Hereditary hair disorders caused by mutations in keratin genes. AD, autosomal dominant; AR, autosomal recessive.
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More than half of the publishers listed alongside IntechOpen (18 out of 30) are Social Science and Humanities publishers. IntechOpen is an exception to this as a leader in not only Open Access content but Open Access content across all scientific disciplines, including Physical Sciences, Engineering and Technology, Health Sciences, Life Science, and Social Sciences and Humanities.
\\n\\nOur breakdown of titles published demonstrates this with 47% PET, 31% HS, 18% LS, and 4% SSH books published.
\\n\\n“Even though ItechOpen has shown the potential of sci-tech books using an OA approach,” other publishers “have shown little interest in OA books.”
\\n\\nAdditionally, each book published by IntechOpen contains original content and research findings.
\\n\\nWe are honored to be among such prestigious publishers and we hope to continue to spearhead that growth in our quest to promote Open Access as a true pioneer in OA book publishing.
\\n\\n\\n\\n
\\n"}]',published:!0,mainMedia:null},components:[{type:"htmlEditorComponent",content:'
Simba Information has released its Open Access Book Publishing 2020 - 2024 report and has again identified IntechOpen as the world’s largest Open Access book publisher by title count.
\n\nSimba Information is a leading provider for market intelligence and forecasts in the media and publishing industry. The report, published every year, provides an overview and financial outlook for the global professional e-book publishing market.
\n\nIntechOpen, De Gruyter, and Frontiers are the largest OA book publishers by title count, with IntechOpen coming in at first place with 5,101 OA books published, a good 1,782 titles ahead of the nearest competitor.
\n\nSince the first Open Access Book Publishing report published in 2016, IntechOpen has held the top stop each year.
\n\n\n\nMore than half of the publishers listed alongside IntechOpen (18 out of 30) are Social Science and Humanities publishers. IntechOpen is an exception to this as a leader in not only Open Access content but Open Access content across all scientific disciplines, including Physical Sciences, Engineering and Technology, Health Sciences, Life Science, and Social Sciences and Humanities.
\n\nOur breakdown of titles published demonstrates this with 47% PET, 31% HS, 18% LS, and 4% SSH books published.
\n\n“Even though ItechOpen has shown the potential of sci-tech books using an OA approach,” other publishers “have shown little interest in OA books.”
\n\nAdditionally, each book published by IntechOpen contains original content and research findings.
\n\nWe are honored to be among such prestigious publishers and we hope to continue to spearhead that growth in our quest to promote Open Access as a true pioneer in OA book publishing.
\n\n\n\n
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(HF) is a skin appendage which exists on the entire skin surface, except for palmoplantar and mucosal regions. During embryogenesis, HF development is operated through reciprocal interactions between skin epithelial cells and underlying dermal cells [1]. The first signal to induce HF formation is considered to originate from the dermal cells. The epithelial cells which receive the dermal signal lead to form a placode (Figure 1). Then a signal from the placode results in forming a dermal condensate just beneath the placode (Figure 1). Additional interaction between these structures induces the downgrowth of the placode and forms a hair germ, which is the source of epithelial components of the HF (Figure 2). The dermal condensate is gradually surrounded by the HF epithelium and becomes a dermal papilla. It has been shown that many signaling molecules, such as Wnt, ectodysplasin (Eda), bone morphogenic protein (Bmp), and sonic hedgehog (Shh), play crucial roles in the HF development [1]. After the HF is generated, it undergoes dynamic cell kinetics, known as the hair cycle, throughout postnatal life, which is composed of three phases: catagen (regressing) phase, telogen (resting) phase and anagen (growing) phase [2]. In human scalp HFs, duration of the catagen, telogen, and anagen phases are 1-2 weeks, 2-3 months, and 2-6 years, respectively. The hair cycle, which is an amazing ability of self-renewal, is maintained by the stem cell niche in bulge portion of the HF, as well as the dermal papilla [3, 4].
Hair follicle placode (mouse embryo; E15.5)
Hair germ (mouse embryo; E16.5)
Human anagen hair follicle.
The anagen HF has a highly complex structure with several distinct cell layers (Figure 3). During the anagen phase, cells from the bulge portion migrate downward to matrix region, while making the outer root sheath (ORS). The matrix cells actively proliferate and differentiate into the hair shaft, the inner root sheath (IRS), and the companion layer of the HF (Figure 3) [4]. The hair shaft shares a common structural organization, in which a multicellular cortex is surrounded by a cuticular layer, occasionally with a medulla layer centrally located within the cortex. The hair shaft is strongly keratinized at the level of keratinizing zone, and forms a rigid structure (Figure 3). Growth of the hair shaft is molded and supported by the IRS, the companion layer, and the ORS. The IRS is composed of three distinct layers: the IRS cuticle, Huxley’s layer, and Henle’s layer (Figure 3).
Recent advances in molecular genetics have led to the identification of numerous genes that are expressed in the HF. Furthermore, mutations in some of these genes have been shown to underlie hereditary hair diseases in humans [2]. Causative genes for the diseases encode various proteins with different functions, such as structural proteins, transcription factors, and signaling molecules. This chapter aims to update recent findings regarding the molecular basis of genetic hair diseases.
Keratins are one of the major structural components of the HF, and are largely divided into type I (acidic) and type II (neutral to basic) keratins. The type I and type II keratins undergo heterodimerization, which leads to form keratin intermediate filaments (KIFs) in the cytoplasm [5]. Based on the amino acid composition, keratins are further classified into two groups: epithelial (soft) keratins and hair (hard) keratins. As compared to the epithelial keratins, the hair keratins show higher sulfur content in their N- and C-terminus, which plays an important role in interacting with hair keratin-associated proteins via disulfide bindings [6, 7]. All the keratin proteins are composed of an N-terminal rod domain, a central rod domain, and a C-terminal tail domain. Importantly, the N-terminal and the C-terminal regions of the rod domain are highly conserved in amino acid sequences, which are called helix initiation motif (HIM) and helix termination motif (HTM), respectively (Figure 4). It is believed that the HIM and the HTM play essential roles in heterodimerization between the keratins. In humans, gene clusters for the type I and type II keratin genes are mapped on chromosomes 17q21 [8] and 12q13 [9], respectively. To date, a total of 54 functional keratin genes (28 type I and 26 type II) have been identified and characterized in humans. It has been shown that during differentiation of the HF, various keratin genes are abundantly and differentially expressed, and contribute to HF keratinization, leading to the formation of a rigid structure [10]. In general, epithelial keratins are mainly expressed in the ORS, the companion layer, the IRS, while hair keratins are predominantly expressed in the hair shaft. In addition, it has recently been reported that some epithelial keratins are expressed in the hair shaft medulla as well [11]. It is noteworthy that mutations in several keratin genes have been reported to underlie hereditary hair disorders in humans (Table 1).
