Class Of Cardinals Research Articles

Embryonic temporal-spatial delineation of excitatory spinal V3 interneuron diversity

Spinal neural circuits that execute movement are composed of cardinal classes of neurons that emerged from distinct progenitor lineages. Each cardinal class contains multiple neuronal subtypes characterized by distinct molecular, anatomical, and physiological characteristics. Through a focus on the excitatory V3 interneuron class, here we demonstrate that interneuron subtype diversity is delineated through a combination of neurogenesis timing and final laminar settling position. We have revealed that early-born and late-born embryonic V3 temporal classes further diversify into subclasses with spatially and molecularly discrete identities. While neurogenesis timing accounts for V3 morphological diversification, laminar settling position accounts for electrophysiological profiles distinguishing V3 subtypes within the same temporal classes. Furthermore, V3 interneuron subtypes display independent behavioral recruitment patterns demonstrating a functional modularity underlying V3 interneuron diversity. These studies provide a framework for how early embryonic temporal and spatial mechanisms combine to delineate spinal interneuron classes into molecularly, anatomically, and functionally relevant subtypes in adults.

Weak Indestructibility and Reflection

AbstractThere is a balance between the amount of (weak) indestructibility one can have and the amount of strong cardinals. It’s consistent relative to large cardinals to have lots of strong cardinals and all of their degrees of strength are weakly indestructible. But this necessitates the destructibility of the partially strong cardinals. Guaranteeing the indestructibility of the partially strong cardinals is shown to be harder. In particular, this work establishes an equiconsistency between: 1.a proper class of cardinals that are strong reflecting strongs; and2.weak indestructibility for (κ+2)-strength for all cardinals κ in the presence of a proper class of strong cardinals.These have a much higher consistency strength than: 3.weak indestructibility for all degrees of strength for a proper class of strong cardinals.This discrepancy holds even if we weaken (2) from the presence of a proper class to just two strong cardinals. (2) is also equivalent to weak indestructibility for all λ-strength for λ far beyond (κ+2); well beyond the next measurable limit of measurables above κ, but before the next μ that is (μ+2)-strong.One direction of the equiconsistency of (1) and (2) is proven using forcing and the other using core model techniques from inner model theory. Additionally, connections between weak indestructibility and the reflection properties associated with Woodin cardinals are discussed, and similar results are derived for supercompacts and supercompacts reflecting supercompacts.Abstract prepared by James Holland.E-mail: jch258@scarletmail.rutgers.eduURL: https://sites.math.rutgers.edu/~jch258/assets/dis.pdf

WEAK INDESTRUCTIBILITY AND REFLECTION

Abstract We establish an equiconsistency between (1) weak indestructibility for all $\kappa +2$ -degrees of strength for cardinals $\kappa $ in the presence of a proper class of strong cardinals, and (2) a proper class of cardinals that are strong reflecting strongs. We in fact get weak indestructibility for degrees of strength far beyond $\kappa +2$ , well beyond the next inaccessible limit of measurables (of the ground model). One direction is proven using forcing and the other using core model techniques from inner model theory. Additionally, connections between weak indestructibility and the reflection properties associated with Woodin cardinals are discussed. This work is a part of my upcoming thesis [7].

Measurable cardinals and choiceless axioms

Kunen refuted the existence of an elementary embedding from the universe of sets to itself assuming the Axiom of Choice. This paper concerns the ramifications of this hypothesis when the Axiom of Choice is not assumed. For example, the existence of such an embedding implies that there is a proper class of cardinals λ such that λ+ is measurable.

Cortical somatostatin interneuron subtypes form cell-type-specific circuits

The cardinal classes are a useful simplification of cortical interneuron diversity, but such broad subgroupings gloss over the molecular, morphological, and circuit specificity of interneuron subtypes, most notably among the somatostatin interneuron class. Although there is evidence that this diversity is functionally relevant, the circuit implications of this diversity are unknown. To address this knowledge gap, we designed a series of genetic strategies to target the breadth of somatostatin interneuron subtypes and found that each subtype possesses a unique laminar organization and stereotyped axonal projection pattern. Using these strategies, we examined the afferent and efferent connectivity of three subtypes (two Martinotti and one non-Martinotti) and demonstrated that they possess selective connectivity with intratelecephalic or pyramidal tract neurons. Even when two subtypes targeted the same pyramidal cell type, their synaptic targeting proved selective for particular dendritic compartments. We thus provide evidence that subtypes of somatostatin interneurons form cell-type-specific cortical circuits.

