Transmutations and spectral parameter power series in eigenvalue problems

We give an overview of recent developments in Sturm-Liouville theory concerning operators of transmutation (transformation) and spectral parameter power series (SPPS). The possibility to write down the dispersion (characteristic) equations corresponding to a variety of spectral problems related to Sturm-Liouville equations in an analytic form is an attractive feature of the SPPS method. It is based on a computation of certain systems of recursive integrals. Considered as families of functions these systems are complete in the $L_{2}$-space and result to be the images of the nonnegative integer powers of the independent variable under the action of a corresponding transmutation operator. This recently revealed property of the Delsarte transmutations opens the way to apply the transmutation operator even when its integral kernel is unknown and gives the possibility to obtain further interesting properties concerning the Darboux transformed Schr\"{o}dinger operators. We introduce the systems of recursive integrals and the SPPS approach, explain some of its applications to spectral problems with numerical illustrations, give the definition and basic properties of transmutation operators, introduce a parametrized family of transmutation operators, study their mapping properties and construct the transmutation operators for Darboux transformed Schr\"{o}dinger operators.Comment: 30 pages, 4 figures. arXiv admin note: text overlap with arXiv:1111.444

Flavaglines Alleviate Doxorubicin Cardiotoxicity: Implication of Hsp27

Background: Despite its effectiveness in the treatment of various cancers, the use of doxorubicin is limited by a potentially fatal cardiomyopathy. Prevention of this cardiotoxicity remains a critical issue in clinical oncology. We hypothesized that flavaglines, a family of natural compounds that display potent neuroprotective effects, may also alleviate doxorubicininduced cardiotoxicity. Methodology/Principal Findings: Our in vitro data established that a pretreatment with flavaglines significantly increased viability of doxorubicin-injured H9c2 cardiomyocytes as demonstrated by annexin V, TUNEL and active caspase-3 assays. We demonstrated also that phosphorylation of the small heat shock protein Hsp27 is involved in the mechanism by which flavaglines display their cardioprotective effect. Furthermore, knocking-down Hsp27 in H9c2 cardiomyocytes completely reversed this cardioprotection. Administration of our lead compound (FL3) to mice attenuated cardiomyocyte apoptosis and cardiac fibrosis, as reflected by a 50 % decrease of mortality. Conclusions/Significance: These results suggest a prophylactic potential of flavaglines to prevent doxorubicin-induce

The p38/MK2/Hsp25 Pathway Is Required for BMP-2-Induced Cell Migration

Background: Bone morphogenetic proteins (BMPs) have been shown to participate in the patterning and specification of several tissues and organs during development and to regulate cell growth, differentiation and migration in different cell types. BMP-mediated cell migration requires activation of the small GTPase Cdc42 and LIMK1 activities. In our earlier report we showed that activation of LIMK1 also requires the activation of PAKs through Cdc42 and PI3K. However, the requirement of additional signaling is not clearly known. Methodology/Principal Findings: Activation of p38 MAPK has been shown to be relevant for a number of BMP-2¿s physiological effects. We report here that BMP-2 regulation of cell migration and actin cytoskeleton remodelling are dependent on p38 activity. BMP-2 treatment of mesenchymal cells results in activation of the p38/MK2/Hsp25 signaling pathway downstream from the BMP receptors. Moreover, chemical inhibition of p38 signaling or genetic ablation of either p38¿ or MK2 blocks the ability to activate the downstream effectors of the pathway and abolishes BMP-2-induction of cell migration. These signaling effects on p38/MK2/Hsp25 do not require the activity of either Cdc42 or PAK, whereas p38/MK2 activities do not significantly modify the BMP-2-dependent activation of LIMK1, measured by either kinase activity or with an antibody raised against phospho-threonine 508 at its activation loop. Finally, phosphorylated Hsp25 colocalizes with the BMP receptor complexes in lamellipodia and overexpression of a phosphorylation mutant form of Hsp25 is able to abolish the migration of cells in response to BMP-2. Conclusions: These results indicate that Cdc42/PAK/LIMK1 and p38/MK2/Hsp25 pathways, acting in parallel and modulating specific actin regulatory proteins, play a critical role in integrating responses during BMP-induced actin reorganization and cell migration