Patrick Lorès

Zine-Eddine Kherraf

Amir Amiri-Yekta

Marjorie Whitfield

Abbas Daneshipour

Laurence Stouvenel

Caroline Cazin

Emma Cavarocchi

Charles Coutton

Marie-Astrid Llabador

Bardet-Biedl Patrick Syndrome

Lorès

Zine-Eddine Kheraff

Christophe Arnoult

Nicolas Thierry-Mieg

Lucile Ferreux

Catherine Patrat

Seyedeh-Hanieh Hosseini

Selima Fourati

Ben Mustapha

Raoudha Zouari

Emmanuel Dulioust

Pierre F Ray

Aminata Touré
email: aminata.toure@inserm.fr

A missense mutation in

Keywords: Infertility, Sperm, MMAF, Intra Flagellar Transport, IFT74

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.

Introduction

The motility of mammalian sperm is provided by the flagellum, an evolutionarily conserved organelle built around a microtubule cytoskeleton, called the axoneme. The axoneme is constituted of nine microtubule doublets surrounding a central pair of microtubules, which is part of the central apparatus. The flagellar axoneme comprises specific components necessary for motility, such as outer and inner dynein arms, nexin-dynein regulatory complex (N-DRC) and Calmodulin-and radial spoke-associated complex (CSC) which are tightly connected to the tubulin backbone to coordinate and orchestrate flagellar beating [START_REF] Ishikawa | Axoneme Structure from Motile Cilia Cold Spring[END_REF]. This axonemal structure is also found in motile cilia, which for instance are present in mammals at the surface of the respiratory epithelium, fallopian tubes and central nervous ependymal canal, where they facilitate the movements of fluids. In addition, the axoneme is present in primary cilia, which coordinate signaling pathways during development and in tissue homeostasis.

Primary cilia are usually immotile solitary organelles extending from the cell surface of most mammalian cells in growth arrest. In these cilia, the structures associated with motility, such as dynein arms and radial spokes are absent, and their tubulin backbone lacks the central pair microtubules. Importantly, the axoneme is present in several ciliated or flagellated unicellular organisms such as Tetrahymena, Chlamydomonas and Trypanosoma, which have proven to constitute useful tools to unravel the molecular mechanisms of assembly and structure of cilia and flagella [START_REF] Vincensini | 1001 model organisms to study cilia and flagella Biology of the cell / under the auspices of the European[END_REF].

The assembly of cilia and flagella was shown to require a molecular motor-driven process, which ensures the selective transport of proteins along the proximal-distal axis of the growing organelle. This process, called Intra Flagellar Transport (IFT) was mainly studied in protists such as Chlamydomonas reinhardtii cilia and Trypanosoma brucei (Avidor-Reiss and Leroux 2015; [START_REF] Ishikawa | Intraflagellar Transport and Ciliary Dynamics Cold Spring[END_REF][START_REF] Reiter | Genes and molecular pathways underpinning ciliopathies[END_REF]. IFT complexes, also called "trains" are multiprotein complexes classified as IFT-A and IFT-B depending on their protein content. The IFT complex A is linked to a kinesin-2 motor to ensure anterograde transport (toward the ciliary and flagellar tips) along axonemal microtubules, whereas the IFT B complex is associated with cytoplasmic dyneins to ensure retrograde transport. IFT trains are specialized for the transport of different sets of protein cargo such as tubulin and are essential to build cilia and flagella. As a result, IFT deficiency is deleterious for cell function and tissue differentiation, and can cause a variety of human diseases and developmental disorders, referred as ciliopathies [START_REF] Reiter | Genes and molecular pathways underpinning ciliopathies[END_REF].

As an exception, the molecular mechanisms of sperm flagellum assembly in mammals are still poorly defined and the presence of an IFT mechanisms in mature sperm flagella was debated due to the absence of protein turnover in this organelle, in contrast to cilia [START_REF] Pedersen | Intraflagellar transport (IFT) role in ciliary assembly, resorption and signalling[END_REF][START_REF] Rosenbaum | Intraflagellar transport[END_REF][START_REF] San Agustin | Intraflagellar transport is essential for mammalian spermiogenesis but is absent in mature sperm[END_REF]. The recent identification of IFT encoding genes, which mutations in mouse models are associated with sperm flagellum assembly defects, indicated an evolutionary conservation of IFT machinery components and potential similar function in mammalian sperm. In the mouse, Ift88 was the first IFT gene shown to be required for sperm flagella assembly [START_REF] Pazour | Chlamydomonas IFT88 and its mouse homologue, polycystic kidney disease gene tg737, are required for assembly of cilia and flagella[END_REF], followed by Spef2 [START_REF] Sironen | Loss of SPEF2 function in mice results in spermatogenesis defects and primary ciliary dyskinesia[END_REF]), Ift20 (Zhang et al. 2016), Ift25 (Liu et al. 2017), Ift27 [START_REF] Zhang | Intraflagellar transporter protein (IFT27), an IFT25 binding partner, is essential for male fertility and spermiogenesis in mice[END_REF]), Ift74 (Shi et al. 2019), Ift81 (Qu et al. 2020), Ift140 [START_REF] Zhang | Intraflagellar transporter protein 140 (IFT140), a component of IFT-A complex, is essential for male fertility and spermiogenesis in mice[END_REF]), Ttc21a (Liu et al. 2019b)and Ttc29 [START_REF] Lores | Mutations in TTC29, Encoding an Evolutionarily Conserved Axonemal Protein, Result in Asthenozoospermia and Male Infertility[END_REF]. Importantly, recent data from genetic analyses of patients showing an isolated phenotype of male sterility due to multiple morphological abnormalities of the sperm flagella (MMAF) also allowed the identification of protein damaging variants affecting IFT genes, such as TTC21A (Liu et al. 2019b), TTC29 [START_REF] Lores | Mutations in TTC29, Encoding an Evolutionarily Conserved Axonemal Protein, Result in Asthenozoospermia and Male Infertility[END_REF], SPEF2 (Liu et al. 2019a;Liu et al. 2019c) and CFAP69 [START_REF] Dong | Absence of CFAP69 Causes Male Infertility due to Multiple Morphological Abnormalities of the Flagella in Human and Mouse[END_REF][START_REF] He | Novel homozygous CFAP69 mutations in humans and mice cause severe asthenoteratospermia with multiple morphological abnormalities of the sperm flagella[END_REF]. In humans, most of those identified IFT-related genes have a predominant expression in the testis and in the case of SPEF2, the mutations were shown to only affect testis-specific isoforms, thus explaining the presence of defects only impacting sperm flagellum structure and leading to an isolated form of male infertility, which is not associated with ciliopathy [START_REF] Toure | The genetic architecture of morphological abnormalities of the sperm tail[END_REF]. To date, their exact function in sperm flagella and their implication in a canonical IFT process remain unknown.

Here, we report the identification of two individuals presenting a MMAF phenotype and carrying a homozygous missense mutation in IFT74, a gene encoding for an essential IFT component. IFT74 was extensively studied in unicellular organisms such as Chlamydomonas [START_REF] Bhogaraju | Molecular basis of tubulin transport within the cilium by IFT74 and[END_REF][START_REF] Brown | Assembly of IFT trains at the ciliary base depends on IFT74[END_REF][START_REF] Kubo | Together, the IFT81 and IFT74 N-termini form the main module for intraflagellar transport of tubulin[END_REF] and was shown to associate with IFT81 for tubulin transport within cilia and to be required for ciliogenesis [START_REF] Kubo | Together, the IFT81 and IFT74 N-termini form the main module for intraflagellar transport of tubulin[END_REF]).

