Structural basis for proapoptotic activation of Bak by the noncanonical BH3-only protein Pxt1.

Bak is a critical executor of apoptosis belonging to the Bcl-2 protein family. Bak contains a hydrophobic groove where the BH3 domain of proapoptotic Bcl-2 family members can be accommodated, which initiates its activation. Once activated, Bak undergoes a conformational change to oligomerize, which leads to mitochondrial destabilization and the release of cytochrome c into the cytosol and eventual apoptotic cell death. In this study, we investigated the molecular aspects and functional consequences of the interaction between Bak and peroxisomal testis-specific 1 (Pxt1), a noncanonical BH3-only protein exclusively expressed in the testis. Together with various biochemical approaches, this interaction was verified and analyzed at the atomic level by determining the crystal structure of the Bak-Pxt1 BH3 complex. In-depth biochemical and cellular analyses demonstrated that Pxt1 functions as a Bak-activating proapoptotic factor, and its BH3 domain, which mediates direct intermolecular interaction with Bak, plays a critical role in triggering apoptosis. Therefore, this study provides a molecular basis for the Pxt1-mediated novel pathway for the activation of apoptosis and expands our understanding of the cell death signaling coordinated by diverse BH3 domain-containing proteins.

Structure of Full-Length SMC and Rearrangements Required for Chromosome Organization.

Multi-subunit SMC complexes control chromosome superstructure and promote chromosome disjunction, conceivably by actively translocating along DNA double helices. SMC subunits comprise an ABC ATPase "head" and a "hinge" dimerization domain connected by a 49 nm coiled-coil "arm." The heads undergo ATP-dependent engagement and disengagement to drive SMC action on the chromosome. Here, we elucidate the architecture of prokaryotic Smc dimers by high-throughput cysteine cross-linking and crystallography. Co-alignment of the Smc arms tightly closes the interarm space and misaligns the Smc head domains at the end of the rod by close apposition of their ABC signature motifs. Sandwiching of ATP molecules between Smc heads requires them to substantially tilt and translate relative to each other, thereby opening up the Smc arms. We show that this mechanochemical gating reaction regulates chromosome targeting and propose a mechanism for DNA translocation based on the merging of DNA loops upon closure of Smc arms.

Crystal structure of Bak bound to the BH3 domain of Bnip5, a noncanonical BH3 domain-containing protein.

The activation or inactivation of B-cell lymphoma-2 (Bcl-2) antagonist/killer (Bak) is critical for controlling mitochondrial outer membrane permeabilization-dependent apoptosis. Its pro-apoptotic activity is controlled by intermolecular interactions with the Bcl-2 homology 3 (BH3) domain, which is accommodated in the hydrophobic pocket of Bak. Bcl-2-interacting protein 5 (Bnip5) is a noncanonical BH3 domain-containing protein that interacts with Bak. Bnip5 is characterized by its controversial effects on the regulation of the pro-apoptotic activity of Bak. In the present study, we determined the crystal structure of Bak bound to Bnip5 BH3. The intermolecular association appeared to be typical at first glance, but we found that it is maintained by tight hydrophobic interactions together with hydrogen/ionic bonds, which accounts for their high binding affinity with a dissociation constant of 775 nM. Structural analysis of the complex showed that Bnip5 interacts with Bak in a manner similar to that of the Bak-activating pro-apoptotic factor peroxisomal testis-enriched protein 1, particularly in the destabilization of the intramolecular electrostatic network of Bak. Our structure is considered to reflect the initial point of drastic and consecutive conformational and stoichiometric changes in Bak induced by Bnip5 BH3, which helps in explaining the effects of Bnip5 in regulating Bak-mediated apoptosis.

Structural studies of a bacterial condensin complex reveal ATP-dependent disruption of intersubunit interactions.

Condensins are key mediators of chromosome condensation across organisms. Like other condensins, the bacterial MukBEF condensin complex consists of an SMC family protein dimer containing two ATPase head domains, MukB, and two interacting subunits, MukE and MukF. We report complete structural views of the intersubunit interactions of this condensin along with ensuing studies that reveal a role for the ATPase activity of MukB. MukE and MukF together form an elongated dimeric frame, and MukF's C-terminal winged-helix domains (C-WHDs) bind MukB heads to constitute closed ring-like structures. Surprisingly, one of the two bound C-WHDs is forced to detach upon ATP-mediated engagement of MukB heads. This detachment reaction depends on the linker segment preceding the C-WHD, and mutations on the linker restrict cell growth. Thus ATP-dependent transient disruption of the MukB-MukF interaction, which creates openings in condensin ring structures, is likely to be a critical feature of the functional mechanism of condensins.

