Le Equazioni Algebriche: i metodi risolutivi nella storia della matematica

Nel presente lavoro si illustrerà  un percorso didattico che usa la metodologia della storia della matematica nell’insegnamento. Si tratteranno, in particolare, i vari metodi risolutivi delle equazioni di primo e di secondo grado nella storia, dal metodo di falsa posizione degli egizi, ai metodi del completamento a quadrato o delle applicazioni delle aree nei greci, fino ai metodi risolutivi di René  Descartes (Cartesio). I metodi geometrici dei greci e di Cartesio sono svolti con il software di geometria dinamica Geogebra. Il percorso si conclude con i riferimenti storici al rinascimento e alle formule risolutive delle equazioni di terzo e quarto grado e a  Evariste Galois

An order-to-disorder structural switch activates the FoxM1 transcription factor

Intrinsically disordered transcription factor transactivation domains (TADs) function through structural plasticity, adopting ordered conformations when bound to transcriptional co-regulators. Many transcription factors contain a negative regulatory domain (NRD) that suppresses recruitment of transcriptional machinery through autoregulation of the TAD. We report the solution structure of an autoinhibited NRD-TAD complex within FoxM1, a critical activator of mitotic gene expression. We observe that while both the FoxM1 NRD and TAD are primarily intrinsically disordered domains, they associate and adopt a structured conformation. We identify how Plk1 and Cdk kinases cooperate to phosphorylate FoxM1, which releases the TAD into a disordered conformation that then associates with the TAZ2 or KIX domains of the transcriptional co-activator CBP. Our results support a mechanism of FoxM1 regulation in which the TAD undergoes switching between disordered and different ordered structures

Structural and mechanistic insights into Helicobacter pylori NikR activation

NikR is a transcriptional metalloregulator central in the mandatory response to acidity of Helicobacter pylori that controls the expression of numerous genes by binding to specific promoter regions. NikR/DNA interactions were proposed to rely on protein activation by Ni(II) binding to high-affinity (HA) and possibly secondary external (X) sites. We describe a biochemical characterization of HpNikR mutants that shows that the HA sites are essential but not sufficient for DNA binding, while the secondary external (X) sites and residues from the HpNikR dimer–dimer interface are important for DNA binding. We show that a second metal is necessary for HpNikR/DNA binding, but only to some promoters. Small-angle X-ray scattering shows that HpNikR adopts a defined conformation in solution, resembling the cis-conformation and suggests that nickel does not trigger large conformational changes in HpNikR. The crystal structures of selected mutants identify the effects of each mutation on HpNikR structure. This study unravels key structural features from which we derive a model for HpNikR activation where: (i) HA sites and an hydrogen bond network are required for DNA binding and (ii) metallation of a unique secondary external site (X) modulates HpNikR DNA binding to low-affinity promoters by disruption of a salt bridge

Effects of robotic upper limb treatment after stroke on cognitive patterns: A systematic review

BACKGROUND: Robotic therapy (RT) has been internationally recognized for the motor rehabilitation of the upper limb. Although it seems that RT can stimulate and promote neuroplasticity, the effectiveness of robotics in restoring cognitive deficits has been considered only in a few recent studies. OBJECTIVE: To verify whether, in the current state of the literature, cognitive measures are used as inclusion or exclusion criteria and/or outcomes measures in robotic upper limb rehabilitation in stroke patients. METHODS: The systematic review was conducted according to PRISMA guidelines. Studies eligible were identified through PubMed/MEDLINE and Web of Science from inception to March 2021. RESULTS: Eighty-one studies were considered in this systematic review. Seventy-three studies have at least a cognitive inclusion or exclusion criteria, while only seven studies assessed cognitive outcomes. CONCLUSION: Despite the high presence of cognitive instruments used for inclusion/exclusion criteria their heterogeneity did not allow the identification of a guideline for the evaluation of patients in different stroke stages. Therefore, although the heterogeneity and the low percentage of studies that included cognitive outcomes, seemed that the latter were positively influenced by RT in post-stroke rehabilitation. Future larger RCTs are needed to outline which cognitive scales are most suitable and their cut-off, as well as what cognitive outcome measures to use in the various stages of post-stroke rehabilitation

Multifaceted SlyD from Helicobacter pylori: implication in [NiFe] hydrogenase maturation

SlyD belongs to the FK506-binding protein (FKBP) family with both peptidylprolyl isomerase (PPIase) and chaperone activities, and is considered to be a ubiquitous cytosolic protein-folding facilitator in bacteria. It possesses a histidine- and cysteine-rich C-terminus binding to selected divalent metal ions (e.g., Ni2+, Zn2+), which is important for its involvement in the maturation processes of metalloenzymes. We have determined the solution structure of C-terminus-truncated SlyD from Helicobacter pylori (HpSlyDΔC). HpSlyDΔC folds into two well-separated, orientation-independent domains: the PPIase-active FKBP domain and the chaperone-active insert-in-flap (IF) domain. The FKBP domain consists of a four-stranded antiparallel β-sheet with an α-helix on one side, whereas the IF domain folds into a four-stranded antiparallel β-sheet accompanied by a short α-helix. Intact H. pylori SlyD binds both Ni2+ and Zn2+, with dissociation constants of 2.74 and 3.79 μM respectively. Intriguingly, binding of Ni2+ instead of Zn2+ induces protein conformational changes around the active sites of the FKBP domain, implicating a regulatory role of nickel. The twin-arginine translocation (Tat) signal peptide from the small subunit of [NiFe] hydrogenase (HydA) binds the protein at the IF domain. Nickel binding and the recognition of the Tat signal peptide by the protein suggest that SlyD participates in [NiFe] hydrogenase maturation processes

