meandrina and P. eydouxi can be difficult to distinguish in the field: our mitochondrial data suggest that these two morphotypes are either a single species or two closely related ones. Regarding P. damicornis, two morphological variants have been described in Hawaii with slight differences in growth form, pigmentation and reproductive timing, suggesting that they may be sympatric cryptic species [START_REF] Richmond | Lunar periodicity in larva release in the reef coral Pocillopora damicornis at Enewetak and Hawaii[END_REF], which could explain our observation of two divergent mitochondrial lineages; in the present study, unfortunately, morphological details of the corals sampled were not recorded, so this hypothesis cannot be tested here.

For all nuclear markers, more than two haplotypes are detected in some individuals

Up to three haplotypes per coral colony are detected for ITS2 and the ATP synthase β subunit, up to four for calmodulin, and up to five for elongation factor-1α (Table 1). As haplotypes have variable lengths, the number of end peaks of a chromatogram can be used as a minimal estimate of the number of haplotypes (Fig. 2); obtaining the sequence of each haplotype, however, is the only way to determine this number, since haplotypes of identical lengths have their end peaks superimposed [START_REF] Flot | Phase determination from direct sequencing of length-variable DNA regions[END_REF].

The occurrence of several dominant ITS types per individual is well documented in various organisms, such as oaks [START_REF] Muir | Three divergent rDNA clusters predate the species divergence in Quercus petraea (Matt.) Liebl. and Quercus robur L[END_REF] and corals [START_REF] Vollmer | Testing the utility of internally transcribed spacer sequences in coral phylogenetics[END_REF], and can be explained by a failure or delay in homogenization among the several hundred copies of ribosomal DNA present in a typical genome [START_REF] Liao | Concerted evolution: molecular mechanism and biological implications[END_REF][START_REF] Dover | Molecular drive: a cohesive mode of species evolution[END_REF][START_REF] Schlötterer | Chromosomal homogeneity of Drosophila ribosomal DNA arrays suggests intrachromosomal exchanges drive concerted evolution[END_REF]. In the case of nuclear introns, however, the finding of more than two sequences per individual comes unexpected, even though similar observations have been previously reported in periwinkles for calmodulin [START_REF] Simpson | Intron analyses reveal multiple calmodulin copies in Littorina[END_REF] and in Penaeus shrimps for elongation factor-1α [START_REF] France | Intraspecific genetic diversity in the marine shrimp Penaeus vannamei: multiple polymorphic elongation factor-1alpha loci revealed by intron sequencing[END_REF]. Presence of more than two gene copies in some individuals could result from gene duplication, but this explanation seems unlikely for the ATP synthase β subunit marker, since it was shortlisted as "likely not to be member of a multigene family" by Jarman et al. [START_REF] Jarman | Oligonucleotide primers for PCR amplification of coelomate introns[END_REF] based on examination of the complete genomes of Homo, Caenorhabditis, and Drosophila. Moreover, our primers were designed overlapping the exon-intron boundaries for enhanced specificity and should have discriminated between paralogous gene copies, except if duplication happened recently or if concerted evolution limits divergence [START_REF] Zimmer | Rapid duplication and loss of genes coding for the alpha chains of hemoglobin[END_REF].

Other mechanisms may be responsible for the increased numbers of haplotypes observed in our study: there is no karyotypic information available for Pocillopora, but variations in chromosome numbers have been reported for corals of the genus Acropora [START_REF] Kenyon | Models of reticulate evolution in the coral genus Acropora based on chromosome numbers: parallels with plants[END_REF][START_REF] Flot | Comparative coral cytogenetics[END_REF], and a study of microsatellite inheritance using controlled crosses in Acropora palmata yielded triploid larvae possessing one paternal and two maternal alleles [START_REF] Baums | Mendelian microsatellite loci for the Caribbean coral Acropora palmata[END_REF]. Chimeric colonies resulting from the fusion of two or more genetically distinct organisms have also been reported in corals of the genus Pocillopora [START_REF] Hidaka | Tissue compatibility between colonies and between newly settled larvae of Pocillopora damicornis[END_REF][START_REF] Hidaka | Contact reactions between young colonies of the coral Pocillopora damicornis[END_REF], which may explain the high numbers of haplotypes per colony observed here. Finally, intraspecific variations in gene copy numbers have recently been discovered in humans [START_REF] Sebat | Large-scale copy number polymorphism in the human genome[END_REF][START_REF] Iafrate | Detection of large-scale variation in the human genome[END_REF] and other mammals (reviewed in [START_REF] Freeman | Copy number variation: New insights in genome diversity[END_REF]), but it is not yet known whether such phenomenon occurs in non-mammalian organisms. In any case, our observation of more than two sequences per individual for each nuclear sequence marker investigated contrasts strongly with the results of previous studies using microsatellites in Pocillopora [START_REF] Magalon | Patterns of genetic variation do not correlate with geographical distance in the reefbuilding coral Pocillopora meandrina in the South Pacific[END_REF][START_REF] Magalon | Development of coral and zooxanthella-specific microsatellites in three species of Pocillopora (Cnidaria, Scleractinia) from French Polynesia[END_REF][START_REF] Starger | Ten polymorphic STR loci in the cosmopolitan reef coral, Pocillopora damicornis[END_REF] that never reported the occurrence of more than two alleles in any single individual: further studies will be required to determine the reason for this discrepancy.

