Consequences of local gauge symmetry in empirical tight-binding theory

A method for incorporating electromagnetic fields into empirical tight-binding theory is derived from the principle of local gauge symmetry. Gauge invariance is shown to be incompatible with empirical tight-binding theory unless a representation exists in which the coordinate operator is diagonal. The present approach takes this basis as fundamental and uses group theory to construct symmetrized linear combinations of discrete coordinate eigenkets. This produces orthogonal atomic-like "orbitals" that may be used as a tight-binding basis. The coordinate matrix in the latter basis includes intra-atomic matrix elements between different orbitals on the same atom. Lattice gauge theory is then used to define discrete electromagnetic fields and their interaction with electrons. Local gauge symmetry is shown to impose strong restrictions limiting the range of the Hamiltonian in the coordinate basis. The theory is applied to the semiconductors Ge and Si, for which it is shown that a basis of 15 orbitals per atom provides a satisfactory description of the valence bands and the lowest conduction bands. Calculations of the dielectric function demonstrate that this model yields an accurate joint density of states, but underestimates the oscillator strength by about 20% in comparison to a nonlocal empirical pseudopotential calculation.Comment: 23 pages, 7 figures, RevTeX4; submitted to Phys. Rev.

Anti-Heparanase Aptamers as Potential Diagnostic and Therapeutic Agents for Oral Cancer

Peer reviewe

ICAR: endoscopic skull‐base surgery

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Development of novel single-stranded nucleic acid aptamers against the pro-Angiogenic and metastatic enzyme heparanase (HPSE1)

Heparanase is an enzyme involved in extracellular matrix remodelling and heparan sulphate proteoglycan catabolism. It is secreted by metastatic tumour cells, allowing them to penetrate the endothelial cell layer and basement membrane to invade target organs. The release of growth factors at the site of cleaved heparan sulphate chains further enhance the potential of the tumour by encouraging the process of angiogenesis. This leads to increased survival and further proliferation of the tumour. Aptamers are single or double stranded oligonucleotides that recognise specific small molecules, peptides, proteins, or even cells or tissues and have shown great potential over the years as diagnostic and therapeutic agents in anticancer treatment. For the first time, single stranded DNA aptamers were successfully generated against the active heterodimer form of heparanase using a modified SELEX protocol, and eluted based on increasing affinity for the target. Sandwich ELISA assays showed recognition of heparanase by the aptamers at a site distinct from that of a polyclonal HPSE1 antibody. The binding affinities of aptamer to immobilised enzyme were high (7×107 to 8×107 M−1) as measured by fluorescence spectroscopy. Immunohistochemistry and immunofluorescence studies demonstrated that the aptamers were able to recognise heparanase with staining comparable or in some cases superior to that of the HPSE1 antibody control. Finally, matrigel assay demonstrated that aptamers were able to inhibit heparanase. This study provides clear proof of principle concept that nucleic acid aptamers can be generated against heparanase. These reagents may serve as useful tools to explore the functional role of the enzyme and in the future development of diagnostic assays or therapeutic reagents