Olivier Masson

Anne-Sophie Bach

Danielle Derocq

Christine Prébois

Valérie Laurent- Matha

Sophie Pattingre

Emmanuelle Liaudet-Coopman

Pathophysiological functions of cathepsin D: targeting its catalytic activity versus its protein binding activity?

Keywords: cathepsin D, protease, cancer, proliferation, apoptosis

The lysosomal aspartic protease cathepsin D (cath-D) is over-expressed and hyper-secreted by epithelial breast cancer cells. This protease is an independent marker of poor prognosis in breast cancer as it is correlated with the incidence of clinical metastasis. In normal cells, cath-D is localized in intracellular vesicles (lysosomes and endosomes). In cancer cells, overexpressed cath-D accumulates in cells, where it may affect their degradative capacities, and the pro-enzyme is hypersecreted in the tumor micro-environment. In addition, during apoptosis, lysosomal cath-D is released into the cytosol, where it may interact with and/or cleave pro-apoptotic, anti-apoptotic, or nuclear proteins. Several studies have shown that cath-D affects various different steps in tumor progression and metastasis. Cath-D stimulates cancer cell growth in an autocrine manner, and also cath-D plays a crucial paracrine role in the tumor micro-environment by stimulating fibroblast outgrowth and tumor angiogenesis. A mutant D231N-cath-D, which is devoid of catalytic activity, remained mitogenic, indicating an additional action of cath-D by protein-protein interaction. Targeting cath-D in cancer may require the use of inhibitors of its catalytic activity, but also the development of new tools to inhibit its protein binding functions. Thus, elucidation of the mechanism of action of cath-D is crucial if an appropriate strategy is to be developed to target this protease in cancer. The discovery of new physiological substrates of cath-D using proteomic approaches can be expected to generate new critical targets. The aim of this review is to describe the roles of the cath-D protease in cancer progression and metastasis, as well as its function in apoptosis, and to discuss how it can be targeted in cancer by inhibiting its proteolytic activity and/or its binding protein activity.

Introduction

Proteases irreversibly hydrolyze the peptide bond in proteins, which results in an important and irreversible post-translational modification. The human genome encodes over 569 proteolytic enzymes or homologs, which constitute the second largest class of human enzymes. Proteases are assigned to five classes on the basis of the active site residue that executes the nucleophilic attack on the target peptide bond: aspartic, cysteine, serine, threonine and metallo-proteinases. These proteases are implicated in normal physiological processes, but deregulation of their expression and/or enzyme activity in disorders such as cancer has profound consequences. Different families of proteases have been implicated in motility, invasion, extravasation, proliferation and metastasis: the serine proteases (uPA, uPAR and PAI1) [START_REF] Smith | Regulation of cell signalling by uPAR[END_REF], the metalloproteinase family [START_REF] Roy | Matrix metalloproteinases as novel biomarkers and potential therapeutic targets in human cancer[END_REF], the cysteine cathepsins (cathepsin-B and cathepsin-L) [START_REF] Palermo | Cysteine cathepsin proteases as pharmacological targets in cancer[END_REF], and the aspartic cathepsin-D (cath-D) [START_REF] Liaudet-Coopman | Cathepsin D: newly discovered functions of a long-standing aspartic protease in cancer and apoptosis[END_REF], respectively. Cathepsin proteases are lysosomal hydrolases that degrade proteins at acidic pH in the lysosomes, or extracellularly in the matrix. Cathepsins can be divided into three subgroups, based on their active-site amino acid (i.e., cysteine (B, C, H, F, K, L, O, S, V, X, and W), aspartate (D and E), or serine (A and G) cathepsins). The possible involvement of cysteine and aspartic cathepsins in cancer has been the subject of more debate than that of metalloproteases and serine proteases. This might result from the assumption that only secreted proteases that are proteolytically active at neutral pH play an active role in cancer, whereas cathepsins, which require a more acidic pH to be proteolytically active, are thought to be likely to play only a minor role. However, it has been demonstrated that cathepsins are hypersecreted in cancer, and cath-B and cath-D have been described as being associated with the cell surface [START_REF] Mohamed | Cysteine cathepsins: multifunctional enzymes in cancer[END_REF][START_REF] Koblinski | Interaction of human breast fibroblasts with collagen I increases secretion of procathepsin B[END_REF]. Recent studies using transgenic mouse models have stimulated fresh interest in the fundamental roles of cathepsins in cancer [START_REF] Joyce | Cathepsin cysteine proteases are effectors of invasive growth and angiogenesis during multistage tumorigenesis[END_REF][START_REF] Joyce | Multiple roles for cysteine cathepsins in cancer[END_REF][START_REF] Gocheva | Cysteine cathepsins and the cutting edge of cancer invasion[END_REF][START_REF] Gocheva | Distinct roles for cysteine cathepsin genes in multistage tumorigenesis[END_REF]. Although historically studies have tended to focus on the role of lysosomal proteases within the endocytic and lysosomal compartments, recent discoveries have shown that these proteases play a critical role in other intracellular compartments, such as the cytosol [START_REF] Ivanova | Lysosomes in apoptosis[END_REF] or the nucleus [START_REF] Chapman | Cathepsins as transcriptional activators?[END_REF], and within the extracellular milieu in the tumoral stroma [START_REF] Mueller | Tumor-stroma interactions directing phenotype and progression of epithelial skin tumor cells[END_REF]. It has become clear that their pattern of expression and their substrate specificities are more complex than was originally envisaged. In cancer, lysosomal proteases are overexpressed and their cellular localizations are profoundly altered, leading to major changes in their targets and consequently in their biological activities.

In addition, cathepsins, metalloproteases and serine proteases act in a cascade-like manner and as part of a proteolytic pathway rather than simply functioning individually [START_REF] Affara | Delineating protease functions during cancer development[END_REF].

Elucidating the cascade of enzymatic activities that contribute to overall proteolysis during carcinogenesis may identify rate-limiting steps or pathways that could be targeted by anticancer treatments [START_REF] Affara | Delineating protease functions during cancer development[END_REF]. The proteolytic cascade of activation of the different classes of proteases strongly suggests that anti-cancer strategies intended to target several classes of proteases simultaneously might be more promising than those that target a single protease or class of proteases.

Recent studies have focused on extracellular proteases as primary targets for drug discovery, because of their differential expression in many pathophysiological processes, including cancer, cardiovascular conditions, and inflammatory, pulmonary, and periodontal diseases [START_REF] Palermo | Cysteine cathepsin proteases as pharmacological targets in cancer[END_REF][START_REF] Cudic | Extracellular proteases as targets for drug development[END_REF]. Interestingly, new extracellular inhibitors of metalloproteases, serine proteases and cysteine proteases are currently under clinical investigation [START_REF] Cudic | Extracellular proteases as targets for drug development[END_REF]. The aim of this review is to present the role of the cath-D protease in cancer progression and metastasis, as well as its function in apoptosis, and to discuss how it could be targeted in cancer by inhibiting its proteolytic activity and/or its protein binding activity.

Structure and trafficking of cath-D

Cath-D [E.C. 3.4.23.5] is a ubiquitous, lysosomal, aspartic endo-proteinase that requires an acidic pH to be proteolytically active (Figure 1). The human cath-D gene contains 9 exons, and is located on chromosome 11p15 [START_REF] Augereau | Cloning and sequencing of the 52K cathepsin D complementary deoxyribonucleic acid of MCF7 breast cancer cells and mapping on chromosome 11[END_REF]. During its transportation to lysosomes, the 52-kDa human pro-cath-D is proteolytically processed to form a 48-kDa, single-chain, intermediate which is an active enzyme located in the endosomes. Further proteolytic processing yields the mature active lysosomal protease, which is composed of both heavy (34 kDa) and light (14 kDa) chains. Cysteine cathepsins are known to be implicated in cath-D processing [START_REF] Samarel | Effects of cysteine protease inhibitors on rabbit cathepsin D maturation[END_REF][START_REF] Gieselmann | Processing of human cathepsin D in lysosomes in vitro[END_REF][START_REF] Laurent-Matha | Processing of human cathepsin D is independent of its catalytic function and auto-activation: involvement of cathepsins L and B[END_REF]. The involvement of cath-B and L has been shown more recently [START_REF] Laurent-Matha | Processing of human cathepsin D is independent of its catalytic function and auto-activation: involvement of cathepsins L and B[END_REF][START_REF] Felbor | Neuronal loss and brain atrophy in mice lacking cathepsins B and L[END_REF][START_REF] Wille | Cathepsin L is involved in cathepsin D processing and regulation of apoptosis in A549 human lung epithelial cells[END_REF]. The human cath-D catalytic site includes two critical aspartic residues (amino acids 33 and 231) located on the 14-kDa and 34-kDa chains, respectively (Figure 1) [START_REF] Metcalf | Two crystal structures for cathepsin D: the lysosomal targeting signal and active site[END_REF]. Cath-D, like other aspartic proteases such as renin, chymosin, pepsinogen, has a bilobed structure. The crystal structures of the native and pepstatin-inhibited form of mature human cath-D [START_REF] Metcalf | Two crystal structures for cathepsin D: the lysosomal targeting signal and active site[END_REF][START_REF] Baldwin | Crystal structures of native and inhibited forms of human cathepsin D: implications for lysosomal targeting and drug design[END_REF][START_REF] Goldfarb | Electrostatic switches that mediate the pH-dependent conformational change of "short" recombinant human pseudocathepsin D[END_REF][START_REF] Lee | Conformational switching in an aspartic proteinase[END_REF] have been shown to have a high degree of tertiary structural similarity with other members of the aspartic protease family (e.g. pepsinogen and human immunodeficiency virus protease). The highresolution structure of pro-cath-D remains to be elucidated. In estrogen receptor (ER)-positive breast cancer cell lines, cath-D is highly up-regulated by estrogens and growth factors (i.e. IGF1, EGF, insulin) [START_REF] Cavailles | Estrogens and growth factors induce the mRNA of the 52K-pro-cathepsin-D secreted by breast cancer cells[END_REF]. In ER-negative breast cancer cell lines, cath-D is constitutively overexpressed. The mechanism for cath-D overexpression in ER-negative breast cancer cells may involve local reorganization of the chromatin structure of the cath-D promoter [START_REF] Giamarchi | Chromatin structure of the regulatory regions of pS2 and cathepsin D genes in hormone-dependent and -independent breast cancer cell lines[END_REF].