Molecular basis for SMC rod formation and its dissolution upon DNA binding.

SMC condensin complexes are central modulators of chromosome superstructure in all branches of life. Their SMC subunits form a long intramolecular coiled coil, which connects a constitutive "hinge" dimerization domain with an ATP-regulated "head" dimerization module. Here, we address the structural arrangement of the long coiled coils in SMC complexes. We unequivocally show that prokaryotic Smc-ScpAB, eukaryotic condensin, and possibly also cohesin form rod-like structures, with their coiled coils being closely juxtaposed and accurately anchored to the hinge. Upon ATP-induced binding of DNA to the hinge, however, Smc switches to a more open configuration. Our data suggest that a long-distance structural transition is transmitted from the Smc head domains to regulate Smc-ScpAB's association with DNA. These findings uncover a conserved architectural theme in SMC complexes, provide a mechanistic basis for Smc's dynamic engagement with chromosomes, and offer a molecular explanation for defects in Cornelia de Lange syndrome.

Development and validation of a sensitive ultra-high-performance liquid chromatography-tandem mass spectrometry method for quantitative analysis of bambermycin in livestock and aquatic products: Implications for food safety control and regulatory enforcement.

A sensitive and accurate analytical method was developed and validated to detect bambermycin, a commonly used antibiotic in animal feed and livestock. The presence of bambermycin residues in food products can pose health risks to consumers, emphasizing the need for a sensitive and accurate analytical method. A reversed-phase analytical column was utilized with a mobile phase comprising 0.005 mol/L ammonium acetate in 5% acetonitrile (A) and 0.005 mol/L ammonium acetate in 95% acetonitrile (B) to achieve effective chromatographic separation. Quantitative determination of bambermycin in various samples, including beef, pork, chicken, milk, eggs, flatfish, eel, and shrimp, was performed using ultra-high-performance liquid chromatography-tandem mass spectrometry. Sample extraction involved a mixture of methanol and a 25% ammonium hydroxide solution, followed by low-temperature purification and phospholipid removal utilizing a Phree cartridge. The method exhibited a satisfactory recovery rate ranging from 69% to 100%. Validation results demonstrated the reliability, robustness, and accuracy of the method, exhibiting good linearity, precision, and recovery. This validated method can be applied for routine analysis of bambermycin residues, assisting in the development of effective monitoring and control measures to ensure the safety of livestock and aquatic products.

Identification of MYC as an antinecroptotic protein that stifles RIPK1-RIPK3 complex formation.

The underlying mechanism of necroptosis in relation to cancer is still unclear. Here, MYC, a potent oncogene, is an antinecroptotic factor that directly suppresses the formation of the RIPK1-RIPK3 complex. Gene set enrichment analyses reveal that the MYC pathway is the most prominently down-regulated signaling pathway during necroptosis. Depletion or deletion of MYC promotes the RIPK1-RIPK3 interaction, thereby stabilizing the RIPK1 and RIPK3 proteins and facilitating necroptosis. Interestingly, MYC binds to RIPK3 in the cytoplasm and inhibits the interaction between RIPK1 and RIPK3 in vitro. Furthermore, MYC-nick, a truncated form that is mainly localized in the cytoplasm, prevented TNF-induced necroptosis. Finally, down-regulation of MYC enhances necroptosis in leukemia cells and suppresses tumor growth in a xenograft model upon treatment with birinapant and emricasan. MYC-mediated suppression of necroptosis is a mechanism of necroptosis resistance in cancer, and approaches targeting MYC to induce necroptosis represent an attractive therapeutic strategy for cancer.

Structural and biochemical analyses of Bcl-xL in complex with the BH3 domain of peroxisomal testis-specific 1.