A Systematic Review on Synthetic and Antimicrobial Bioactivity of the Multifaceted Hydrazide Derivatives

: To overcome the upsurge of antimicrobial resistance that has emerged in recent years, there is a need for the development of newer hits having satisfying anti-infective activity. Hydrazides incorporated with an azomethine hydrogen account for a cardinal class of molecules for the development of newer derivatives. Hydrazide derivatives have gained considerable interest of medicinal chemists owing to their diverse bioactivity. In the present review, we have attempted to compile the recent trends in the synthesis of hydrazides and their substituted derivatives. The structural features that lead to the desired antimicrobial activity are highlighted, which will lead the way for synthetic and medicinal chemists to focus on newer designs in this arena.

Conserved genetic signatures parcellate cardinal spinal neuron classes into local and projection subsets.

Motor and sensory functions of the spinal cord are mediated by populations of cardinal neurons arising from separate progenitor lineages. However, each cardinal class is composed of multiple neuronal types with distinct molecular, anatomical, and physiological features, and there is not a unifying logic that systematically accounts for this diversity. We reasoned that the expansion of new neuronal types occurred in a stepwise manner analogous to animal speciation, and we explored this by defining transcriptomic relationships using a top-down approach. We uncovered orderly genetic tiers that sequentially divide groups of neurons by their motor-sensory, local-long range, and excitatory-inhibitory features. The genetic signatures defining neuronal projections were tied to neuronal birth date and conserved across cardinal classes. Thus, the intersection of cardinal class with projection markers provides a unifying taxonomic solution for systematically identifying distinct functional subsets.

A novel temporal identity window generates alternating Eve+/Nkx6+ motor neuron subtypes in a single progenitor lineage

BackgroundSpatial patterning specifies neural progenitor identity, with further diversity generated by temporal patterning within individual progenitor lineages. In vertebrates, these mechanisms generate “cardinal classes” of neurons that share a transcription factor identity and common morphology. In Drosophila, two cardinal classes are Even-skipped (Eve)+ motor neurons projecting to dorsal longitudinal muscles, and Nkx6+ motor neurons projecting to ventral oblique muscles. Cross-repressive interactions prevent stable double-positive motor neurons. The Drosophila neuroblast 7–1 (NB7–1) lineage uses a temporal transcription factor cascade to generate five distinct Eve+ motor neurons; the origin and development of Nkx6+ motor neurons remains unclear.MethodsWe use a neuroblast specific Gal4 line, sparse labelling and molecular markers to identify an Nkx6+ VO motor neuron produced by the NB7–1 lineage. We use lineage analysis to birth-date the VO motor neuron to the Kr+ Pdm+ neuroblast temporal identity window. We use gain- and loss-of-function strategies to test the role of Kr+ Pdm+ temporal identity and the Nkx6 transcription factor in specifying VO neuron identity.ResultsLineage analysis identifies an Nkx6+ neuron born from the Kr+ Pdm+ temporal identity window in the NB7–1 lineage, resulting in alternation of cardinal motor neuron subtypes within this lineage (Eve>Nkx6 > Eve). Co-overexpression of Kr/Pdm generates ectopic VO motor neurons within the NB7–1 lineage – the first evidence that this TTF combination specifies neuronal identity. Moreover, the Kr/Pdm combination promotes Nkx6 expression, which itself is necessary and sufficient for motor neuron targeting to ventral oblique muscles, thereby revealing a molecular specification pathway from temporal patterning to cardinal transcription factor expression to motor neuron target selection.ConclusionsWe show that one neuroblast lineage generates interleaved cardinal motor neurons fates; that the Kr/Pdm TTFs form a novel temporal identity window that promotes expression of Nkx6; and that the Kr/Pdm > Nkx6 pathway is necessary and sufficient to promote VO motor neuron targeting to the correct ventral muscle group.