In the mouse, Shi et al. demonstrated that IFT74 deficiency in male germ cells induces male sterility, with immotile and short-tailed sperm cells [START_REF] Shi | Intraflagellar transport protein 74 is essential for spermatogenesis and male fertility in micedagger[END_REF]. Importantly, in humans, IFT74 deficiency was associated with two cases of Bardet-Biedl syndrome (BBS), a rare multisystemic ciliopathy resulting in retinal dystrophy, obesity, polydactyly, intellectual disability, renal dysfunction, urogenital malformations and male hypogonadism [START_REF] Kleinendorst | Second case of Bardet-Biedl syndrome caused by biallelic variants in IFT74[END_REF][START_REF] Lindstrand | Copy-Number Variation Contributes to the Mutational Load of Bardet-Biedl Syndrome[END_REF]. The work we present here indicates that in humans, mutations in IFT74 can induce isolated male sterility due to impaired flagellogenesis and confirms the importance of IFT machinery for proper assembly and elongation of mammalian sperm flagella.

Results

Identification of an IFT74 bi-allelic missense mutation in two unrelated infertile individuals with MMAF

Whole-exome sequencing (WES) data from a cohort of 167 MMAF-affected individuals were analyzed in order to identify new candidate genes for severe asthenozoospermia due to sperm flagella defects. Previous analyses of this cohort permitted to identify bi-allelic variants in a total of 76 men (45.5%) in 16 confirmed MMAF-associated genes (AK7, ARMC2, CFAP43, CFAP44, CFAP65, CFAP69, CFAP70, CFAP91 (MAATS1), CFAP251 (WDR66), DNAH1, DNAH8, FSIP2, QRICH2, SPEF2, TTC21 and TTC29). In the remaining undiagnosed individuals, we identified a homozygous missense variation c.256G>A; p.Gly86Ser, absent from the genetic variation databases (gnomAD, ClinVar) in IFT74 (Intra Flagellar Transport, Gene ID 80173). We considered this variant to be a good candidate since two unrelated individuals presented the same homozygous variant and IFT74 was shown to be essential for spermatogenesis and male fertility in mice [START_REF] Shi | Intraflagellar transport protein 74 is essential for spermatogenesis and male fertility in micedagger[END_REF]. IFT74 is located on 9p21.2 and is subject to alternative splicing resulting in multiple transcripts and protein isoforms. The canonical IFT74 transcript (ENST00000443698; GenBank: NM_025103) contains 19 coding exons (19/20), predicting a 600-amino-acid protein (UniProtKB: Q96LB3) (Figure 1A). Based on public tissue expression databases (EMBL-EBI Expression Atlas, NCBI, Human protein atlas, and GTEx), IFT74 is highly and preferentially expressed in testes. The protein was also detected by proteomic analyses of human whole sperm [START_REF] Wang | In-depth proteomic analysis of the human sperm reveals complex protein compositions[END_REF]) and human airways ciliary samples [START_REF] Blackburn | Quantitative Proteomic Analysis of Human Airway Cilia Identifies Previously Uncharacterized Proteins of High Abundance[END_REF][START_REF] Wang | In-depth proteomic analysis of the human sperm reveals complex protein compositions[END_REF] and comprises an amino-terminal region with basic residues and a unique large coil-coiled domain extending from amino acid 98 to 482 (Figure 1A). The identified variant, c.256G>A; p.Gly86Ser, impacts the last nucleotide of exon 3 (Figure 1A). According to this location, next to the splice donor consensus site, the variant is predicted to be deleterious for U2 type splicing; it is also scored as deleterious by both adaptive boosting (ada_score > 0.99999) and random forests (rf_score = 0.998), using dbscSNV tool. At the protein level, the variant is predicted to be probably damaging (0.997) according to PolyPhen2, and disease causing (probability = 1) according to Mutation Taster.

We confirmed the presence of the variant at the homozygous state by Sanger sequencing on DNA samples from both MMAF individuals, as illustrated in Figure 1B.

Clinical and biological features

Individual IFT74_1 (i.e. III.5) originated from Tunisia and his parents were not consanguineous (Figure 1B). He reported a 3-year primary infertility with his first wife. After they separated, the woman had a child with another partner. After 18 months of infertility with his second wife, the patient approached our reproductive center for medical help. Medical history was free from any medical or surgical previous events. The patient reported no genital, urinary or other particular symptom. A detailed medical interrogation failed to evidence any exposure to potentially gonadotoxic compounds or factors, either professional or in his life mode. The patient displayed no clinical signs of hypogonadism nor hypoandrogenism; secondary sex characteristics were strictly normal. The only clinical feature deserving specific care was excess weight (BMI 27.9, 75 kg for 1.64 m). No diabetes, nor hypertension were reported. The patient had four sisters, all of them with children, and three brothers (Figure 1C). One of the brothers was also infertile (III.6). The two other brothers were fertile; one of them (III.8) had fathered four children, two healthy daughters and two sons who deceased in the neonatal period; the cause of these deaths was not known. No familial nor genetic pathology were documented in the family.

Semen analyses evidenced a very low progressive sperm motility, contrasting with normal sperm counts and near normal vitality rate (Table 1). The percentage of morphologically normal sperm cells was significantly reduced (14%, lower limit 23%) and detailed analysis of the morphological anomalies indicated sperms with short tails (16%). The pattern of the other abnormalities showed no specificity. In addition, a further analysis performed on a sperm fraction selected through centrifugation on a density gradient showed that instead of being improved as is usual in men with normal semen parameters, motility was markedly decreased after this selection, whereas percentages of vitality and of normal sperms remained close to the initial values.

Individual IFT74_2 originated from Algeria and was recruited in Tunisia at the Polyclinique les Jasmins, Tunis. No history of familial consanguinity has been reported. He has three brothers and two sisters. His three male siblings were married and fertile. His past medical history was marked by a unilateral varicocele treated 6 years before the date of the recruitment.

Analyses of its ejaculate evidenced a low sperm count (7 million/ml) associated with a total sperm immotility and 0% of typical forms with 100% of flagellar abnormalities (Table 1). The majority of the flagella presented an irregular caliber (84%) and/or a short length (73%). The vitality was also dramatically reduced (22%). Additional characterization of the sperm defect was not possible for this patient as he did not volunteer to give any additional samples.

As illustrated for individual IFT74_1 (Figure 2A), sperm morphological analysis of the patients indicated a typical MMAF phenotype defined by sperm with absent, short and irregular flagella in rates largely the distribution ranges observed in control fertile men [START_REF] Auger | Another look at human sperm morphology[END_REF]) (Table 1). Ultrastructure analysis of sperm from individual IFT74_1 was performed by transmission electron microscopy (TEM) and showed abnormal mitochondrial sheath and cytoplasmic bags containing unassembled flagellar components, as previously described for the MMAF phenotype (Figure 2B). Analysis of a total number of 26 transversal sections of sperm cells from individual IFT74_1, evidenced 27% of abnormal axonemal structure, all characterized by the absence of some peripheral doublets; no morphological anomalies were observed on the other transversal sections even at the highest possible magnification and the central pair of the axoneme was always present. Such level of axonemal disorganization appears lower than what was previously reported for MMAF individuals carrying mutations in genes encoding for axonemal or associated structural components such as CFAP43, CFAP44, AK7 and DNAH8 [START_REF] Coutton | Mutations in CFAP43 and CFAP44 cause male infertility and flagellum defects in Trypanosoma and human[END_REF][START_REF] Liu | Bi-allelic DNAH8 Variants Lead to Multiple Morphological Abnormalities of the Sperm Flagella and Primary Male Infertility[END_REF][START_REF] Lores | Homozygous missense mutation L673P in adenylate kinase 7 (AK7) leads to primary male infertility and multiple morphological anomalies of the flagella but not to primary ciliary dyskinesia[END_REF]; the same observation was previously made for patients carrying mutations in TTC29, a gene also encoding for a component of the IFT machinery [START_REF] Lores | Mutations in TTC29, Encoding an Evolutionarily Conserved Axonemal Protein, Result in Asthenozoospermia and Male Infertility[END_REF].