Antiapoptotic B-cell lymphoma-2 (Bcl-2) proteins suppress apoptosis by interacting with proapoptotic regulators. They commonly contain a hydrophobic groove where the Bcl-2 homology 3 (BH3) domain of Bcl-2 family members or BH3 domain-containing non-Bcl-2 family proteins can be accommodated. Peroxisomal testis-specific 1 (Pxt1) was previously identified as a male germ cell-specific protein whose overexpression causes germ cell apoptosis and infertility in male mice. Sequence and biochemical analyses also showed that human Pxt1, which is composed of 134 amino acids and is longer than mouse Pxt1 consisting of only 51 amino acids, has a BH3 domain that interacts with antiapoptotic Bcl-2 proteins, including Bcl-2 and Bcl-xL. In this study, we determined the crystal structure of Bcl-xL bound to the human Pxt1 BH3 domain. The five BH3 consensus residues are well conserved in the human Pxt1 BH3 domain and make a critical contribution to the complex formation in a canonical manner. Structural and biochemical analyses also demonstrated that Bcl-xL interacts with the BH3 domain of human Pxt1 but not with that of mouse Pxt1, and that residues 76-83 of human Pxt1, absent in mouse Pxt1, play a pivotal role in the intermolecular binding to Bcl-xL. While Bcl-xL consistently colocalized with human Pxt1 in mitochondria, it did not do so with mouse Pxt1, when expressed in HeLa cells. Collectively, these data verified that human and mouse Pxt1 differ in their binding ability to the antiapoptotic regulator Bcl-xL, which might affect their functionality in controlling apoptosis.

Structural basis for recognition of the tumor suppressor protein PTPN14 by the oncoprotein E7 of human papillomavirus.

Human papillomaviruses (HPVs) are causative agents of various diseases associated with cellular hyperproliferation, including cervical cancer, one of the most prevalent tumors in women. E7 is one of the two HPV-encoded oncoproteins and directs recruitment and subsequent degradation of tumor-suppressive proteins such as retinoblastoma protein (pRb) via its LxCxE motif. E7 also triggers tumorigenesis in a pRb-independent pathway through its C-terminal domain, which has yet been largely undetermined, with a lack of structural information in a complex form with a host protein. Herein, we present the crystal structure of the E7 C-terminal domain of HPV18 belonging to the high-risk HPV genotypes bound to the catalytic domain of human nonreceptor-type protein tyrosine phosphatase 14 (PTPN14). They interact directly and potently with each other, with a dissociation constant of 18.2 nM. Ensuing structural analysis revealed the molecular basis of the PTPN14-binding specificity of E7 over other protein tyrosine phosphatases and also led to the identification of PTPN21 as a direct interacting partner of E7. Disruption of HPV18 E7 binding to PTPN14 by structure-based mutagenesis impaired E7's ability to promote keratinocyte proliferation and migration. Likewise, E7 binding-defective PTPN14 was resistant for degradation via proteasome, and it was much more effective than wild-type PTPN14 in attenuating the activity of downstream effectors of Hippo signaling and negatively regulating cell proliferation, migration, and invasion when examined in HPV18-positive HeLa cells. These results therefore demonstrated the significance and therapeutic potential of the intermolecular interaction between HPV E7 and host PTPN14 in HPV-mediated cell transformation and tumorigenesis.

R-catcher, a potent molecular tool to unveil the arginylome.

Protein arginylation is a critical regulator of a variety of biological processes. The ability to uncover the global arginylation pattern and its associated signaling pathways would enable us to identify novel disease targets. Here, we report the development of a tool able to capture the N-terminal arginylome. This tool, termed R-catcher, is based on the ZZ domain of p62, which was previously shown to bind N-terminally arginylated proteins. Mutating the ZZ domain enhanced its binding specificity and affinity for Nt-Arg. R-catcher pulldown coupled to LC-MS/MS led to the identification of 59 known and putative arginylated proteins. Among these were a subgroup of novel ATE1-dependent arginylated ER proteins that are linked to diverse biological pathways, including cellular senescence and vesicle-mediated transport as well as diseases, such as Amyotrophic Lateral Sclerosis and Alzheimer's disease. This study presents the first molecular tool that allows the unbiased identification of arginylated proteins, thereby unlocking the arginylome and provide a new path to disease biomarker discovery.

Thirteen-week subcutaneous repeated dose toxicity study of butylparaben and its toxicokinetics in rats.