EQUIVALENT DEFINITIONS OF SUPERSTABILITY IN TAME ABSTRACT ELEMENTARY CLASSES

AbstractIn the context of abstract elementary classes (AECs) with a monster model, several possible definitions of superstability have appeared in the literature. Among them are no long splitting chains, uniqueness of limit models, and solvability. Under the assumption that the class is tame and stable, we show that (asymptotically) no long splitting chains implies solvability and uniqueness of limit models implies no long splitting chains. Using known implications, we can then conclude that all the previously-mentioned definitions (and more) are equivalent:Corollary.LetKbe a tame AEC with a monster model. Assume thatKis stable in a proper class of cardinals. The following are equivalent:(1)For all high-enough λ,Khas no long splitting chains.(2)For all high-enough λ, there exists a good λ-frame on a skeleton ofKλ.(3)For all high-enough λ,Khas a unique limit model of cardinality λ.(4)For all high-enough λ,Khas a superlimit model of cardinality λ.(5)For all high-enough λ, the union of any increasing chain of λ-saturated models is λ-saturated.(6)There exists μ such that for all high-enough λ,Kis (λ,μ) -solvable.This gives evidence that there is a clear notion of superstability in the framework of tame AECs with a monster model.

Diversity of molecularly defined spinal interneurons engaged in mammalian locomotor pattern generation.

Mapping the expression of transcription factors in the mouse spinal cord has identified ten progenitor domains, four of which are cardinal classes of molecularly defined, ventrally located interneurons that are integrated in the locomotor circuitry. This review focuses on the properties of these interneuronal populations and their contribution to hindlimb locomotor central pattern generation. Interneuronal populations are categorized based on their excitatory or inhibitory functions and their axonal projections as predictors of their role in locomotor rhythm generation and coordination. The synaptic connectivity and functions of these interneurons in the locomotor central pattern generators (CPGs) have been assessed by correlating their activity patterns with motor output responses to rhythmogenic neurochemicals and sensory and descending fibers stimulations as well as analyzing kinematic gait patterns in adult mice. The observed complex organization of interneurons in the locomotor CPG circuitry, some with seemingly similar physiological functions, reflects the intricate repertoire associated with mammalian motor control and is consistent with high transcriptional heterogeneity arising from cardinal interneuronal classes. This review discusses insights derived from recent studies to describe innovative approaches and limitations in experimental model systems and to identify missing links in current investigational enterprise.

Genetic dissection of Gata2 selective functions during specification of V2 interneurons in the developing spinal cord.

Motor activities are controlled by neural networks in the ventral spinal cord and consist in motor neurons and a set of distinct cardinal classes of spinal interneurons. These interneurons arise from distinct progenitor domains (p0-p3) delineated according to a transcriptional code. Neural progenitors of each domain express a unique combination of transcription factors (TFs) that largely contribute to determine the fate of four classes of interneurons (V0-V3) and motor neurons. In p2 domain, at least four subtypes of interneurons namely V2a, V2b, V2c, and Pax6(+) V2 are generated. Although genetic and molecular mechanisms that specify V2a and V2b are dependent on complex interplay between several TFs including Nkx6.1, Irx3, Gata2, Foxn4, and Ascl1, and signaling pathways such as Notch and TGF-β, the sequence order of the activation of these regulators and their respective contribution are not completely elucidated yet. Here, we provide evidence by loss- or gain-of-function experiments that Gata2 is necessary for the normal development of both V2a and V2b neurons. We demonstrate that Nkx6.1 and Dll4 positively regulate the activation of Gata2 and Foxn4 in p2 progenitors. Gata2 also participates in the maintenance of p2 domain by repressing motor neuron differentiation and exerting a feedback control on patterning genes. Finally, Gata2 promotes the selective activation of V2b program at the expense of V2a fate. Thus our results provide new insights on the hierarchy and complex interactions between regulators of V2 genetic program.