Alteration of IFT74 splicing in Sperm from Patient With Homozygous IFT74 mutation

In order to demonstrate the pathogenicity of the identified c.256G>A;p.Gly86Ser variant, we analyzed the transcript and protein levels in semen samples available from individual IFT74_1.

We first performed semi-quantitative RT-PCR to amplify IFT74 transcripts in sperm cells from control individual and individual IFT74_1, using primers located in exons 2, 4 and 5 (Figure 3A). Semi-quantitative analysis of the ubiquitous housekeeping gene HPRT, showed no difference between control individual and individual IFT74_1 (Figure 3A), indicating that there was no major difference in the quantity and quality of the analyzed mRNA. The signal intensity of IFT74 transcripts appearing slightly decreased in sperm cells from individual IFT74_1, compared with control sperm (Figure 3A), we performed real time quantitative PCR analysis.

This was performed as a single experiment due to limited amount of biological material but the results indicated normal transcript amount in sperm from individual IFT74_1; the ratio of transcript even being slightly increased for the patient (Supplemental Figure S1A). This observation indicates that the mutated transcripts in sperm from individual IFT74_1 were not or only marginally subjected to mRNA decay. However, we note that the PCR amplicons generated in sperm from the control individual formed a sharp band while the amplicons generated with the same primers in sperm from individual IFT74_1 appeared as a smear and were likely heterogeneous. We confirmed the presence of heterogenous transcripts by Sanger sequencing of the amplicons and analysis of the electropherograms; the electropherogram clearly indicated a mixture of at least 2 different transcripts in sample from individual IFT74_1 (Figure 3B). To elucidate the consequences of the c.256G>A mutation and to define the nature of the different transcripts, we individually cloned and sequenced the heterogeneous PCR products generated from individual IFT74_1. We isolated and sequenced 16 clones and we identified the following different transcripts: i.) type 1: normally spliced transcripts carrying the c.256G>A missense mutation in exon 3 (9/16 clones; 56%), ii.) type 2: abnormally spliced transcripts using a cryptic donor site located 30 bp upstream the normal splicing site, which induces an in-frame deletion of 10 amino-acids within exon 3 (5/16 clones, 31%). These two main mutated transcripts isolated in sperm from individual IFT74_1, namely type 1 and type 2, are illustrated in Figure 3C along with the theoretically encoded proteins. In addition, two minor transcripts were detected as spliced transcripts using cryptic donor sites present in intron 3 (2/16 clones, 13%) (Supplemental Figure S1). Type 3 retains 18 bp of intron 3, and encodes for a mutant protein carrying an in-frame insertion of 6 amino-acids. Type 4 retains 108 bp of intron 3, which induces a frameshift and a truncated protein (p.Gly86Ser*13) (Supplemental Figure S1).

Production of IFT74 Mutated Proteins in Sperm from Patient With Homozygous IFT74 mutation

We next performed western blot experiments using two different antibodies raised against IFT74 epitopes, which are located downstream the mutation site (HPA026684 and HPA020247, Sigma Aldrich ®). Using both antibodies, the protein was detected as a single band at the predicted molecular weight of 69 kDa in sperm protein extracts from control individuals. For antibody HPA020247, a shorter exposure of the western blot also clearly indicated a unique band in control sample (data not shown). In contrast, for individual IFT74_1, the protein signal appears as a very tight doublet, which corresponds to the expected sizes of the two principal mutated proteins described above: ENSP00000404122.1:p.Gly86Ser (69.13kDa ; missense mutation) and ENSP00000404122.1:p.Leu77_Gly86del (68.13 kDa ; in frame deletion of 10 aa) (FIGURE 4A).

Alteration of IFT74 Protein localization in Sperm from Patient With Homozygous IFT74 mutation

We then performed immunodetection assays using IFT74 antibody HPA026684. In control individuals we observed that IFT74 was homogeneously distributed along the sperm flagellum.

However, we noticed that in sperm cells from individual IFT74_1 which achieved to assemble a correct length of flagella (visible by Tubulin staining), IFT74 staining was weaker and its distribution was different (Figure 4B). When compared to Tubulin staining, the mutated IFT74 proteins appeared concentrated in the proximal part of the flagellum. This feature was observed in 89,4% of normomorphic sperm cells, and was specific for the IFT74 mutant proteins, as sperm from a MMAF individual mutated in TTC29, referred as i.e. TTC29_1, and harboring wild type IFT74 alleles [START_REF] Lores | Mutations in TTC29, Encoding an Evolutionarily Conserved Axonemal Protein, Result in Asthenozoospermia and Male Infertility[END_REF], did not show such abnormal distribution, although IFT process is likely to be impaired in those cells. Considering that in Chlamydomonas, IFT74 was shown to associated with IFT81 and to form the main module for intraflagellar transport of Tubulin [START_REF] Bhogaraju | Molecular basis of tubulin transport within the cilium by IFT74 and[END_REF][START_REF] Kubo | Together, the IFT81 and IFT74 N-termini form the main module for intraflagellar transport of tubulin[END_REF], we performed IFT81 immunodetection assays and observed that IFT81 protein was also abnormally concentrated in the proximal part of the flagellum, while the staining was homogenously distributed along the sperm flagellum from control individual (Figure 5A). Again, such abnormal localization of IFT81 protein was not observed in sperm from a MMAF individual mutated in TTC29. Interestingly, when analyzing SPAG6, an axonemal component localizing to the central pair, we observed that both sperm from individual IFT74_1 and TTC29_1, displayed a normal distribution pattern along the flagellum (Figure 5B).

Discussion

We report the identification of the IFT74 c.256G>A;p.Gly86Ser bi-allelic missense mutation, in two unrelated infertile men with sperm flagellum assembly defects. We showed that the mutation induces the production of two main mutant IFT74 proteins: one carrying a missense mutation (p.Gly86Ser), the other carrying a 10 amino-acids in-frame deletion (p.Leu77_Gly86del). We suspect that these mutated proteins retain some functional activity, and supporting this hypothesis, we observed a moderate axonemal disorganization in sperm from an IFT74 mutated individual. In particular the central pair was not affected, in contrast to previously investigated MMAF individuals harboring truncating mutations in CFPA43, CFAP44, AK7 and DNAH8, for instance [START_REF] Coutton | Mutations in CFAP43 and CFAP44 cause male infertility and flagellum defects in Trypanosoma and human[END_REF][START_REF] Liu | Bi-allelic DNAH8 Variants Lead to Multiple Morphological Abnormalities of the Sperm Flagella and Primary Male Infertility[END_REF][START_REF] Lores | Homozygous missense mutation L673P in adenylate kinase 7 (AK7) leads to primary male infertility and multiple morphological anomalies of the flagella but not to primary ciliary dyskinesia[END_REF].

