Asymptotic Property of Eigenvalues and Eigenfunctions of the Laplace Operator in Domain with a Perturbed Boundary

2000 Mathematics Subject Classification: 35J05, 35C15, 44P05

The domain derivative in rough-surface scattering and rigorous estimates for first-order perturbation theory

We investigate Fréchet differentiability of the scattered field with respect to variation in the boundary in the case of time–harmonic acoustic scattering by an unbounded, sound–soft, one–dimensional rough surface. We rigorously prove the differentiability of the scattered field and derive a characterization of the Fréchet derivative as the solution to a Dirichlet boundary value problem. As an application of these results we give rigorous error estimates for first–order perturbation theory, justifying small perturbation methods that have a long history in the engineering literature. As an application of our rigorous estimates we show that a plane acoustic wave incident on a sound–soft rough surface can produce an unbounded scattered field.

Three distinct structural environments of a transmembrane domain in the inwardly rectifying potassium channel ROMK1 defined by perturbation.

To probe the protein environment of an ion channel, we have perturbed the structure of a transmembrane domain by substituting side chains with those of two different sizes by using site-specific mutagenesis. We have used Trp and Ala as a high- and a low-impact perturbation probe, respectively, to replace each of 18 consecutive residues within the putative second transmembrane segment, M2, of an inwardly rectifying potassium channel, ROMK1. Our rationale is that a change in the channel function as a consequence of these mutations at a particular position will reflect the structural environment of the altered side chain. Each position can then be assigned to one of three classes of environments, as grated by different levels of perturbation: very tolerant (channel functions with both Trp and Ala substitutions), tolerant (function preserved with Ala but not with Trp substitution), and intolerant (either Ala or Trp substitution destroys function). We identify the very tolerant environment as being lipid-facing, tolerant as protein-interior-facing, and intolerant as pore-facing. We observe a strikingly ordered pattern of perturbation of all three environmental classes. This result indicates that M2 is a straight alpha-helix.

Quantum fluctuations on domain walls, strings, and vacuum bubbles

We develop a covariant quantum theory of fluctuations on vacuum domain walls and strings. The fluctuations are described by a scalar field defined on the classical world sheet of the defects. We consider the following cases: straight strings and planar walls in flat space, true vacuum bubbles nucleating in false vacuum, and strings and walls nucleating during inflation. The quantum state for the perturbations is constructed so that it respects the original symmetries of the classical solution. In particular, for the case of vacuum bubbles and nucleating strings and walls, the geometry of the world sheet is that of a lower-dimensional de Sitter space, and the problem reduces to the quantization of a scalar field of tachyonic mass in de Sitter space. In all cases, the root-mean-squared fluctuation is evaluated in detail, and the physical implications are briefly discussed.

Nuclear magnetic resonance structure shows that the severe acute respiratory syndrome coronavirus-unique domain contains a macrodomain fold

The nuclear magnetic resonance (NMR) structure of a central segment of the previously annotated severe acute respiratory syndrome (SARS)-unique domain (SUD-M, for "middle of the SARS-unique domain") in SARS coronavirus (SARS-CoV) nonstructural protein 3 (nsp3) has been determined. SUD-M(513-651) exhibits a macrodomain fold containing the nsp3 residues 528 to 648, and there is a flexibly extended N-terminal tail with the residues 513 to 527 and a C-terminal flexible tail of residues 649 to 651. As a follow-up to this initial result, we also solved the structure of a construct representing only the globular domain of residues 527 to 651 [SUD-M(527-651)]. NMR chemical shift perturbation experiments showed that SUD-M(527-651) binds single-stranded poly(A) and identified the contact area with this RNA on the protein surface, and electrophoretic mobility shift assays then confirmed that SUD-M has higher affinity for purine bases than for pyrimidine bases. In a further search for clues to the function, we found that SUD-M(527-651) has the closest three-dimensional structure homology with another domain of nsp3, the ADP-ribose-1 ''-phosphatase nsp3b, although the two proteins share only 5% sequence identity in the homologous sequence regions. SUD-M(527-651) also shows three-dimensional structure homology with several helicases and nucleoside triphosphate-binding proteins, but it does not contain the motifs of catalytic residues found in these structural homologues. The combined results from NMR screening of potential substrates and the structure-based homology studies now form a basis for more focused investigations on the role of the SARS-unique domain in viral infection.