Cath-D overexpression leads to the hypersecretion of the 52-kDa, proteolytically-inactive proenzyme, and the accumulation of intracellular cath-D [START_REF] Capony | Increased secretion, altered processing, and glycosylation of pro-cathepsin D in human mammary cancer cells[END_REF]. Release of mature cath-D by exocytosis has been observed in specialized cells [START_REF] Castino | Prolactin promotes the secretion of active cathepsin D at the basal side of rat mammary acini[END_REF]. Mannose-6-phosphate (M6P) receptors are involved in cath-D lysosomal routing, and in the cellular uptake of secreted pro-cath-D, although cath-D may also be targeted to the lysosomes, and undergo endocytosis independently of M6P receptors (Figure 1) [START_REF] Laurent-Matha | Endocytosis of pro-cathepsin D into breast cancer cells is mostly independent of mannose-6phosphate receptors[END_REF][START_REF] Capony | Specific mannose-6-phosphate receptor-independent sorting of pro-cathepsin D in breast cancer cells[END_REF]. The LRP1 receptor has been excluded as a possible receptor mediating the alternative endocytosis of pro-cath-D on the basis of the inability of the protein chaperone RAP, which competes with ligands that bind to the alpha chain of LRP1, to prevent cath-D endocytosis [START_REF] Laurent-Matha | Procathepsin D interacts with prosaposin in cancer cells but its internalization is not mediated by LDL receptor-related protein[END_REF]. It has recently been shown that sortilin functions as an alternative sorting receptor to the M6P receptors for cath-D and cath-H [START_REF] Canuel | Sortilin mediates the lysosomal targeting of cathepsins D and H[END_REF].

The tight control of cath-D expression and catalytic function is fundamental in normal cells

During fetal development, the level of cath-D increases gradually in all tissues, suggesting a gradual maturation of the lysosomal system [START_REF] Kageyama | Development-dependent expression of cathepsins d and e in various rat tissues, with special reference to the high expression of cathepsin e in fetal liver[END_REF]. A reduction of cath-D expression or catalytic activity leads to devastating neurodegenerative disorders. Cath-D knockout mice die shortly after birth, and display a neuronal accumulation of ceroid lipofuscin, accompanied by neurodegeneration in the retina and central nervous system, and the accumulation of autophagic vacuoles [START_REF] Saftig | Mice deficient for the lysosomal proteinase cathepsin D exhibit progressive atrophy of the intestinal mucosa and profound destruction of lymphoid cells[END_REF][START_REF] Koike | Cathepsin D deficiency induces lysosomal storage with ceroid lipofuscin in mouse CNS neurons[END_REF][START_REF] Koike | Involvement of two different cell death pathways in retinal atrophy of cathepsin D-deficient mice[END_REF][START_REF] Walls | Altered regulation of phosphatidylinositol 3-kinase signaling in cathepsin D-deficient brain[END_REF]. Cath-D-deficient Drosophila recapitulates the key features of neuronal ceroid lipofuscinoses (NCLs) [START_REF] Myllykangas | Cathepsin D-deficient Drosophila recapitulate the key features of neuronal ceroid lipofuscinoses[END_REF]. Congenital cath-D mutations leading to reduced expression of cath-D and/or the production of enzymatically-inactive protein result in typical NCL in dogs and humans [START_REF] Tyynela | A mutation in the ovine cathepsin D gene causes a congenital lysosomal storage disease with profound neurodegeneration[END_REF][START_REF] Awano | A mutation in the cathepsin D gene (CTSD) in American Bulldogs with neuronal ceroid lipofuscinosis[END_REF][START_REF] Siintola | Cathepsin D deficiency underlies congenital human neuronal ceroidlipofuscinosis[END_REF][START_REF] Steinfeld | Cathepsin D deficiency is associated with a human neurodegenerative disorder[END_REF][START_REF] Tyynela | Congenital ovine neuronal ceroid lipofuscinosis--a cathepsin D deficiency with increased levels of the inactive enzyme[END_REF][START_REF] Fritchie | Novel mutation and the first prenatal screening of cathepsin D deficiency (CLN10)[END_REF]. More recently, cath-D deficiency has been shown to be associated with Parkinson disease [START_REF] Cullen | Cathepsin D expression level affects alpha-synuclein processing, aggregation, and toxicity in vivo[END_REF].

In contrast, an increase in cath-D expression can also lead to fatal disorders. A recent study indicates that increased cardiac cath-D expression and activity induces heart failure. This is attributable to a 16-kDa cath-D-cleaved form of prolactin that mediates postpartum cardiomyopathy [START_REF] Hilfiker-Kleiner | A cathepsin D-cleaved 16 kDa form of prolactin mediates postpartum cardiomyopathy[END_REF]. Increased cath-D levels have also been observed in the cerebellum of autistic subjects, suggesting that altered activities of cath-D may play an important role in the pathogenesis of autism [START_REF] Sheikh | Cathepsin D and apoptosis related proteins are elevated in the brain of autistic subjects[END_REF].

Function of cath-D in apoptosis

Cysteine and aspartic cathepsins play key roles in tumor cell death via the mediation of apoptosis [START_REF] Liaudet-Coopman | Cathepsin D: newly discovered functions of a long-standing aspartic protease in cancer and apoptosis[END_REF][START_REF] Ivanova | Lysosomes in apoptosis[END_REF][START_REF] Emert-Sedlak | Involvement of cathepsin D in chemotherapy-induced cytochrome c release, caspase activation, and cell death[END_REF][START_REF] Vasiljeva | Dual contrasting roles of cysteine cathepsins in cancer progression: apoptosis versus tumour invasion[END_REF][START_REF] Minarowska | Regulatory role of cathepsin D in apoptosis[END_REF]. The function of cath-D in apoptosis needs further investigation, since this protease has both anti-apoptotic and pro-apoptotic functions.

Anti-apoptotic characteristics of cath-D

Even though cath-D gene expression outlines the areas of physiological cell death during embryo development [START_REF] Zuzarte-Luis | Cathepsin D gene expression outlines the areas of physiological cell death during embryonic development[END_REF], cath-D deficiency in mice has revealed its anti-apoptotic function under physiological conditions [START_REF] Saftig | Mice deficient for the lysosomal proteinase cathepsin D exhibit progressive atrophy of the intestinal mucosa and profound destruction of lymphoid cells[END_REF][START_REF] Koike | Cathepsin D deficiency induces lysosomal storage with ceroid lipofuscin in mouse CNS neurons[END_REF][START_REF] Koike | Involvement of two different cell death pathways in retinal atrophy of cathepsin D-deficient mice[END_REF]. Indeed, cath-D knock-out mice developed apoptosis in the thymus and in the retina [START_REF] Saftig | Mice deficient for the lysosomal proteinase cathepsin D exhibit progressive atrophy of the intestinal mucosa and profound destruction of lymphoid cells[END_REF][START_REF] Koike | Cathepsin D deficiency induces lysosomal storage with ceroid lipofuscin in mouse CNS neurons[END_REF][START_REF] Koike | Involvement of two different cell death pathways in retinal atrophy of cathepsin D-deficient mice[END_REF]. Some other studies have also suggested that cath-D may have an anti-apoptotic role in cancer. Our own immunohistochemical studies have revealed that xenografts of cancer cells overexpressing cath-D displayed less tumor apoptosis than mock-transfected cancer cells [START_REF] Berchem | Cathepsin-D affects multiple tumor progression steps in vivo: proliferation, angiogenesis and apoptosis[END_REF]. More recently, cath-D has been shown to protect human neuroblastoma cells from doxorubicin-induced cell death [START_REF] Sagulenko | Cathepsin D protects human neuroblastoma cells from doxorubicin-induced cell death[END_REF].

