Conventional and Atypical Deep Penetrating Nevus, Deep Penetrating Nevus-like Melanoma, and Related Variants

Simple Summary Atypical deep penetrating nevus (DPN) is a unique skin tumor with an uncertain biologic/metastatic potential that may be difficult to distinguish from DPN (an indolent lesion) and DPN-like melanoma (an aggressive lesion) based on the results of histomorphologic analysis and commonly employed molecular studies such as fluorescence in situ hybridization and comparative genomic hybridization alone. Herein, we review the clinical, histomorphological, immunohistochemical, molecular, and cytogenetic characteristics of the DPN spectrum of lesions to try to better understand the prognosis of these lesions and possible treatment approaches. Abstract Deep penetrating nevus (DPN) is an uncommon acquired melanocytic lesion with a distinct histopathological appearance that typically behaves in an indolent manner. The lesion is characterized by a symmetrical proliferation of epithelioid to spindled melanocytes associated with abundant melanophages and wedge-shaped extension to the deep reticular dermis and subcutis. Pronounced cytologic atypia and mitotic figures are usually absent, which helps distinguish DPN from melanoma with a deep penetrating growth pattern. Recently, the concept of atypical DPN has been proposed for lesions that demonstrate borderline histomorphologic features and may be associated with lymph node deposits but lack the copy number aberrations typical of melanoma by either fluorescence in situ hybridization or comparative genomic hybridization. While most of these lesions have a favorable clinical course, rare lesions may progress to melanoma. In this review, we summarize the current literature on atypical DPNs with uncertain behavior/metastatic potential and outline the characteristics that distinguish these lesions from conventional DPN and melanoma with DPN-like features.


Introduction
Melanocytic tumors are a heterogeneous group of lesions with wide variation in histomorphology and biologic behavior. Melanocytic tumors range from conventional acquired nevi, with unequivocally bland histopathological features and completely indolent clinical courses, to melanomas, with strikingly atypical histopathological features and inarguable potential for metastatic and aggressive disease [1]. In between is a spectrum of lesions with ambiguous histopathological features and unclear biologic potential that pose challenges in regard to their correct classification and management. The most recent edition of the World Health Organization Classification of Skin Tumors outlines a series of terms that have been used to describe lesions within this category, including "superficial atypical melanocytic proliferation of uncertain significance (SAMPUS)", "melanocytic tumor of uncertain malignant potential (MELTUMP)", "intermediate lesion", "melanocytic neoplasm of low malignant potential", and "melanocytoma" [1]. Melanocytoma has been defined as "a tumorigenic neoplasm of melanocytes that generally has increased cellularity and/or atypia (compared with a common nevus) and an increased (although generally still low) probability of neoplastic progression" [1]. These borderline melanocytic lesions often pose significant diagnostic difficulty and necessitate expert consultation and ancillary molecular testing [2][3][4].
Deep penetrating nevus (DPN) is an uncommon acquired melanocytic lesion that was first reported by Seab et al. in 1989 [5]. It lies along a histological continuum with plexiform spindle cell nevus (PLEXSCN), described by Barnhill et al. in 1991 [6], and clonal/inverted type A nevus, described by Ball and Golitz in 1994 [7]. DPN has a distinct histopathological appearance and has been generally accepted as behaving in an indolent manner. It can be distinguished from melanoma with a deep penetrating growth pattern, which usually shows unequivocally aggressive histomorphological features, including pronounced cytologic atypia and significantly increased mitotic activity.
Recently, a borderline lesion has been described within the DPN spectrum of tumors, referred to as atypical DPN or deep penetrating melanocytoma. This is a histologically ambiguous lesion that demonstrates borderline features similar to those of melanoma and is sometimes associated with lymph node deposits but often lacks the copy number aberrations typical of melanoma by either fluorescence in situ hybridization (FISH) or comparative genomic hybridization (CGH) [8]. Although this lesion appears to have an overall favorable clinical course, it can exhibit potential for progression to melanoma [8,9].
In this review, we will outline the current literature on conventional DPN, atypical DPN, and DPN-like melanoma; describe the clinical, histopathological, immunohistochemical, molecular, and cytogenetic characteristics that distinguish these lesions from each other and the other DPN histological variants; and highlight treatment approaches. Atypical DPNs are an area of ongoing research, and our review describes the most current literature on this topic.

