Umbilicity and characterization of Pansu spheres in the Heisenberg group

For $n\geq 2$ we define a notion of umbilicity for hypersurfaces in the Heisenberg group $H_{n}$. We classify umbilic hypersurfaces in some cases, and prove that Pansu spheres are the only umbilic spheres with positive constant $p$(or horizontal)-mean curvature in $H_{n}$ up to Heisenberg translations.Comment: 32 pages, 2 figures; in Crelle's journal, 201

Umbilic hypersurfaces of constant sigma-k curvature in the Heisenberg group

We study immersed, connected, umbilic hypersurfaces in the Heisenberg group $H_{n}$ with $n$ $\geq$ $2.$ We show that such a hypersurface, if closed, must be rotationally invariant up to a Heisenberg translation. Moreover, we prove that, among others, Pansu spheres are the only such spheres with positive constant sigma-k curvature up to Heisenberg translations.Comment: 28 pages, 6 figure

Protein subcellular localization prediction based on compartment-specific features and structure conservation

BACKGROUND: Protein subcellular localization is crucial for genome annotation, protein function prediction, and drug discovery. Determination of subcellular localization using experimental approaches is time-consuming; thus, computational approaches become highly desirable. Extensive studies of localization prediction have led to the development of several methods including composition-based and homology-based methods. However, their performance might be significantly degraded if homologous sequences are not detected. Moreover, methods that integrate various features could suffer from the problem of low coverage in high-throughput proteomic analyses due to the lack of information to characterize unknown proteins. RESULTS: We propose a hybrid prediction method for Gram-negative bacteria that combines a one-versus-one support vector machines (SVM) model and a structural homology approach. The SVM model comprises a number of binary classifiers, in which biological features derived from Gram-negative bacteria translocation pathways are incorporated. In the structural homology approach, we employ secondary structure alignment for structural similarity comparison and assign the known localization of the top-ranked protein as the predicted localization of a query protein. The hybrid method achieves overall accuracy of 93.7% and 93.2% using ten-fold cross-validation on the benchmark data sets. In the assessment of the evaluation data sets, our method also attains accurate prediction accuracy of 84.0%, especially when testing on sequences with a low level of homology to the training data. A three-way data split procedure is also incorporated to prevent overestimation of the predictive performance. In addition, we show that the prediction accuracy should be approximately 85% for non-redundant data sets of sequence identity less than 30%. CONCLUSION: Our results demonstrate that biological features derived from Gram-negative bacteria translocation pathways yield a significant improvement. The biological features are interpretable and can be applied in advanced analyses and experimental designs. Moreover, the overall accuracy of combining the structural homology approach is further improved, which suggests that structural conservation could be a useful indicator for inferring localization in addition to sequence homology. The proposed method can be used in large-scale analyses of proteomes

Computational analysis of a novel mutation in ETFDH gene highlights its long-range effects on the FAD-binding motif

<p>Abstract</p> <p>Background</p> <p>Multiple acyl-coenzyme A dehydrogenase deficiency (MADD) is an autosomal recessive disease caused by the defects in the mitochondrial electron transfer system and the metabolism of fatty acids. Recently, mutations in electron transfer flavoprotein dehydrogenase (<it>ETFDH</it>) gene, encoding electron transfer flavoprotein:ubiquinone oxidoreductase (ETF:QO) have been reported to be the major causes of riboflavin-responsive MADD. To date, no studies have been performed to explore the functional impact of these mutations or their mechanism of disrupting enzyme activity.</p> <p>Results</p> <p>High resolution melting (HRM) analysis and sequencing of the entire <it>ETFDH </it>gene revealed a novel mutation (p.Phe128Ser) and the hotspot mutation (p.Ala84Thr) from a patient with MADD. According to the predicted 3D structure of ETF:QO, the two mutations are located within the flavin adenine dinucleotide (FAD) binding domain; however, the two residues do not have direct interactions with the FAD ligand. Using molecular dynamics (MD) simulations and normal mode analysis (NMA), we found that the p.Ala84Thr and p.Phe128Ser mutations are most likely to alter the protein structure near the FAD binding site as well as disrupt the stability of the FAD binding required for the activation of ETF:QO. Intriguingly, NMA revealed that several reported disease-causing mutations in the ETF:QO protein show highly correlated motions with the FAD-binding site.</p> <p>Conclusions</p> <p>Based on the present findings, we conclude that the changes made to the amino acids in ETF:QO are likely to influence the FAD-binding stability.</p

Strong maximum principle for mean curvature operators on subRiemannian manifolds

We study the strong maximum principle for horizontal (p-)mean curvature operator and p-(sub)Laplacian operator on subRiemannian manifolds including, in particular, Heisenberg groups and Heisenberg cylinders. Under a certain Hormander type condition on vector fields, we show the strong maximum principle holds in higher dimensions for two cases: (a) the touching point is nonsingular; (b) the touching point is an isolated singular point for one of comparison functions. For a background subRiemannian manifold with local symmetry of isometric translations, we have the strong maximum principle for associated graphs which include, among others, intrinsic graphs with constant horizontal (p-)mean curvature. As applications, we show a rigidity result of horizontal (p-)minimal hypersurfaces in any higher dimensional Heisenberg cylinder and a pseudo-halfspace theorem for any Heisenberg group