Structure of keratin proteins.
disease | inheritance pattern | OMIM# | main symptoms | gene | protein, function |
Monilethrix | AD | 158000 | moniliform hair, perifollicular papules | KRT81 KRT83 KRT86 | K81 (basic hair keratin) K83 (basic hair keratin) K86 (basic hair keratin) |
Pure hair and nail ectodermal dysplasia | AR | 602032 | hypotrichosis, spoon nails | KRT85 | K85 (basic hair keratin) |
Autosomal dominant woolly hair (ADWH)/ hypotrichosis | AD | 194300/613981 | WH/ hypotrichosis | KRT74 KRT71 | K74 (basic epithelial keratin) K71 (basic epithelial keratin) |
Hereditary hair disorders caused by mutations in keratin genes. AD, autosomal dominant; AR, autosomal recessive.
Monilethrix is characterized clinically by fragile scalp hair shafts and diffuse perifollicular papules with erythema. As the hair of affected individuals with monilethrix is easily broken, they frequently show sparse hair (hypotrichosis). In most cases, monilethrix shows an autosomal dominant inheritance pattern (MIM 158000), while autosomal recessive forms (MIM 252200) also exist. Under microscopy, the hair shaft of affected individuals with monilethrix dysplays a characteristic anomaly, known as beaded or moniliform hair, which shows periodic changes in hair diameter. As a result, the hair leads to the formation of nodes and internodes (Figure 5) [12]. Autosomal dominant form of the disease is caused by heterozygous mutations in KRT81, KRT83, and KRT86 genes, which encode type II hair keratins K81, K83, and K86, respectively [13, 14]. All the mutations identified to date result in a deleterious amino acid substitution within either the HIM or the HTM of the rod domain. These hair keratins are predominantly expressed in the keratinizing zone of the hair shaft cortex (Figure 6) [15]. Although precise mechanisms to cause moniliform hair remain elusive, mutations in these hair keratin genes are predicted to result in disruption of the KIF formation, leading to an abnormal hair shaft keratinization.
Moniliform hair. N, node; in, internode.
Expression of hair keratin K86 in the human hair shaft cortex.
Pure hair and nail ectodermal dysplasia (PHNED; MIM 602032) is characterized by absent or sparse hair, as well as nail dystrophy [16]. Hairs of affected individuals with PHNED are short and thin, and perifollicular papules can also be observed. In addition, their nails typically show koilonychia (spoon nails). The disease can show either an autosomal dominant or recessive inheritance trait. The autosomal recessive form has been mapped to chromosome 17p12-q21.2 [17] and 12p11.1-q21.1 [18] which contain the type I and type II keratin gene clusters, respectively. Subsequently, homozygous mutations in KRT85 gene have been identified in families with autosomal recessive PHNED [18, 19]. The KRT85 gene encodes the type II hair keratin K85, which is abundantly expressed in the matrix region of both the HF and the nail units [15, 20]. Molecular basis for autosomal dominant PHNED is yet unknown.
In addition to hair keratins, it has recently been reported that mutations in HF-specific epithelial keratin genes are associated with hereditary woolly hair (WH)/hypotrichosis. WH is defined as an abnormal variant of tightly curled hair and is considered to be a kind of hair growth deficiency [21]. There are both syndromic and non-syndromic forms of WH. The non-syndromic forms of WH can show either an autosomal-dominant (ADWH; MIM 194300) or -recessive (ARWH; MIM 278150) inheritance pattern. It is well-known that WH is frequently associated with hypotrichosis. Recently, heterozygous mutations in KRT74 and KRT71 genes have been identified in families with ADWH/hypotrichosis (Figure 7) [22-24]. Importantly, the KRT74 and the KRT71 genes encode the IRS-specific type II epithelial keratins K74 and K71, respectively (Figure 8) [25]. It can be postulated that disruption of the KIF formation in the IRS results in a failure to guide the hair growth, and leads to WH phenotype. Interestingly, KRT71 mutations have also been identified in mice, rats, cats, and dogs, all of which show wavy coat phenotypes [26-30]. These data strongly suggest crucial roles of the IRS-specific epithelial keratins in the HF development and hair growth across mammalian species.
Clinical features of autosomal dominant woolly hair/hypotrichosis caused by a mutation in the KRT71 gene.
Expression of the IRS-specific karatin K71 in the human hair follicle.
Similar to epidermis, the HF epithelium possess a number of cell-cell adhesion structures, such as desmosomes, corneodesmosomes, adherens junctions, gap junctions, and tight junctions, which play important roles in maintaining the structure and the function of the HF. It has been shown that disruption of any of these structures can result in hereditary hair disorders in humans (Table 2).
Desmosome is a critical structure for cell-cell adhesion in most epithelial tissues, including the HF. The major structural component of the desmosome is the desmosomal cadherin family, which is comprised of the desmogleins (DSGs) and desmocollins (DSCs). In humans, 4 DSG genes (DSG1-DSG4) and 3 DSC genes (DSC1-DSC3) are located on chromosome 18q12. These desmosomal cadherin family members are glycoproteins with single-pass transmembrane domain, and are involved in Ca2+-dependent cell-cell adhesion, connecting with each other using their extracellular domains [31]. Within the cytoplasm, they interact with several other proteins, known as desmosomal plaque proteins, which include plakoglobin, plakophilin, and desmoplakin. The desmosomal plaque proteins contribute to anchor the KIF near the cell membrane. As such, the cell integrity and the cell-cell adhesion are maintained [31]. Recessively-inherited mutations in the DSG4 gene have been shown to cause a non-syndromic form of hereditary hair disorder known as localized autosomal recessive hypotrichosis 1 (LAH1; MIM 607903) [32]. Affected individuals with LAH1 show sparse hairs on the scalp, chest, arms, and legs. The eyebrows and beard are less dense than normal, and the axillary hair, pubic hair, and eyelashes look normal in most cases. It is noteworthy that hair shafts of affected individuals with DSG4 mutations are fragile and often show moniliform hair [33-35]. Therefore, the DSG4 can also be regarded as a causative gene for autosomal recessive monilethrix. DSG4 is the only desmoglein member that is expressed in the hair shaft (Figure 9) [36], and its expression in the hair shaft cortex finely overlaps with K81, K83, and K86, of which mutations cause autosomal dominant monilethrix. More recently, a homozygous nonsense mutation in the DSC3 gene has been identified in a family with an autosomal recessive form of hypotrichosis [37]. The disease is characterized by sparse scalp hairs and small vesicle formation on the scalp and extremities (hypotrichosis and recurrent skin vesicles; MIM 613102) [37], while there is an argument that the vesicles may be keratosis pilaris [38]. In addition, mutations in genes encoding desmosomal plaque proteins can also show hair phenotypes (Table 2). For example, mutations in junctional plakoglobin (JUP) and desmoplakin (DSP) genes are known to underlie Naxos disease (MIM 601214) and Carvajal syndrome (MIM 605676), respectively [39, 40]. Both diseases show an autosomal recessive inheritance pattern and are characterized by woolly hair, palmoplantar keratoderma, and severe cardiomyopathy. Furthermore, loss of function mutations in plakophilin 1 (PKP1) gene cause a rare autosomal recessive disease named ectodermal dysplasia/skin fragility syndrome (MIM 604536) [41].