Clinical Features
Conventional DPN is a benign melanocytic lesion that affects patients of all ages, has a predilection for women under the age of 40 years, and is usually found on the head and neck, trunk, and upper extremities [5,[10][11][12]. DPN presents as a solitary, less than 1 cm in diameter, symmetrical, well-circumscribed, nonulcerated, dome-shaped papule or nodule with dark pigmentation (Figure 1) [5,10,13]. DPN can be brown to blue to black with occasional color variegation and may seem to suddenly appear, which may raise clinical concern regarding melanoma and hence the need for biopsy [10,14]. Most patients with DPN do not have a personal or family history of melanoma [14]. DPN arising in a congenital nevus has been reported [15]. Multiple DPNs arising in linear arrangement have also been reported [16]. The dermoscopic features of DPN are not well established [14].

Histopathological Criteria
On histopathological examination (Figure 2), DPN is usually a small, well-circumscribed, symmetrical lesion composed of enlarged fusiform, spindled, and/or epithelioid melanocytes arranged in fascicles, cords, and nests extending into the deep dermis and subcutis in a wedge-shaped (inverted triangle) pattern [5,10,11,17]. A grenz zone may be present [13,14]. There may be peripheral collagen trapping, as seen in dermatofibromas. The bundles of melanocytes are usually associated with neurovascular and adnexal structures, giving a plexiform appearance [5,10,17]. There is no associated necrosis or loss or invasion of adnexal structures [13]. Sparse to abundant heavily pigmented melanophages and a lymphocytic infiltrate may be present [5,11,13]. There may be a limited junctional component [5,13].

Histopathological Criteria
On histopathological examination (Figure 2), DPN is usually a small, well-circumscribed, symmetrical lesion composed of enlarged fusiform, spindled, and/or epithelioid melanocytes arranged in fascicles, cords, and nests extending into the deep dermis and subcutis in a wedge-shaped (inverted triangle) pattern [5,10,11,17]. A grenz zone may be present [13,14]. There may be peripheral collagen trapping, as seen in dermatofibromas. The bundles of melanocytes are usually associated with neurovascular and adnexal structures, giving a plexiform appearance [5,10,17]. There is no associated necrosis or loss or invasion of adnexal structures [13]. Sparse to abundant heavily pigmented melanophages and a lymphocytic infiltrate may be present [5,11,13]. There may be a limited junctional component [5,13].
DPN may exist in a pure form but is often associated with a second nevoid subtype (conventional, blue, or Spitz nevus) as part of a combined nevus ( Figure 3) [10][11][12]18].
Some immunohistochemical features of DPNs are highlighted in Figure 4.
Some immunohistochemical features of DPNs are highlighted in Figure 4.

Molecular Biology
DPNs demonstrate activation of the WNT pathway, most commonly through gainof-function mutations of CTNNB1 (exon 3), which encodes β-catenin protein, and rarely through inactivation of APC [22]. WNT signaling increases melanocyte size and pigmentation, which results in the apparent lack of maturation seen in DPNs [22]. DPNs show diffuse expression of AXIN2, a marker of β-catenin transcription, by RNA in situ hybridization [22]. Mutations of genes in the mitogen-activated protein kinase (MAPK) pathway, such as BRAF (usually p.V600E), MAP2K1 (also referred to as MEK1), or HRAS, may also be present [22]. Most DPNs arise from common acquired nevi, in which case the CTNNB1 mutation is limited to only the DPN component, whereas the MAPK-activating mutation is found in both components [12,22]. Mutations of the β-catenin and MAPK pathways result in activation of LEF1, a transcription factor that facilitates the epithelial-mesenchymal transition and promotes tumorigenesis [23].
Although DPNs were once thought to be closely related to blue nevi given their shared diffuse expression of HMB45, GNAQ and GNA11 mutations, which are common in blue nevi, are not found in DPNs [30]. However, the presence of HRAS mutations in DPNs does suggest a possible relationship with Spitz nevi [30]. ALK rearrangements are not a common feature in DPNs [31].

