Non-trivial, non-negative periodic solutions of a system of singular-degenerate parabolic equations with nonlocal terms

We study the existence of non-trivial, non-negative periodic solutions for systems of singular-degenerate parabolic equations with nonlocal terms and satisfying Dirichlet boundary conditions. The method employed in this paper is based on the Leray-Schauder topological degree theory. However, verifying the conditions under which such a theory applies is more involved due to the presence of the singularity. The system can be regarded as a possible model of the interactions of two biological species sharing the same isolated territory, and our results give conditions that ensure the coexistence of the two species.Comment: 39 page

Inhibition of ERK5 elicits cellular senescence in melanoma via the cyclin-dependent kinase inhibitor p21

2021 The Authors.Melanoma is the deadliest skin cancer with a very poor prognosis in advanced stages. Although targeted and immune therapies have improved survival, not all patients benefit from these treatments. The mitogen-activated protein kinase ERK5 supports the growth of melanoma cells in vitro and in vivo. However, ERK5 inhibition results in cell-cycle arrest rather than appreciable apoptosis. To clarify the role of ERK5 in melanoma growth, we performed transcriptomic analyses following ERK5 knockdown in melanoma cells expressing BRAFV600E and found that cellular senescence was among the most affected processes. In melanoma cells expressing either wild-type or mutant (V600E) BRAF, both genetic and pharmacologic inhibition of ERK5 elicited cellular senescence, as observed by a marked increase in senescence-associated β-galactosidase activity and p21 expression. In addition, depletion of ERK5 from melanoma cells resulted in increased levels of CXCL1, CXCL8, and CCL20, proteins typically involved in the senescence-associated secretory phenotype. Knockdown of p21 suppressed the induction of cellular senescence by ERK5 blockade, pointing to p21 as a key mediator of this process. In vivo, ERK5 knockdown or inhibition with XMD8–92 in melanoma xenografts promoted cellular senescence. Based on these results, small-molecule compounds targeting ERK5 constitute a rational series of prosenescence drugs that may be exploited for melanoma treatment.The work in E. Rovida’s lab was supported by grants from Associazione Italiana per la Ricerca sul Cancro (AIRC, IG-15282 and IG-21349), by Ente Fondazione Cassa di Risparmio di Firenze (ECRF), and Universita degli Studi di Firenze (Fondo di Ateneo ex-60%). A. Tubita was supported by a “Carlo Zanotti” Fondazione Italiana per la Ricerca sul Cancro (FIRC)-AIRC fellowship (ID-23847)

Non-trivial, non-negative periodic solutions of a system of singular-degenerate parabolic equations with nonlocal terms

We study the existence of nontrivial, nonnegative periodic solutions for systems of singular-degenerate parabolic equations with nonlocal terms and satisfying Dirichlet boundary conditions. The method employed in this paper is based on the Leray-Schauder topological degree theory. However, verifying the conditions under which such a theory applies is more involved due to the presence of the singularity. The system can be regarded as a possible model of the interactions of two biological species sharing the same isolated territory, and our results give conditions that ensure the coexistence of the two species

Erratum to: Guidelines for the use and interpretation of assays for monitoring autophagy (3rd edition) (Autophagy, 12, 1, 1-222, 10.1080/15548627.2015.1100356

non present