disease | inheritance pattern | OMIM# | main symptoms | gene | protein, function |
Localized autosomal recessive hypotrichosis 1 (LAH1)/monilethrix | AR | 607903/ 252200 | hypotrichosis, moniliform hair, perifollicular papules | DSG4 | desmoglein 4 |
Hypotrichosis and recurrent skin vesicles | AR | 613102 | Hypotrichosis, skin vesicles or keratosis pilaris | DSC3 | desmocollin 3 |
Naxos disease | AR | 601214 | WH, PPK, right ventricular cardiomyopathy | JUP | junctional plakoglobin |
Carvajal syndrome | AR | 605676 | WH, PPK, left ventricular cardiomyopathy | DSP | desmoplakin |
Ectodermal dysplasia/skin fragility syndrome | AR | 604536 | Hypotrichosis, fragile skin, nail dystrophy | PKP1 | plakophilin 1 |
Hypotrichosis simplex of the scalp | AD | 146520 | Scalp-limited hypotrichosis | CDSN | corneodesmosin |
Netherton syndrome | AR | 256500 | ichthyosiform erythroderma, atopic manifestation, bamboo hair | SPINK5 | LEKTI (serine protease inhibitor) |
Ichthyosis with hypotrichosis | AR | 610765 | ichthyosis, hypotrichosis | ST14 | matriptase (serine protease) |
Hypotrichosis with juvenile macular dystrophy | AR | 601553 | Hypotrichosis, weak eyesight | CDH3 | P-cadherin |
Ectodermal dysplasia, ectrodactyly, macular dystrophy (EEM) syndrome | AR | 225280 | Hypotrichosis, weak eyesight, ectrodactyly | CDH3 | P-cadherin |
Hidrotic ectodermal dysplasia (Clouston syndrome) | AD | 129500 | hypotrichosis, PPK, nail dystrophy | GJB6 | connexin 30 |
Keratitis ichthyosis deafness (KID) syndrome | AD | 148210 | vascularizing keratitis, sensorial deafness, erythrokeratoderma, hypotrichosis | GJB2 GJB6 | connexin 26 connexin 30 |
Ichthyosis, leukocyte vacuoles, alopecia, and sclerosing cholangitis | AR | 607626 | Hypotrichosis, ichthyosis, jaundice, hapatomegaly, | CLDN1 | claudin 1 |
Hereditary hair disorders caused by disruption of cell-cell adhesion structures and the related molecules.
Expression of desmoglein 4 (DSG4) in the human hair shaft.
Corneodesmosome is a modified desmosome in the stratum corneum (SC) of the epidermis, and plays a crucial in the desquamation process. One of the major components of the corneodesmosome is corneodesmosin (CDSN). CDSN is secreted by cytoplasmic vesicles into the extracellular core of desmosomes, and is progressively proteolysed by several serine proteases, such as kallikrein-related peptidases, which leads to the loss of cell-cell adhesivity in the SC and causes desquamation [42]. CDSN is also expressed predominantly in the IRS of the HF, and thus is considered to be important for terminal differentiation, as well as subsequent degradation of the IRS [43]. In 2003, heterozygous nonsense mutations in the CDSN gene have been identified in patients with hereditary hypotrichosis simplex of the scalp (HHSS; MIM 146520), which is an autosomal dominant disorder characterized by sparse hairs limited to the scalp region without any obvious hair shaft anomalies (Figure 10) [44]. Histologically, the IRS of the patients’ HF was disturbed, which was consistent with the expression of CDSN in the IRS. Furthermore, aggregates of abnormal CDSN were detected around the HF, as well as in the papillary dermis in patients’ skin [44]. These aggregates have recently been shown to be an amyloid protein derived from the mutant CDSN, which is likely to be toxic to the HF cells [45]. Therefore, the mutant CDSN protein appears to function in a dominant negative manner, affect growth of the HF, and lead to HHSS. In addition to HHSS, it has been reported that mutations in other genes functionally related with CDSN can show some hair phenotypes associated with congenital ichthyosis. Of these, Netherton syndrome (NS; MIM 256500) is a rare autosomal recessive condition characterized by ichthyosiform erythroderma, atopic manifestation, and the hair shaft anomaly, known as bamboo hair (trichorrhexis invaginata) (Figure 11). The NS is caused by loss of function mutations in SPINK5 gene which encodes a serine protease inhibitor named LEKTI (lymphoepithelial Kazal-type-related inhibitor) [46]. Disruption of LEKTI has been shown to result in upregulation of serine proteases and excess desquamation due to premature proteolysis of CDSN [47, 48]. Furthermore, it has been reported that recessively-inherited mutations in ST14 gene, which encodes a member of serine proteases (matriptase), underlie ichthyosis with hypotrichosis syndrome (MIM 610765) [49]. Sum of these genetic data suggest that balanced expression of CDSN, serine proteases, and their inhibitors is critical for the HF differentiation.
Clinical features of hypotrichosis simplex of the scalp.
Bamboo hair (trichorrhexis invaginata).
E- and P-cadherins are classical cadherins which are a major component of adherens junctions in the HF. When the HF placode is formed during embryogenesis, the expression of E-cadherin is markedly downregulated, while P-cadherin is simultaneously upregulated, and prominant expression of P-cadherin persists in the proximal portion of the HF. This phenomenon, known as cadherin switching, is believed to be essential for the HF morphogenesis [50]. In addition, P-cadherin has recently been shown to be important for postnatal hair growth and cycling as well [51]. The critical role of these classical cadherins in the HF has been further supported by two hereditary diseases resulting from mutations in the P-cadherin gene (CDH3). First, mutations in the CDH3 gene are known to underlie hypotrichosis with juvenile macular dystrophy (HJMD; MIM 601553), which is an autosomal recessive disease characterized by sparse hair and weak eyesight due to macular dystrophy of the retina [52]. In addition, it has been reported that another disease, ectodermal dysplasia, ectrodactyly and macular dystrophy (EEM syndrome; MIM 225280), is also caused by recessively-inherited mutations in the CDH3 gene [53]. Affected individuals with EEM syndrome show common hair and eye phenotype with HJMD. However, EEM patients also shows split hand/foot malformation (ectrodactyly), suggesting crucial roles of P-cadherin in the development of not only hair and retina, but also the limbs in humans. There are no clear genotype-phenotype correlations in CDH3 mutations, as it has been reported that a same mutation in the CDH3 gene caused HJMD in one family [54], while EEM syndrome in another family [53]. Identification of modifier gene(s) may reveal this paradox in the future.
Gap junction (GJ) is a specialized intercellular structure that provides a pathway for both metabolic and ionic coupling between adjacent cells and maintains tissue homeostasis [55]. Connexins (Cxs) are 4-pass transmembrane proteins and the major component of the GJs. Clouston syndrome (MIM 129500), also known as hidrotic ectodermal dysplasia, is an autosomal dominant condition characterized by hypotrichosis, nail dystrophy, and palmoplantar keratoderma. The disease is caused by mutations in GJB6 gene which encodes Cx30 [56]. In addition, mutations in GJB2 gene encoding Cx26 are known to underlie keratitis-ichthyosis-deafness syndrome (KID; MIM 148210) [57]. The triad of KID is vascularizing keratitis, profound sensorial hearing loss, and erythrokeratoderma. Additionally, patients with KID show severe hypotrichosis in high frequency. Interestingly, it has been reported that a mutation in the GJB6 gene (V37E) can show phenotypes resembling KID [58]. These Cx proteins are mainly expressed in the ORS of the HF (Figure 12) [59, 60], and thus they may play some roles in maintaining the function of the HF stem cells.