Molecular Biology
DPNs demonstrate activation of the WNT pathway, most commonly through gainof-function mutations of CTNNB1 (exon 3), which encodes β-catenin protein, and rarely through inactivation of APC [22]. WNT signaling increases melanocyte size and pigmentation, which results in the apparent lack of maturation seen in DPNs [22]. DPNs show diffuse expression of AXIN2, a marker of β-catenin transcription, by RNA in situ hybridization [22]. Mutations of genes in the mitogen-activated protein kinase (MAPK) pathway, such as BRAF (usually p.V600E), MAP2K1 (also referred to as MEK1), or HRAS, may also be present [22]. Most DPNs arise from common acquired nevi, in which case the CTNNB1 mutation is limited to only the DPN component, whereas the MAPK-activating mutation is found in both components [12,22]. Mutations of the β-catenin and MAPK pathways result in activation of LEF1, a transcription factor that facilitates the epithelial-mesenchymal transition and promotes tumorigenesis [23].
Although DPNs were once thought to be closely related to blue nevi given their shared diffuse expression of HMB45, GNAQ and GNA11 mutations, which are common in blue nevi, are not found in DPNs [30]. However, the presence of HRAS mutations in DPNs does suggest a possible relationship with Spitz nevi [30]. ALK rearrangements are not a common feature in DPNs [31].

Cytogenetic Findings
Conventional DPNs lack cytogenetic abnormalities on FISH or CGH.

Prognosis and Treatment
Conventional DPNs are benign, rarely progress to melanoma, and typically are not associated with local recurrences and distant metastases [5,14,32]. Treatment consists of conservative and complete surgical excision [13,14].

Cytogenetic Findings
Conventional DPNs lack cytogenetic abnormalities on FISH or CGH.

Prognosis and Treatment
Conventional DPNs are benign, rarely progress to melanoma, and typically are not associated with local recurrences and distant metastases [5,14,32]. Treatment consists of conservative and complete surgical excision [13,14].

Clinical Features
Atypical DPNs (also known as deep penetrating melanocytomas, atypical DPNs with uncertain malignant potential, and borderline DPNs) are considered intermediate-grade lesions and are an area of ongoing study with limited literature. These are rare tumors that have more atypical clinical features than conventional DPNs, including larger size and more frequent asymmetry [1]. An early review of seven cases by Magro et al. showed a male predilection and mean age at presentation of 22.3 years (range, 14-36 years) [9]. In a subsequent review of 40 atypical DPN-type lesions, Magro et al. showed that these lesions had a slight female predilection (1.5:1 female to male ratio) and wide range of age at presentation (range, 10-62 years), with a median age at presentation of 34.5 years [8]. The lesions were more commonly distributed on the face, upper and mid back, and forearm and rarely on the lower torso and lower extremity [8]. A series of 13 cases reported by Muhlbauer et al. also confirmed a female predilection and showed a mean age of 36 years (range, 11-66 years) and the back and arm as common locations [3]. In a series of 21

Histopathological Criteria
Atypical DPN may arise in a background characteristic of conventional DPN. Compared to conventional DPN, atypical DPN has increased architectural and cytologic atypia. However, the atypical features fall short of those diagnostic of melanoma ( Figure 5). Atypical architectural features include asymmetry, hypercellularity with expansile nodular or diffuse sheet-like architecture, and infiltrative borders [8,33,35]. A junctional component with cells cytologically similar to those seen in the dermis and pagetoid upward migration of melanocytes may be present [8]. Although random cytologic atypia may be present in conventional DPN, the atypia found in atypical DPN appears more than random and is most conspicuous within the areas of hypercellularity [8,33]. Lesional cells demonstrate moderate to severe cytologic atypia, including pleomorphism, high nuclear to cytoplasmic ratios, conspicuous cherry-red nucleoli, variable cytoplasmic melanin pigment, amphophilic cytoplasm, rare multinucleation, and 1 to 3 mitotic figures per square millimeter [8,33,35] [8]. Despite the increased mitotic activity, atypical mitotic figures are usually not seen [33]. A lymphocytic infiltrate may be commonly seen [33,34]. The case reported by Abraham et al. showed focal necrosis [34]. Atypical DPNs may exist in their pure form or as part of a combined nevus [33].  Atypical DPNs may show nodal deposits on sentinel lymph node (SLN) biopsy ( Figure 6).