Pro-apoptotic characteristics of cath-D

Cath-D is a key mediator of induced-apoptosis, and its proteolytic activity has often been shown to be involved in this event [START_REF] Emert-Sedlak | Involvement of cathepsin D in chemotherapy-induced cytochrome c release, caspase activation, and cell death[END_REF][START_REF] Deiss | Cathepsin D protease mediates programmed cell death induced by interferon-gamma, Fas/APO-1 and TNF-alpha[END_REF][START_REF] Ollinger | Inhibition of cathepsin D prevents free-radical-induced apoptosis in rat cardiomyocytes[END_REF][START_REF] Kagedal | The lysosomal protease cathepsin D mediates apoptosis induced by oxidative stress[END_REF][START_REF] Roberg | Oxidative stress causes relocation of the lysosomal enzyme cathepsin D with ensuing apoptosis in neonatal rat cardiomyocytes[END_REF][START_REF] Takuma | Roles of cathepsins in reperfusion-induced apoptosis in cultured astrocytes[END_REF][START_REF] Johansson | Cathepsin D mediates cytochrome c release and caspase activation in human fibroblast apoptosis induced by staurosporine[END_REF][START_REF] Beaujouin | Overexpression of both catalytically active and -inactive cathepsin D by cancer cells enhances apoptosis-dependent chemo-sensitivity[END_REF][START_REF] Gan | HCCS1 overexpression induces apoptosis via cathepsin D and intracellular calcium, and HCCS1 disruption in mice causes placental abnormality[END_REF][START_REF] Miura | Translocation of lysosomal cathepsin D caused by oxidative stress or proteasome inhibition in primary cultured neurons and astrocytes[END_REF]. During apoptosis, mature lysosomal cath-D is translocated to the cytosol due to lysosomal membrane permeabilization (LMP) [56-58, 60, 64, 65]. Cytoplasmic cath-D has been shown to cleave Bid to form tBid [START_REF] Heinrich | Cathepsin D links TNFinduced acid sphingomyelinase to Bid-mediated caspase-9 and -3 activation[END_REF][START_REF] Blomgran | Cathepsin-cleaved Bid promotes apoptosis in human neutrophils via oxidative stress-induced lysosomal membrane permeabilization[END_REF], which triggers the insertion of Bax into the mitochondrial membrane [START_REF] Gan | HCCS1 overexpression induces apoptosis via cathepsin D and intracellular calcium, and HCCS1 disruption in mice causes placental abnormality[END_REF][START_REF] Bidere | Cathepsin D triggers Bax activation, resulting in selective apoptosis-inducing factor (AIF) relocation in T lymphocytes entering the early commitment phase to apoptosis[END_REF], and leads in turn to the mitochondrial release of cytochrome c into the cytosol, and the activation of pro-caspases 9 and 3 [START_REF] Ollinger | Inhibition of cathepsin D prevents free-radical-induced apoptosis in rat cardiomyocytes[END_REF][START_REF] Johansson | Cathepsin D mediates cytochrome c release and caspase activation in human fibroblast apoptosis induced by staurosporine[END_REF][START_REF] Roberg | Microinjection of cathepsin d induces caspasedependent apoptosis in fibroblasts[END_REF][START_REF] Heinrich | Cathepsin D links TNFinduced acid sphingomyelinase to Bid-mediated caspase-9 and -3 activation[END_REF]. Cath-D is also involved in caspase-independent apoptosis by activating Bax independently of Bid cleavage, and leading in turn to the mitochondrial release of the apoptosis inducing factor (AIF) [START_REF] Bidere | Cathepsin D triggers Bax activation, resulting in selective apoptosis-inducing factor (AIF) relocation in T lymphocytes entering the early commitment phase to apoptosis[END_REF]. More recently, it has been shown that cath-D can also activate pro-caspase 8, initiating neutrophil apoptosis during the resolution of inflammation [START_REF] Conus | Caspase-8 is activated by cathepsin D initiating neutrophil apoptosis during the resolution of inflammation[END_REF]. Interestingly, a recent report indicates the presence of mature cath-D in the nucleus during cell death [START_REF] Zhao | Nuclear translocation of mitochondrial cytochrome c, lysosomal cathepsins B and D, and three other death-promoting proteins within the first 60 minutes of generalized seizures[END_REF], and it has been proposed that nuclear cath-D may mediate the proteolytic activation of endonuclease 23 during cryonecrotic cell death [START_REF] Grdovic | Proteolytic events in cryonecrotic cell death: Proteolytic activation of endonuclease P23[END_REF].

Since cath-D is one of the lysosomal enzymes that requires a more acidic pH to be proteolytically-active than lysosomal cysteine enzymes, such as cath-B and cath-L, it is open to question whether cytosolic cath-D is able to cleave the substrate(s) implicated in the apoptotic cascade. In some studies, pepstatin A, an inhibitor of the enzyme, partially delayed the apoptosis induced by IFN-gamma and FAS/APO [START_REF] Deiss | Cathepsin D protease mediates programmed cell death induced by interferon-gamma, Fas/APO-1 and TNF-alpha[END_REF], staurosporin [START_REF] Johansson | Cathepsin D mediates cytochrome c release and caspase activation in human fibroblast apoptosis induced by staurosporine[END_REF][START_REF] Bidere | Cathepsin D triggers Bax activation, resulting in selective apoptosis-inducing factor (AIF) relocation in T lymphocytes entering the early commitment phase to apoptosis[END_REF], TNF-alpha [START_REF] Deiss | Cathepsin D protease mediates programmed cell death induced by interferon-gamma, Fas/APO-1 and TNF-alpha[END_REF][START_REF] Heinrich | Cathepsin D links TNFinduced acid sphingomyelinase to Bid-mediated caspase-9 and -3 activation[END_REF][START_REF] Demoz | Endosomallysosomal proteolysis mediates death signalling by TNFalpha, not by etoposide, in L929 fibrosarcoma cells: evidence for an active role of cathepsin D[END_REF], serum deprivation [START_REF] Shibata | Participation of cathepsins B and D in apoptosis of PC12 cells following serum deprivation[END_REF], oxidative stress [START_REF] Ollinger | Inhibition of cathepsin D prevents free-radical-induced apoptosis in rat cardiomyocytes[END_REF][START_REF] Kagedal | The lysosomal protease cathepsin D mediates apoptosis induced by oxidative stress[END_REF][START_REF] Takuma | Roles of cathepsins in reperfusion-induced apoptosis in cultured astrocytes[END_REF], or when pepstatin A was co-micro-injected with cath-D [START_REF] Roberg | Microinjection of cathepsin d induces caspasedependent apoptosis in fibroblasts[END_REF]. Other studies indicate that the effect of a mutant cath-D deprived of catalytic activity was indistinguishable from that of the normal enzyme [START_REF] Beaujouin | Overexpression of both catalytically active and -inactive cathepsin D by cancer cells enhances apoptosis-dependent chemo-sensitivity[END_REF][START_REF] Tardy | Stress-induced apoptosis is impaired in cells with a lysosomal targeting defect but is not affected in cells synthesizing a catalytically inactive cathepsin D[END_REF].

Furthermore, microinjection of the inactive precursor pro-cath-D into cytosol confirmed that the pro-apoptotic effect of cytosolic cath-D may be also independent of its catalytic activity [START_REF] Schestkowa | The catalytically inactive precursor of cathepsin D induces apoptosis in human fibroblasts and HeLa cells[END_REF]. In conclusion, cath-D can promote apoptosis by mechanisms that may be dependent on and/or independent of its active site.

Roles of cath-D in cancer

Cath-D is an independent marker of a poor prognosis in breast cancer

In the 1990s, several independent clinical studies showed that the cath-D level in primary breast cancer cytosols is an independent prognostic parameter correlated with the incidence of clinical metastasis and shorter survival times [START_REF] Westley | Prognostic value of cathepsin D in breast cancer[END_REF]. A meta-analysis of studies on nodenegative breast cancer [START_REF] Ferrandina | Relationship between cathepsin-D content and disease-free survival in node-negative breast cancer patients: a meta-analysis[END_REF], as well as a complete study of 2810 patients in Rotterdam [START_REF] Foekens | Cathepsin-D in primary breast cancer: prognostic evaluation involving 2810 patients[END_REF],

indicate that high concentrations of cath-D are an effective marker of aggressiveness. Cath-D is now recognized as an independent marker of poor prognosis in breast cancer associated with metastatic risk [START_REF] Fitzgibbons | Prognostic factors in breast cancer. College of American Pathologists Consensus Statement[END_REF]. In recent years, independent studies have confirmed the prognostic value of cath-D in breast cancer [START_REF] Harbeck | Long-term follow-up confirms prognostic impact of PAI-1 and cathepsin D and L in primary breast cancer[END_REF][START_REF] Greco | Co-expression of thymidine kinase and cathepsin D in 200 primary breast carcinomas[END_REF][START_REF] Gaci | Prognostic impact of cathepsin D and c-erbB-2 oncoprotein in a subgroup of node-negative breast cancer patients with low histological grade tumors[END_REF][START_REF] Bossard | Keeping data continuous when analyzing the prognostic impact of a tumor marker: an example with cathepsin D in breast cancer[END_REF][START_REF] Kute | Prognostic markers in node-negative breast cancer: a prospective study[END_REF][START_REF] Rodriguez | Clinical significance of cathepsin D concentration in tumor cytosol of primary breast cancer[END_REF][START_REF] Anim | Relationship between the expression of various markers and prognostic factors in breast cancer[END_REF][START_REF] Cheng | Identificating cathepsin D as a biomarker for differentiation and prognosis of nasopharyngeal carcinoma by laser capture microdissection and proteomic analysis[END_REF][START_REF] Vasudev | Pre-operative urinary cathepsin D is associated with survival in patients with renal cell carcinoma[END_REF]. The main cath-D producing cells appear to be cancer cells and stromal macrophages [START_REF] Roger | Cathepsin D immunostaining in paraffin-embedded breast cancer cells and macrophages: correlation with cytosolic assay[END_REF]. Pro-cath-D is also increased in the plasma of patients with metastatic breast cancer [START_REF] Brouillet | Increased cathepsin D level in the serum of patients with metastatic breast carcinoma detected with a specific pro-cathepsin D immunoassay[END_REF][START_REF] Szajda | Cathepsin D and carcino-embryonic antigen in serum, urine and tissues of colon adenocarcinoma patients[END_REF][START_REF] Szajda | Activity of cathepsin D in the blood serum and urine of patients with cancer of the stomach, pancreas and liver[END_REF], indicating that some of the pro-cath-D secreted by tumors can be released into the circulation. Interestingly, proteomic studies have recently confirmed the up-regulation of cath-D in many types of cancer [START_REF] Cheng | Identificating cathepsin D as a biomarker for differentiation and prognosis of nasopharyngeal carcinoma by laser capture microdissection and proteomic analysis[END_REF][START_REF] Selicharova | 2-DE analysis of breast cancer cell lines 1833 and 4175 with distinct metastatic organ-specific potentials: comparison with parental cell line MDA-MB-231[END_REF][START_REF] Roth | Differential expression proteomics of human colorectal cancer based on a syngeneic cellular model for the progression of adenoma to carcinoma[END_REF].