Parabens are widely used preservatives in cosmetics and pharmaceutical products and are approved as food additives. These chemicals have been considered safe for many years. However, the literature classifies parabens as endocrine-disrupting chemicals, and an assessment of their influence on the endocrine system and systemic toxicity is important. This study explored long-term systemic toxicity, effects on the endocrine system, and toxicokinetic behavior after repeated subcutaneous administration of butylparaben to Sprague-Dawley rats. Rats were treated with vehicle (4% Tween 80) or butylparaben at dose levels of 2, 10, and 50 mg/kg/day for 13 weeks. Assessment of systemic toxicity and endocrine-disrupting effects was based on mortality; clinical signs; body weight; food and water consumption; ophthalmological findings; urinalysis; hematology and clinical biochemistry; organ weights; necropsy and histopathological findings; regularity and length of the estrous cycle; semen quality; and toxicokinetic behavior. Female uterine weight and estrous cycle, and male semen quality indicated no estrogenic effects. Butylparaben induced local irritation at the injection site in both sexes at a dose of 50 mg/kg/day, but systemic toxicity was not observed. Therefore, the no-observed-adverse-effect level of butylparaben is set at 50 mg/kg/day in rats of both sexes. Butylparaben was without endocrine system effects at this dose. Butylparaben displays dose-dependent systemic exposure up to the maximum dose of 50 mg/kg/day and repeated administration of butylparaben for 13 weeks shows no bioaccumulation.

Targeted knockout of a chemokine-like gene increases anxiety and fear responses.

Emotional responses, such as fear and anxiety, are fundamentally important behavioral phenomena with strong fitness components in most animal species. Anxiety-related disorders continue to represent a major unmet medical need in our society, mostly because we still do not fully understand the mechanisms of these diseases. Animal models may speed up discovery of these mechanisms. The zebrafish is a highly promising model organism in this field. Here, we report the identification of a chemokine-like gene family, samdori (sam), and present functional characterization of one of its members, sam2 We show exclusive mRNA expression of sam2 in the CNS, predominantly in the dorsal habenula, telencephalon, and hypothalamus. We found knockout (KO) zebrafish to exhibit altered anxiety-related responses in the tank, scototaxis and shoaling assays, and increased crh mRNA expression in their hypothalamus compared with wild-type fish. To investigate generalizability of our findings to mammals, we developed a Sam2 KO mouse and compared it to wild-type littermates. Consistent with zebrafish findings, homozygous KO mice exhibited signs of elevated anxiety. We also found bath application of purified SAM2 protein to increase inhibitory postsynaptic transmission onto CRH neurons of the paraventricular nucleus. Finally, we identified a human homolog of SAM2, and were able to refine a candidate gene region encompassing SAM2, among 21 annotated genes, which is associated with intellectual disability and autism spectrum disorder in the 12q14.1 deletion syndrome. Taken together, these results suggest a crucial and evolutionarily conserved role of sam2 in regulating mechanisms associated with anxiety.

Quantification of spinosyn A and spinosyn D in animal-derived products using multiwalled carbon nanotubes coupled with LC-MS/MS for analysis.

An analytical method was developed for the quantification of spinosad (sum of spinosyns A and D) in five animal-derived products (chicken breast, pork, beef, egg, and milk) using LC-MS/MS. The sample was extracted using acetonitrile/1% acetic acid and a combination of magnesium sulfate and sodium acetate salts. The sample was purified using multiwalled carbon nanotubes as sorbent via a dispersive-solid-phase extraction procedure. Matrix-matched calibration (seven-point) provided good linearity with coefficient of determination (R2 ) ≥0.99 for each product. The limits of detection and quantification (LOQs) ranged between 0.0003-0.03 and 0.001-0.1 mg/kg, respectively. Method validation was carried out after spiking the target standard to blank matrices at the concentration levels of LOQ, 2 × LOQ, and 10 × LOQ with three replicates for each. The average recoveries were between 74 and 104%, with relative standard deviations ≤9.68, which were within the acceptable range designated by the international organizations. The developed method was successfully applied for monitoring market samples collected throughout the Korean Peninsula, and none of the samples tested positive for the target analytes. It has therefore been shown that dehydration and acidification were effective to extract spinosad from animal-derived products.

Quantum Artificial Neural Network Approach to Derive a Highly Predictive 3D-QSAR Model for Blood-Brain Barrier Passage.