Cx30 expression in the human hair follicle.
In addition to the cell-cell adhesion structures described above, tight junction (TJ) also exists in the HF epithelium and expression patterns of TJ-associated proteins in the HF have previously been characterized [61]. Disruption of CLDN1 gene encoding claudin 1, a major structural component of TJ, has recently been shown to cause a severe autosomal recessive syndrome, known as ichthyosis, leukocyte vacuoles, alopecia, and sclerosing cholangitis (MIM 607626) [62].
During the past 20 years, numerous genes that are expressed in the HF have been identified, and various transcription factors have been shown to be involved in transcriptional regulation of these genes. Of these, p63 is one of the main transcription factors expressed in the HF. During the HF morphogenesis, p63 is abundantly expressed in the HF placode (Figure 13). In the postnatal stage, it is strongly expressed in the ORS and the matrix region of the HF (Figure 14). It has previously been reported that mutations in TP63 gene encoding p63 cause several autosomal dominant diseases including ectodermal dysplasia, ectrodactyly, cleft lip/palate (EEC) syndrome (MIM 604292), ankyloblepharon, ectodermal defects, and cleft lip/palate (AEC) syndrome (MIM 106260) and Rapp-Hodgkin syndrome (MIM 129400) (Table 3) [63-65]. In most cases, patients with these syndromes result in scarring alopecia, and their hair shafts are coarse and twisted (Figure 15). It is noteworthy that affected individuals with TP63 mutations show large phenotypic overlaps in hair and limbs with P-cadherin (CDH3) mutations. p63 colocalizes with P-cadherin in developing HF placode and limb buds during mouse embryogenesis. Importantly, it has been demonstrated that the CDH3 is a direct target gene of p63 [66].
P63 expression in the developing mouse hair follicle placode.
p63 expression in the human hair follicle.
disease | inheritance pattern | OMIM# | main symptoms | gene | Protein, function |
Ectrodactyly, ectodermal dysplasia, and cleft lip/palate (EEC ) syndrome | AD | 604292 | hypotrichosis, ectrodactyly, cleft lip/palate, hypodontia | TP63 | tumor protein p63 |
Ankyloblepharon, ectodermal defects, and cleft lip/palate (AEC) syndrome | AD | 106260 | hypotrichosis, ankyloblepharon, skin erosion, cleft lip/palate, hypodontia | TP63 | tumor protein p63 |
Rapp-Hodgkin syndrome | AD | 129400 | hypotrichosis, cleft lip/palate, hypodontia | TP63 | tumor protein p63 |
T cell immunodeficiency, congenital alopecia, and nail dystrophy (human nude phenotype) | AR | 601705 | atrichia, nail dystrophy, T-cell immuodeficiency | FOXN1 | Forkhead box N1 |
Atrichia with papular lesions | AR | 209500 | atrichia, papules | HR | Hair less (transcriptional corepressor) |
Marie-Unna hereditary hypotrichosis | AD | 146550 | Hypotrichosis, wiry hair | U2HR | Small peptide that regulates translation of the HR protein |
Trichorhinophalangeal syndrome type I/type III | AD | 190350/190351 | Hypotrichosis, peer-shaped nose, brachydactyly, clinodactyly | TRPS1 | Zing finger transcription factor |
Hypotrichosis-lymphedema-telangiectasia syndrome | AD/AR | 607823 | Hypotrichosis, lymphedema, telangiectasia (easily visible blood vessels) | SOX18 | SRY-BOX 18 |
Trichodontoosseous syndrome | AD | 190320 | WH, hypodontia, bone anomalies | DLX3 | Distal-less homeobox 3 |
Hereditary hair disorders resulting from mutations in transcription factors.
FOXN1, also known as WHN, is a transcription factor expressed in the matrix and the hair shaft of the HF, and has been shown to regulate the expression of several hair keratin genes [67]. FOXN1 is expressed in not only the HF, but also in the nail units and thymus. Mutations in the FOXN1 gene have been reported to underlie T-cell immunodeficiency, congenital alopecia, and nail dystrophy (MIM 601705), which is an autosomal recessive disease and represents the human counterpart of the nude mouse phenotype, suggesting the crucial roles of FOXN1 in development of skin appendages, as well as thymus in both humans and mice [68].
Clinical features of Rapp-Hodgkin syndrome.
Hairless (HR) is a putative single zinc-finger transcription factor which is known to regulate the catagen phase of the hair cycle [69]. Recessively-inherited mutations in the HR gene have been shown to underlie atrichia with popular lesions (APL; MIM 209500) [70]. APL is characterized by early onset of generalized complete hair loss (atrichia), which is followed by papular eruptions due to formation of dermal cyst after an abnormal first catagen phase [71]. Mutations responsible for APL have been found in coding exons or exon-intron boundary sequences of the HR gene, all of which were predicted to result in loss of expression and/or function of the HR protein. Recently, another disease, known as Marie-Unna hypotrichosis (MUH; MIM 146550), has been shown to be associated with the HR gene. MUH is a non-syndromic hereditary hair disorder showing an autosomal dominant inheritance pattern. Affected individuals with MUH typically exhibit sparse scalp and facial hair at birth. Subsequently, coarse, wiry, and twisted hairs develop in early childhood. Hair loss progresses with aging, which leads to a complete alopecia or a phenotype just like androgenetic alopecia. MUH was previously mapped to the HR locus on chromosome 8p21.3 [72]. However, direct sequencing analysis of coding sequences of the HR gene failed to detect mutations. Later on, Wen et al. found that the promoter region of the HR gene has four potential upstream open reading frames (uORFs), which were designated U1HR-U4HR. Strikingly, direct sequencing analysis of the U1HR-U4HR in patients with MUH has led to the identification of mutations within the U2HR sequences, which encode a small peptide of 34 amino acid residues [73]. In vitro studies have suggested that this small peptide encoded by the U2HR downregulates the HR expression at the translational level, and loss-of-function mutations in the U2HR results in overexpression of the HR protein [73]. Besides these findings, actual consequences resulting from U2HR mutations in vivo remain elusive.
TRPS1 is a transcription factor with GATA-type and Ikaros-type zinc finger domains, which has been shown to be abundantly expressed in both epithelial and mesenchymal components in the developing mouse HFs [74]. Furthermore, it has recently been reported that Trps1 plays crucial roles in regulating the expression of several Wnt inhibitors and various transcription factors during vibrissa follicle morphogenesis in mice [75]. In humans, mutations in the TRPS1 gene are known to cause trichorhinophalangeal syndrome type I (TRPS I; MIM 190350) or type III (TRPS III; MIM 190351), both of which show an autosomal dominant inheritance trait, and are characterized by sparse hair and a number of craniofacial and skeletal abnormalities, such as peer-shaped nose and brachydactyly. Hypotrichosis is the most prominent in the temporal region of the scalp (Figure 16) [76, 77].
