Nonsoluble and non-p-soluble length of finite groups

Every finite group G has a normal series each of whose factors either is soluble or is a direct product of nonabelian simple groups. We define the nonsoluble length λ(G) as the number of nonsoluble factors in a shortest series of this kind. Upper bounds for λ(G) appear in the study of various problems on finite, residually finite, and profinite groups. We prove that λ(G) is bounded in terms of the maximum 2-length of soluble subgroups of G, and that λ(G) is bounded by the maximum Fitting height of soluble subgroups. For an odd prime p, the non-p-soluble length λ p (G) is introduced, and it is proved that λ p (G) does not exceed the maximum p-length of p-soluble subgroups. We conjecture that for a given prime p and a given proper group variety V the non-p-soluble length λ p (G) of finite groups G whose Sylow p-subgroups belong to V is bounded. In this paper we prove this conjecture for any variety that is a product of several soluble varieties and varieties of finite exponent. As an application of the results obtained, an error is corrected in the proof of the main result of the second author’s paper Multilinear commutators in residually finite groups, Israel Journal of Mathematics 189 (2012), 207–224

Locally finite groups containing a 2 -element with Chernikov centralizer

Suppose that a locally finite group G has a 2-element g with Chernikov centralizer. It is proved that if the involution in ⟨g⟩ has nilpotent centralizer, then G has a soluble subgroup of finite index

Murine GRPR and Stathmin Control in Opposite Directions both Cued Fear Extinction and Neural Activities of the Amygdala and Prefrontal Cortex

Extinction is an integral part of normal healthy fear responses, while it is compromised in several fear-related mental conditions in humans, such as post-traumatic stress disorder (PTSD). Although much research has recently been focused on fear extinction, its molecular and cellular underpinnings are still unclear. The development of animal models for extinction will greatly enhance our approaches to studying its neural circuits and the mechanisms involved. Here, we describe two gene-knockout mouse lines, one with impaired and another with enhanced extinction of learned fear. These mutant mice are based on fear memory-related genes, stathmin and gastrin-releasing peptide receptor (GRPR). Remarkably, both mutant lines showed changes in fear extinction to the cue but not to the context. We performed indirect imaging of neuronal activity on the second day of cued extinction, using immediate-early gene c-Fos. GRPR knockout mice extinguished slower (impaired extinction) than wildtype mice, which was accompanied by an increase in c-Fos activity in the basolateral amygdala and a decrease in the prefrontal cortex. By contrast, stathmin knockout mice extinguished faster (enhanced extinction) and showed a decrease in c-Fos activity in the basolateral amygdala and an increase in the prefrontal cortex. At the same time, c-Fos activity in the dentate gyrus was increased in both mutant lines. These experiments provide genetic evidence that the balance between neuronal activities of the amygdala and prefrontal cortex defines an impairment or facilitation of extinction to the cue while the hippocampus is involved in the context-specificity of extinction

Brain and blood biomarkers of tauopathy and neuronal injury in humans and rats with neurobehavioral syndromes following blast exposure

Traumatic brain injury (TBI) is a risk factor for the later development of neurodegenerative diseases that may have various underlying pathologies. Chronic traumatic encephalopathy (CTE) in particular is associated with repetitive mild TBI (mTBI) and is characterized pathologically by aggregation of hyperphosphorylated tau into neurofibrillary tangles (NFTs). CTE may be suspected when behavior, cognition, and/or memory deteriorate following repetitive mTBI. Exposure to blast overpressure from improvised explosive devices (IEDs) has been implicated as a potential antecedent for CTE amongst Iraq and Afghanistan Warfighters. In this study, we identified biomarker signatures in rats exposed to repetitive low-level blast that develop chronic anxiety-related traits and in human veterans exposed to IED blasts in theater with behavioral, cognitive, and/or memory complaints. Rats exposed to repetitive low-level blasts accumulated abnormal hyperphosphorylated tau in neuronal perikarya and perivascular astroglial processes. Using positron emission tomography (PET) and the [18F]AV1451 (flortaucipir) tau ligand, we found that five of 10 veterans exhibited excessive retention of [18F]AV1451 at the white/gray matter junction in frontal, parietal, and temporal brain regions, a typical localization of CTE tauopathy. We also observed elevated levels of neurofilament light (NfL) chain protein in the plasma of veterans displaying excess [18F]AV1451 retention. These findings suggest an association linking blast injury, tauopathy, and neuronal injury. Further study is required to determine whether clinical, neuroimaging, and/or fluid biomarker signatures can improve the diagnosis of long-term neuropsychiatric sequelae of mTBI

