Coincidence and common fixed point theorems for Suzuki type hybrid contractions and applications

Coincidence and common fixed point theorems for a class of Suzuki hybrid contractions involving two pairs of single-valued and multivalued maps in a metric space are obtained. In addition, the existence of a common solution for a certain class of functional equations arising in a dynamic programming is also discussed.

Pata contractions and coupled type fixed points

A new coupled fixed point theorem related to the Pata contraction for mappings having the mixed monotone property in partially ordered complete metric spaces is established. It is shown that the coupled fixed point can be unique under some extra suitable conditions involving mid point lower or upper bound properties. Also the corresponding convergence rate is estimated when the iterates of our function converge to its coupled fixed point.

Characterisation of patients with brachydactyly type E associated or not with hormonal resistance: clinical, genetic and radiological approach

334 p.

Current Approaches for Predicting a Lack of Response to Anti-EGFR Therapy in KRAS Wild-Type Patients

Targeting epidermal growth factor receptor (EGFR) has been one of the most effective colorectal cancer strategies. Anti-EGFR antibodies function by binding to the extracellular domain of EGFR, preventing its activation, and ultimately providing clinical benefit. KRAS mutations in codons 12 and 13 are recognized prognostic and predictive biomarkers that should be analyzed at the clinic prior to the administration of anti-EGFR therapy. However, still an important fraction of KRAS wild-type patients do not respond to the treatment. The identification of additional genetic determinants of primary or secondary resistance to EGFR targeted therapy for further improving the selection of patients is urgent. Herein, we review the latest published literature highlighting the most important genes that may predict resistance to anti-EGFR monoclonal antibodies in colorectal cancer patients. According to the available findings, the evaluation of BRAF, NRAS, PIK3CA, and PTEN status could be the right strategy to select patients who are likely to respond to anti-EGFR therapies. In the future, the combination of those biomarkers will help establish consensus that can be introduced into clinical practice.

A New Type of Coincidence and Common Fixed Point Theorem with Applications

Coincidence and common fixed point theorems for a class of 'Ciric-Suzuki hybrid contractions involving a multivalued and two single-valued maps in a metric space are obtained. Some applications including the existence of a common solution for certain class of functional equations arising in a dynamic programming are also discussed..

Análise da via Wnt e seu envolvimento no processo da tumorigênese do câncer colo-retal

O câncer colo-retal (CCR) representa o quarto tipo de câncer mais freqüente no Brasil entre homens e mulheres e a sobrevida para esse tipo de neoplasia é considerada boa, se a doença for diagnosticada em estádio inicial. Neste tipo de câncer a progressão do adenoma (tumor benigno) para o adenocarcinoma (tumor maligno) é dependente do acúmulo de mutações em diversos oncogenes e genes supressores de tumor. Estas mutações podem levar a alterações de importantes vias de sinalização que controlam estes eventos como, por exemplo, as vias Wnt e EGFR. No entanto, os mecanismos moleculares e celulares mediados por estas vias durante a progressão do CCR permanecem por serem definidos. Neste trabalho foi avaliada a participação da via Wnt e do EGFR durante a progressão do CCR usando células Caco-2, uma linhagem celular derivada de adenocarcinoma de cólon humano como modelo. As células foram tratadas com EGF, ativador da via EGFR, e cloreto de lítio (LiCl), um conhecido inibidor da enzima GSK-3β e conseqüentemente, ativador da via Wnt, ou alternativamente com a combinação de ambas drogas. Após os tratamentos, foi avaliada a morfologia celular, localização e expressão de proteínas juncionais, os padrões proliferativos e do ciclo celular e o potencial tumorigênico (migração e formação de colônias). Nossos resultados mostram que a localização subcelular das proteínas juncionais claudina-1 e β-catenina foi alterada após tratamento com EGF e LiCl, porém a expressão não foi afetada. A localização nuclear de β-catenina, um marcador da ativação da via Wnt, foi observada após tratamento com ambos os compostos, no entanto estes agentes modularam a enzima GSK-3β de forma diferencial. Além disso, tratamento com EGF aumentou a capacidade proliferativa e migratória da célula, mas não alterou a formação de colônias. LiCl, apesar de ser um conhecido ativador da via Wnt, inibiu o aumento da proliferação e migração causado pelo EGF, como visto pelo tratamento das células com EGF+LiCl, e reduziu a formação de colônias. Nossos resultados revelaram que LiCl possui uma atividade supressora de tumor o que pode representar um novo papel para este composto como um possível agente terapêutico para o tratamento do CCR.

Pseudohypoparathyroidism Type Ib Associated with Novel Duplications in the GNAS Locus

Context Pseudohypoparathyroidism type 1b (PHP-Ib) is characterized by renal resistance to PTH (and, sometimes, a mild resistance to TSH) and absence of any features of Albright's hereditary osteodystrophy. Patients with PHP-Ib suffer of defects in the methylation pattern of the complex GNAS locus. PHP-Ib can be either sporadic or inherited in an autosomal dominant pattern. Whereas familial PHP-Ib is well characterized at the molecular level, the genetic cause of sporadic PHP-Ib cases remains elusive, although some molecular mechanisms have been associated with this subtype. Objective The aim of the study was to investigate the molecular and imprinting defects in the GNAS locus in two unrelated patients with PHP-Ib. Design We have analyzed the GNAS locus by direct sequencing, Methylation-Specific Multiplex Ligation-dependent Probe Amplification, microsatellites, Quantitative Multiplex PCR of Short Fluorescent fragments and array-Comparative Genomic Hybridization studies in order to characterize two unrelated families with clinical features of PHP-Ib. Results We identified two duplications in the GNAS region in two patients with PHP-Ib: one of them, comprising similar to 320 kb, occurred 'de novo' in the patient, whereas the other one, of similar to 179 kb in length, was inherited from the maternal allele. In both cases, no other known genetic cause was observed. Conclusion In this article, we describe the to-our-knowledge biggest duplications reported so far in the GNAS region. Both are associated to PHP-Ib, one of them occurring 'de novo' and the other one being maternally inherited.