IFT74 is required for ciliogenesis and was shown to associate with IFT81 to form the main module for intraflagellar transport of Tubulin. In vitro, the N-terminus of IFT81 is able to directly bind to tubulin, and IFT74 N-terminus, which is positively charged, enhances the affinity of this interaction with the highly acidic C-terminal tails of -tubulin [START_REF] Bhogaraju | Molecular basis of tubulin transport within the cilium by IFT74 and[END_REF]). Brown et al demonstrated that in Chlamydomonas, the N-terminus of IFT74 is required for the recruitment of retrograde IFT-A subcomplexes to IFT-B, for the assembly of new trains at the base of the cilium and their injection into the cilium [START_REF] Brown | Assembly of IFT trains at the ciliary base depends on IFT74[END_REF]. Our observation that IFT81 protein is mislocalized and retained in the proximal region of the flagellum, in sperm from individual carrying homozygous IFT74 mutation, suggests that such molecular complex is conserved and functional in mammalian sperm too.

The MMAF phenotype and the male sterility observed in IFT74 homozygous mutated individuals is in line with the phenotype observed in Chlamydomonas reinhardtii, and in mouse invalidated for IFT74. In Chlamydomonas, IFT74 null mutation abrogates flagella assembly [START_REF] Brown | Assembly of IFT trains at the ciliary base depends on IFT74[END_REF][START_REF] Kubo | Together, the IFT81 and IFT74 N-termini form the main module for intraflagellar transport of tubulin[END_REF], and in the mouse, its specific deletion in male germ cells was associated with infertility due to reduced production of sperm with short or absent tails [START_REF] Shi | Intraflagellar transport protein 74 is essential for spermatogenesis and male fertility in micedagger[END_REF]. However, in human, individuals carrying biallelic IFT74 loss of function mutations were reported to display Bardet-Biedl Syndrome (BBS), a rare developmental genetic disorder linked to severe impairment of primary cilia function [START_REF] Kleinendorst | Second case of Bardet-Biedl syndrome caused by biallelic variants in IFT74[END_REF][START_REF] Lindstrand | Copy-Number Variation Contributes to the Mutational Load of Bardet-Biedl Syndrome[END_REF]. Mutations in IFT81 were also associated with short-Rib polydactyly syndrome, a group of bone malformations characterized by a narrow thorax and polydactyly [START_REF] Duran | Destabilization of the IFT-B cilia core complex due to mutations in IFT81 causes a Spectrum of Short-Rib Polydactyly[END_REF]. BBS is a genetically heterogeneous disease with considerable phenotypic variability. To date more than 20 genes (BBS1-BBS20) were mapped to the disease; those BBS genes encode for components of the BBSome complex located at ciliary basal body (BBS1, 2, 4, 5, 7, 8, 9), for chaperone and microtubule associated proteins [START_REF] Khan | Genetics of human Bardet-Biedl syndrome, an updates[END_REF][START_REF] Priya | Bardet-Biedl syndrome: Genetics, molecular pathophysiology, and disease management[END_REF]). The disease is typified by mixed rod-cone dystrophy, polydactyly associated sometimes with syndactyly and/or brachydactyly. Mental retardation is also present in about 50% of cases, obesity in about 70%, associated with insulin resistance, type 2 diabetes, dyslipidemia, and hypertension [START_REF] Tsang | Ciliopathy: Bardet-Biedl Syndrome[END_REF]. So far BBS patients were reported with hypogonadotropic hypogonadism and urogenital malformations with renal anomalies present in about 40% of the patients [START_REF] Tsang | Ciliopathy: Bardet-Biedl Syndrome[END_REF]). However, the two BBS patients identified with IFT74 null mutations were suffering from obesity, polydactyly, retinal dystrophy, but no renal abnormality was diagnosed and only one of the patients had intellectual disability [START_REF] Kleinendorst | Second case of Bardet-Biedl syndrome caused by biallelic variants in IFT74[END_REF][START_REF] Lindstrand | Copy-Number Variation Contributes to the Mutational Load of Bardet-Biedl Syndrome[END_REF]). Considering our present data, those patients could also display spermiogenesis defects and male sterility; however, no fertility phenotype was stated in the above studies. While writing this manuscript, a study from Koscinski et al. reported the first characterization of the reproductive functions for a series of 11 adult male BBS patients aged of 18 to 39. Those patients carried mutations in BBS1, 3, 5, 9, 10 and 12 and some of them displayed hypogonadism and urogenital anomalies (unilateral or bilateral cryptorchidism, micropenis, short scrotum, epididymal cysts …). However, these anomalies were not systematically present, which indicated that the reproductive features of BBS patient are also extremely variable [START_REF] Koscinski | Reproduction Function in Male Patients With Bardet Biedl Syndrome[END_REF]. None of those 11 patients were reported by the authors with a typical MMAF phenotype nor with ultra-structural defects of the sperm axoneme, while reduced sperm motility was frequently observed, which the authors assumed to result from an altered spermatogenesis due an abnormal thermoregulation caused by the obesity and genital anomalies of the tested subjects [START_REF] Dieterich | The Aurora Kinase C c.144delC mutation causes meiosis I arrest in men and is frequent in the North African population[END_REF].

Importantly, following a comprehensive clinical examination of the two MMAF individuals we report herein with the IFT74 c. 256G>A mutation, no clinical features indicative of a ciliopathy nor of the BBS were observed. In particular, genital and urogenital malformations, which are part of the BBS phenotype [START_REF] Tsang | Ciliopathy: Bardet-Biedl Syndrome[END_REF] were not detected in the two MMAF patients. The patients did not suffer from intellectual disability neither; one of them (individual IFT74_1) was occupying an engineer position. No diabetes nor hypertension were reported. Only weight excess was reported for individual IFT74_1, which remains limited as compare to the severe obesity usually found in BBS patients. Sperm production was quantitatively normal for individual IFT74_1, which again excluded the presence of hypogonadism, which is so far the only reproductive phenotype described for BBS patients in association with urogenital malformations [START_REF] Koscinski | Reproduction Function in Male Patients With Bardet Biedl Syndrome[END_REF]. Individual IFT74_2 had a significantly reduced sperm count but this patient also suffered from unilateral varicocele, which was treated six years earlier. As numerous studies have reported an association between varicocele and altered semen parameters, the reduced sperm count of this patient may be partly caused by the varicocele. Overall, the examinations and clinical signs reported for both patients carrying the IFT74 c. 256G>A mutation, indicated a phenotype of isolated male infertility, with sperm anomalies associated with a MMAF phenotype but no major clinical signs of BBS.

It is of particular interest to understand why spermiogenesis is affected and ciliogenesis preserved in IFT74 mutated patients while IFT74 appears essential for IFT and for both cilia and flagella assembly. We showed that the c. 256G>A missense mutation induces the production of two main mutated IFT74 proteins: one carrying a missense mutation (p.Gly86Ser), the other carrying an in-frame 10 amino-acids deletion, (p.Leu77_Gly86del).

Considering the site of these mutations, both types of mutant proteins could be affected in their N-terminal domain, which is known to be required for Tubulin binding. Binding and transport of the Tubulin is therefore expected to be impacted in cells from the patients. However, we suspect that the mutated IFT74 proteins are partly functional and could be sufficient to maintain IFT in most cilia but not in sperm flagella, thus inducing male sterility but not BBS. Such sperm-restricted phenotype was previously observed for a somatic missense mutation in AK7, encoding a Cilia and flagella Adenylate kinase, which only induces male sterility but not Primary Ciliary Dyskinesia in human [START_REF] Lores | Homozygous missense mutation L673P in adenylate kinase 7 (AK7) leads to primary male infertility and multiple morphological anomalies of the flagella but not to primary ciliary dyskinesia[END_REF]. The greater sensibility of sperm flagellum towards these mutations, denotes some specificities in the molecular mechanisms of flagellum assembly and/or a reduced redundancy in functional proteins in this organelle. This point is reinforced by the observation that in mice, the invalidation of several genes demonstrated to be involved in human BBS (Bbs1, Bbs2, Bbs4, Bbs6 and Bbs7), only induced male sterility due to absent or abnormal sperm flagella while the cilia were properly assembled [START_REF] Koscinski | Reproduction Function in Male Patients With Bardet Biedl Syndrome[END_REF].

