Evolution of epithelial sodium channels: current concepts and hypotheses

The conquest of freshwater and terrestrial habitats was a key event during vertebrate evolution. Occupation of low-salinity and dry environments required significant osmoregulatory adaptations enabling stable ion and water homeostasis. Sodium is one of the most important ions within the extracellular liquid of vertebrates, and molecular machinery for urinary reabsorption of this electrolyte is critical for the maintenance of body osmoregulation. Key ion channels involved in the fine-tuning of sodium homeostasis in tetrapod vertebrates are epithelial sodium channels (ENaCs), which allow the selective influx of sodium ions across the apical membrane of epithelial cells lining the distal nephron or the colon. Furthermore, ENaC-mediated sodium absorption across tetrapod lung epithelia is crucial for the control of liquid volumes lining the pulmonary surfaces. ENaCs are vertebrate-specific members of the degenerin/ENaC family of cation channels; however, there is limited knowledge on the evolution of ENaC within this ion channel family. This review outlines current concepts and hypotheses on ENaC phylogeny and discusses the emergence of regulation-defining sequence motifs in the context of osmoregulatory adaptations during tetrapod terrestrialization. In light of the distinct regulation and expression of ENaC isoforms in tetrapod vertebrates, we discuss the potential significance of ENaC orthologs in osmoregulation of fishes as well as the putative fates of atypical channel isoforms in mammals. We hypothesize that ancestral proton-sensitive ENaC orthologs might have aided the osmoregulatory adaptation to freshwater environments whereas channel regulation by proteases evolved as a molecular adaptation to lung liquid homeostasis in terrestrial tetrapods.

REPRESENTATIONS OF IDEALS IN POLISH GROUPS AND IN BANACH SPACES

We investigate ideals of the form {A⊆ω: Σn∈Axnis unconditionally convergent} where (xn)n∈ωis a sequence in a Polish group or in a Banach space. If an ideal onωcan be seen in this form for some sequence inX, then we say that it is representable inX.After numerous examples we show the following theorems: (1) An ideal is representable in a Polish Abelian group iff it is an analytic P-ideal. (2) An ideal is representable in a Banach space iff it is a nonpathological analytic P-ideal.We focus on the family of ideals representable inc0. We characterize this property via the defining sequence of measures. We prove that the trace of the null ideal, Farah’s ideal, and Tsirelson ideals are not representable inc0, and that a tallFσP-ideal is representable inc0iff it is a summable ideal. Also, we provide an example of a peculiar ideal which is representable inℓ1but not in ℝ.Finally, we summarize some open problems of this topic.

Radium223—Where Does It Fit in the Metastatic Castration-resistant Prostate Cancer Treatment Landscape?

Radium223 is approved for symptomatic castration-resistant prostate cancer patients with osseous involvement. Selecting patients and defining sequence strategies are challenging, with the limited available data, but there is a trend toward greater impact in higher volume disease. Combination and/or consolidation strategies for Radium223 will be of significant interest as data emerge from ongoing trials.

Stereotyped B-cell receptors in one-third of chronic lymphocytic leukemia: a molecular classification with implications for targeted therapies

Mounting evidence indicates that grouping of chronic lymphocytic leukemia (CLL) into distinct subsets with stereotyped BCRs is functionally and prognostically relevant. However, several issues need revisiting, including the criteria for identification of BCR stereotypy and its actual frequency as well as the identification of “CLL-biased” features in BCR Ig stereotypes. To this end, we examined 7596 Ig VH (IGHV-IGHD-IGHJ) sequences from 7424 CLL patients, 3 times the size of the largest published series, with an updated version of our purpose-built clustering algorithm. We document that CLL may be subdivided into 2 distinct categories: one with stereotyped and the other with nonstereotyped BCRs, at an approximate ratio of 1:2, and provide evidence suggesting a different ontogeny for these 2 categories. We also show that subset-defining sequence patterns in CLL differ from those underlying BCR stereotypy in other B-cell malignancies. Notably, 19 major subsets contained from 20 to 213 sequences each, collectively accounting for 943 sequences or one-eighth of the cohort. Hence, this compartmentalized examination of VH sequences may pave the way toward a molecular classification of CLL with implications for targeted therapeutic interventions, applicable to a significant number of patients assigned to the same subset.

Layered circle packings

Given a bounded sequence of integers{d0,d1,d2,…},6≤dn≤M, there is an associated abstract triangulation created by building up layers of vertices so that vertices on thenth layer have degreedn. This triangulation can be realized via a circle packing which fills either the Euclidean or the hyperbolic plane. We give necessary and sufficient conditions to determine the type of the packing given the defining sequence{dn}.

On Fréchet algebras of power series

If the indeterminate X in a Fréchet algebra A of power series is a power series generator for A, then either A is the algebra of all formal power series or is the Beurling-Fréchet algebra on non-negative integers defined by a sequence of weights. Let the topology of A be defined by a sequence of norms. Then A is an inverse limit of a sequence of Banach algebras of power series if and only if each norm in the defining sequence satisfies certain closability condition and an equicontinuity condition due to Loy. A non-Banach uniform Fréchet algebra with a power series generator is a nuclear space. A number of examples are discussed; and a functional analytic description of the holomorphic function algebra on a simply connected planar domain is obtained.

A quasianalytic singular spectrum with respect to the Denjoy-Carleman class

Making use of the FBI (Fourier-Bros-Iagolnitzer) transforms we simplify the quasianalytic singular spectrum for the Fourier hyperfunctions, which was defined for distributions by Hörmander as follows; for any Fourier hyperfunction u, (x0, ξ0) does not belong to the quasianalytic singular spectrum W FM(u) if and only if there exist positive constants C, γ and N, and a neighborhood of x0 and a conic neighborhood Г of ξ0 such thatfor all x ∈ U, |ξ| ∈ Γ and |ξ| ≥ N, where M(t) is the associated function of the defining sequence Mp. This result simplifies Hörmander’s definition and unify the singular spectra for the C∞ class, the analytic class and the Denjoy-Carleman class, both quasianalytic and nonquasianalytic.