Easton functions and supercompactness

Suppose is -supercompact witnessed by an elementary embedding j : V ! M with critical point , and further suppose that F is a function from the class of regular cardinals to the class of cardinals satisfying the requirements of Easton's theorem: (1)8

Interneuron cell types are fit to function

Understanding brain circuits begins with an appreciation of their component parts - the cells. Although GABAergic interneurons are a minority population within the brain, they are crucial for the control of inhibition. Determining the diversity of these interneurons has been a central goal of neurobiologists, but this amazing cell type has so far defied a generalized classification system. Interneuron complexity within the telencephalon could be simplified by viewing them as elaborations of a much more finite group of developmentally specified cardinal classes that become further specialized as they mature. Our perspective emphasizes that the ultimate goal is to dispense with classification criteria and directly define interneuron types by function.

Identification of Multiple Subsets of Ventral Interneurons and Differential Distribution along the Rostrocaudal Axis of the Developing Spinal Cord

The spinal cord contains neuronal circuits termed Central Pattern Generators (CPGs) that coordinate rhythmic motor activities. CPG circuits consist of motor neurons and multiple interneuron cell types, many of which are derived from four distinct cardinal classes of ventral interneurons, called V0, V1, V2 and V3. While significant progress has been made on elucidating the molecular and genetic mechanisms that control ventral interneuron differentiation, little is known about their distribution along the antero-posterior axis of the spinal cord and their diversification. Here, we report that V0, V1 and V2 interneurons exhibit distinct organizational patterns at brachial, thoracic and lumbar levels of the developing spinal cord. In addition, we demonstrate that each cardinal class of ventral interneurons can be subdivided into several subsets according to the combinatorial expression of different sets of transcription factors, and that these subsets are differentially distributed along the rostrocaudal axis of the spinal cord. This comprehensive molecular profiling of ventral interneurons provides an important resource for investigating neuronal diversification in the developing spinal cord and for understanding the contribution of specific interneuron subsets on CPG circuits and motor control.

Borel Tukey morphisms and combinatorial cardinal invariants of the continuum

We discuss the Borel Tukey ordering on cardinal invariants of the continuum. We observe that this ordering makes sense for a larger class of cardinals than has previously been considered. We then provide a Borel version of a large portion of van Douwen's diagram. For instance, although the usual proof of the inequality $\mathfrak p\leq\mathfrak b$ does not provide a Borel Tukey map, we show that in fact there is one. Afterwards, we revisit a result of Mildenberger concerning a generalization of the unsplitting and splitting numbers. Lastly, we show that the inclusion ordering on $\mathcal P(\omega)$ embeds into the Borel Tukey ordering on cardinal invariants.

Large cardinals and definable well-orders on the universe

AbstractWe use a reverse Easton forcing iteration to obtain a universe with a definable well-order, while preserving the GCH and proper classes of a variety of very large cardinals. This is achieved by coding using the principle , at a proper class of cardinals κ. By choosing the cardinals at which coding occurs sufficiently sparsely, we are able to lift the embeddings witnessing the large cardinal properties without having to meet any non-trivial master conditions.

A differential developmental pattern of spinal interneuron apoptosis during synaptogenesis: insights from genetic analyses of the protocadherin-γ gene cluster

Although the role of developmental apoptosis in shaping the complement and connectivity of sensory and motoneurons is well documented, the extent to which cell death affects the 13 cardinal classes of spinal interneurons is unclear. Using a series of genetic manipulations in vivo, we demonstrate for the first time a differential pattern of developmental apoptosis in molecularly identified spinal interneuron populations, and implicate the adhesion molecule family encoded by the 22-member protocadherin-gamma (Pcdh-gamma) gene cluster in its control. In constitutive Pcdh-gamma null mouse embryos, many interneuron populations undergo increased apoptosis, but to differing extents: for example, over 80% of En1-positive V1 neurons are lost, whereas only 30% of Chx10-positive V2a neurons are lost and there is no reduction in the number of V1-derived Renshaw cells. We show that this represents an exacerbation of a normal, underlying developmental pattern: the extent of each population's decrease in Pcdh-gamma mutants is precisely commensurate both with the extent of its loss during normal embryogenesis and with the extent of its increase in Bax(-/-) mice, in which apoptosis is genetically blocked. Interneuron apoptosis begins during the first wave of synaptogenesisis in the spinal cord, occurring first among ventral populations (primarily between E14 and E17), and only later among dorsal populations (primarily after P0). Utilizing a new, conditional Pcdh-gamma mutant allele, we show that the gamma-Pcdhs can promote survival non-cell-autonomously: mutant neurons can survive if they are surrounded by normal neurons, and normal neurons can undergo apoptosis if they are surrounded by mutant neurons.