Immunohistochemical Features
Atypical DPNs demonstrate nuclear and cytoplasmic β-catenin expression [33]. The Ki67 proliferative index may be increased [34]. Atypical DPNs may show reduced expression of 5-hydroxymethylcytosine compared to conventional DPN [36]. Atypical DPNs that have progressed to melanoma may not show PRAME expression [35]. Some typical immunohistochemical features of atypical DPN are highlighted in Figure 7.

Molecular Biology
Atypical DPNs demonstrate mutational profiles similar to those of conventional DPN. Next-generation sequencing (NGS) performed on 21 atypical DPNs by Manca et al. showed frequent mutations of β-catenin pathway genes (most commonly CTNNB1 mutations and less commonly APC mutations) and MAPK pathway genes (BRAF, HRAS, and MAP2K1) [33]. IDH mutations were found in 33% of cases [33]. Their single case with nodal disease demonstrated alterations in the β-catenin pathway and mutations in IDH1 and NRAS [33]. Comprehensive mutation analysis showed low genetic heterogeneity for the main gene pathways [33]. No significant associations were found between specific gene mutations and histomorphologic features [33].

Cytogenetic Findings
Atypical DPNs usually demonstrate negative cytogenetic profiles on FISH and CGH. In the review of 40 cases of atypical DPN by Magro et al., FISH targeting 6p25 (RREB1), 6q23 (MYB), 11q13 (CCND1), and Cep6 performed in 10 of the 40 cases showed cytogenetic abnormalities characteristic of melanoma in three cases despite borderline histomorphologic features [8]. Oligo-array-based CGH performed in six of their cases (including two of the cases with melanoma profiles on FISH) did not show any significant chromosomal abnormalities [8]. In a FISH analysis of 13 atypical DPNs performed by Muhlbauer et al., only 3 lesions demonstrated abnormal FISH profiles [3]. The case reported by Abraham et al. did not demonstrate cytogenetic abnormalities on CGH [34]. In the case reported by Isales et al., FISH targeting RREB1, MYB, CCND1, Cep6, 9p21 (CDKN2A), and Cep9 performed on the initial atypical DPN lesion was negative [35].

Immunohistochemical Features
Atypical DPNs demonstrate nuclear and cytoplasmic β-catenin expression [33]. The Ki67 proliferative index may be increased [34]. Atypical DPNs may show reduced expression of 5-hydroxymethylcytosine compared to conventional DPN [36]. Atypical DPNs that have progressed to melanoma may not show PRAME expression [35]. Some typical immunohistochemical features of atypical DPN are highlighted in Figure 7.

Molecular Biology
Atypical DPNs demonstrate mutational profiles similar to those of conventional DPN. Next-generation sequencing (NGS) performed on 21 atypical DPNs by Manca et al. showed frequent mutations of β-catenin pathway genes (most commonly CTNNB1 mutations and less commonly APC mutations) and MAPK pathway genes (BRAF, HRAS, and MAP2K1) [33]. IDH mutations were found in 33% of cases [33]. Their single case with nodal disease demonstrated alterations in the β-catenin pathway and mutations in IDH1 and NRAS [33]. Comprehensive mutation analysis showed low genetic heterogeneity for the main gene pathways [33]. No significant associations were found between specific gene mutations and histomorphologic features [33]. Atypical DPNs may demonstrate normal cytogenetic profiles on initial biopsies at the borderline stage but then demonstrate chromosomal aberrations once they have morphologically progressed to melanoma [3]. One of the cases in the series reported by Magro et al. demonstrated normal cytogenetic profiles on both FISH and CGH on the initial biopsy but demonstrated unequivocal histomorphologic and cytogenetic progression into a DPN-like melanoma on subsequent biopsies (gains of RREB1 and CCND1 and loss of MYB1 on FISH and amplification of 3p21.1-p11.1 and loss of 8p23.3-p11.21 on CGH) [8]. In the case reported by Isales et al., FISH targeting RREB1, MYB, CCND1, Cep6, CDKN2A, and Cep9 performed on the initial atypical DPN lesion was negative [35]. However, when the lesion recurred and was thought to be more morphologically consistent with melanoma, FISH showed clonal gains at 6p25.35.