Overall the consequences of the IFT74 missense mutation described in this report confirms that the IFT machinery is certainly required for sperm flagellum assembly in mammals, in contrast to previous assumption that were done for both Drosophila and mammalian sperm. Moreover, a large body of studies now shows that despite common molecular alterations [START_REF] Koscinski | Reproduction Function in Male Patients With Bardet Biedl Syndrome[END_REF]Niederlova et al. 2019) ciliopathies encompass a collection of distinct clinical features. We show here that the nature of the mutation affecting a particular gene required for ciliogenesis may induce different pathologies, adding a level of complexity to the clinical manifestations of ciliary dysfunction.

Materials and methods

Whole exome sequencing and variants filtering

Genomic DNA was isolated from saliva using the Oragen DNA extraction kit (DNAgenotech®, Ottawa, Canada). Coding regions and intron/exon boundaries were sequenced on the Novogen platform based in China (agilent v6, HiSeqX,) after enrichment with Agilent kits (Agilent Technologies, Wokingham, UK).

Bioinformatics analyses: All datasets were reanalyzed using our updated bioinformatics pipeline, following the GATK 3.7 best practice recommendations. Briefly: sequencing reads were aligned against the GRCh38 reference genome using BWA-MEM 0.7.17, resulting BAM files were cleaned and sorted and duplicates were marked using Picard 2.7.1, and variants were called using GATK HaplotypeCaller to produce GVCF files. The GVCF files were then merged with a custom script (https://github.com/bcm-uga/mergeGVCFs) to obtain a single GVCF, and a final VCF file was produced with GATK Genotype GVCFs.

Variants filtering: The most promising candidate variants were identified using an in-house bioinformatics pipeline (Perl scripts available upon request), as follows: Low-quality variant calls (DP<5, GQ<20, or less than 15% of reads supporting the ALT allele) were removed. We used Variant Effect Predictor (VEP version 92) [START_REF] Mclaren | The Ensembl Variant Effect Predictor[END_REF] to annotate the variants and predict their impact. variants with a minor allele frequency greater than 5% in the NHLBI ESP6500 [Exome Variant Server, NHLBI GO Exome Sequencing Project (ESP), Seattle, WA], greater than 3% in 1000 Genomes Project phase 3 datasets, or greater than 1% in gnomAD v2.0 (https://gnomad.broadinstitute.org/) were discarded. We also compared these variants to an inhouse database of over 200 control exomes enriched for North African subjects. All variants present in homozygous state in this control database were excluded. We then only retained variants impacting splice donor or acceptor sites or causing frameshifts, in-frame insertions or deletions, stop gain, stop loss or missense variants except those scored as "tolerated" by SIFT (https://sift.bii.a-star.edu.sg/) and as "benign" by Polyphen-2 (http://genetics.bwh.harvard.edu/pph2/). Gene expression data from the Genotype-Tissue Expression, GTEx project (https://gtexportal.org/home/) were added and used to strengthen the likely implication of the selected candidate variants.

Sanger Sequencing

The identified variants in IFT74 were validated by Sanger sequencing performed on ABI 3500XL (Applied Biosystems). Data analyses were performed using SeqScape software (Applied Biosystems). Sequences of primers used and the expected product sizes are summarized in Table 1.

Semen Analysis

Semen samples were obtained by masturbation after a period of 2 to 7 days of sexual abstinence.

Semen samples were incubated at 37°C for 30 min for liquefaction and semen parameters were evaluated according to World Health Organization (WHO) guidelines [START_REF] Cooper | World Health Organization reference values for human semen characteristics[END_REF].

Sperm vitality was assessed by eosin staining, and sperm morphology was analyzed on Schorr stained semen smears according to David's classification [START_REF] Auger | Another look at human sperm morphology[END_REF]. Moreover, as usual for patients requiring medically assisted procreation, a further analysis was performed on a sperm fraction recovered after selection by centrifugation (300g, 20 minutes) on density gradient.

Transmission Electron Microscopy analysis of sperm cells

Human sperm cells (10 millions) were fixed by incubation in 0.1 M phosphate buffer pH 7 supplemented with 3% glutaraldehyde (Grade I; Sigma-Aldrich Co. Saint-Louis, MO, USA)

for 2 h at room temperature. After two washes in PBS, sperm cells were resuspended in 0.2 M sodium cacodylate buffer and the samples were post-fixed by incubation with 1% osmium tetroxide (Electron Microscopy Sciences, Hatfield, UK). Samples were then dehydrated by immersion in a graded series of alcohol solutions and embedded in Epon resin (Polysciences Inc., Warrington, USA). Semi-thin sections were cut and stained with toluidine blue-Azur II.

Ultra-thin sections (90 nm) were cut with a Reichert Ultracut S ultramicrotome (Reichert-Jung AG, Wien, Austria) and were then stained with uranyl acetate and lead citrate. Sections were analyzed with a JEOL 1011 microscope and digital images were acquired with a Gatan

Erlangshen CCD camera and Digital Micrograph software.

RT-PCR Analysis of Sperm Cells

200-800 ng of total RNA was extracted from 5-10 million human spermatozoa using NucleoSpin RNA kit (Macherey Nagel) and subjected to reverse transcription with High-Capacity cDNA Reverse Transcription kit (Applied Biosystems, Fisher Scientific) following the manufacturer's instructions. PCR reactions were performed from 50 ng of retrotranscripted mRNA with GoTaq DNA polymerase (Promega) using IFT74 specific primers with 40 cycles of amplification ( 95°C, 30s; 55°C, 30s; 72°C, 1min). Amplicons were gel purified and either directly sequenced (Eurofins Genomics), or cloned before sequencing using TA cloning vector (Thermo Fisher Scientific). Sequences of primers used and expected product sizes are summarized in Table S1.

RT-qPCR Analysis of Sperm Cells

cDNA prepared from one semen sample were used as template for real-time fluorescence quantitative PCR with SensiFAST SYBR® No-ROX Kit (Bioline). IFT74 and HPRT qPCR primer pairs were obtained from OriGene. The quantification of mRNA was performed in triplicate with HPRT as an internal control, according to the -2 Ct method. Sequences of primers used and expected product sizes are summarized in Supplemental Table S1.

Western Blot Analysis on Sperm Cells

Denaturized protein samples corresponding to 1-2 million of spermatozoa from control or patient were loaded on SDS-PAGE (8% acrylamide/bisacrylamide [40% 37.5:1]) and transferred onto nitrocellulose membranes. The membranes were blocked in 5% milk in PBS-Tween 0.1%, and immunoblot analysis was performed using the indicated primary antibodies.

Details of antibodies and dilutions used for western blot assays are provided in Table 2.

