The Conley index in Hilbert spaces and its applications

We present a generalization of the classical Conley index defined for flows on locally compact spaces to flows on an infinite-dimensional real Hilbert space H generated by vector fields of the form f: H → H, f(x) = Lx + K(x), where L: H → H is a bounded linear operator satisfying some technical assumptions and K is a completely continuous perturbation. Simple examples are presented to show how this new invariant can be applied in searching critical points of strongly indefinite functionals having asymptotically linear gradient

Diverse and cancer type‑specific roles of the p53 R248Q gain‑of‑function mutation in cancer migration and invasiveness

Gain‑of‑function (GOF) mutations in the TP53 gene lead to acquisition of new functions by the mutated tumor suppressor p53 protein. A number of the over‑represented 'hot spot' mutations, including the ones in codons 175, 248 or 273, convey GOF phenotypes. Such phenotypes may include resistance to chemotherapeutics or changes in motility and invasiveness. Whereas the prevalent notion is that the acquisition of the p53 GOF phenotype translates into poorer prognosis for the patient, the analysis of a human somatic p53 mutations dataset demonstrated earlier tumor onset, but decreased frequency and altered location of metastases in patients with the p53‑R248Q allele. Therefore, the GOF activities of p53‑R248Q and p53‑D281G were analyzed in triple negative breast cancer MDA‑MB‑231 and lung adenocarcinoma H1299 cell lines with regard to invasive and metastatic traits. The expression of p53‑D281G increased the motility and invasiveness of the lung cancer cells, but not those of the breast cancer cells. In contrast, the expression of p53‑R248Q decreased the motility and invasiveness of the breast and lung cancer cells in a p53 transactivation‑dependent manner. The intravenous xenotransplantation of MDA‑MB‑231 cells expressing p53‑R248Q into zebrafish embryos resulted in an alteration of the distribution of cancer cells in the body of the fish. In p53‑R248Q‑expressing H1299 cells a decrease in the expression of TCF8/ZEB1 and N‑cadherin was observed, suggesting partial mesenchymal‑to‑epithelial transition. In the two cell lines expressing p53‑R248Q a decrease was noted in the expression of myosin light chain 2, a protein involved in actomyosin‑based motility. To the best of our knowledge, the present study is one of only few reports demonstrating the mutated p53 GOF activity resulting in a decrease of a malignant trait in human cancer.Animal science

Bifurcation of periodic solutions in differential inclusions

summary:Ordinary differential inclusions depending on small parameters are considered such that the unperturbed inclusions are ordinary differential equations possessing manifolds of periodic solutions. Sufficient conditions are determined for the persistence of some of these periodic solutions after multivalued perturbations. Applications are given to dry friction problems