Cath-D affects multiple steps of cancer progression and metastasis

Cath-D is overexpressed and hypersecreted in a multitude of cancer types (breast cancer, ovarian cancer, endometrial cancer, cancer of the head and neck, bladder cancer, malignant glioma, melanoma). In cancer cells, overexpressed cath-D accumulates in cells where it may affect their degradative capacities, and the pro-enzyme is hypersecreted in the tumor microenvironment (Figure 2). Cath-D hypersecreted by cancer cells may affect stromal cell behavior and/or degrade components of the extracellular matrix, thus modifying the tumor micro-environment (Figure 2). Secreted pro-cath-D may act as a mitogen by competing with IGF2 for interaction with the M6P moieties of the M6P/IGF2 receptor, displacing IGF2 from the IGF1 receptor, and resulting in the activation of the mitogenic IGF1 receptor pathway [START_REF] Mathieu | Interactions of cathepsin-D and insulin-like growth factor-II (IGF-II) on the IGF-II/mannose-6-phosphate receptor in human breast cancer cells and possible consequences on mitogenic activity of IGF-II[END_REF][START_REF] Faridi | Modulation of cathepsin D routing by IGF-II involves IGF-II binding to IGF-II/M6P receptor in MCF-7 breast cancer cells[END_REF]. Many publications have suggested that the interaction of a part of the cath-D pro-fragment (amino acids 27 to 44) with an unknown cell surface receptor is implicated in its mitogenic function [START_REF] Fusek | Mitogenic function of human procathepsin D: the role of the propeptide[END_REF][START_REF] Ohri | The propeptide of cathepsin D increases proliferation, invasion and metastasis of breast cancer cells[END_REF][START_REF] Vetvicka | Role of enzymatically inactive procathepsin D in lung cancer[END_REF][START_REF] Vetvicka | Procathepsin D in breast cancer: what do we know? Effects of ribozymes and other inhibitors[END_REF][START_REF] Vetvicka | Anti-human procathepsin D activation peptide antibodies inhibit breast cancer development[END_REF][START_REF] Vashishta | Role of activation peptide of procathepsin D in proliferation and invasion of lung cancer cells[END_REF]. Alternatively, it has also been suggested that the catalytic activity of secreted cath-D may be implicated in releasing growth factors, such as FGF2, from the extracellular matrix [START_REF] Briozzo | MCF7 mammary cancer cells respond to bFGF and internalize it following its release from extracellular matrix: a permissive role of cathepsin D[END_REF]. Even though, the extracellular pH in tumors is generally more acidic than that in the corresponding normal tissues [START_REF] Griffiths | Are cancer cells acidic?[END_REF], the question remains as to whether secreted pro-cath-D could be activated extra-cellularly in a sufficiently acidic milieu. We have demonstrated that a mutated D231N cath-D, which is devoid of proteolytic activity, was still mitogenic for cancer cells both in vitro, in three-dimensional (3D) matrices, and in athymic nude mice [START_REF] Berchem | Cathepsin-D affects multiple tumor progression steps in vivo: proliferation, angiogenesis and apoptosis[END_REF][START_REF] Glondu | A mutated cathepsin-D devoid of its catalytic activity stimulates the growth of cancer cells[END_REF], suggesting that cath-D can also act by protein-protein interaction [START_REF] Rochefort | Cathepsin D in cancer metastasis: a protease and a ligand[END_REF].

Interactions between stromal and epithelial cells are important in cancer progression and metastasis [START_REF] Mueller | Friends or foes -bipolar effects of the tumour stroma in cancer[END_REF][START_REF] Liotta | The microenvironment of the tumour-host interface[END_REF][START_REF] Masson | In vivo evidence that the stromelysin-3 metalloproteinase contributes in a paracrine manner to epithelial cell malignancy[END_REF]. Stromal and tumor cells can exchange numerous tumor-promoting factors, such as growth factors, cytokines, and proteases. The fibroblast is a major cell type of the stromal compartment and, as such, is intimately involved in orchestrating the stromal side of the dialogue in tissue homeostasis. Cath-D is localized on the surface of breast fibroblasts [START_REF] Koblinski | Interaction of human breast fibroblasts with collagen I increases secretion of procathepsin B[END_REF], and can be taken up by fibroblasts [START_REF] Laurent-Matha | Endocytosis of pro-cathepsin D into breast cancer cells is mostly independent of mannose-6phosphate receptors[END_REF][START_REF] Laurent-Matha | Catalytically inactive human cathepsin D triggers fibroblast invasive growth[END_REF][START_REF] Heylen | Fibroblasts capture cathepsin D secreted by breast cancer cells: possible role in the regulation of the invasive process[END_REF]. Cath-D has been shown to play a crucial paracrine role in the tumor micro-environment by stimulating fibroblast outgrowth and tumor angiogenesis [START_REF] Berchem | Cathepsin-D affects multiple tumor progression steps in vivo: proliferation, angiogenesis and apoptosis[END_REF][START_REF] Hu | Thrombin up-regulates cathepsin D which enhances angiogenesis, growth, and metastasis[END_REF], and possibly by inhibiting anti-tumor responses [START_REF] Wolf | Cathepsin D specifically cleaves the chemokines macrophage inflammatory protein-1 alpha, macrophage inflammatory protein-1 beta, and SLC that are expressed in human breast cancer[END_REF]. More recently, endothelial cells have been shown to secrete pro-cath-D via the action of inflammatory cytokines [START_REF] Erdmann | Inflammatory cytokines increase extracellular procathepsin D in permanent and primary endothelial cell cultures[END_REF]. A mutant version of cath-D (D231N) that was devoid of catalytic activity, still proved to be mitogenic for fibroblasts, suggesting a mechanism involving protein-protein interaction [START_REF] Laurent-Matha | Catalytically inactive human cathepsin D triggers fibroblast invasive growth[END_REF].

Interestingly, some reports have indicated that the cysteine lysosomal cathepsins, cath-L and cath-F, which lack a signal peptide, localize in the nucleus [START_REF] Goulet | A cathepsin L isoform that is devoid of a signal peptide localizes to the nucleus in S phase and processes the CDP/Cux transcription factor[END_REF][START_REF] Maubach | Nuclear cathepsin F regulates activation markers in rat hepatic stellate cells[END_REF]. Nuclear cath-L proteolytically processes CDP/Cux transcription factor [START_REF] Chapman | Cathepsins as transcriptional activators?[END_REF][START_REF] Goulet | A cathepsin L isoform that is devoid of a signal peptide localizes to the nucleus in S phase and processes the CDP/Cux transcription factor[END_REF] and histone H3 [START_REF] Duncan | Cathepsin L proteolytically processes histone H3 during mouse embryonic stem cell differentiation[END_REF][START_REF] Ceru | Stefin B interacts with histones and cathepsin L in the nucleus[END_REF],

and has important functions in the control of cell transformation [START_REF] Goulet | Increased expression and activity of nuclear cathepsin L in cancer cells suggests a novel mechanism of cell transformation[END_REF][START_REF] Sullivan | Localization of nuclear cathepsin L and its association with disease progression and poor outcome in colorectal cancer[END_REF] as well as in differentiation [START_REF] Duncan | Cathepsin L proteolytically processes histone H3 during mouse embryonic stem cell differentiation[END_REF]. It has been shown that translation initiation at downstream AUG sites within cath-L mRNA is the first requirement in the chain of events that leads to the presence of active cath-L in the nucleus [START_REF] Goulet | A cathepsin L isoform that is devoid of a signal peptide localizes to the nucleus in S phase and processes the CDP/Cux transcription factor[END_REF]. There is, at present, no clear evidence for the presence of cath-D in the nucleus, and the nuclear function of cath-D in cancer is still unknown. However, our preliminary experiments strongly suggest the presence of cath-D in the nucleus of cancer cells. This may be due to translation initiation at downstream AUG sites within the cath-D mRNA (Figure 2). Indeed, it is worth noting that, like that of cath-L [START_REF] Goulet | A cathepsin L isoform that is devoid of a signal peptide localizes to the nucleus in S phase and processes the CDP/Cux transcription factor[END_REF], the coding sequence of cath-D contains several AUG codons that are located downstream of the first AUG codons. Alternatively, two recent reports have suggested that cytosolic mature cath-D may reach the nucleus in apoptosis (Figure 2) [START_REF] Zhao | Nuclear translocation of mitochondrial cytochrome c, lysosomal cathepsins B and D, and three other death-promoting proteins within the first 60 minutes of generalized seizures[END_REF]. One important question concerns the ability of cath-D to act as a functional enzyme at the neutral pH of the nucleus. Since enzymatic activity by cath-D is achieved at acidic pH, we can reasonably assume that cath-D might be only weakly active in the nuclear milieu. However, even limited cath-D activity in the nucleus could be compatible with a role in the proteolytic processing of specific nuclear proteins. In contrast, the optimal activity of cathepsins in the acidic environment of the lysosomes is necessary for the terminal degradation of proteins. Thus, the suboptimal pH that prevails in the nucleus should not be taken as an obstacle, but rather as an important element that enables cath-D to play a role in the limited proteolysis of nuclear proteins. Another possibility is that nuclear cath-D may sequester transcription repressors and/or activators, modulating the composition of the complexes implicated in the tight control of transcription.