Prognosis and Treatment
Although SLN deposits may be common in atypical DPN, reported transformation to melanoma and fatal outcomes are rare.
In the review of seven patients with atypical DPN by Magro et al., four patients developed positive SLN, and one patient who developed recurrence as melanoma died Biology 2022, 11, 460 9 of 13 of widespread metastatic disease [9]. In their larger series of 40 patients with atypical DPN, Magro et al. had follow-up data for 37 of the 40 patients, with the follow-up period ranging from 5 months to 5.42 years (mean, 2.22 years) [8]. Thirty-five of the patients underwent re-excision, most commonly wide re-excision with 1-to 2-cm margins [8]. Of the 19 patients who underwent SLN biopsy, 6 had small subcapsular tumor deposits. Of these six patients, one had extensive parenchymal disease and developed recurrence one year after the wide excision; four underwent completion lymphadenectomy but did not have additional nodal disease; and two received adjuvant interferon alpha therapy [8]. Thirty-four patients remained without further metastatic or recurrent disease [8]. Two patients who were not initially diagnosed as having atypical DPN and did not undergo wide re-excision developed DPN-like melanoma and widespread metastases within three years and four years, respectively, after initial diagnosis and subsequently died [8]. A patient with atypical DPN who did undergo re-excision and had a positive SLN but normal CGH findings later developed recurrence as melanoma [8]. Two of the three patients with atypical DPN and positive FISH findings underwent SLN biopsy, and only one was positive for lymph node deposits [8]. All three patients remained alive and well at the time of the publication [8].
In the case reported by Isales et al., the patient did not undergo re-excision, despite the presence of positive margins on the initial biopsy, and developed recurrence 5 years later as melanoma with widespread SLN disease, including extracapsular extension, and 1 of 24 lymph nodes positive on completion lymphadenectomy [35]. The patient was treated with pembrolizumab with no subsequent recurrence for four years [35].
In the series of 21 cases reported by Manca et al., most patients were treated with simple excision without a further surgical procedure. Two patients underwent re-excision; one of these patients also underwent a SLN biopsy, which showed a positive node, with subsequent complete lymphadenectomy demonstrating 1 of 20 lymph nodes positive [33]. Follow-up data for 19 patients with a mean follow-up period of 38.1 months (range: 5-226 months) showed that all patients were alive and well and demonstrated no other local recurrences or distant metastases [33].
The patient reported by Abraham et al. had multiple small nodal deposits on SLN biopsy [34].
As outlined, a wide variety of treatment approaches have been utilized in cases of atypical DPN, including no further treatment after initial biopsy, re-excision with conservative to wide margins, SLN biopsy, completion lymphadenectomy, and systemic therapy. The most cautious course of action in atypical DPN, like in other histologically ambiguous cases, may be to manage these lesion as melanoma, however, this may be influenced by key factors including the age of the patient and the grade of cytological and architectural atypia [2,8,37]. It has been recommended that treatment of atypical DPN include complete excision with wide clear margins up to 1 cm [8,37,38]. We also recommend close clinical follow-up, which may include occasional full body examination, although definitive clinical guidelines are not available on this [14]. Although discussion of SLN biopsy may also be considered, in their reprise of the atypical DPN case by Abraham et al., McCalmont and Bastian emphasized that SLN biopsy is controversial in the evaluation of ambiguous melanocytic lesions and should be used as a staging tool rather than a diagnostic or predictive one [39]. There may be false positives and SLN biopsy is not considered standard management.

Clinical Features
DPN-like melanoma has also been termed plexiform melanoma [40]. DPN-like melanomas usually affect young patients and are present on the face or upper body [40]. Like most melanomas, clinically, these lesions may demonstrate asymmetry, poor circumscription, color variegation, large size, and evolution over time.

Molecular Biology
DPN-like melanoma may share activation of the WNT pathway with DPN, suggesting that some DPNs can progress to melanoma. A biphenotypic epithelioid and plexiform melanoma with DPN-like features was shown to demonstrate BRAF and PTEN mutations in both components but a CTNNB1 mutation only in the DPN-like areas [41]. NGS performed on five cases of DPN-like melanoma by Yeh et al. showed MAPK pathway activating mutations of BRAF or NRAS in all cases and activating mutations in the β-catenin pathway in three cases [22]. All cases showed additional oncogenic alterations, including CDKN2A, TERT, TP53, ARID1A, and TET2 mutations, and genomic copy number aberrations [22]. Isales et al., in their case of atypical DPN progressing to melanoma, showed mutations of CTNNB1, NRAS, IDH1, ERBB4, GRIN2A, and MECOM in both tumors using NGS [35]. The melanoma additionally had mutations of TERT, DNMT3A, and PRSS3 and imbalanced chromosomal copy number gains in BRCA2, RET, FGFR1 (also referred to as FLT2), and IGF2 [35].
Evidence from molecular studies to date indicates that BRAF or MAP2K mutation leads to a conventional nevus, and subsequent CTNNB1 mutation results in the pheno-

