Supersymmetrical Separation of Variables for Scarf II Model: Partial Solvability

Recently, a new quantum model - two-dimensional generalization of the Scarf II - was completely solved analytically by SUSY method for the integer values of parameter. Now, the same integrable model, but with arbitrary values of parameter, will be studied by means of supersymmetrical intertwining relations. The Hamiltonian does not allow the conventional separation of variables, but the supercharge operator does allow, leading to the partial solvability of the model. This approach, which can be called as the first variant of SUSY-separation, together with shape invariance of the model, provides analytical calculation of the part of spectrum and corresponding wave functions (quasi-exact-solvability). The model is shown to obey two different variants of shape invariance which can be combined effectively in construction of energy levels and wave functions.Comment: 6 p.p., accepted for publication in EP

Ten years of anti-vascular endothelial growth factor therapy.

The targeting of vascular endothelial growth factor A (VEGFA), a crucial regulator of both normal and pathological angiogenesis, has revealed innovative therapeutic approaches in oncology and ophthalmology. The first VEGFA inhibitor, bevacizumab, was approved by the US Food and Drug Administration in 2004 for the first-line treatment of metastatic colorectal cancer, and the first VEGFA inhibitors in ophthalmology, pegaptanib and ranibizumab, were approved in 2004 and 2006, respectively. To mark this tenth anniversary of anti-VEGFA therapy, we discuss the discovery of VEGFA, the successes and challenges in the development of VEGFA inhibitors and the impact of these agents on the treatment of cancers and ophthalmic diseases

Finding New Partnerships: The Function of Individual Extracellular Receptor Domains in Angiogenic Signalling by VEGF Receptors

Vascular endothelial growth factors (VEGFs) constitute a family of polypeptides regulating blood and lymphatic vessel development. VEGFs bind to type V receptor tyrosine kinases (RTKs), VEGFR-1, VEGFR-2, and VEGFR-3, but also bind directly to neuropilins and heparan sulphate glycosaminoglycans (HSPG), or indirectly to co-receptors such integrins and semaphorins. VEGFR activation results from ligand-induced dimerisation, which is mediated by the extracellular receptor domain (ECD). Recent studies established that dimerisation is necessary, but not sufficient, for receptor activation, since it was shown that only distinct orientations of receptor monomers give rise to active receptor dimers that are capable to instigate transmembrane signalling. Additional complexity in VEGFR signalling arises from association with specific co-receptors, which is determined by ligand- and ECD-specific interaction domains. In the following, the role of the different extracellular subdomains in VEGFR activation and signalling is discussed. We give an overview of the mechanistic concepts arising from recent structural studies that led to the development of novel allosteric receptor inhibitors and discuss their possible application in therapies aimed at pathological angiogenesis