Our preliminary results indicate that cath-D can indeed interact with a nuclear repressor implicated in cancer. Future studies will clarify whether cath-D participates in the regulation of transcription in cancer by cleaving and/or interacting with nuclear proteins, and thus modulates their activity.

Targeting cath-D in cancer

Cathepsins have long been known to play an important role in the progression and metastasis of cancer. Cath-D stimulates cancer cell proliferation, fibroblast outgrowth, tumor angiogenesis, and metastasis. In cancer cells, overexpressed cath-D accumulates in cells where it may affect their degradation capacities, and the pro-enzyme is hypersecreted in the tumor micro-environment (Figure 2). Therefore, inhibiting cath-D action requires the development of inhibitors targeting extracellular cath-D, and/or intracellular cath-D located in different parts of the cell (e.g. intracellular vesicles, cytosol, or nucleus).

Inhibitors of cath-D proteolytic activity

In recent years, research interest in the development of potent inhibitors of various aspartic peptidases has arisen, fuelled by the growing evidence of their involvement in human diseases [START_REF] Dash | Aspartic peptidase inhibitors: implications in drug development[END_REF], such as that of renin in hypertension [START_REF] Riccioni | Aliskiren, the first approved renin inhibitor: Clinical application and safety in the treatment of hypertension[END_REF], -secretase in Alzheimer's disease [START_REF] Bjorklund | Design and synthesis of potent and selective BACE-1 inhibitors[END_REF], plasmepsins in malaria [START_REF] Johansson | Design and synthesis of potent inhibitors of the malaria aspartyl proteases plasmepsin I and II. Use of solid-phase synthesis to explore novel statine motifs[END_REF], HIV-1 peptidase in acquired immune deficiency syndrome [START_REF] Lefebvre | Resilience to resistance of HIV-1 protease inhibitors: profile of darunavir[END_REF], and secreted aspartic peptidases in Candida infections [START_REF] Estes | Pharmacology and antifungal properties of anidulafungin, a new echinocandin[END_REF]. As opposed to other proteinases (e.g. serine proteases, metalloproteinases or cysteine cathepsins), no mammalian endogenous lysosomal or cytoplasmic cath-D inhibitor is known to exist. When released into the plasma, cath-D is inactivated by its interaction with 2-macroglobulin at a neutral pH, but not at an acidic pH [START_REF] Gonias | Conformation and protease binding activity of binary and ternary human alpha 2-macroglobulin-protease complexes[END_REF][START_REF] Barrett | The interaction of alpha 2-macroglobulin with proteinases. Characteristics and specificity of the reaction, and a hypothesis concerning its molecular mechanism[END_REF]. Since cath-D requires an acidic pH to be proteolytically active, acidic pH may be the physiological regulator of human cath-D activity.

In normal cells, cath-D is only active in acidic intracellular vesicles, and therefore uncontrolled proteolysis is avoided. However, no endogenous cath-D inhibitor is known to exist at acidic pH. It is worth noting that, in cancer, cath-D hypersecreted into the acidic extracellular tumor microenvironment may have a profound effect on matrix remodeling or extracellular factor proteolysis. Most exogenous cath-D inhibitors are synthetic compounds: peptides and polypeptides produced by micro-organisms, plants and lower animals [START_REF] Gacko | Cathepsin D inhibitors[END_REF][START_REF] Minarowska | Quantitative determination and localization of cathepsin D and its inhibitors[END_REF].

Organic compounds that esterify the carboxyl group of the Asn33 or Asp231 are synthetic cath-D inhibitors. Studies coupling the complementary methods of combinatorial chemistry and structure-based design, yielded low nanomolar inhibitors of cath-D [START_REF] Kick | Structure-based design and combinatorial chemistry yield low nanomolar inhibitors of cathepsin D[END_REF][START_REF] Ellman | Combinatorial methods to engineer small molecules for functional genomics[END_REF][START_REF] Bi | Novel cathepsin D inhibitors block the formation of hyperphosphorylated tau fragments in hippocampus[END_REF][START_REF] Wood | Substrate activity screening: a fragment-based method for the rapid identification of nonpeptidic protease inhibitors[END_REF][START_REF] Srivastava | Synthesis of gallic acid based naphthophenone fatty acid amides as cathepsin D inhibitors[END_REF]. Cath-D activity is inhibited by structural analogs of synthetic substrates in which an L-amino acid has been replaced by a D-amino acid [START_REF] Gacko | Cathepsin D inhibitors[END_REF]. The cath-D propeptide segment, which is cleaved off during zymogen activation, has been reported to inhibit pro-cath-D by blocking the active site at neutral pH [START_REF] Goldfarb | Electrostatic switches that mediate the pH-dependent conformational change of "short" recombinant human pseudocathepsin D[END_REF][START_REF] Lee | Conformational switching in an aspartic proteinase[END_REF][START_REF] Fusek | Inhibition of aspartic proteinases by propart peptides of human procathepsin D and chicken pepsinogen[END_REF][START_REF] Masa | Cathepsin D propeptide: mechanism and regulation of its interaction with the catalytic core[END_REF]. At high pH, a stable conformational species of cath-D exists in which the active site is blocked [START_REF] Lee | Conformational switching in an aspartic proteinase[END_REF]. More recently, a pH-dependent conformational change has been shown to be mediated by electrostatic switches [START_REF] Goldfarb | Electrostatic switches that mediate the pH-dependent conformational change of "short" recombinant human pseudocathepsin D[END_REF]. Peptide fragments derived from the propeptide have been shown to display some inhibitory potency against mature cath-D, suggesting that the development of new classes of pro-peptide-derived inhibitors of cath-D may be promising [START_REF] Masa | Cathepsin D propeptide: mechanism and regulation of its interaction with the catalytic core[END_REF]. Pepstatin A, an inhibitor of aspartic proteases produced by a micro-organism, is the most potent polypeptide inhibitor of cath-D so far identified [START_REF] Knight | Interaction of human cathepsin D with the inhibitor pepstatin[END_REF]. This is a hexa-peptide containing the unusual amino acid, statin (Sta, (3S,4S)-4-amino-3-hydroxy-6-methylheptanoic acid), and has the sequence Iva-Val-Val-Sta-Ala-Sta. It was originally isolated from cultures of various species of Actinomyces due to its ability to inhibit pepsin at picomolar concentrations. It was later found to be a potent inhibitor of nearly all acidic proteases and, as such, has become a valuable research tool. Pepstatin is commonly used to study the role of cath-D in in-vitro systems and in cells. Some studies have seemed to show that pepstatin A administered in vivo induces a significant reduction in the number of metastases, whereas other studies have not confirmed this effect [START_REF] Tumminello | Evaluation of antitumor and antimetastatic activity of pepstatin A in some experimental tumor models[END_REF]. Inhibition of cath-D by tripeptides containing statin analogs has also been reported [START_REF] Bessodes | Inhibition of cathepsin D by tripeptides containing statine analogs[END_REF]. Cath-D polypeptide inhibitors have also been identified in many plants [START_REF] Gacko | Cathepsin D inhibitors[END_REF], such as tomato leaves [START_REF] Lison | A novel function for the cathepsin D inhibitor in tomato[END_REF] and potato tubers [START_REF] Cater | Aspartic proteinase inhibitors from tomato and potato are more potent against yeast proteinase A than cathepsin D[END_REF]. Cath-D inhibitors are also produced by lower animals, such as equistatin from Actinia equina [START_REF] Lenarcic | Thyroglobulin type-1 domains in equistatin inhibit both papainlike cysteine proteinases and cathepsin D[END_REF][START_REF] Strukelj | Equistatin, a protease inhibitor from the sea anemone actinia equina, is composed of three structural and functional domains[END_REF] that can also inhibit cysteine cathepsin activity.

Interestingly, it has been shown that deoxyribonucleic acids (DNA fragments) can inhibit cath-D proteolytic activity [START_REF] Shibata | Cathepsin D is specifically inhibited by deoxyribonucleic acids[END_REF].