Clinical features of TRPS I.
In addition to the transcription factors described above, several other members are also associated with hereditary hair diseases. For instance, both dominantly- and recessively-inherited mutations in SOX18 gene underlie hypotrichosis-lymphedema-telangiectasia syndrome (MIM 607823) [78] and dominantly-inherited mutations in DLX3 gene cause trichodontoosseous syndrome (MIM 190320), respectively (Table 3) [79].
It has been shown via analyses using mice models that several signaling pathways play crucial roles in the HF morphogenesis and development. In humans, disruption of these signaling pathways has been demonstrated to underlie various hereditary hair disorders (Table 4). In addition, information obtained from the analysis of hereditary hair diseases has highlighted a novel signaling pathway that had not previously been known to play a role in the HF development.
disease | inheritance pattern | OMIM# | main symptoms | gene | protein, function |
Hypohidrotic ectodermal dysplasia | XR | 305100 | Hypotrichosis, hypohidrosis, hypodontia | EDA | ectodysplasin A1 (EDA-A1) |
AD | 129490 | EDAR EDARADD TRAF6 | EDA-A1 receptor EDAR-associated death domain TNF receptor-associated factor 6 | ||
AR | 224900 | EDAR EDARADD | EDA-A1 receptor EDAR-associated death domain | ||
Odontoonychodermal dysplasia | AR | 257980 | Hypotrichosis, hypodontia, nail dystrophy, PPK | WNT10A | Wnt ligand |
Generalized hereditary hypotrichosis simplex | AD | 605389 | hypotrichosis | APCDD1 | Wnt inhibitor |
Localized autosomal recessive hypotrichosis 2 (LAH2)/autosomal recessive woolly hair 2 (ARWH2) | AR | 604379 | WH, hypotrichosis | LIPH | phosphatidic acid-selective phospholipase A1α (PA-PLA1α) |
LAH3/ARWH1 | AR | 611452/278150 | WH, hypotrichosis | LPAR6 | LPA6 (LPA receptor) |
Inflammatory skin and bowel disease | AR | 614328 | erythema, diarrhea, WH | ADAM17 | Tumor necrosis factor converting enzyme (TACE) |
Hereditary hair disorders associated with disruption of signaling pathways.
Hypohidrotic ectodermal dysplasia (HED), also known as Christ-Siemens-Touraine syndrome, is a rare genetic disease characterized by abnormal development of hair, teeth, and sweat glands. Most cases of HED show an X-linked recessive inheritance pattern (MIM 305100), while a minority of HED is inherited as either an autosomal dominant (MIM 129490) or an autosomal recessive trait (MIM 224900). During the last 15 years, the molecular basis for HED has gradually been disclosed. X-linked HED is caused by mutations in ectodysplasin (EDA) gene [80], and autosomal forms of HED are resulting from mutations in either EDA-receptor (EDAR) [81] or EDAR-associated death domain (EDARADD) [82] genes. The EDA gene encodes several isoforms of a type II transmembrane protein via alternative splicing [83]. Of these, ectodysplasin-A1 (EDA-A1) is the longest isoform which belongs to the tumor necrosis factor (TNF) ligand superfamily. EDAR, the receptor of EDA-A1 [84], is a type I transmembrane protein and a member of the TNF receptor superfamily with a potential death domain in its intracellular region. During the development of ectoderm-derived organs, EDA-A1 binds to its receptor EDAR, which subsequently associates with its adaptor EDARADD. Additionally, EDARADD protein interacts with TNF receptor-associated factor 6 (TRAF6), which further forms a complex with TGFβ-activated kinase 1 (TAK1) and TAK1-binding protein 2 (TAB2) within the cytoplasm, leading to activate the downstream NF-κB [85]. Most recently, a heterozygous mutation in the TRAF6 gene has been identified in a patient showing typical clinical features of HED [86]. Since EDA-A1, EDAR, EDARADD, and TRAF6 are closely related to each other in a signaling pathway, mutations in any of these four pathway components result in identical phenotypic characteristics among patients.
Odontoonychodermal dysplasia (OODD; MIM 257980) is an autosomal recessive disease which is characterized by various ectodermal abnormalities including hypotrichosis, hypodontia, nail dystrophy, and palmoplantar keratoderma. It has recently been shown that OODD is caused by loss of function mutations in the WNT10A gene, which encodes a WNT ligand [87]. It is noted that some affected individuals with WNT10A mutations can show phenotypes resembling HED [88], indicating the close relationship between EDA-A1/EDAR signaling and Wnt signaling, which has also been suggested by experiments in mice models [89].
In addition to Wnt ligands, abnormal function of Wnt inhibitors has recently been shown to cause a hereditary hair disorder in humans. Generalized hypotrichosis simplex (GHS; MIM 605389) is an autosomal dominant non-syndromic hair disorder which is characterized by progressive loss of scalp and body hairs starting in the middle of the first decade of life and almost complete baldness by the third decade [90]. In several families with GHS, an identical heterozygous missense mutation (L9R) has been identified in APCDD1 gene on chromosome 18p11.22 [91, 92]. The APCDD1 gene encodes a single-pass transmembrane protein which is abundantly expressed in the dermal papilla, the matrix and the hair shaft of human HF. Functional studies in cultured cells, chick embryos, and xenopus have revealed that APCDD1 inhibits Wnt signaling potentially via interacting Wnt ligands and their co-receptors LRPs [91]. In addition, it has been demonstrated that the L9R-mutant APCDD1 protein functions in a dominant negative manner against wild-type APCDD1 protein [91]. Therefore, Wnt activity is predicted to be upregulated in patients’ HFs. It is postulated that chronic stimulation by Wnt signaling may result in depletion of stem cell pool in the HF bulge, leading to GHS.
Recently, a signaling of lipid mediators has been shown to play essential roles in hair growth. About a decade ago, phosphatidic acid, has been demonstrated to promote hair growth in organ culture system, suggesting a potential role of lipids in hair growth [93]. Later on, it has been reported that mutations in lipase H (LIPH) gene underlies an autosomal recessively-inherited hypotrichosis (Localized autosomal recessive hypotrichosis 2 (LAH2); MIM 604379) [94]. Affected individuals with LAH2 show sparse hair on their scalp and extremities, whereas facial and sexual hairs look normal. In addition, it is noteworthy that patients with LIPH mutations show woolly hair (WH) in high frequency (Figure 17) [95], thus the LIPH can be regarded as a causative gene responsible for autosomal recessive WH (ARWH). Most affected individuals with LIPH mutations showed mainly WH during early childhood, and then exhibited wide variability in the hypotrichosis phenotype with aging [96].
Clinical features of LAH2/woolly hair caused by mutations in the LIPH gene.