Molecular Characterization of Spontaneous Mesenchymal Stem Cell Transformation

Background. We previously reported the in vitro spontaneous transformation of human mesenchymal stem cells (MSC) generating a population with tumorigenic potential, that we termed transformed mesenchymal cells (TMC). Methodology/Principal Findings. Here we have characterized the molecular changes associated with TMC generation. Using microarrays techniques we identified a set of altered pathways and a greater number of downregulated than upregulated genes during MSC transformation, in part due to the expression of many untranslated RNAs in MSC. Microarray results were validated by qRT-PCR and protein detection. Conclusions/Significance. In our model, the transformation process takes place through two sequential steps; first MSC bypass senescence by upregulating c-myc and repressing p16 levels. The cells then bypass cell crisis with acquisition of telomerase activity, Ink4a/Arf locus deletion and Rb hyperphosphorylation. Other transformation-associated changes include modulation of mitochondrial metabolism, DNA damage-repair proteins and cell cycle regulators. In this work we have characterized the molecular mechanisms implicated in TMC generation and we propose a two-stage model by which a human MSC becomes a tumor cell

Functionalized Poly(3-hexylthiophene)s via Lithium–Bromine Exchange

Poly(3-hexylthiophene) (P3HT) is one of the most extensively investigated conjugated polymers and has been employed as the active material in many devices including field-effect transistors, organic photovoltaics and sensors. As a result, methods to further tune the properties of P3HT are desirable for specific applications. Herein, we report a facile postpolymerization modification strategy to functionalize the 4-position of commercially available P3HT in two simple steps–bromination of the 4-position of P3HT (Br–P3HT) followed by lithium−bromine exchange and quenching with an electrophile. We achieved near quantitative lithium–bromine exchange with Br–P3HT, which requires over 100 thienyl lithiates to be present on a single polymer chain. The lithiated-P3HT is readily combined with functional electrophiles, resulting in P3HT derivatives with ketones, secondary alcohols, trimethylsilyl (TMS) group, fluorine, or an azide at the 4-position. We demonstrated that the azide-modified P3HT could undergo Cu-catalyzed or Cu-free click chemistry, significantly expanding the complexity of the structures that can be appended to P3HT using this method.National Science Foundation (U.S.) (ECCS-0939514

Loss of Function of the Cik1/Kar3 Motor Complex Results in Chromosomes with Syntelic Attachment That Are Sensed by the Tension Checkpoint

The attachment of sister kinetochores by microtubules emanating from opposite spindle poles establishes chromosome bipolar attachment, which generates tension on chromosomes and is essential for sister-chromatid segregation. Syntelic attachment occurs when both sister kinetochores are attached by microtubules from the same spindle pole and this attachment is unable to generate tension on chromosomes, but a reliable method to induce syntelic attachments is not available in budding yeast. The spindle checkpoint can sense the lack of tension on chromosomes as well as detached kinetochores to prevent anaphase onset. In budding yeast Saccharomyces cerevisiae, tension checkpoint proteins Aurora/Ipl1 kinase and centromere-localized Sgo1 are required to sense the absence of tension but are dispensable for the checkpoint response to detached kinetochores. We have found that the loss of function of a motor protein complex Cik1/Kar3 in budding yeast leads to syntelic attachments. Inactivation of either the spindle or tension checkpoint enables premature anaphase entry in cells with dysfunctional Cik1/Kar3, resulting in co-segregation of sister chromatids. Moreover, the abolished Kar3-kinetochore interaction in cik1 mutants suggests that the Cik1/Kar3 complex mediates chromosome movement along microtubules, which could facilitate bipolar attachment. Therefore, we can induce syntelic attachments in budding yeast by inactivating the Cik1/Kar3 complex, and this approach will be very useful to study the checkpoint response to syntelic attachments

Built Shallow to Maintain Homeostasis and Persistent Infection: Insight into the Transcriptional Regulatory Network of the Gastric Human Pathogen Helicobacter pylori

Transcriptional regulatory networks (TRNs) transduce environmental signals into coordinated output expression of the genome. Accordingly, they are central for the adaptation of bacteria to their living environments and in host–pathogen interactions. Few attempts have been made to describe a TRN for a human pathogen, because even in model organisms, such as Escherichia coli, the analysis is hindered by the large number of transcription factors involved. In light of the paucity of regulators, the gastric human pathogen Helicobacter pylori represents a very appealing system for understanding how bacterial TRNs are wired up to support infection in the host. Herein, we review and analyze the available molecular and “-omic” data in a coherent ensemble, including protein–DNA and protein–protein interactions relevant for transcriptional control of pathogenic responses. The analysis covers ∼80% of the annotated H. pylori regulators, and provides to our knowledge the first in-depth description of a TRN for an important pathogen. The emerging picture indicates a shallow TRN, made of four main modules (origons) that process the physiological responses needed to colonize the gastric niche. Specific network motifs confer distinct transcriptional response dynamics to the TRN, while long regulatory cascades are absent. Rather than having a plethora of specialized regulators, the TRN of H. pylori appears to transduce separate environmental inputs by using different combinations of a small set of regulators