Inhibitors of cath-D binding activity

Cath-D can also act by protein-protein interaction. Studies of the role of secreted pro-cath-D as a mitogen through its protein binding activity in cancer suggest the involvement of a part of the cath-D profragment (position 27-44) in an interaction with an unknown cell surface receptor [START_REF] Fusek | Mitogenic function of human procathepsin D: the role of the propeptide[END_REF][START_REF] Ohri | The propeptide of cathepsin D increases proliferation, invasion and metastasis of breast cancer cells[END_REF][START_REF] Vetvicka | Role of enzymatically inactive procathepsin D in lung cancer[END_REF][START_REF] Vetvicka | Procathepsin D in breast cancer: what do we know? Effects of ribozymes and other inhibitors[END_REF][START_REF] Vetvicka | Anti-human procathepsin D activation peptide antibodies inhibit breast cancer development[END_REF][START_REF] Vashishta | Role of activation peptide of procathepsin D in proliferation and invasion of lung cancer cells[END_REF]. Interestingly, an anti-procath-D antibody directed against peptide 27-44 can reverse the growth of human breast tumors in athymic nude mice [START_REF] Vetvicka | Procathepsin D in breast cancer: what do we know? Effects of ribozymes and other inhibitors[END_REF][START_REF] Vetvicka | Anti-human procathepsin D activation peptide antibodies inhibit breast cancer development[END_REF][START_REF] Vetvicka | Analysis of the interaction of procathepsin D activation peptide with breast cancer cells[END_REF]. Secreted pro-cath-D may also act as a mitogen via its interaction with the M6P moieties of the M6P/IGF-2 receptor, displacing IGF2 from the IGF1 receptor, and leading to the activation the mitogenic IGF1 receptor pathway [START_REF] Mathieu | Interactions of cathepsin-D and insulin-like growth factor-II (IGF-II) on the IGF-II/mannose-6-phosphate receptor in human breast cancer cells and possible consequences on mitogenic activity of IGF-II[END_REF][START_REF] Faridi | Modulation of cathepsin D routing by IGF-II involves IGF-II binding to IGF-II/M6P receptor in MCF-7 breast cancer cells[END_REF]. We have demonstrated that a mutant D231N cath-D that is devoid of proteolytic activity is still mitogenic for cancer cells and fibroblasts both in vitro in three dimensional (3D) matrices, and in athymic nude mice [START_REF] Berchem | Cathepsin-D affects multiple tumor progression steps in vivo: proliferation, angiogenesis and apoptosis[END_REF][START_REF] Glondu | A mutated cathepsin-D devoid of its catalytic activity stimulates the growth of cancer cells[END_REF]. These findings suggest that pro-cath-D may act as an extracellular binding protein by directly or indirectly triggering an as-yet unidentified cell surface receptor. Our unpublished results also indicate that pro-cath-D hypersecreted by cancer cells triggers fibroblast invasive growth in a 3D matrix by interacting with a newly-identified fibroblastic cell surface receptor (submitted). The GST pull-down experiments revealed that this novel cath-D receptor binds the 52-, 34-and 14-kDa cath-D fragments, but only poorly to the 4-kDa cath-D profragment, indicating that the interaction interface spans both 34-and 14-kDa cath-D sub-units (submitted). Taken together, these observations suggest the importance of targeting extracellular pro-cath-D, and open new perspectives for the therapeutic inhibition of protease function in cancer by means other than the use of classical catalytic activity inhibitors.

Because of the pleotrophic action of secreted cath-D as a binding protein, the best strategy may be to inhibit the extracellular action of pro-cath-D through the use of neutralizing antibodies, rather than by targeting an individual cath-D partner.

Studies in apoptosis also strongly suggest that mature cytosolic cath-D may have an additional role involving protein-protein interaction. So far, no apoptosis-related binding partner of cath-D has yet been identified. The search for cath-D partners using the yeast-two hybrid approach may elucidate the pro-apoptotic function of cath-D independently of its catalytic activity. Our unpublished results using this approach show that cath-D does indeed interact with a pro-apoptotic constituent of the apoptotic pathway. However, it would be premature to envisage blocking the interaction of cath-D using a component of the apoptotic machinery within the cell.

Cath-D substrates in cancer

The discovery of new cath-D physiological substrates is likely to generate new critical targets for cancer therapy. To understand the functions of proteases, it is crucial to identify their substrates. Cath-D cleaves preferentially -Phe-Phe-, -Leu-Tyr-, -Tyr-Leu-, and -Phe-Tyr-bonds in peptide chains containing at least five amino acids at an acidic pH [START_REF] Dunn | The two sides of enzyme-substrate specificity: lessons from the aspartic proteinases[END_REF].

These peptides contain L-amino acids, and also contain hydrophobic amino acid residues at the site cleaved by cath-D. Recently, proteome-derived database-searchable peptide libraries have been developed to identify endoprotease cleavage sites [START_REF] Schilling | Proteome-derived, database-searchable peptide libraries for identifying protease cleavage sites[END_REF]. This approach may be applicable for cath-D. For a long time the main function of cath-D was thought to be to degrade proteins in lysosomes at an acidic pH. In addition to its established role as a major protein-degrading enzyme in lysosomes and phagosomes, it has been shown that cath-D can also activate precursors of biologically-active proteins, such as prolactin and osteopontin in specialized cells [START_REF] Lkhider | Cathepsin D released by lactating rat mammary epithelial cells is involved in prolactin cleavage under physiological conditions[END_REF][START_REF] Piwnica | A new mechanism for prolactin processing into 16K PRL by secreted cathepsin D[END_REF][START_REF] Sevlever | Cathepsin D is the main lysosomal enzyme involved in the degradation of alpha-synuclein and generation of its carboxy-terminally truncated species[END_REF][START_REF] Sakaguchi | Truncation of annexin A1 is a regulatory lever for linking epidermal growth factor signaling with cytosolic phospholipase A2 in normal and malignant squamous epithelial cells[END_REF][START_REF] Christensen | Osteopontin is cleaved at multiple sites close to its integrin-binding motifs in milk and is a novel substrate for plasmin and cathepsin D[END_REF]. Many cath-D substrates have been reported in vitro, but no endogenous substrates of cath-D in cancer have yet been clearly identified. In proteomics, the set of proteins that can be hydrolyzed by a protease is named its substrate degradome or degradomics [START_REF] Schilling | Proteomic discovery of protease substrates[END_REF]. A method termed Terminal Amine Isotopic Labeling of Substrates (TAILS) has recently been developed to identify extracellular and membrane protease substrates using iTRAQ labeling and mass spectrometry [START_REF] Overall | In search of partners: linking extracellular proteases to substrates[END_REF][START_REF] Doucet | Protease proteomics: revealing protease in vivo functions using systems biology approaches[END_REF][START_REF] Butler | Membrane protease degradomics: proteomic identification and quantification of cell surface protease substrates[END_REF]. This powerful proteomic approach, which permitted the discovery of the MMP-2 substrate degradome [START_REF] Dean | Proteomics discovery of metalloproteinase substrates in the cellular context by iTRAQ labeling reveals a diverse MMP-2 substrate degradome[END_REF], can also be applied to the identification of cath-D substrates using cells that do or do not express cath-D.

Conclusion

Cath-D is a key protease that affects many fundamental functions in cells. The molecular mechanism by which cath-D affects cancer progression remains largely unknown. Furthermore, we still do not have any specific cath-D inhibitors that could be used to target its action in cancer. Since this protease may also act by protein-protein interaction, it will be crucial to identify its partners in order to develop inhibitors to block its protein binding function.

  Several reports have indicated that cath-D stimulates cancer cell proliferation[START_REF] Vignon | Autocrine growth stimulation of the MCF 7 breast cancer cells by the estrogen-regulated 52 K protein[END_REF][START_REF] Garcia | Overexpression of transfected cathepsin D in transformed cells increases their malignant phenotype and metastatic potency[END_REF][START_REF] Fusek | Mitogenic function of human procathepsin D: the role of the propeptide[END_REF][START_REF] Vetvicka | Effect of human procathepsin D on proliferation of human cell lines[END_REF][START_REF] Liaudet | Transfected cathepsin D stimulates high density cancer cell growth by inactivating secreted growth inhibitors[END_REF][START_REF] Ohri | Depletion of procathepsin D gene expression by RNA interference: a potential therapeutic target for breast cancer[END_REF][START_REF] Ohri | The propeptide of cathepsin D increases proliferation, invasion and metastasis of breast cancer cells[END_REF] , and increases the metastatic potential[START_REF] Garcia | Overexpression of transfected cathepsin D in transformed cells increases their malignant phenotype and metastatic potency[END_REF][START_REF] Ohri | Depletion of procathepsin D gene expression by RNA interference: a potential therapeutic target for breast cancer[END_REF][START_REF] Liaudet | Cathepsin D maturation and its stimulatory effect on metastasis are prevented by addition of KDEL retention signal[END_REF][START_REF] Glondu | Down-regulation of cathepsin-D expression by antisense gene transfer inhibits tumor growth and experimental lung metastasis of human breast cancer cells[END_REF][START_REF] Vashishta | Ribozyme-targeting procathepsin D and its effect on invasion and growth of breast cancer cells: an implication in breast cancer therapy[END_REF]. Cath-D stimulates cancer cell growth in an autocrine manner[START_REF] Fusek | Mitogenic function of human procathepsin D: the role of the propeptide[END_REF][START_REF] Vetvicka | Effect of human procathepsin D on proliferation of human cell lines[END_REF][START_REF] Glondu | A mutated cathepsin-D devoid of its catalytic activity stimulates the growth of cancer cells[END_REF][START_REF] Vetvicka | Effect of procathepsin D and its activation peptide on prostate cancer cells[END_REF][START_REF] Vetvicka | Role of enzymatically inactive procathepsin D in lung cancer[END_REF]. Various different mechanisms have been proposed to explain the mitogenicity of cath-D. Intracellular cath-D stimulates high density cancer cell growth by inactivating secreted growth inhibitors, such as heat shock 70 protein[START_REF] Liaudet | Transfected cathepsin D stimulates high density cancer cell growth by inactivating secreted growth inhibitors[END_REF][START_REF] Nirde | Heat shock cognate 70 protein secretion as a new growth arrest signal for cancer cells[END_REF].

Figure 1 .

 1 Figure 1. Schematic representation of the human cath-D 52 kDa pro-cath-D sequence

Figure 2 .

 2 Figure 2. Localization of cath-D in cancer cells

Acknowledgement

Grant sponsors 'ANR Jeunes chercheurs Jeunes chercheuses' ANR-05-JCJC-0215-01, and EU FP6; Grant number: LSHC-CT-2007-037665.


Alain Y Kibangou
email: alain.kibangou@ujf-grenoble.fr

BLIND RECEIVERS FOR MISO COMMUNICATION SYSTEMS USING A NONLINEAR PRECODER

In this paper, we propose two blind decoding approaches for multi-input single-output (MISO) communication systems. We first introduce a nonlinear precoding scheme that allows viewing the received signal as a Volterra-like model with the following properties: the input solely depends on the coding sequence, assumed to be known to the receiver, while the kernel is a multiway array depending on informative data and on the channel parameters. We show that such a kernel admits a PARAFAC tensor model. After estimating the kernel by using the coding sequence, the data symbols are then recovered. For this purpose, two methods are proposed. The first one directly computes the PARAFAC loading factors by means of an alternating least squares method. The second one solves the problem by means of a joint diagonalization of matrices constructed with the slices of the tensor. The performance of the proposed methods is evaluated by means of simulations.