A successful passage of the blood-brain barrier (BBB) is an essential prerequisite for the drug molecules designed to act on the central nervous system. The logarithm of blood-brain partitioning (LogBB) has served as an effective index of molecular BBB permeability. Using the three-dimensional (3D) distribution of the molecular electrostatic potential (ESP) as the numerical descriptor, a quantitative structure-activity relationship (QSAR) model termed AlphaQ was derived to predict the molecular LogBB values. To obtain the optimal atomic coordinates of the molecules under investigation, the pairwise 3D structural alignments were conducted in such a way to maximize the quantum mechanical cross correlation between the template and a target molecule. This alignment method has the advantage over the conventional atom-by-atom matching protocol in that the structurally diverse molecules can be analyzed as rigorously as the chemical derivatives with the same scaffold. The inaccuracy problem in the 3D structural alignment was alleviated in a large part by categorizing the molecules into the eight subsets according to the molecular weight. By applying the artificial neural network algorithm to associate the fully quantum mechanical ESP descriptors with the extensive experimental LogBB data, a highly predictive 3D-QSAR model was derived for each molecular subset with a squared correlation coefficient larger than 0.8. Due to the simplicity in model building and the high predictability, AlphaQ is anticipated to serve as an effective computational screening tool for molecular BBB permeability.

Signaling Pathways Regulated by UBR Box-Containing E3 Ligases.

UBR box E3 ligases, also called N-recognins, are integral components of the N-degron pathway. Representative N-recognins include UBR1, UBR2, UBR4, and UBR5, and they bind destabilizing N-terminal residues, termed N-degrons. Understanding the molecular bases of their substrate recognition and the biological impact of the clearance of their substrates on cellular signaling pathways can provide valuable insights into the regulation of these pathways. This review provides an overview of the current knowledge of the binding mechanism of UBR box N-recognin/N-degron interactions and their roles in signaling pathways linked to G-protein-coupled receptors, apoptosis, mitochondrial quality control, inflammation, and DNA damage. The targeting of these UBR box N-recognins can provide potential therapies to treat diseases such as cancer and neurodegenerative diseases.

Residual detection of naproxen, methyltestosterone and 17α-hydroxyprogesterone caproate in aquatic products by simple liquid-liquid extraction method coupled with liquid chromatography-tandem mass spectrometry.

In the present study, we aimed to develop a reliable screening method based on liquid chromatography coupled with tandem mass spectrometry (LC-MS/MS) for the detection and quantification of naproxen, methyltestosterone and 17α-hydroxyprogesterone caproate residues. The target analytes were extracted from samples of eel, flatfish and shrimp using acetonitrile with 1% acetic acid, followed by liquid-liquid purification with n-hexane. Chromatographic separation was achieved on a reversed-phase analytical column using 0.1% formic acid containing 10 mm ammonium formate in distilled water (A) and methanol (B) as mobile phases. All the matrix-matched calibration curves were linear (R2 ≥ 0.99) over the concentration range of the tested analytes. Recovery at three spiking levels (0.005, 0.01 and 0.02 mg/kg) ranged from 68 to 117% with intra- and inter-day precisions <10%. Five market samples for each matrix (eel, flatfish and shrimp) were collected and tested for method application. In summary, the proposed method is feasible to screen and quantify the analytes with high selectivity in aquatic food products meant for human consumption.

Development and validation of a solid-phase extraction method coupled with LC-MS/MS for the simultaneous determination of 16 antibiotic residues in duck meat.

The present study was carried out to determine 16 antibiotics belonging to seven different groups (tetracyclines, sulfonamides, penicillins, fluoroquinolones, macrolides, lincosamides and trimethoprims) in duck meat. A solid-phase extraction method based on Oasis HLB cartridges coupled with liquid chromatography-electrospray ionization tandem mass spectrometry was developed. Solutions of 0.1 m ethylenediaminetetraacetic acid disodium salt and 2% trifluoroacetic acid were used for the preliminary extraction of the target antibiotics from duck meat and n-hexane was used for purification prior to solid-phase extraction. Mobile phases composed of 0.1% trifluoroacetic acid in distilled water (solvent A) and 0.1% trifluoroacetic acid in methanol (solvent B), combined with a reversed-phase C18 analytical column, provided the optimal separation and signal intensity. The linearity of the method was assessed using six concentrations (5, 10, 20, 30, 40, and 50 µg/kg), and the recoveries, which were calculated at three spiking concentrations (5, 10 and 20 µg/kg), were in the range 69.8-103.3% with relative standard deviations (RSDs) ≤ 6.9% for the 16 tested antibiotics. Matrix effects ranging from -47.2 to -13.5% were observed for all the analytes, and the limits of quantitation (LOQ), which ranged from 4.93 to 26.21 µg/kg, were much lower than the maximum residue limits (MRLs) set by various regulatory authorities. Ten samples from a market were tested, and none of the target analytes were detected. Thus, a simple and versatile protocol has been developed to detect and quantify 16 antibiotics in duck meat samples.