The LIPH gene encodes cell membrane-associated phosphatidic acid-selective phospholipase A1α (PA-PLA1α) which produces 2-acyl lysophosphatidic acid (LPA) from phosphatidic acid [97]. As LPA activates cells through binding with its receptor, the existence of LPA receptor(s) in the HF had been expected, which has been idenitified by the analyses of additional families with ARWH/hypotrichosis without carrying mutations in the LIPH gene. Affected individuals in these families showed WH and associated hypotrichosis (Localized autosomal recessive hypotrichosis 3 (LAH3); MIM611452), which were almost identical phenotypes to those with LIPH mutations. Linkage studies and positional cloning have led to the identification of mutations in LPAR6 gene, also known as P2RY5, in these families [98, 99]. The LPAR6 gene encodes a G protein-coupled receptor LPA6 (P2Y5), which has clearly been proved to be a receptor of LPA [100]. Both PA-PLA1α and LPA6 are mainly expressed in the IRS of human HF [24, 99]. Importantly, their expression overlaps with K71 and K74, of which mutations underlie autosomal dominant WH/hypotrichosis. Sum of these data strongly suggest the crucial roles of PA-PLA1α/LPA/LPA6 pathway in the HF differentiation and hair growth, and its downstream signaling may be involved in regulating expression of the IRS-specific keratins. More recently, significant findings have been reported, which have revealed the downstream signaling of the PA-PLA1α/LPA/LPA6 pathway. Inoue et al. have produced Liph-knockout (KO) mice which exhibited a wavy coat phenotype resembling WH in humans [101]. In addition, a series of expression studies in the mutant mice, as well as detailed in vitro analyses, have demonstrated that the PA-PLA1α/LPA/LPA6 axis regulates differentiation and maturation of mouse HF via a signaling pathway composed of tumor necrosis factor converting enzyme (TACE), transforming growth facor (TGF)-α, and epidermal growth factor receptor (EGFR) [101]. It has been shown that LPA produced by PA-PLA1α stimulated its receptor LPA6, which subsequently activated TACE. Then, TACE induced ectodomain shedding of TGF-α, which resulted in transactivation of EGFR (Figure 18) [101]. Notably, in the HF of the Liph-KO mice, the expression of cleaved TGF-α, tyrosine-phosphorylated EGFR, LPA, and the IRS-specific K71, were significantly reduced [101]. Most recently, a recessively-inherited mutation in ADAM17 gene encoding TACE have been shown to cause inflammatory skin and bowel disease (MIM 614328) in humans, and affected individuals with the ADAM17 mutation appear to show WH phenotypes, similar to patients with LIPH or LPAR6 mutations [102]. These findings strongly suggest that the PA-PLA1α/LPA/LPA6 signaling can be involved in activating TACE in humans as well.
Schematic representation of the PA-PLA1α/LPA/LPA6 signaling pathway.
To identify causative genes responsible for hereditary hair disorders, as well as to disclose the functional relationship between these genes, has provided precious information to better understand the complex mechanisms for the HF development and cycling in humans. It is highly expected that recently-established methods in molecular genetics, especially whole genome sequencing [103], will enable us to find additional causative genes for the diseases. These genes may be associated with not only rare hair disorders, but also determining the hair texture in healthy individuals and/or more common hair diseases, such as alopecia areata and androgenetic alopecia.
I appreciate Drs. Atsushi Fujimoto and Hiroki Fujikawa (Niigata University, Japan) for their assistance to make figures. This work was supported in part by the Special Coordination Funds for Promoting Science and Technology from the Ministry of Education, Culture, Sports, Science and Technology of Japan (MEXT) to Y.S.
Bitcoin is a digital currency built on a peer-to-peer network and on the blockchain, a public ledger where all transactions are recorded and made available to all nodes. Opposite to traditional banking transactions, based on trust for counterparty, Bitcoin relies on cryptography and on a consensus protocol for the network. The entire system is founded on an open source software created in 2009 by a computer scientist known under the pseudonym Satoshi Nakamoto, whose identity is still unknown (see [1]). Hence, Bitcoin is an independent digital currency, not subject to the control of central authorities and without inflation; furthermore, transactions in the network are pseudonymous and irreversible.
\nBitcoin and the underlying blockchain technology have gained much attention in the last few years. Research on Bitcoin often deals with cybersecurity and legitimacy issues such as the analysis of double spending possibilities and other cyber-threats; recently, high returns and volatility have attracted research toward the analysis of Bitcoin price efficiency as well as its dynamics (see, among others, [2, 3, 4]). Moreover, many contributions claim that Bitcoin price is driven by attention or sentiment about the Bitcoin system itself; see [5, 6, 7, 8]. Possible driving factors for the sentiment about the Bitcoin system are the volume of Google searches or Wikipedia requests as in [5], or more traditional indicators as the number or volume of transactions, as suggested in [6]. In [9], the author suggests a time series model in order to identify the dynamic relation between speculation activity and price.
\nIn this chapter, after having introduced the basic concepts underlying Bitcoin, we sum up and describe to a broader audience the recent outcomes of the research reported in [10], by avoiding unnecessary technicalities. Some new insights are also given by looking at possible extensions in order to take into account the presence of bubble effects or the special feature of Bitcoin being traded in different online platforms (exchanges) that will be further investigated in our future research.
\nWe recall that Bitcoin was first introduced as an electronic payment system between peers by Satoshi Nakamoto (pseudonym) in [1]. Opposite to traditional transactions, which are based on the trust in financial intermediaries, this system relies on the network, on the fixed rules and on cryptography. Bitcoins can be purchased on appropriate websites that allow to change usual currencies in the cryptocurrency.
\nThe Bitcoin network has several attractive properties for its users:
No central bank authority for money supply and no regulator;
Transactions are 24/7 and without any country border;
Transaction cost are almost negligible with respect to traded amount;
Transaction are anonymous;
The security of each transaction is guaranteed by cryptography and digital signature;
The security of the whole network is guaranteed by construction unless more than 50% of the network nodes agree on a deceptive action.
As a digital payment system, Bitcoins may be used to pay for several online services and goods. Special applications have been designed for smartphones and tablets for transactions in Bitcoins and some ATMs have appeared all over the world (see Coin ATM radar) to change traditional currencies in Bitcoins. Accepting Bitcoins as a payment method is also related to an advertisement opportunity for companies. However, the high returns achieved in the last few years have transformed Bitcoin in a speculative asset affecting its use as a form of payment.
\nThe Bitcoin system has been subject to many cracks but has proven to be very resilient as the value of the cryptocurrency was able to rise again after all the falls. Nevertheless, at the time of writing, Bitcoin was experiencing a fall in its exchange rate with main fiat currencies.
\nTwo of the main crackdowns were China enforcement in December 2013 and Mt. Gox bankruptcy in February 2014.
\nBesides technical and regulation issues, the Bitcoin system also faces reputational concerns.
\nIn fact, the ambiguity of anonymous transactions has blamed the network of allowing several criminal activities such as buying illegal goods, money laundering or the financing of terrorism actions. As a representative example, we recall that The Silk Road was a website that started selling narcotics and illegal drugs in 2011, payable in Bitcoins. The website was finally shutdown by 2013 and the owner was arrested and sentenced to life in prison. Again, anonymous transactions make it possible to use huge quantities of money, exchanged in Bitcoins, without declaring its origin, hence allowing for possible money laundering. However, according to a research performed by the UK government, the highest score related to money laundering is still cash, followed by the bank, accountancy and legal service providers (see
It is worth noticing that while counterparties are represented by secret addresses and are anonymous, all transactions are recorded and might be traced. Investigation is hence favored by this feature of the network.