Immunofluorescence Analysis of Sperm Cells

10 μL of semen samples were spread onto a Superfrost Plus slide (Menzel Glasbearbeitungswerk, GmbH & Co. KG). Sperm was fixed by incubation with PBS/4% paraformaldehyde for 10 min. The slides were incubated 20 min at 95°C in citrate buffer (H-3300, VectorLabs). The slides were next treated with 0.2% Triton in PBS for permeabilization and then blocked by incubation in 10% goat serum for 1 h. They were then incubated overnight with primary antibodies at 4°C and then with secondary antibodies for 1 h at room temperature.

The slides were mounted in Vectashield medium (Vector Laboratories) supplemented with 0.5 μg/mL DAPI. Slides were analyzed with a Zeiss Axiophot epifluorescence microscope. Digital images were acquired with a cooled charge-coupled device (CCD) camera (Hamamatsu Co.), under identical instrument settings, with MetaMorph software (Molecular Devices). Details of antibodies and dilutions used for immunofluorescence assays are provided in table S2. respectively. Two other transcripts resulting from abnormal splicing of exon3 (intron retention), type 3 and type 4, were identified (each 7.5%) and encode for mutant proteins with an in-frame insertion of 7 amino acids and a truncated protein, respectively. The higher panel represents de nucleotide sequences of all types of transcripts as compared to the control sequence (WT); in red are highlighted the mutated nucleotides: missense, deletion (-) or intronic insertion. The lower panel represents the encoded proteins with mutated residues highlighted in red: missense, deletion (-) or insertion.

Values are expressed in percent, unless specified otherwise. ND: not determined. a Lower and upper reference limits (5th centiles and their 95% confidence intervals) according to the World Health Organization (WHO) standards [START_REF] Cooper | World Health Organization reference values for human semen characteristics[END_REF]), David's Classification (for typical sperm morphology) and the distribution range of morphologically abnormal spermatozoa observed in fertile individuals [START_REF] Auger | Another look at human sperm morphology[END_REF].

7

(5-9) 1 (0-2)

42

(39-45)

FiguresFigure 1 .

 1 Figures

Figure 2 .

 2 Figure 2. Characterization of the sperm morphological and ultra-structural phenotype of

Figure 3 .

 3 Figure 3. IFT74 splicing and transcript analysis in Sperm from Individual Carrying

Figure 4 .

 4 Figure 4. Analysis of IFT74 Proteins in Sperm from Individual Carrying homozygous

Table 1 .

 1 Semen parameters and sperm morphological defects (flagellum and head) of MMAF individuals carrying mutations in IFT74

	General Semen Characteristics	Flagellum defects

(57)(58)(59)[START_REF] Rosenbaum | Intraflagellar transport[END_REF](61)(62)(63)

Acknowledgements

We thank all the individuals and their families for their cooperation, as well as all the referring physicians. We thank all the technicians from the Service de Biologie de la Reproduction at the Hôpital Cochin (Paris) for routine semen sample evaluation (Jacques Bras, Nathalie Chériau, Véronique Hernandorena, Jean-Claude Cambronne and Caroline Villalon). We thank Cellular Imaging Facility of the Institut Cochin for electron microscopy procedures.

Funding Information

This work was supported by Institut National de la Santé et de la Recherche Médicale (INSERM), Centre National de la Recherche Scientifique (CNRS), Université Paris Descartes, University Grenoble-Alpes and Agence Nationale de la Recherche : grant MASFLAGELLA ANR-14-CE15 and grant FLAGEL-OME ANR-19-CE17-0014 to PR, NTM and AT, grant DIVERCIL-17-CE13-0023 to AT.

Data Availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

Accession numbers

The IFT74 variant reported in this manuscript is accessible in ClinVar with the submission number SUB8577098.

DECLARATIONS Competing Interests

The authors have no conflict of interest to declare.

Author contribution

All authors contributed to the study conception and design. AT designed and supervised the study. M-AL, LF, CP, SFBM, RZ and ED recruited the patients, performed clinical analysis and characterization. NTM, CC and PR performed exome and bioinformatics analysis. PL, Z-EK, AA-Y, AD, CCa and S-HH performed experimental work (Sanger sequencing, RT-PCR, Sequencing, Immunofluorescence, Immunoblotting). AT performed MO and TEM analysis. PL and AT performed data illustrations. PL, MW, LS and EC, ED and AT analysed the data. PL and AT wrote the manuscript. The first draft of the manuscript was written by PL and AT, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Animal Research

Not applicable

Ethics approval

The study was performed according to the principle of the Declaration of Helsinki. The use of human samples and the genetic studies were approved by local and governmental committees:

Consent to Participate

Informed consent was obtained from all individuals included in the study.

Consent to Publish

Agreement for data publication was obtained from all individuals included in the study.

Supplementary Figures

Supplemental Figure 1


D Fournier

M Marangolo

M Eddrief

N N Kolesnikov

C Fretigny

Straightforward measurement of thermal properties of anisotropic materials: the case of Bi 2 Se 3 single crystal

We show that by a simple two-steps measurement protocol one can extract the thermal properties of anisotropic insulator materials. We focus on Bi 2 Se 3 single crystal, a layered crystal with individual sheets held together by Van der Waals force, presenting strong heat diffusion anisotropy. Since the shape of the sample does not allow experiments in the perpendicular direction the challenge is to measure the in plane and out of plane thermal properties by in plane measurements. The optical properties of Bi 2 Se 3 being known (opaque sample for the pump and probe beams), thermoreflectance microscopy experiments can be done on the bare substrate. In this case, the lateral heat diffusion is governed by the in plane thermal diffusivity. A 100 nm gold layer is then deposited on the sample. In this second experiment it is straightforward to demonstrate that the perpendicular thermal properties of the layer rule the lateral diffusivity. The good agreement of theoretical curves obtained by thermal models with experimental data permit us to evaluate the thermal conductivity coefficients of bulk Bi2Se3.

Introduction

Thermal conductivity k is one of the leading parameters employed to describe the transport phenomena in solid state systems. Its formal definition comes from Boltzmann transport equations that clearly put into evidence the tensorial nature of k and incite experimentalists to measure its directional values. This is particularly important in layered system like di-chalcogenides systems (MX 2 with M=Mo,W; X=S, Se, Te), black phosphorus and selenides (Bi 2 Se 3 ) and tellurides (Bi 2 Te 3 ) of Bismuth. Indeed, in these compounds the Van der Waals bonding between layers makes the cross-plane thermal conductivity k z much lower than the in-plane one k r [see for example, Ref 1,2]. Most of these layered systems have been extensively studied in bulk because of their thermoelectric applications since their very low values of k are accompanied by significant electrical conductivity () and high Seebeck coefficient (S) leading to high dimensionless figure of merit

k σT S = ZT / 2
, with T the absolute temperature. Inevitably, the genuine anisotropic character of k is lost when such materials are employed in their polycristalline form (e.g. in industrial thermoelectric applications) leading to effective k parameters that are affected not only by the intrinsic (i.e. depending of the electronic and phononic band structure) k z and k r values of the compound but also by extrinsic characteristics of the manufactured material (grain boundaries, disorder, defects, etc..). Interestingly, similar considerations can be done when bulk layered materials are compared with ultra thin (one or few layers) 2D materials that have attracted the attention of current research because of their electronic, spintronic and optoelectronic properties. Indeed, thermal conductivity of 2D materials is affected by nanoscale properties like phonon confinement, thermal diffusion into the underlying substrates and peculiar intrinsic properties like topology insulating states (ex. Bi 2 Se 3 and Bi 2 Te 3 ) and electronic band gap modifications (MoS 2 ).