Residue analysis of tebufenozide and indoxacarb in chicken muscle, milk, egg and aquatic animal products using liquid chromatography-tandem mass spectrometry.

We developed an analytical method using liquid-liquid extraction (LLE) and liquid chromatography-tandem mass spectrometry (LC-MS/MS) to detect and quantify tebufenozide (TEB) and indoxacarb (IND) residues in animal and aquatic products (chicken muscle, milk, egg, eel, flatfish, and shrimp). The target compounds were extracted using 1% acetic acid (0.1% acetic acid for egg only) in acetonitrile and purified using n-hexane. The analytes were separated on a Gemini-NX C18 column using (a) distilled water with 0.1% formic acid and 5 mm ammonium acetate and (b) methanol with 0.1% formic acid as the mobile phase. All six-point matrix-matched calibration curves showed good linearity with coefficients of determination (R2 ) ≥0.9864 over a concentration range of 5-50 µg/kg. Intra- and inter-day accuracy was expressed as the recovery rate at three spiking levels and ranged between 73.22 and 114.93% in all matrices, with a relative standard deviation (RSD, corresponding to precision) ≤13.87%. The limits of quantification (LOQ) of all target analytes ranged from 2 to 20 µg/kg, which were substantially lower than the maximum residue limits (MRLs) specified by the regulatory agencies of different countries. All samples were collected from different markets in Seoul, Republic of Korea, and tested negative for tebufenozide and indoxacarb residues. These results show that the method developed is robust and may be a promising tool to detect trace levels of the target analytes in animal products.

Simultaneous determination of spinosad, temephos, and piperonyl butoxide in animal-derived foods using LC-MS/MS.

Pesticides, which are used as plant protection products, can enter the food chain, and exposure to these xenobiotics can cause a wide array of health problems in humans. Therefore, the objective of the present study was to develop an analytical method for the simultaneous determination of residual spinosad (sum of spinosyn A and D), temephos and piperonyl butoxide in porcine muscle, egg, milk, eel, flatfish and shrimp (sampling period: February to June 2018) using liquid chromatography-triple quadrupole tandem mass spectrometry (LC-MS/MS). The target analytes were extracted with a combination of acidified acetonitrile and ethyl acetate and subsequently purified with original QuEChERS kits (composed of magnesium sulfate and sodium chloride) as well as n-hexane. All analytes were separated on a reversed-phase analytical column using a mobile phase of (A) 0.1% formic acid containing 10 mm ammonium formate in distilled water and (B) methanol. Good linearity (R2 ≥ 0.980) was achieved over the tested concentration range (3.5-35 µg/kg for spinosyn A; 1.5-15 µg/kg for spinosyn D; 5-50 µg/kg for temephos and piperonyl butoxide) in matrix-matched standard calibrations. Fortified samples at three spiking levels yielded recoveries in the range of 71-105% with relative standard deviations ≤9.2%. The applicability of the method was evaluated via evaluating samples collected from a large wholesale market located in Seoul, and none of the samples contained any of the target analytes. In conclusion, the current approach is simple, efficient and reliable and can successfully determine the residual levels of spinosad, temephos and piperonyl butoxide in complex animal-derived food products.

Time-harmonic convention of exp(-iωt) can be preferable to exp(+iωt) (L).

Since (±i)2 = -1, there are two time-harmonic conventions, namely, exp(+iωt) and exp(-iωt) with ω and t for angular frequency and time, respectively. Both conventions are mathematically valid. However, a question may still be asked whether a specific acoustic problem can favor one or the other convention. This letter reports one such example in which the use of exp(-iωt) can be preferable when the principal value of the square root of a complex number is considered as an argument of the Hankel functions in the context of 2.5-dimensional problems.