The underground secant: a tour in search of a definition. Italian pupils and students interpretation

The mathematical concept of secant has an intrinsic double nature: formal and informal, the second, often, is a result of a visual approach. We can apply to the secant what Sfard (2008, p. 39) states, i.e. that “there are some specialized keywords we use without ever being exposed to their explicit definitions”. We consider the word and the mathematical meaning of secant as an example of what Sfard notices and we can name ‘underground curriculum’. As to secant, the assumption is that informal, visual, content should be enough for to appreciate the formal definition but this assertion clashes with the result of a questionnaire administered to pupils of grade 11–13 (16–18 year old) and first enrolled in university students. A widespread didactic practice strictly connects the mathematical concept of secant with the derivative through the construction of the tangent to the curve. Therefore misunderstanding the concept of ‘secant’ could negatively affect the comprehension of Calculus

Success and Pitfalls of Genetic Testing in Undiagnosed Diseases: Whole Exome Sequencing and Beyond

Novel approaches to uncover the molecular etiology of neurodevelopmental disorders (NDD) are highly needed. Even using a powerful tool such as whole exome sequencing (WES), the diagnostic process may still prove long and arduous due to the high clinical and genetic heterogeneity of these conditions. The main strategies to improve the diagnostic rate are based on family segregation, re-evaluation of the clinical features by reverse-phenotyping, re-analysis of unsolved NGS-based cases and epigenetic functional studies. In this article, we described three selected cases from a cohort of patients with NDD in which trio WES was applied, in order to underline the typical challenges encountered during the diagnostic process: (1) an ultra-rare condition caused by a missense variant in MEIS2, identified through the updated Solve-RD re-analysis; (2) a patient with Noonan-like features in which the NGS analysis revealed a novel variant in NIPBL causing Cornelia de Lange syndrome; and (3) a case with de novo variants in genes involved in the chromatin-remodeling complex, for which the study of the epigenetic signature excluded a pathogenic role. In this perspective, we aimed to (i) provide an example of the relevance of the genetic re-analysis of all unsolved cases through network projects on rare diseases; (ii) point out the role and the uncertainties of the reverse phenotyping in the interpretation of the genetic results; and (iii) describe the use of methylation signatures in neurodevelopmental syndromes for the validation of the variants of uncertain significance

Genetic Basis of Breast and Ovarian Cancer: Approaches and Lessons Learnt from Three Decades of Inherited Predisposition Testing

Germline variants occurring in BRCA1 and BRCA2 give rise to hereditary breast and ovarian cancer (HBOC) syndrome, predisposing to breast, ovarian, fallopian tube, and peritoneal cancers marked by elevated incidences of genomic aberrations that correspond to poor prognoses. These genes are in fact involved in genetic integrity, particularly in the process of homologous recombination (HR) DNA repair, a high-fidelity repair system for mending DNA double-strand breaks. In addition to its implication in HBOC pathogenesis, the impairment of HR has become a prime target for therapeutic intervention utilizing poly (ADP-ribose) polymerase (PARP) inhibitors. In the present review, we introduce the molecular roles of HR orchestrated by BRCA1 and BRCA2 within the framework of sensitivity to PARP inhibitors. We examine the genetic architecture underneath breast and ovarian cancer ranging from high- and mid- to low-penetrant predisposing genes and taking into account both germline and somatic variations. Finally, we consider higher levels of complexity of the genomic landscape such as polygenic risk scores and other approaches aiming to optimize therapeutic and preventive strategies for breast and ovarian cancer