NMR structure shows that the SARS-unique domain contains a macrodomain fold

The NMR structure of a central segment of the previously annotated "SARS-unique domain" (SUD-M; "middle of the SARS-unique domain") in the SARS coronavirus (SARS-CoV) non-structural protein 3 (nsp3) has been determined. SUD-M(513-651) exhibits a macrodomain fold containing the nsp3-residues 528-648, and there is a flexibly extended N-terminal tail with the residues 513-527 and a C-terminal flexible tail of residues 649-651. As a follow-up to this initial result, we also solved the structure of a construct representing only the globular domain of residues 527-651 [SUD-M(527-651)]. NMR chemical shift perturbation experiments showed that SUD-M(527-651) binds single-stranded poly-A and identified the contact area with this RNA on the protein surface, and electrophoretic mobility shift assays then confirmed that SUD-M has higher affinity for purine bases than for pyrimidine bases. In further search for clues to the function, we found that SUD-M(527-651) has the closest three-dimensional structure homology with another domain of nsp3, the ADP-ribose-1''-phosphatase nsp3b, although the two proteins share only 5% sequence identity in the homologous sequence regions. SUD-M(527-651) also shows 3D structure homology with several helicases and NTP-binding proteins, but it does not contain the motifs of catalytic residues found in these structural homologues. The combined results from NMR screening of potential substrates and the structure-based homology studies now form a basis for more focused investigations on the role of the SARS-unique domain in viral infection.

SARS coronavirus unique domain: three-domain molecular architecture in solution and RNA binding

Nonstructural protein 3 of the severe acute respiratory syndrome (SARS) coronavirus includes a "SARS-unique domain" (SUD) consisting of three globular domains separated by short linker peptide segments. This work reports NMR structure determinations of the C-terminal domain (SUD-C) and a two-domain construct (SUD-MC) containing the middle domain (SUD-M) and the C-terminal domain, and NMR data on the conformational states of the N-terminal domain (SUD-N) and the SUD-NM two-domain construct. Both SUD-N and SUD-NM are monomeric and globular in solution; in SUD-NM, there is high mobility in the two-residue interdomain linking sequence, with no preferred relative orientation of the two domains. SUD-C adopts a frataxin like fold and has structural similarity to DNA-binding domains of DNA-modifying enzymes. The structures of both SUD-M (previously determined) and SUD-C (from the present study) are maintained in SUD-MC, where the two domains are flexibly linked. Gel-shift experiments showed that both SUD-C and SUD-MC bind to single-stranded RNA and recognize purine bases more strongly than pyrimidine bases, whereby SUD-MC binds to a more restricted set of purine-containing RNA sequences than SUD-M. NMR chemical shift perturbation experiments with observations of (15)N-labeled proteins further resulted in delineation of RNA binding sites (i.e., in SUD-M, a positively charged surface area with a pronounced cavity, and in SUD-C, several residues of an anti-parallel beta-sheet). Overall, the present data provide evidence for molecular mechanisms involving the concerted actions of SUD-M and SUD-C, which result in specific RNA binding that might be unique to the SUD and, thus, to the SARS coronavirus.

LARGE-ORDER PERTURBATION EXPANSIONS FOR THE CHARGED HARMONIC-OSCILLATOR

The charged oscillator, defined by the Hamiltonian H = -d2/dr2+ r2 + lambda/r in the domain [0, infinity], is a particular case of the family of spiked oscillators, which does not behave as a supersingular Hamiltonian. This problem is analysed around the three regions lambda --> infinity, lambda --> 0 and lambda --> -infinity by using Rayleigh-Ritz large-order perturbative expansions. A path is found to connect the large lambda regions with the small lambda region by means of the renormalization of the series expansions in lambda. Finally, the Riccati-Pade method is used to construct an implicit expansion around lambda --> 0 which extends to very large values of Absolute value of lambda.

Solution structure and peptide binding studies of the C-terminal Src homology 3-like domain of the diphtheria toxin repressor protein

The diphtheria toxin repressor (DtxR) is the best-characterized member of a family of homologous proteins that regulate iron uptake and virulence gene expression in the Gram-positive bacteria. DtxR contains two domains that are separated by a short, unstructured linker. The N-terminal domain is structurally well-defined and is responsible for Fe2+ binding, dimerization, and DNA binding. The C-terminal domain adopts a fold similar to eukaryotic Src homology 3 domains, but the functional role of the C-terminal domain in repressor activity is unknown. The solution structure of the C-terminal domain, consisting of residues N130-L226 plus a 13-residue N-terminal extension, has been determined by using NMR spectroscopy. Residues before A147 are highly mobile and adopt a random coil conformation, but residues A147-L226 form a single structured domain consisting of five β-strands and three helices arranged into a partially orthogonal, two-sheet β-barrel, similar to the structure observed in the crystalline Co2+ complex of full-length DtxR. Chemical shift perturbation studies demonstrate that a proline-rich peptide corresponding to residues R125-G139 of intact DtxR binds to the C-terminal domain in a pocket formed by residues in β-strands 2, 3, and 5, and helix 3. Binding of the proline-rich peptide by the C-terminal domain of DtxR presents an example of peptide binding by a prokaryotic Src homology 3-like protein. The results of this study, combined with previous x-ray studies of intact DtxR, provide insights into a possible biological function of the C-terminal domain in regulating repressor activity.

Structure and function of the C-terminal PABC domain of human poly(A)-binding protein

We have determined the solution structure of the C-terminal quarter of human poly(A)-binding protein (hPABP). The protein fragment contains a protein domain, PABC [for poly(A)-binding protein C-terminal domain], which is also found associated with the HECT family of ubiquitin ligases. By using peptides derived from PABP interacting protein (Paip) 1, Paip2, and eRF3, we show that PABC functions as a peptide binding domain. We use chemical shift perturbation analysis to identify the peptide binding site in PABC and the major elements involved in peptide recognition. From comparative sequence analysis of PABC-binding peptides, we formulate a preliminary PABC consensus sequence and identify human ataxin-2, the protein responsible for type 2 spinocerebellar ataxia (SCA2), as a potential PABC ligand.