V3 Spinal Neurons Establish a Robust and Balanced Locomotor Rhythm during Walking

A robust and well-organized rhythm is a key feature of many neuronal networks, including those that regulate essential behaviors such as circadian rhythmogenesis, breathing, and locomotion. Here we show that excitatory V3-derived neurons are necessary for a robust and organized locomotor rhythm during walking. When V3-mediated neurotransmission is selectively blocked by the expression of the tetanus toxin light chain subunit (TeNT), the regularity and robustness of the locomotor rhythm is severely perturbed. A similar degeneration in the locomotor rhythm occurs when the excitability of V3-derived neurons is reduced acutely by ligand-induced activation of the allatostatin receptor. The V3-derived neurons additionally function to balance the locomotor output between both halves of the spinal cord, thereby ensuring a symmetrical pattern of locomotor activity during walking. We propose that the V3 neurons establish a regular and balanced motor rhythm by distributing excitatory drive between both halves of the spinal cord.

Ultrabright multikilovolt coherent tunable x-ray source at λ ∼ 2.71–2.93Å

Detailed molecular structural information of the living state is of enormoussignificance to the medical and biological communities. Since hydrated biologicallyactive structures are small delicate complex three-dimensional (3D) entities,it is essential to have molecular scale spatial resolution, high contrast,distortionless, direct 3D modalities of visualization of naturally functioningspecimens in order to faithfully reveal their full molecular architectures. Anx-ray holographic microscope equipped with an x-ray laser as the illuminatorwould be uniquely capable of providing these images. A quantitative interlockingconcordance of physical evidence, that includes (a) the observation ofstrong enhancement of selected spectral components of several Xeq+ hollow-atomtransition arrays (q = 31,32, 34, 35, 36, 37) radiated axially from confined plasma channels, (b)the measurement of line narrowing that is spectrally correlated with theamplified transitions, (c) evidence for spectral hole-burning in thespontaneous emission, a manifestation of saturated amplification, thatcorresponds spectrally with the amplified lines, and (d) the detection ofan intense narrow (δθx ∼ 0.2 mrad)directed beam of radiation, (1) experimentally demonstratesin the λ ∼ = 2.71–2.93 Årange (ℏωx ∼ = 4230–4570 eV)the operation of a new concept capable of producing the ideal conditions foramplification of multikilovolt x-rays and (2) proves the feasibility of acompact x-ray illuminator that can cost-effectively achieve the missionof biological x-ray microholography. The measurements also (α) establish theproperty of tunability in the quantum energy over a substantial fraction of the spectralregion exhibiting amplification (Δℏωx ∼ 345 eV) and(β)demonstrate the coherence of the x-ray output through the observation of acanonical spatial mode pattern. An analysis of the physical scaling revealed bythese results indicates that the capability of the x-ray source potentially includessingle-molecule microimaging, the key for the in situ structural analysis ofmembrane proteins, a cardinal class of drug targets. An estimate of the peakbrightness achieved in these initial experiments gives a value of ∼1031–1032 photons s−1 mm−2 mrad−2/(0.1% bandwidth),a magnitude that is ∼107–108-foldhigher than presently available synchrotron technology.

On a universal ultrametric space

For every cardinal τ we construct a universal ultrametric space LW τ such that any ultrametric space of weight ≤τ can be embedded isometrically in LW τ . The weight of LW τ is τ ℵ 0 and we show that for all cardinals τ≤c and for a wide class of cardinals >c the weight of a universal ultrametric space can not be smaller