Molecular Biology
DPN-like melanoma may share activation of the WNT pathway with DPN, suggesting that some DPNs can progress to melanoma. A biphenotypic epithelioid and plexiform melanoma with DPN-like features was shown to demonstrate BRAF and PTEN mutations in both components but a CTNNB1 mutation only in the DPN-like areas [41]. NGS performed on five cases of DPN-like melanoma by Yeh et al. showed MAPK pathway activating mutations of BRAF or NRAS in all cases and activating mutations in the β-catenin pathway in three cases [22]. All cases showed additional oncogenic alterations, including CDKN2A, TERT, TP53, ARID1A, and TET2 mutations, and genomic copy number aberrations [22]. Isales et al., in their case of atypical DPN progressing to melanoma, showed mutations of CTNNB1, NRAS, IDH1, ERBB4, GRIN2A, and MECOM in both tumors using NGS [35]. The melanoma additionally had mutations of TERT, DNMT3A, and PRSS3 and imbalanced chromosomal copy number gains in BRCA2, RET, FGFR1 (also referred to as FLT2), and IGF2 [35].
Evidence from molecular studies to date indicates that BRAF or MAP2K mutation leads to a conventional nevus, and subsequent CTNNB1 mutation results in the phenotypic switch to DPN. Finally, additional molecular oncogenic alterations, including alterations in CDKN2A, TERT, and other genes, cause DPN-like melanoma [22].

Cytogenetic Findings
DPN-like melanoma may show abnormal cytogenetic profiles on FISH and CGH.

Prognosis and Treatment
DPN-like melanomas are associated with metastatic potential and an aggressive disease course [40]. It has been proposed that these lesions may be less aggressive than nonplexiform variants of melanoma of the same thickness [40]. Complete excision with wide, clear margins and SLN biopsy is recommended.

Plexiform Spindle Cell Nevus (PLEXSCN)
PLEXSCN is considered a variant of DPN [1]. Clinically, PLEXSCN lesions are darkly pigmented raised lesions that present in young adults without sex predilection on the upper torso [6]. The main histological differences between PLEXSCN and DPN are that PLEXSCN demonstrates plexiform architecture instead of a wedge shape, a more superficial depth with localization along the neurovascular plexus, and greater amount of intervening collagen between fascicles of lesional cells. PLEXSCN lesions may have a junctional component and can be part of a combined nevus. PLEXSCN lesions are usually benign; however, complete excision with clear margins is recommended [42]. An atypical form of PLEXSCN with increased mitotic activity, hypercellularity, and cytologic atypia and potential for lymph node involvement has also been described [42,43].

Clonal/Inverted Type A Nevus
Clonal/inverted type A nevus (also known as melanocytic nevus with focal atypical epithelioid cell components) is also considered a variant of DPN [1,44]. It demonstrates clinical and histological features similar to those of DPN [44,45]. However, clonal nevus is a more superficial dermis-based lesion composed of only epithelioid melanocytes and may include a junctional component [44,45]. Like conventional DPNs, clonal/inverted type A nevi are usually benign lesions [7]. Complete excision is recommended [44].

Conclusions
The DPN spectrum of melanocytic lesions is a diagnostically challenging group, for which cytogenetic findings may not always confer useful information for classification and risk stratification. This highlights the importance of astute histopathological examination in the evaluation of these lesions. Although NGS may have utility in identifying additional driver mutations, such as TERT promotor mutations, which may help in differentiating atypical DPN from DPN-like melanoma, this molecular technique may not be available at all centers. Until NGS enters widespread clinical use, in ambiguous cases, a cautious approach to management including complete excision with wide, clear margins and close clinical follow-up. SLN biopsy is controversial in these lesions.
Author Contributions: P.G. drafted the manuscript including the literature review, preparation of images, and revisions. P.P.A. conceived and designed the manuscript and critically reviewed the manuscript. All authors have read and agreed to the published version of the manuscript.