We study the relation of mutual strong Birkhoff–James orthogonality in two classical
C
∗
-algebras: the
C
∗
-algebra
B
(
H
)
of all bounded linear operators on a complex Hilbert space
H
and the ...commutative, possibly nonunital,
C
∗
-algebra. With the help of the induced graph it is shown that this relation alone can characterize right invertible elements. Moreover, in the case of commutative unital
C
∗
-algebras, it can detect the existence of a point with a countable local basis in the corresponding compact Hausdorff space.
Heterotrimeric G proteins are immediate transducers of G protein-coupled receptors-the biggest receptor family in metazoans-and play innumerate functions in health and disease. A set of de novo point ...mutations in
and
, the genes encoding the α-subunits (Gαo and Gαi1, respectively) of the heterotrimeric G proteins, have been described to cause pediatric encephalopathies represented by epileptic seizures, movement disorders, developmental delay, intellectual disability, and signs of neurodegeneration. Among such mutations, the Gln52Pro substitutions have been previously identified in
and
. Here, we describe the case of an infant with another mutation in the same site, Gln52Arg. The patient manifested epileptic and movement disorders and a developmental delay, at the onset of 1.5 weeks after birth. We have analyzed biochemical and cellular properties of the three types of dominant pathogenic mutants in the Gln52 position described so far: GαoGln52Pro, Gαi1Gln52Pro, and the novel GαoGln52Arg. At the biochemical level, the three mutant proteins are deficient in binding and hydrolyzing GTP, which is the fundamental function of the healthy G proteins. At the cellular level, the mutants are defective in the interaction with partner proteins recognizing either the GDP-loaded or the GTP-loaded forms of Gαo. Further, of the two intracellular sites of Gαo localization, plasma membrane and Golgi, the former is strongly reduced for the mutant proteins. We conclude that the point mutations at Gln52 inactivate the Gαo and Gαi1 proteins leading to aberrant intracellular localization and partner protein interactions. These features likely lie at the core of the molecular etiology of pediatric encephalopathies associated with the codon 52 mutations in
/
.
The introduction of immunotherapy in the treatment of non-small cell lung cancer (NSCLC) has resulted in a radical change in patients' treatment responses and survival rates. The increased percentage ...of long survivors, improved toxicity profiles compared to chemotherapy, and the possible applications for different NSCLC scenarios, have led to immune checkpoint inhibitors (ICIs) becoming the cornerstone of NSCLC treatment. Therefore, the objective of this review is to describe the current and future perspectives of NSCLC treatment.
A systematic review according to the PRISMA criteria has been performed based on clinical trials with immunotherapy in NSCLC from the start of these treatments until June 2022.
The use of ICIs is widespread across both first- and second-line treatments with anti-PD-1, anti-PD-L1, and anti-CTLA-4 drugs. New indications for immunotherapy in NSCLC have focused on adjuvant (atezolizumab) and neoadjuvant (nivolumab), with ICIs now present in all stages of NSCLC treatment. Given the promising results seen in clinical trials, new ICIs anti- lymphocyte activation gene-3 (LAG-3) or IDO1 currently under development, will soon be used as standard treatment for NSCLC.
Immunotherapy is the mainstay of NSCLC treatment in all stages, including adjuvant, neoadjuvant and advanced tumors. The development of new molecules will revolutionize the treatment of NSCLC in the coming years.
The roots of polynomials over Cayley-Dickson algebras over an arbitrary field and of arbitrary dimension are studied. It is shown that the spherical roots of a polynomial f(x) are also roots of its ...companion polynomial
. We generalize the classical theorems for complex and real polynomials by Gauss-Lucas and Jensen to locally-complex Cayley-Dickson algebras: it is proved that the spherical roots of
belong to the convex hull of the roots of
, and we also show that all roots of
are contained in the snail of f(x), as defined by Ghiloni and Perotti.
Graph defined by Birkhoff–James orthogonality relation in normed spaces is studied. It is shown that (i) in a normed space of sufficiently large dimension there always exists a nonzero vector which ...is mutually Birkhoff–James orthogonal to each among a fixed number of given vectors, and (ii) in nonsmooth norms the cardinality of the set of pairwise Birkhoff–James orthogonal vectors may exceed the dimension of the vector space, but this cardinality is always bounded above by a function of the dimension. It is further shown that any given pair of elements in a normed space can be extended to a finite tuple such that each consecutive elements are mutually Birkhoff–James orthogonal; the exact minimal length of the tuple is also determined.
For an arbitrary normed space
X
over a field
F
∈
{
R
,
C
}
,
we define the directed graph
Γ
(
X
)
induced by Birkhoff–James orthogonality on the projective space
P
(
X
)
,
and also its nonprojective ...counterpart
Γ
0
(
X
)
.
We show that, in finite-dimensional normed spaces,
Γ
(
X
)
carries all the information about the dimension, smooth points, and norm’s maximal faces. It also allows to determine whether the norm is a supremum norm or not, and thus classifies finite-dimensional abelian
C
∗
-algebras among other normed spaces. We further establish the necessary and sufficient conditions under which the graph
Γ
0
(
R
)
of a (real or complex) Radon plane
R
is isomorphic to the graph
Γ
0
(
F
2
,
‖
·
‖
2
)
of the two-dimensional Hilbert space and construct examples of such nonsmooth Radon planes.
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