As a matter of fact, thermoreflectance techniques are currently employed to extract directional k values [see for example Ref.3]. Basically, this kind of pump-probe experiments demands two light beams: one for the creation of the heat source and the other for the measurement of the enhanced local temperature. Light reflectance is affected by the temperature field associated to the heat diffusion, permitting to extract thermal properties by adopting convenient models. It's important to underline that k r measurements demand a quite simple set-up where thermoreflectance is measured as a function of the lateral distance between two distinct laser sources (the pump and the probe). Moreover, no absolute temperature evaluation is needed. On the other hand, k z demands either an absolute temperature evaluation in frequency mode [4][5][6][7][8][9][10][11][12][13] or picosecond acoustics and time delay measurements in time mode. [14][15][16][17][18][19] thermoreflectance based on. In the following, after a brief recall of thermoreflectance techniques, we will present a heat diffusion model in the frequency domain that permits us to envisage a new method to extract k z in bulk materials in a straightforward way without absolute temperature evaluation. Our calculations put into evidence that similarly to k r , k z can be measured by lateral measurements once the bad thermal conductor sample is covered by a thin high thermal conductivity film (gold in our case). This method permitted us to measure the k r and k z values of bulk Bi 2 Se 3 , a well known thermoelectric material and topological insulator.

Theory in the case of semi-infinite sample

In this section, we calculate the spatio-temporal temperature field induced on the surface of a semiinfinite sample by a modulated point heat source. The sample presents a uniaxial symmetry with the symmetry axis along the normal of the surface plane. It's convenient to write the heat diffusion equation in a cylindrical coordinate system [20,21,22] in the following manner:

Where T(r,z,t) is the heat modulated temperature variation, k r and k z are the values of the thermal conductivities in-and out-of plane directions, respectively. After a t-Fourier transform and an r-Hankel transform z,t) T(r, becomes ω) z, Θ(λ, . In the transformed space, the solution of Eq. 1 is:

Eq.2 exp 2 z) k C i + λ k k ( A = ω) z, Θ(λ, r z r  
The sample region corresponds to z < 0. A is obtained from the boundary conditions given by the conservation of heat flux through the interface and by the temperature continuity at the interface (z = 0). If we suppose no loss in air above the sample the heat flux conservation at z = 0 reads:

Φ = z ω) z, Θ(λ, k z z 0    
,  being the source heat flux deposited on the surface at radial frequency . It is worthwhile to notice that only k z appears in the boundary condition for the anisotropic case. This gives:

Eq.1 1 2 2 2 2 t t) z, T(r, ρC = ) r t) z, T(r, r + r t) z, T(r, ( k + z t) z, T(r, k r z         Eq.3 exp 2 2 r z r r z r k C iω + λ k k z) k C iω + λ k k ( Φ = ω) z, Θ(λ,   
The surface temperature (z=0) in the real space is obtained after an inverse Hankel transform:

Eq.4 ) 0 0 2 0     d r ( J k C iω + λ k k Φ = ω) , T(r, r z r  
By integration, the analytical expression of the spherical thermal wave is obtained. It characterizes the surface heat diffusion from a point source in a semi-infinite medium: µ r being the lateral thermal diffusion length and D r the lateral thermal diffusivity:

ω D = μ ρC k = D r r r r

and

Obviously, in the case of an isotropic sample

k = k = k z r
, Eq.5 reads:

A careful comparison of equations 5 (anisotropic case) and 5 bis (isotropic case) reveals that the surface temperature modulation equations just differ by the conductivity terms. It turns out that the effective conductivity in the anisotropic case is just the geometric mean of the in-and out-of-plane conductivities while the in-plane diffusivity is unchanged. In the next chapter we will show that these useful relationships are preserved in the case of an anisotropic substrate capped by an isotropic layer.

Theory in the case of layered sample.

Our discussion starts from the mathematical evidence that equation 1 can be written in the following way:

Here we have supposed that the symmetry axis of the medium is parallel to the z axis and we have rescaled the z-coordinate as

z k k = Z r z [23], i.e. z k k = Z Z r z 1 , 1 , 0  and z k k = Z Z r z 2 , 2 , 1



for the two different materials. Similarly to the isotropic case, it is meaningful to define a diffusion coefficient equal Eq.6

1 ~2 2 2 2 t t) Z, (r, T k ρC = ) r t) Z, (r, T r + r t) Z, (r, T ( + Z t) Z, (r, T r         bis Eq.5 exp exp 0 ) μ r i ( ) μ r ( k Φ = ω) , T(r,   Eq.5 exp exp 0 ) μ r i ( ) μ r ( k k Φ = ω) , T(r, r r z r   to ρC k = D
r . Now, we write the boundary conditions at the interface (

i z = z
) characterized by the heat flux conservation and the equality of the temperature in the case of isotropic media:

i z = z z, i z = z z, | z t) z, (r, T k = | z t) z, (r, T k     1 1 0 0 and ) , ( ) , ( 1 0 t z r T t z r T i i



When the z-coordinate is rescaled it is possible to write for z=z i : In the following we will study the case of an isotropic layer deposited on an anisotropic substrate. This is the case of our experimental samples, i.e. evaporated gold on anisotropic uniaxial Bi 2 Se 3 . First of all we recall that the surface temperature of a sample consisting of an isotropic layer (1) whose thickness is h 1 on the top of a semi-infinite isotropic substrate (0) heated by a modulated point source can be expressed as [5,15]: Eq.7 0

1 1 1 1 1 0 0 0 0 0 ~Z t) , Z (r, T k k = Z t) , Z (r, T k k r, Z, r, Z,     and ) , ( ) , ( ~1 0 t Z r T t Z r T i i
0 0 0 1 1 1 1 1 1 1 1 0 0 0 1 1 (λλr)λd J σ k + ) σ th(h σ k σ k + ) σ th(h σ k σ k Φ = ω) , T(r,   0.
substrate in the and 1 layer in the vector wave the is where

0 0 2 0 1 1 2 1 k C iω + λ = σ k C iω + λ = σ 0 1

 

Let us underline that in this case, no closed form solution can be found. From the discussion above, when the substrate is anisotropic, surface temperature is obtained by replacing the substrate conductivity with its effective value in the above solution (z rescaling has no effect since the layer is supposed isotropic):

Eq.7bis 0

0 0 2 0 0 1 1 1 1 1 1 1 1 0 2 0 0 0 1 1 (λλr)λd J k C iω + λ k k + ) σ th(h σ k σ k + ) σ th(h k C iω + λ k k σ k Φ = ω) , T(r, r r z r r z    
Without getting too specific, one can say that in the case of a layered structure, the heat diffusion process is strongly depending upon the thermal properties of each component. It may be useful to describe the two asymptotic regimes reported in Fig. 1 Fig. 1 Lateral diffusion scheme in the case of layered structure. Left: bad thermal conductor deposited on conductor substrate Right: good thermal conductor on insulator.

1) If the layer has a low thermal conductivity as compared to the substrate (Fig. 1, left), the asymptotic behavior reflects the substrate lateral diffusion [8]:

2) In the opposite case (Fig. 1, right) (highly conductive layer on an insulating substrate,

0 1 >> k k and 0 1 >> D D
), the lateral heat diffusion corresponds to confined heat regime and the slopes of the amplitude and the phase of the asymptotic modulation temperature are neither that of the layer nor that of the substrate, as shown in references [12] and [13]: As reported in [12,13] specific combinations of a and b can be written as:

0 1 0 1 0 1 0 2 2 1 2 1 1 2    Eq.10
The former expression, which does not depend on h, shows that the thermal diffusivity of the upper layer can be experimentally obtained even if the thickness of the layer is unknown. The latter expression attests that the thermal properties of the substrate appear as a ratio Finally, the important point of our theoretical approach is that a set of two experiments (the former on a bare anisotropic substrate and the latter on the same sample covered by an isotropic layer), permits to measure separately the sample in plane thermal diffusivity D r and the effusivity

ρC k = e z .
Consequently, if the density and specific heat are known, one can obtain the values of k r and k z . In the following, after a brief description of the experimental set up, we will present thermal conductivities measurements of Bi 2 Se 3 bulk samples.