INTRODUCTION

Multi-input Single Output (MISO) communication channel modelling occurs when the communication system exhibits multiple antennas and/or transmitters whereas the receiver has a single antenna (see Fig. 1). In both cases several space-time block processing coding and modulation schemes (in a distributed or cooperative way in the second case) have been proposed in the literature. For scenarios in which there is perfect channel state information (CSI), several linear precoding systems have been proposed (see [START_REF] Sidiropoulos | Khatri-Rao space-time codes[END_REF] and references therein). However, in practice the CSI at the transmitter suffers from inaccuracies caused by errors in channel estimation and/or limited, delayed or erroneous feedback [START_REF] Kwon | Multi-user MISO broadcast channel with user-cooperating decoder[END_REF]. The derivation of robust coding methods with few or no knowledge on the transmission channel is then a topic of particular interest.

BS

In MISO communication channels, the propagation scenario can be viewed as a highly underdetermined mixture of sources having more sources than sensors. Systems with one single output sensor have received considerably less attention (see [START_REF] Fernandes | Blind identification of MISO-FIR channels[END_REF] and references therein).

In this paper, we introduce a nonlinear precoding scheme where the CSI is not required. From such a scheme, we derive blind decoding approaches for a MISO communication system. The proposed nonlinear precoding scheme gives rise to a homogeneous Volterra-like input-output equation whose inputs depend on the coding sequence whereas the kernel depends on the informative symbols and on the channel parameters.

It is now well known that Volterra kernels of order higher than two can be viewed as tensors or multiway array. We show that the kernel of the resulting Volterra-like model admits a PARAFAC model. PARAFAC (PARallel FACtors analysis) [START_REF] Harshman | Foundation of the PARAFAC procedure: models and conditions for an "explanatory" multimodal factor analysis[END_REF] is certainly the most famous tensor model proposed in the literature. In the last decade, several PARAFAC or more generally tensor based signal processing methods have been proposed in the literature devoted to communications [START_REF] Sidiropoulos | Blind PARAFAC receivers for DS-CDMA systems[END_REF][START_REF] De Almeida | PARAFAC-based unified tensor modeling for wireless communication systems with application to blind multiuser equalization[END_REF][START_REF] Nion | An enhanced line search scheme for complex-valued tensor decompositions. Application in DS-CDMA[END_REF][START_REF] Rajih | Enhanced line search : a novel method to accelerate PARAFAC[END_REF][START_REF] Kibangou | Blind equalization of nonlinear channels using tensor decompositions with code/space/time diversities[END_REF]. Most of them make use of the spatial diversity induced by multiple receive antennas. The contribution of this paper is to provide a nonlinear precoding scheme at the transmitter end and appropriate algorithms for blind decoding. The first decoding approach is based on the alternating least squares algorithm whereas in the second one the problem is solved by means of a joint diagonalization of a set of matrices constructed from tensor slices. The paper is organized as follows. In section 2, we explain the nonlinear encoding scheme and deduce the overall system model. In section 3, two-steps decoding schemes are derived. In section 4, the performance of the derived methods are evaluated by means of simulations before concluding the paper in section 5. Notations: Vectors are written as boldface lower-case letters (a,b,• • • ) and matrices as boldface capitals (A,B,• • • ). Tensors are written using calligraphic letters X . A i. and A . j denote respectively the ith row and the jth column of the I × J matrix A. A T stands for the transpose of A whereas A H stands for its complex conjugate. A † stands for the matrix pseudo-inverse. diag(.) is the operator that forms a diagonal matrix from its vector argument whereas vec(.) forms a vector by stacking the columns of its matrix argument. For X ∈ C I×R and Y ∈ C J×R , the Khatri-Rao product, denoted by , is defined as follows:

X Y =   Ydiag(X 1. ) . . . Ydiag(X I. )   ∈ C IJ×R (1)
It can also be viewed as a column-wise Kronecker product.

X Y = ( X .1 ⊗ Y .1 • • • X .R ⊗ Y .R ) ∈ C IJ×R , ( 2
)
⊗ denoting the Kronecker product.

SYSTEM MODEL

The considered communication system has K multiple transmitters or antennas. Each user transmits digital signals at the same time and using the same bandwidth. The output at the receiver is then a superposition of K signal waveforms.

For each user, the QM-length symbol stream is first parsed into M × 1 symbol vectors s

(k) q = s (k) 1,q • • • s (k) M,q T , q = 1, • • • , Q.
The nonlinear precoding considered herein is a two-stage one. First, each of the symbol vectors s (k) q is linearly precoded by an N × M matrix A. We get b

(k) q = As (k) q .
Note that the linear coding matrix is the same for all the users. Then, the codewords c (k) q to be transmitted are obtained through a nonlinear mapping f (.):

c (k) q = f (b (k) q ) = f (As (k) q ). (3)
The codewords are modulated by a pulse-shape filter g k (t) so that the baseband signal x k,q (t) transmitted by the kth user is given by

x k,q (t) = N ∑ n=1 c (k) n,q g k (t -(n -1) T ) ,
T being an appropriately chosen fraction of the symbol period T s . We assume that each of the signals

x k,q (t), k = 1, • • • , K, is
received via a single path characterized by a fading-factor α k and a delay τ k that holds propagation delay and asynchronism. In baseband, the received signal y q (t) is then given by:

y q (t) = K ∑ k=1 α k x k,q (t -τ k ) + w q (t),
w q (t) denoting the additive noise. By sampling at The discrete-time baseband equivalent model for the received data is then given by:

y n,q = y q (t)| t=(n-1)T = K ∑ k=1 h k,q c (k) n,q + w n,q with h k,q = α k g k (t -(n -1) T -τ k ) | t=(n-1)
T assumed to be quasi-static, i.e. constant during the transmission of the qth data block.

In the sequel, we consider that the nonlinear function f (.) involved in the encoding process (3) is a pth degree monomial. Therefore, elementwise the received data can be written as follows:

y n,q = K ∑ k=1 h k,q c (k) n,q + w n,q = K ∑ k=1 h k,q f ( M ∑ m=1 a n,m s (k) m,q ) + w n,q = K ∑ k=1 h k,q M ∑ m=1 a n,m s (k) m,q p + w n,q = K ∑ k=1 M ∑ m 1 =1 • • • M ∑ m p =1 h k,q p ∏ j=1 a n,m j s (k) m j ,q + w n,q . ( 4
)
The aim of our study is to derive estimators of the data symbols s

(k)
m,q solely from the received data y n,q . We assume that the linear precoding matrix A is known to the receiver. By defining

β m 1 ,••• ,m p ,q = K ∑ k=1 h k,q p ∏ j=1 s (k) m j ,q , ( 5
)
we can rewrite (4) as:

y n,q = M ∑ m 1 =1 • • • M ∑ m p =1 β m 1 ,••• ,m p ,q p ∏ j=1 a n,m j . ( 6
)
We can note from ( 6) that the received signal is linear in the unknown β m 1 ,••• ,m p ,q but nonlinear in the coding matrix entries. In fact, in a system theory point-of-view, Eq. ( 6) can be viewed as the input-output equation of a pth-order homogeneous Volterra model [START_REF] Schetzen | The Volterra and Wiener theories of nonlinear systems[END_REF], where β m 1 ,••• ,m p ,q and a n,m represent respectively the Volterra kernel and the input sequence. Moreover, the structure of the kernel (5) looks like that of a parallel cascade Wiener model (see [START_REF] Kibangou | Identification of parallel-cascade Wiener systems using joint diagonalization of third-order Volterra kernel slices[END_REF]). Therefore, in the sequel, we derive two-stage receivers. The first step consists in estimating the parameters β m 1 ,••• ,m p ,q in the least squares sense whereas the second one make use of the algebraic structure of the estimated parameters.

In the sequel, we restrict our study to the third-order case, p = 3.

BLIND RECEIVERS

The parameters β m 1 ,m 2 ,m 3 ,q can be viewed as entries of a symmetric tensor. Indeed, for any permutation π(.) of the indices (m 1 ,m 2 ,m 3 ), we have β p 1 ,p 2 ,p 3 ,q = β m 1 ,m 2 ,m 3 ,q with (p 1 , p 2 , p 3 ) = π(m 1 , m 2 , m 3 ). We can then rewrite [START_REF] De Almeida | PARAFAC-based unified tensor modeling for wireless communication systems with application to blind multiuser equalization[END_REF], in the noiseless case, as

y n,q = M ∑ m 1 =1 M ∑ m 2 =m 1 M ∑ m 3 =m 2 βm 1 ,m 2 ,m 3 ,q 3 ∏ j=1 a n,m j . ( 7
)
where

βm 1 ,m 2 ,m 3 ,q =          β m 1 ,m 2 ,m 3 ,q if m 1 = m 2 = m 3 3β m 1 ,m 2 ,m 3 ,q m 1 = m 2 = m 3 3β m 1 ,m 2 ,m 3 ,q m 1 = m 3 = m 2 3β m 1 ,m 2 ,m 3 ,q m 2 = m 3 = m 1 6β m 1 ,m 2 ,m 3 ,q m 1 = m 2 = m 3
In matrix form, Eq. ( 7) can be written as follows:

y q = ( y 1,q • • • y N,q ) T = Φ Φ Φθ q , ( 8
)
where θ q is a Q × 1 vector containing the parameters βm 1 ,m 2 ,m 3 ,q to be estimated, Φ Φ Φ is an N × Q matrix defined as

Φ Φ Φ = Ψ Ψ Ψ A Ω Ω Ω, with Ψ Ψ Ψ A   A 1. ⊗ A 1. ⊗ A 1. . . . A N. ⊗ A N. ⊗ A N.   , Ω Ω Ω is a M 3 × Q
column selection matrix, and Q = (M + 2)(M + 1)M/6. The least square solution of ( 8) is given by:

θq = Φ Φ Φ † y q (9)
provided Φ Φ Φ is full column rank. Therefore, the most important criterion for designing the coding matrix A is to ensure that Φ Φ Φ be full column rank. The design of the encoder is then decoupled from the channel knowledge. However, in order to improve the quality of the estimates in a noisy framework it could be necessary to increase N.