\nDespite the flaws in the system, Bitcoin has achieved a notwithstanding rise in recent years.
\nIn Figure 1, we report Bitcoin price and returns from January 2012 to December 2017 (source
Bitcoin price (top) and returns (bottom) from January 2012 to December 2017.
The model we suggest in what follows is motivated by findings in [5, 6, 8, 11] where it is showed that Bitcoin price is related to investors’ attention measured by the trading volume and/or the number of searches in engines such as Google and Wikipedia. Bitcoin is treated as a financial stock as suggested in [12] and the suggested model may be applied in principle to other assets that are proven to depend on market attention.
\nConsider a probability space \n
Let us denote the Bitcoin price process as \n
where \n
It is well known that the above dynamics for the attention factor is a geometric Brownian motion, the solution of which is given by \n
We collect in this subsection the properties of the logarithmic returns obtained by the price process defined in Eq. (1).
\nConsider the discrete process \n
Theorem 2.1. The random vector \n
Proof. In order to prove the theorem it suffices to remind that, for i = 1, 2, …, n, the random variable \n
As for the unconditional distribution, it is easy to obtain, for \n
where \n
Proposition 2.2. The joint probability density of the vector \n
where \n
The proof follows from Bayes’ rule and application of Theorem 2.1.
\nIt is worth to remark that the probability density \n
Precisely, we have that \n
We apply the outcomes above in order to estimate model parameters according to the maximum-likelihood method (see for example [14, 15]) where the likelihood is approximated by applying the Levy approximation [13].
\nParameter estimates are obtained as
\nwhere
The first step in our procedure is to identify possible measures of investors’ attention. As already mentioned in the introduction, we consider the total trading volume on Bitcoin available from
The trading volume of exchange is a classical measure of the attractiveness of a traded asset for an investor; besides, in [16], the authors find evidence that the latter captures the attention of retail/uniformed investors.
\nWe consider daily data from January 1, 2015, to June 30, 2017, for the total volume and the SVI Index. As for the daily value of the Bitcoin, we have considered the average mean across main exchanges represented by the Index in
In Table 1, the outcomes for parameter estimates, obtained by maximizing the approximate likelihood given the observed time series, are summed up.
\n\n | \n\n | \n\n\n | \n\n\n | \n\n\n | \n
---|---|---|---|---|
A = Vol | \n0.9571 | \n1.1346 | \n0.0218 | \n0.0829 | \n
A = SVI | \n1.3584 | \n1.0687 | \n0.0743 | \n0.1559 | \n
Parameter estimates for the model in Eq. (1) fitted on daily observations from January 2015 to June 2017.
In this section, we show how to characterize the price of European call options on Bitcoins in the underlying market model. Let us fix a finite time horizon \n
where \n
Lemma 3.1. Every equivalent martingale measure \n
where \n
The proof can be deduced from that of Lemma 1.4 in [10], where they also account for a possible delay between the attention factor and its effect on Bitcoin prices trend. The process \n
is an \n
Equivalently, we can write the discounted Bitcoin price process \n
Clearly, under the minimal martingale measure \n
where \n
Remark 3.2. Note that, under any equivalent martingale measure that keeps the drift of the attention factor dynamics linear in \n
Now, we compute the fair price of a Bitcoin European call option via the risk-neutral evaluation approach, so it can be expressed as expected value of the terminal payoff under the selected pricing measure, that is, the minimal martingale measure. Let CT = (ST − K)+ be the \n
where
\nand \n
Here, \n
The following result provides the risk-neutral price of the option under the minimal martingale measure \n
Proposition 3.3. The risk-neutral price \n
where the function \n
Hence, the resulting risk-neutral pricing formula when evaluated in \n
In order to appreciate the performance of the pricing formula in Eq. (19), we compute model prices for option traded on the online platform
T-K | \nMarket bid | \nMarket ask | \nModel volume | \nModel Google SVI | \nBenchmark BS | \n
---|---|---|---|---|---|
Aug-2200 | \n0.1662 | \n0.2318 | \n0.2029 | \n0.2282 | \n0.1967 | \n
Aug-2300 | \n0.1670 | \n0.2072 | \n0.1737 | \n0.2032 | \n0.1655 | \n
Aug-2400 | \n0.1390 | \n0.1845 | \n0.1469 | \n0.1802 | \n0.1369 | \n
Aug-2500 | \n0.1142 | \n0.1638 | \n0.1228 | \n0.1591 | \n0.1112 | \n
Aug-2600 | \n0.0922 | \n0.1376 | \n0.1014 | \n0.1399 | \n0.0887 | \n
Aug-2700 | \n0.0749 | \n0.1202 | \n0.0828 | \n0.1226 | \n0.0695 | \n
Aug-2800 | \n0.0572 | \n0.1047 | \n0.0684 | \n0.107 | \n0.0535 | \n
Aug-2900 | \n0.0442 | \n0.0983 | \n0.0549 | \n0.0931 | \n0.0405 | \n
Sept-2200 | \n0.1991 | \n0.2648 | \n0.2546 | \n0.3204 | \n0.2173 | \n
Sept-2300 | \n0.1766 | \n0.2432 | \n0.2321 | \n0.3019 | \n0.1906 | \n
Sept-2400 | \n0.1890 | \n0.2230 | \n0.2113 | \n0.2844 | \n0.1662 | \n
Sept-2500 | \n0.1375 | \n0.2042 | \n0.1919 | \n0.2679 | \n0.1439 | \n
Sept-2600 | \n0.1207 | \n0.1828 | \n0.1741 | \n0.2523 | \n0.1239 | \n
Sept-2700 | \n0.1120 | \n0.1668 | \n0.1576 | \n0.2377 | \n0.1060 | \n
Sept-2800 | \n0.0953 | \n0.1504 | \n0.1463 | \n0.2239 | \n0.0903 | \n
Sept-2900 | \n0.0848 | \n0.1422 | \n0.1325 | \n0.2109 | \n0.0764 | \n
Motivated by empirical evidences (see for example [21, 22]), we discuss a generalization of the model introduced in Section 3.1, which is capable to describe speculative bubbles in Bitcoin markets.
\nPrecisely, we fix a finite time horizon \n
Without loss of generality, we assume that the interest rate is fixed and equal to zero. In this setting, the discounted Bitcoin price trend and the market attention factor dynamics are described by
\nwhere we have set \n
By simulating trajectories for the asset price \n
Simulated trajectories with n = 250 daily observations for the attention process (red) and the corresponding Bitcoin price dynamics for \n\nρ\n=\n0\n\n (black), \n\nρ\n=\n0.5\n\n(green), and \n\nρ\n=\n1\n\n (blue).
Indeed, we will show formally that the possibility of Bitcoin speculative bubbles is related to the sign of the correlation parameter \n
The mathematical theory of financial bubbles is developed, among others, in [23, 24, 25]. Precisely, we introduce the following definition from [23].