Nuclear sequence markers yield clusters of individuals that are also compatible with morphology

For ITS2 (Fig. 3), two clusters are detected that comprise more than a single individual: one includes all individuals of the P. ligulata morphotype, and the other all individuals of the P. eydouxi morphotype. In addition, two clusters of a single individual are detected, each of them of the P. damicornis morphotype. For calmodulin (Fig. 4), a single cluster of individuals is detected that comprises three samples of the P. meandrina morphotype. For elongation factor-1α (Fig. 5), two clusters stand out, each of them made of a single P. eydouxi individual, whereas for the ATP synthase β subunit (Fig. 6), only one cluster of one P. damicornis coral sample is detected.

None of these clusters comprises colonies of different morphotypes; hence, our nuclear datasets do not contradict previous morphological hypotheses, but do not support many of them either. Despite their higher variability in terms of haplotype numbers and of differences between haplotypes, nuclear markers turn out to be less informative than mitochondrial ones for delimiting clusters of individuals. The same apparent paradox is observed when comparing ITS2 and the other nuclear markers: haplotypes are fewer and less divergent for ITS2 than for calmodulin, elongation factor-1α and the ATP synthase β subunit, but nevertheless ITS2 seems to yield more clusters of individuals.

Two main hypotheses can be proposed to explain why fewer clusters of individuals are detected by using nuclear markers than by looking at mitochondrial DNA. First, it might be that individuals belonging to different mitochondrial clusters are exchanging genes through sexual reproduction; however, in that case, it would be difficult to explain why clusters of mitochondrial and nuclear haplotypes are compatible with morphology, unless some strong environmental selection is acting concomitantly on both genomes. Such selection may explain part of the molecular differences observed between P. damicornis and P. eydouxi, two morphotypes Fig. 3. Network of ITS2 haplotypes. Coloured curves connect haplotypes that co-occur in at least one individual, and their width is drawn proportional to the number of individuals in which the two haplotypes co-occur. Mutations are shown in red on the branches (numbers refer to positions in the alignments). The colour code for the curves is the same as for the haplotypes (dark blue: P. damicornis; pink: P. meandrina; green: P. ligulata; pale blue: P. eydouxi; red: P. molokensis). Clusters of haplotypes that correspond to clusters of individuals are enclosed in dashed circle: for instance, all P. ligulata haplotypes fall into one such cluster, and each of the two pools of co-occurring haplotypes observed within this cluster corresponds to a distinct potential field for recombination (FFR). The P. eydouxi cluster on the right side of the network comprises a single pool of co-occurring haplotypes; hence, in our dataset all individuals of the P. eydouxi morphotype are part of a single FFR.

found in contrasting reef environments in Hawaii (calm shallow waters for P. damicornis, deeper exposed locations for P. eydouxi) but not between P. ligulata and P. meandrina that are usually found interspersed among each other on shallow reef parts exposed to wave action.

Alternatively, second, the different mitochondrial clusters may correspond to reproductively isolated sympatric populations (i.e., biological species), in which case incomplete lineage sorting and retention of a shared ancestral polymorphism could explain why these species cannot be distinguished using nuclear intron sequences. A prediction from this second hypothesis would be that, among nuclear markers, those with shorter coalescence time due to concerted evolution, such as ITS2, should yield clearer patterns than other genes; and this is precisely what is observed here.

Conclusions

Our results show that mitochondrial data obtained by sequencing the putative control region and the recently described open reading frame can be useful for resolving interpopulational relationships among pocilloporid corals. On the other hand, nuclear markers in Pocillopora are plagued with high numbers of haplotypes in some individuals that make sequencing cumbersome and costly; moreover, these markers turn out not to be very informative in terms of clusters of individuals. Among nuclear markers, ITS2 provides a slightly clearer picture than nuclear gene introns, but apparently does not resolve all potential interspecific relationships, i.e. does not allow identification of the more restricted clusters delineated by mitochondrial and morphological data. Had our nuclear markers displayed only one or two haplotypes per individual as expected, we could have tried to sort individuals into clusters by using population genetic models that are not hindered by shared ancestral haplotypes [START_REF] Pritchard | Inference of population structure using multilocus genotype data[END_REF]. However, since orthology/paralogy relationships among our sequences are unclear, the actual number of copies of each marker remains unknown, and a population genetic analysis of our data is impossible.