TDP : a two-dimensional perturbation calculation code based on TDC, for IBM-7090, Deck B 516 /

Work performed at CANEL.

A Putative Otu Domain-containing Protein 1 Deubiquitinating Enzyme Is Differentially Expressed In Thyroid Cancer And Identifies Less-aggressive Tumours.

This study aimed to identify novel biomarkers for thyroid carcinoma diagnosis and prognosis. We have constructed a human single-chain variable fragment (scFv) antibody library that was selected against tumour thyroid cells using the BRASIL method (biopanning and rapid analysis of selective interactive ligands) and phage display technology. One highly reactive clone, scFv-C1, with specific binding to papillary thyroid tumour proteins was confirmed by ELISA, which was further tested against a tissue microarray that comprised of 229 thyroid tissues, including: 110 carcinomas (38 papillary thyroid carcinomas (PTCs), 42 follicular carcinomas, 30 follicular variants of PTC), 18 normal thyroid tissues, 49 nodular goitres (NG) and 52 follicular adenomas. The scFv-C1 was able to distinguish carcinomas from benign lesions (P=0.0001) and reacted preferentially against T1 and T2 tumour stages (P=0.0108). We have further identified an OTU domain-containing protein 1, DUBA-7 deubiquitinating enzyme as the scFv-binding antigen using two-dimensional polyacrylamide gel electrophoresis and mass spectrometry. The strategy of screening and identifying a cell-surface-binding antibody against thyroid tissues was highly effective and resulted in a useful biomarker that recognises malignancy among thyroid nodules and may help identify lower-risk cases that can benefit from less-aggressive management.

Applications Of Visual Evoked Potentials And Fourier-domain Optical Coherence Tomography In Parkinson's Disease: A Controlled Study.

The goal of this cross-sectional observational study was to quantify the pattern-shift visual evoked potentials (VEP) and the thickness as well as the volume of retinal layers using optical coherence tomography (OCT) across a cohort of Parkinson's disease (PD) patients and age-matched controls. Forty-three PD patients and 38 controls were enrolled. All participants underwent a detailed neurological and ophthalmologic evaluation. Idiopathic PD cases were included. Cases with glaucoma or increased intra-ocular pressure were excluded. Patients were assessed by VEP and high-resolution Fourier-domain OCT, which quantified the inner and outer thicknesses of the retinal layers. VEP latencies and the thicknesses of the retinal layers were the main outcome measures. The mean age, with standard deviation (SD), of the PD patients and controls were 63.1 (7.5) and 62.4 (7.2) years, respectively. The patients were predominantly in the initial Hoehn-Yahr (HY) disease stages (34.8% in stage 1 or 1.5, and 55.8 % in stage 2). The VEP latencies and the thicknesses as well as the volumes of the retinal inner and outer layers of the groups were similar. A negative correlation between the retinal thickness and the age was noted in both groups. The thickness of the retinal nerve fibre layer (RNFL) was 102.7 μm in PD patients vs. 104.2 μm in controls. The thicknesses of retinal layers, VEP, and RNFL of PD patients were similar to those of the controls. Despite the use of a representative cohort of PD patients and high-resolution OCT in this study, further studies are required to establish the validity of using OCT and VEP measurements as the anatomic and functional biomarkers for the evaluation of retinal and visual pathways in PD patients.

Effects Of Misalignments In The Retinal Nerve Fiber Layer Thickness Measurements With Spectral Domain Optical Coherence Tomography.

Purpose. To investigate misalignments (MAs) on retinal nerve fiber layer thickness (RNFLT) measurements obtained with Cirrus(©) SD-OCT. Methods. This was a retrospective, observational, cross-sectional study. Twenty-seven healthy and 29 glaucomatous eyes of 56 individuals with one normal exam and another showing MA were included. MAs were defined as an improper alignment of vertical vessels in the en face image. MAs were classified in complete MA (CMA) and partial MA (PMA), according to their site: 1 (superior, outside the measurement ring (MR)), 2 (superior, within MR), 3 (inferior, within MR), and 4 (inferior, outside MR). We compared RNFLT measurements of aligned versus misaligned exams in all 4 sectors, in the superior area (sectors 1 + 2), inferior area (sectors 3 + 4), and within the measurement ring (sectors 2 + 3). Results. RNFLT measurements at 12 clock-hour of eyes with MAs in the superior area (sectors 1 + 2) were significantly lower than those obtained in the same eyes without MAs (P = 0.043). No significant difference was found in other areas (sectors 1 + 2 + 3 + 4, sectors 3 + 4, and sectors 2 + 3). Conclusion. SD-OCT scans with superior MAs may present lower superior RNFLT measurements compared to aligned exams.