Experimental results

The sample Bi 2 Se 3 single crystals were grown by high-pressure vertical zone melting, the method technically close to one described earlier in [24]. The initial load was pre-synthesized from elements with 99,9999 % purity in evacuated silica ampoules. The growth process was carried out in graphite crucibles with the zone movement rate of 2-4 mm/h and temperature gradient on the crystallization front of 30-40 deg. Celsius. The ambient medium was argon at 2.0 MPa pressure. The exfoliation along (0001) was carried out mechanically after cutting the crystal perpendicularly to the mentioned plane.

The setup

The sample surface is illuminated with an intensity modulated pump beam (532 nm laser) focused on the sample surface (around 1 µm diameter spot). The pump wavelength is chosen in order to be totally or partially absorbed by the sample. Thermal waves are then excited in the sample and monitored by the reflectivity change of another focused laser beam (probe beam). We use a 488 nm laser diode probe beam to maximize the probe sensitivity to the thermal field when the sample is covered with a gold thin film. The scanning is carried out by rotating a dichroic mirror controlled by stepper motors. A photodiode and a lock-in amplifier record the AC sample reflectivity component, in a frequency range between 1 kHz and 1MHz. Data collection and stepper motors positioning were performed by home-written software in LabVIEW ® (National Instruments). We have used very low power for the pump (532 nm laser -1 mW) and probe beam (488 nm laser diode -0.2 mW) to measuring bare Bi 2 Se 3 crystal, which is opaque for the two pump and probe beams [23].

Bulk Bi 2 Se 3

Figure 2 shows the experimental results (amplitude and phase) obtained by scanning the surface around the heat source point on the bare substrate. The three experimental data sets correspond to three modulation frequencies that is to say to three penetrations of the heat in the material because the thermal diffusion length is depending upon the frequency. We succeeded in obtaining a reliable set of parameters ( thermal diffusivity, spot diameter) for the fit of the three curves obtained by adopting Eq.5 ( spherical thermal waves). The good agreement obtained for each modulation frequency corroborates the thermal transport model at different probing depths ( 2-5 micrometers range). As discussed in the previous section, the measurement of the bare sample permits us to evaluate the in plane thermal diffusivity, Dr. It turns out that the Dr is estimated to 2.5 10 -6 m 2 /s with an uncertainty of 0.25 m 2 /s.

C D k r r  
can be evaluated by considering the C product C =1.4 10 6 J/m 3 K [7.51 g/cm 3 and C running [25] between 125 and 130 JK -1 mol -1 ] giving k r = 3.5 W/mK. The sample was then covered by a 100nm evaporated Gold layer (with a hanging layer to improve adhesion). Figure 3 shows the experimental results obtained on this layered sample. As expected, the heat diffusion regime is strongly modified and differs of the previous spherical wave regime (Eq.5). Indeed, the amplitude measurements presents a r 1 trend corresponding to a confined heat diffusion [13]. The gold layer is a very good thermal conductor deposited to a thermal insulator (the case 2 discussed in the previous chapter). By a careful evaluation of the slopes of the amplitude and phase curves [12] we obtain the effusivity of the Bi 2 Se 3 crystal (Fig. 3). From this value



Discussion

Our experimental protocol consisting of two distinct experiments one on the bare substrate and the other one on the sample covered by a thin gold layer. The first one permitted us to evaluate the radial thermal diffusivity D r = 2.5 10 -6 m 2 /s and the second one the perpendicular thermal conductivity k z = 0.9 W/mK of an anisotropic material, i.e. Bi 2 Se 3 . It turns out that a fitting procedure based on an anisotropic thermal transport model gives D r = 2.5 10 -6 m 2 /s, k r = 3.5 W/mK and k z = 0.82 W/mK, D z = 6.1 10 -7 m 2 /s the density and the specific heat being close to C = 1.40 10 6 Ws/m 3 K. These results are in good agreement with recent measurements reported in literature [26,27]. The following considerations are also worthwhile to be reported:

1 Our measurements are not affected by the size of the pump and of the probe spots since they are based on the asymptotic part of the record.

2 The optical absorption coefficient of the bare substrate which can lead to an eventual penetration depth of the light [23] is not a binding factor since only the asymptotic behavior of the slope of the phase is taken in consideration.

3 An eventual interface resistance between the gold layer and Bi 2 Se 3 due to a poor adhesion of the metallic layer plays a minor role. Indeed, an overevaluation of the interface resistance such as R = 5 10 -8 m 2 K/W would lower k z to 0.65 W/mK, which is within the error bar of the measurements. 4 We corroborated our two steps protocol by performing uncomfortable measurements on a lateral side of the layered Bi 2 Se 3 sample, i.e. the plane containing the c-and the a-axis of the rhombohedral structure. This permits to obtain D z = 8.2 10 -7 m 2 /s and k z = 1.1 W/mK, as attested by the good agreement between experimental data and fitting curves in Fig. 4.

Conclusion

We proposed a very simple method to put into evidence and to measure the thermal anisotropy of a poor thermal conductor sample. This was done with experiments performed only radially. This kind of experiments is well suited when the shape or the nature of the sample do not permit to perform thermoreflectance experiments on different faces of the. We have shown that thermoreflectance measurements on the bare crystal gives the radial thermal diffusivity, while the measurements on the same sample covered by a thin gold layer gives the perpendicular thermal conductivity. We notice that sample a strong contrast of the thermal conductivity of the two materials in needed in our approach. Our experimental protocol permitted us to measure the following Bi 2 Se 3 thermal properties: D r = 2.5±0.25 10 -6 m 2 /s, k r = 3.5±0.3 W/mK k z = 0.82± 0.18 W/mK, D z = 6.7± 10 -7 m 2 /s. These values are in good agreement with previous experimental values reported in litterature [26,27].



  This equation written by rescaling the z-coordinate by a factor r z k k reveals that the thermal conductivity of an anisotropic material is given by the geometrical mean,

  the thermal properties of the upper layer are known, the substrate thermal effusivity the case of an anisotropic substrate, only the effusivity of the substrate can be deduced:

Fig. 2

 2 Fig.2 Thermo reflectance phase data on the Bi 2 Se 3 bare sample at 50-100-200kHz Circles: experimental data ; Lines: theoretical model with D r = 2.5 ±0.25 10 -6 m 2 /s -C D k r r

Fig 3 :

 3 Fig 3: 100nm Gold deposited on Bi 2 Se 3 Points: experimental data at 4 frequencies 100 kHz, 200 kHz, 400 kHz, 800 kHz Lines: theoretical model with 100nm gold k=250 W/mK -D = 1 10 -4 m 2 /s Bi 2 Se 3 effusivity =1100 ± 100 Ws/m 2 K, mK W C e k z / 0.18 82 . 0 2    

Fig 4 :

 4 Fig 4: Experiments on two faces (top and lateral faces) of bare Bi 2 Se 3 Points: experimental data at 100 kHz black points 001 axe c , red points a-axis of the rhombohedral structure Lines: theoretical model with D r = 2.55 10 -6 m 2 /s axe c and D r = 8.2 10 -7 m 2 /s axe a