Endocytic Sorting and Downregulation of the M2 Acetylcholine Receptor is Regulated by Ubiquitin and the ESCRT Complex

Acknowledgements The authors would like to thank Professor Mark von Zastrow from the University of California, San Francisco for sharing critical constructs. We would like to thank Kevin MacKenzie and the University of Aberdeen Microscopy core and the Iain Fraser Flow cytometry core for their assistance in the acquisition of data, and Professor Lynda Erskine for critical reading of the manuscript. This work was supported by a PhD studentship from the University of Aberdeen (DZ) and by funding from the Royal Society and Tenovus Scotland (JNH)Peer reviewedPostprin

Conductivity and the current-current correlation measure

We review various formulations of conductivity for one-particle Hamiltonians and relate them to the current-current correlation measure. We prove that the current-current correlation measure for random Schr\"odinger operators has a density at coincident energies provided the energy lies in a localization regime. The density vanishes at such energies and an upper bound on the rate of vanishing is computed. We also relate the current-current correlation measure to the localization length

Solving the Coulomb scattering problem using the complex scaling method

Based on the work of Nuttall and Cohen [Phys. Rev. {\bf 188} (1969) 1542] and Resigno et al{} [Phys. Rev. A {\bf 55} (1997) 4253] we present a rigorous formalism for solving the scattering problem for long-range interactions without using exact asymptotic boundary conditions. The long-range interaction may contain both Coulomb and short-range potentials. The exterior complex scaling method, applied to a specially constructed inhomogeneous Schr\"odinger equation, transforms the scattering problem into a boundary problem with zero boundary conditions. The local and integral representations for the scattering amplitudes have been derived. The formalism is illustrated with numerical examples.Comment: 3 pages, 3 figure

Singular Modes of the Electromagnetic Field

We show that the mode corresponding to the point of essential spectrum of the electromagnetic scattering operator is a vector-valued distribution representing the square root of the three-dimensional Dirac's delta function. An explicit expression for this singular mode in terms of the Weyl sequence is provided and analyzed. An essential resonance thus leads to a perfect localization (confinement) of the electromagnetic field, which in practice, however, may result in complete absorption.Comment: 14 pages, no figure

Lieb-Thirring Bound for Schr\"odinger Operators with Bernstein Functions of the Laplacian

A Lieb-Thirring bound for Schr\"odinger operators with Bernstein functions of the Laplacian is shown by functional integration techniques. Several specific cases are discussed in detail.Comment: We revised the first versio

Sufficient conditions for two-dimensional localization by arbitrarily weak defects in periodic potentials with band gaps

We prove, via an elementary variational method, 1d and 2d localization within the band gaps of a periodic Schrodinger operator for any mostly negative or mostly positive defect potential, V, whose depth is not too great compared to the size of the gap. In a similar way, we also prove sufficient conditions for 1d and 2d localization below the ground state of such an operator. Furthermore, we extend our results to 1d and 2d localization in d dimensions; for example, a linear or planar defect in a 3d crystal. For the case of D-fold degenerate band edges, we also give sufficient conditions for localization of up to D states.Comment: 9 pages, 3 figure

Coral development: from classical embryology to molecular control

The phylum Cnidaria is the closest outgroup to the triploblastic metazoans and as such offers unique insights into evolutionary questions at several levels. In the post-genomic era, a knowledge of the gene complement of representative cnidarians will be important for understanding the relationship between the expansion of gene families and the evolution of morphological complexity among more highly evolved metazoans. Studies of cnidarian development and its molecular control will provide information about the origins of the major bilaterian body axes, the origin of the third tissue layer, the mesoderm, and the evolution of nervous system patterning. We are studying the cnidarian Acropora millepora, a reef building scleractinian coral, and a member of the basal cnidarian class, the Anthozoa. We review ourwork on descriptive embryology and studies of selected transcription factor gene families, where our knowledge from Acropora is particularly advanced relative to other cnidarians. We also describe a recent preliminary whole genome initiative, a coral EST database.Eldon E. Ball, David C. Hayward, John S. Reece-Hoyes, Nikki R. Hislop, Gabrielle Samuel, Robert Saint, Peter L. Harrison and David J. Mille

Radiogenomics map-based molecular and imaging phenotypical characterization in localised prostate cancer using pre-biopsy biparametric MR imaging

Objective: To create a radiogenomics map and evaluate the correlation between molecular and imaging phenotypes in localized prostate cancer (PCa), using radical prostatectomy histopathology as a reference standard.Methods: Radiomic features were extracted from T2-weighted (T2WI) and Apparent Diffusion Coefficient (ADC) images of clinically localized PCa patients (n=15) across different Gleason scorebased risk categories. DNA extraction was performed on formalin-fixed, paraffin-embedded (FFPE) samples. Gene expression analysis of androgen receptor expression, apoptosis, and hypoxia was conducted using the Chromosome Analysis Suite (ChAS) application and OSCHIP files. The relationship between gene expression alterations and textural features was assessed using Pearson's correlation analysis. Receiver operating characteristic (ROC) analysis was utilized to evaluate the predictive accuracy of the model.Results: A significant correlation was observed between radiomic texture features and copy number variation (CNV) of genes associated with apoptosis, hypoxia, and androgen receptor (p-value= ≤ 0.05). The identified radiomic features, including Sum Entropy ADC, Inverse Difference ADC, Sum Variance T2WI, Entropy T2WI, Difference Variance T2WI, and Angular Secondary Moment T2WI, exhibited potential for predicting cancer grade and biological processes such as apoptosis and hypoxia. Incorporating radiomics and genomics into a prediction model significantly improved the prediction of prostate cancer grade (clinically significant prostate cancer), yielding an AUC of 0.95.Conclusion: Radiomic texture features significantly correlate with genotypes for apoptosis, hypoxia, and androgen receptor expression in localised prostate cancer. Integration of these into prediction model improved prediction accuracy of clinically significant prostate cancer