Once the parameters βm1,m 2 ,m 3 ,q have been estimated, we can deduce β m1,m2,m3,q . Therefore, we will estimate the informative symbols from the estimated parameters β m1,m2,m3,q , which can be viewed as the entries of a third-order tensor. In the sequel, we remove the index q since the decoding process is per-block.

PARAFAC tensor model

Let us denote by B the M × M × M third-order symmetric tensor with β m 1 ,m 2 ,m 3 as entries. From Eq. ( 5), we can deduce that B admits a PARAFAC model [START_REF] Harshman | Foundation of the PARAFAC procedure: models and conditions for an "explanatory" multimodal factor analysis[END_REF] with S and Sdiag(h) as factor matrices. Using the Kruskal operator [START_REF]Three-way arrays: rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics[END_REF][START_REF] Kolda | Tensor decompositions and applications[END_REF], we get:

B = [S, S, Sdiag(h)] with h = ( h 1,q • • • h K,q ) T and S =     s (1) 1,q • • • s (K) 1,q . . . . . . . . . s (1) M,q • • • s (K) M,q    
the matrix of the data symbols assumed to be full column rank, which implies M ≥ K.

From the sufficient condition stated by Kruskal [START_REF]Three-way arrays: rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics[END_REF], we can deduce that, the factor matrices are essentially unique, i.e. unique up to column permutation and scaling, if k S ≥ 2 3 (K + 2), where k S denotes the Kruskal-rank of S. It is also called k-rank and is defined as the greatest integer k S such that any set of k S t columns of S is independent. Moreover, since the columns of S are associated with independent users, for M ≥ K, S is full column rank with a high probability. As a consequence, the above inequality is always satisfied. Hence, the factor matrices can be obtained up to a scaling factor. The scaling ambiguity can be removed by considering differential modulation or by setting the first row of S equals to one.

Before deriving the estimation algorithm for fitting the PARAFAC model, we define the following matrix representations of the tensor. The slices of B are given by

B m.. = B .m. = B ..m =   β 1,1,m • • • β 1,M,m . . . . . . . . . β M,1,m • • • β M,M,m   = Sdiag(S m. )diag(h)S T . ( 10
)
By concatenating these slices, we get the unfolding matrix

B =   B 1.. . . . B M..   =   B 1.. . . . B M..   =   B 1.. . . . B M..   = (S S) diag(h t )S T . ( 11
)
For fitting the parameters of the PARAFAC model, we make use of an Alternating least squares algorithm. For this purpose, we define A 1 = S, A 2 = S and A 3 = Sdiag(h), so that we can rewrite the unfolding matrix as follows:

B = (A 1 A 2 ) A T 3 = (A 2 A 3 ) A T 1 = (A 3 A 1 ) A T 2 .
The alternating least squares algorithm consists in alternating minimization of the cost functions

J 1 = B -(A 2 A 3 ) A T 1 2 F , J 2 = B -(A 3 A 1 ) A T 2 2 F , J 3 = B -(A 1 A 2 ) A T 3 2
F . For each cost functions, given the two matrices involved in the Khatri-Rao product, the least squares solutions are respectively:

ÂT 1 = (A 2 A 3 ) † B, ÂT 2 = (A 3 A 1 ) † B, ÂT 3 = (A 1 A 2 ) † B.
After convergence, assuming that S has 1s as entries of its first row, its estimate is given by:

Ŝ = 1 3 A 1 + A 2 + A 3 diag(a) -1
with a the first row of A 3 . We can summarize the ALS estimation method as follows:

1. Initialize Â(i) 1 and Â(i) 2 , i = 0. 2. Increment i = i + 1. 3. Compute Â(i) 3 = A (i-1) 1
A (i-1) 2 † B T . 4. Compute Â(i) 1 = A (i-1) 2
A (i) 3 † B T . 5. Compute Â(i) 2 = A (i) 3
A (i) 1 † B T .
6. Go to step 2 until a stoping criterion is reached.

7. Compute Ŝ = 1 3 A (i) 1 + A (i) 2 + A (i) 3 diag(a (i) ) -1
, where a (i) denotes the first row of A (i) 3 .

Joint diagonalization approach

Assuming that S is full column rank, we can deduce that S S is also full column rank [START_REF] Sidiropoulos | Parallel factor analysis in sensor array processing[END_REF]. Obviously, diag(h)S T is full row rank, and therefore rank(B) = K, i.e. B is a rank deficient matrix if M > K.

Let us now consider the reduced singular value decomposition (SVD) of B:

B = UΣ Σ ΣV T , ( 12
)
the column-orthonormal matrices U and V, with respective dimensions M 2 × K and M × K, containing the left and right singular vectors of B respectively, whereas the K × K diagonal matrix Σ Σ Σ is formed with the nonzero singular values of B.

From equations ( 11) and ( 12), and the fact that rank(B T ) = K, we deduce that V and S span the same column space. So, there exists a nonsingular matrix F, with dimensions K × K, such that

S = VF. (13)
We can then rewrite the tensor slices as follows:

B ..m = VFdiag(S m. )diag(h)F T V T .
Now, let us define the following symmetric matrices:

G m = V T B ..m V = Fdiag(S m. )diag(h)F T , ( 14
)
with m = 1, • • • , M. We can conclude that F jointly diagonalizes the matrices G m , m = 1, • • • , M. Therefore F can be obtained by solving a joint diagonalization problem using one of the joint diagonalization algorithms proposed in the literature ( [START_REF] Ziehe | A fast algorithm for joint diagonalization with non-orthogonal transformations and its application to blind source separation[END_REF] for example). Then, S is estimated using [START_REF] Kolda | Tensor decompositions and applications[END_REF]. The decoding process is summarized as follows:

1. Compute the matrix V of the K right singular vectors of B.

Construct the set of matrices G

m , m = 1, • • • , M as fol- lows G m = V T B ..m V. 3.
Find the K × K matrix F that jointly diagonalizes the matrices G. 4. Compute the data matrix as Ŝ = VF.

SIMULATION RESULTS

In this section, we give some simulation results. The simulated communication system was characterized by the following parameters: K = M = 3. The data sequences was BPSK ones. Both channel parameters and encoding matrix were driven from a uniform distribution. The results presented below are averaged values over 100 Monte Carlo trials. The decoding performance is evaluated in terms of biterror-rate (BER). The joint diagonalization method used in the second decoding approach is the FFDIAG method [START_REF] Ziehe | A fast algorithm for joint diagonalization with non-orthogonal transformations and its application to blind source separation[END_REF].

For each decoding method, in Fig. 2 and 3 we plot the BER according to the signal-to-noise ratio (SNR).

In general, the proposed decoding methods give good results. Significant improvements are obtained by increasing the number N of rows for the encoding matrix A. That is an expected result since by increasing the number of rows for the encoding matrix, the least squares estimation of the data tensor is improved. The improvement is particularly significant for SNR values higher than 2 dB.

In figures 4, 5, and 6 we compare the two decoding methods for different values of N. We obtain comparable results with both methods. The joint diagonalization approach gives slightly better results. Note that the ALS-PARAFAC were randomly initialized. We considered 10 different initialization and then that giving the best results was selected. The algorithm were stopped after 100 iterations. For these simulations the joint diagonalization approach seems to have more desirable features.

CONCLUSION

In this paper, we have proposed two blind decoding schemes for multi-input single-output (MISO) communication systems. At the transmitter end, we have introduced a new nonlinear precoding scheme that consists in first linearly precoding the informative symbol with the same matrix for all the users and then nonlinearly mapping the linearly encoded data. By considering a polynomial mapping of degree higher than two, the received signal can be written as the output of an homogeneous Volterra-like model. The input of this model solely depend of the coding sequence assumed to be known to the receiver while the kernel is a multilinear array depending on informative data and on the channel parameters. The proposed decoding scheme is a two-stage one. First, the data kernel is estimated in the least squares sense. Second, the kernel is decomposed using the ALS-PARAFAC method or a joint diagonalization of matrices constructed from the tensor slices. We have shown the efficiency of the proposed methods through simulation results.

Figure 1 :

 1 Figure 1: Multi Input Single Output communication systems.

3 Figure 2 :

 32 Figure 2: Performance evaluation with different number of rows for the encoding matrix (ALS-PARAFAC case).

3 Figure 3 :

 33 Figure 3: Performance evaluation with different number of rows for the encoding matrix (Joint diagonalization).

Figure 4 :

 4 Figure 4: Comparison of the decoding methods (N = M 3 ).

Figure 5 :

 5 Figure 5: Comparison of the decoding methods (N = 2M 3 ).

Figure 6 :

 6 Figure 6: Comparison of the decoding methods (N = 3M 3 ).