\nDefinition 4.1. The Bitcoin price process \n
The term strict \n
Recall that the absence of arbitrage opportunities is “essentially” equivalent to the existence of a probability measure \n
Remark 4.2. Note that stock bubbles arise if \n
Then, to exclude arbitrage opportunities from the market, we define the process \n
where \n
To ensure that \n
and we can consider the corresponding family of equivalent (local) martingale measures \n
where the \n
\n\n
Now, suppose that the risk perception process is zero, that is, \n
is a true \n
Proposition 4.3. In the model outlined in Eq. (24), the Bitcoin price process \n
The proof is based on the application of some of Sin’s results given in [27], where the existence of risk-neutral measures for the Hull-White stochastic volatility model [19] and for similar frameworks is determined by the possibility of explosion in finite time for solutions of certain auxiliary stochastic differential equations. Precisely, it is possible to show that the martingale property of the discounted stock price \n
Let us generalize the model introduced in Eq. (1) by assuming a possible delay \n
where \n
Analogous results as those in Section 2 can be derived by similar computations, and model parameters, for a fixed delay, can be estimated by means of the maximum likelihood method. In order to estimate the delay parameter, we maximize the profile likelihood as defined in [15]. Details of this procedure can be found in [10]. The estimation results of model in Eq. (27) on the same daily data considered in Section 2 are summed up in Table 3.
\n\n | \n\n | \n\n\n | \n\n\n | \n\n\n | \n\n\n | \n
---|---|---|---|---|---|
A = Vol | \n1 day | \n0.4881 | \n1.0459 | \n0.0282 | \n0.0924 | \n
A = SVI | \n7 days | \n1.0964 | \n0.9946 | \n0.1005 | \n0.1885 | \n
Parameter estimates for model in Eq. (27) fitted on daily observations from January 2015 to June 2017.
In Figure 3, we plot simulated trajectories of the price process in Eq. (27) by letting the delay parameter vary.
\nSimulated trajectories of n = 250 daily observations of the attention factor (red) and the Bitcoin price according to model in Eq. (27) when the delay parameter is \n\nτ\n=\n1\n\n day (black) and \n\nτ\n=\n10\n\n days (blue).
The different delays result in a shift to the south-east between the faster and slower reacting trajectories; in the picture, this behavior is sharp since the other model parameters are kept constant. By looking at the picture, the idea to model the price of Bitcoin in different exchanges by the same model in Eq. (27) but allowing different parameters naturally arises.
\nIn particular, considering for instance two exchanges, we have
\nwhere \n
Note that within this model, prices for Bitcoin traded in different exchanges are perfectly correlated. Indeed, this is what happens in observed data; considering daily prices from January 2015 to June 2017 for Bitstamp, Kraken, Cex.io, Gdax, and The Rock exchanges we get cross-correlation values larger than 0.999.
\nWe fit model in Eq. (28) for the Bitstamp and Gdax exchanges on daily observations of Bitcoin price from January 2015 to June 2017 obtaining the outcomes reported in Table 4, when the attention is measured by the trading volume, and in Table 5, when attention is measured by the Google SVI index.
\nExchange | \n\n\n | \n\n\n | \n\n\n | \n\n\n | \n\n\n | \n
---|---|---|---|---|---|
Bitstamp | \n1 | \n0.4994 | \n1.0461 | \n0.0281 | \n0.0896 | \n
Gdax | \n2 | \n0.4997 | \n1.0420 | \n0.0326 | \n0.1036 | \n
Model fitting with delay parameter: outcomes for Bitstamp and Gdax exchanges when attention is measured by the trading volume.
Exchange | \n\n\n | \n\n\n | \n\n\n | \n\n\n | \n\n\n | \n
---|---|---|---|---|---|
Bitstamp | \n7 days | \n1.0934 | \n0.9946 | \n0.0992 | \n0.1782 | \n
Gdax | \n7 days | \n1.0964 | \n0.9946 | \n0.1160 | \n0.2087 | \n
Model fitting with delay parameter: outcomes for Bitstamp and Gdax exchanges when attention is measured by the SVI index.
It is evident from the outcomes in Table 4 that the model parameters are not significantly different while the delay might be quite different as if the reaction to the attention factor is faster for some exchanges and slower for others. On the contrary, when attention is measured by the Google SVI Index, the delay is unchanged, but the difference between estimated parameters for the price dynamics is nonnegligible.
\nBy analyzing the outcomes and considering the shift effect as depicted in Figure 3, it is tempting to conjecture that the faster reaction determines the leader exchanges and that the slower exchange will then follow. If we could forecast that the next day price of the slower exchange will reach the price today for the faster one, we could obtain a profit by suitably investing in the two exchanges. However, it is worth noticing that the estimation of the delay parameter is obtained by maximizing the likelihood over a whole time series and is a product of averaging so arbitrage cannot be achieved in a direct way.
\nNevertheless, in a multivariate setting as ours, the theory guarantees that arbitrage opportunities are ruled out if the market price of risk in the market is unique. Without entering technical details and assuming \n
It is evident that these values are not equal if we plug parameter estimates in Eq. (30); hence, arbitrage opportunities are not ruled out at least from a theoretical point of view. We will address this issue more precisely in future research.
\nIn this chapter, we have introduced a model in continuous time in order to describe the dynamics of Bitcoin price depending on an exogenous stochastic factor, which represents market attention on the Bitcoin system. Market attention is measured either by the total trading volume in Bitcoins or by means of the Google Search Volume Index, which, as suggested in [16], is a direct measure of the revealed attention for uniformed retail investors. More precisely, the attention factor affects directly the instantaneous mean and volatility of logarithmic returns; in addition, it may be also correlated with the price changes. An estimation procedure to fit the model to observed data is also suggested and, under the assumption of no correlation, a closed formula for standard European option prices on Bitcoin is provided.
\nBy applying outcomes within the mathematical theory of bubbles [23, 24, 25, 27], we are able to show that Bitcoin boosts in a bubble if and only if there is a positive correlation between changes in the price and in the attention factor. This finding is reasonable and claims that a stronger positive dependence between the two processes in Eq. (21) may result in an explosion of the price process.
\nFinally, we allow for a delay on the effect of market attention on the Bitcoin price, and, based on this generalized model, we introduce a multivariate setting for our model (Eq. (28)) in order to take into account the special feature of multiple exchanges where it is possible to trade in Bitcoins. Preliminary results indicate that arbitrage opportunities may arise in two exchanges that are characterized by different delays.
\nWe gratefully acknowledge Marco Patacca for having provided the routines in Matlab® to develop the empirical sections of the paper and for useful suggestions and comments. We also acknowledge funding from Fondazione Cassa di Risparmio di Perugia (Grant 2015:0459013) and Bank of Italy (Grant 407660/16).
\nThe authors declare no conflict of interest.
Gianna Figà-Talamanca gratefully acknowledges interesting discussions on the topic of this chapter with colleagues of the Department of Finance and Risk Engineering where she was visiting professor while preparing this research. The authors also wish to thank Stefano Bistarelli for having introduced them to the intriguing and worth to explore world of cryptocurrencies.
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