The data presented here bring partial support to the morphological delimitation of species in Hawaiian corals of the genus Pocillopora. ITS2 and mitochondrial data concur with the delimitation of P. ligulata as a distinct populational unit of possible species level, whereas mitochondrial data also strongly support the distinctiveness of P. molokensis: these results may have significant implications regarding conservation, since these two morphospecies are listed as putative Hawaiian endemics [START_REF] Maragos | Revised checklist of extant shallow-water stony coral species from Hawaii (Cnidaria: Anthozoa: Scleractinia), Bishop Mus[END_REF]. However, and with regard to the high level of intra-and interpopulational variation, determining whether these Hawaiian morphological and genetic clusters may belong to more widespread genetic clusters will require further investigation. It is also unclear whether the two mitochondrial lineages identified among corals of the P. damicornis morphotype are two cryptic species or just an instance of intraspecific variation similar to the one previously reported for corals of the genus Montastrea [START_REF] Fukami | Analysis of complete mitochondrial DNA sequences of three members of the Montastraea annularis coral species complex (Cnidaria, Anthozoa, Scleractinia)[END_REF]. Moreover, further research will be needed to clarify the status of the P. meandrina and P. eydouxi morphotypes that could only be distinguished using ITS2, not using mitochondrial markers: given our small sample size for P. eydouxi, the hypothesis that these two morphotypes may be growth forms of a single species cannot be rejected. Hence, this report is a first step toward a molecular reassessment of species boundaries in the coral genus Pocillopora, but examination of a larger number of specimens collected over the whole area of distribution of this genus will be required before more general conclusions can be reached.

  open-reading frame; CR: putative mitochondrial control region; ITS2: internal transcribed spacer 2; Calm: calmodulin; EF-1α: elongation factor-1α; ATPSβ: ATP synthase β subunit. reaction mixes containing 20 µl H 2 O, 2.5 µl Red Taq buffer (Sigma), 1 µl dNTP mix (6.6 mmol l -1 total), 1.3 µl DMSO, 0.3 µl primers (25 µmol l -1 ), 0.3 µl Red Taq (Sigma) and 0.5 µl undiluted DNA extract (containing about 15 ng of total DNA). PCR conditions comprised an initial denaturation step of 60 s at 94 • C, followed by 40 cycles (30 s denaturation at 94 • C, 30 s annealing at 53 • C, 75 s elongation at 72 • C) and a final 5-min elongation step at 72 • C. PCR products were cleaned using a mix of exonuclease I and shrimp alkaline phosphatase and sequenced in both directions with the same primers as for amplification. Sequences were assembled and cleaned using Sequencher 4 (Gene Codes).

Fig. 1 .

 1 Fig. 1. Median-joining network of mitochondrial haplotypes. Coloured circles represent haplotypes and their area is proportional to the number of times a given haplotype was sampled. Colours within the circles indicate the morphotypes of the individuals in which each haplotype was detected (dark blue: P. damicornis; pink: P. meandrina; green: P. ligulata; pale blue: P. eydouxi; red: P. molokensis). Mutations are shown in red on the branches (numbers refer to positions in the alignments), and haplotype clusters are enclosed in dashed circles.

Fig. 2 .

 2 Fig. 2. Examples of traces showing variation in the number of end peaks due to different numbers of haplotypes per individual. From top to bottom: ATP synthase, sample 9; ATP synthase, sample 2; ATP synthase, sample 4; calmodulin, sample 37. All ATP synthase haplotypes end with a C (a A overhang is added by the polymerase during the PCR process), whereas calmodulin haplotypes end with a A that appears artefactually larger than the actual end peak.

Fig. 4 .

 4 Fig. 4. Network of calmodulin haplotypes (dark blue: P. damicornis; pink: P. meandrina; green: P. ligulata; pale blue: P. eydouxi; red: P. molokensis).

Fig. 5 .

 5 Fig. 5. Network of elongation factor-1α haplotypes (dark blue: P. damicornis; pink: P. meandrina; green: P. ligulata; pale blue: P. eydouxi; red: P. molokensis).

Fig. 6 .

 6 Fig. 6. Network of ATP synthase β subunit haplotypes (dark blue: P. damicornis; pink: P. meandrina; green: P. ligulata; pale blue: P. eydouxi; red: P. molokensis).

Table 2

 2 List of primers used for PCR amplificationMarker Primer name Primer sequence

Acknowledgements

Research by J.-F. Flot was supported by a PhD scholarship from the French Ministry of Research and Education and by a research grant from the MNHN program État et structure phylogénétique de la biodiversité actuelle et fossile. Support from the Consortium national de recherche en génomique is acknowledged (agreement No. 2005/67 on the project 'Macrophylogeny of life' directed by Guillaume Lecointre). This project benefited greatly from the assistance of Annie Tillier, Josie Lambourdière, and Céline Bonillo at the Service de systématique moléculaire (MNHN CNRS IFR 101). Thanks to Evelyn Cox, Frank Stanton and Daniel Thornhill for helping with sample collection during the 2002 Pauley Summer Program 'Molecular Biology of Corals'; participation of J.-F. Flot in this program was supported by the E. W. Pauley Foundation. Thanks also to Keoki Stender for providing field information, to Marie-Catherine Boisselier, Magalie Castelin, Julien Lorion, and Nicolas Puillandre for useful discussions, and to Sarah Samadi for critically reading an earlier version of this paper.