Lmo4 in the Basolateral Complex of the Amygdala Modulates Fear Learning

Pavlovian fear conditioning is an associative learning paradigm in which mice learn to associate a neutral conditioned stimulus with an aversive unconditioned stimulus. In this study, we demonstrate a novel role for the transcriptional regulator Lmo4 in fear learning. LMO4 is predominantly expressed in pyramidal projection neurons of the basolateral complex of the amygdala (BLC). Mice heterozygous for a genetrap insertion in the Lmo4 locus (Lmo4gt/+), which express 50% less Lmo4 than their wild type (WT) counterparts display enhanced freezing to both the context and the cue in which they received the aversive stimulus. Small-hairpin RNA-mediated knockdown of Lmo4 in the BLC, but not the dentate gyrus region of the hippocampus recapitulated this enhanced conditioning phenotype, suggesting an adult- and brain region-specific role for Lmo4 in fear learning. Immunohistochemical analyses revealed an increase in the number of c-Fos positive puncta in the BLC of Lmo4gt/+ mice in comparison to their WT counterparts after fear conditioning. Lastly, we measured anxiety-like behavior in Lmo4gt/+ mice and in mice with BLC-specific downregulation of Lmo4 using the elevated plus maze, open field, and light/dark box tests. Global or BLC-specific knockdown of Lmo4 did not significantly affect anxiety-like behavior. These results suggest a selective role for LMO4 in the BLC in modulating learned but not unlearned fear

Gastrin-Releasing Peptide Signaling Plays a Limited and Subtle Role in Amygdala Physiology and Aversive Memory

Links between synaptic plasticity in the lateral amygdala (LA) and Pavlovian fear learning are well established. Neuropeptides including gastrin-releasing peptide (GRP) can modulate LA function. GRP increases inhibition in the LA and mice lacking the GRP receptor (GRPR KO) show more pronounced and persistent fear after single-trial associative learning. Here, we confirmed these initial findings and examined whether they extrapolate to more aspects of amygdala physiology and to other forms of aversive associative learning. GRP application in brain slices from wildtype but not GRPR KO mice increased spontaneous inhibitory activity in LA pyramidal neurons. In amygdala slices from GRPR KO mice, GRP did not increase inhibitory activity. In comparison to wildtype, short- but not long-term plasticity was increased in the cortico-lateral amygdala (LA) pathway of GRPR KO amygdala slices, whereas no changes were detected in the thalamo-LA pathway. In addition, GRPR KO mice showed enhanced fear evoked by single-trial conditioning and reduced spontaneous firing of neurons in the central nucleus of the amygdala (CeA). Altogether, these results are consistent with a potentially important modulatory role of GRP/GRPR signaling in the amygdala. However, administration of GRP or the GRPR antagonist (D-Phe6, Leu-NHEt13, des-Met14)-Bombesin (6–14) did not affect amygdala LTP in brain slices, nor did they affect the expression of conditioned fear following intra-amygdala administration. GRPR KO mice also failed to show differences in fear expression and extinction after multiple-trial fear conditioning, and there were no differences in conditioned taste aversion or gustatory neophobia. Collectively, our data indicate that GRP/GRPR signaling modulates amygdala physiology in a paradigm-specific fashion that likely is insufficient to generate therapeutic effects across amygdala-dependent disorders

Increased Stathmin1 Expression in the Dentate Gyrus of Mice Causes Abnormal Axonal Arborizations

Pituitary adenylate cyclase-activating polypeptide (PACAP) is involved in multiple brain functions. To clarify the cause of abnormal behavior in PACAP deficient-mice, we attempted the identification of genes whose expression was altered in the dentate gyrus of PACAP-deficient mice using the differential display method. Expression of stathmin1 was up-regulated in the dentate gyrus at both the mRNA and protein levels. PACAP stimulation inhibited stathmin1 expression in PC12 cells, while increased stathmin1expression in neurons of the subgranular zone and in primary cultured hippocampal neurons induced abnormal arborization of axons. We also investigated the pathways involved in PACAP deficiency. Ascl1 binds to E10 box of the stathmin1 promoter and increases stathmin1 expression. Inhibitory bHLH proteins (Hes1 and Id3) were rapidly up-regulated by PACAP stimulation, and Hes1 could suppress Ascl1 expression and Id3 could inhibit Ascl1 signaling. We also detected an increase of stathmin1 expression in the brains of schizophrenic patients. These results suggest that up-regulation of stathmin1 in the dentate gyrus, secondary to PACAP deficiency, may create abnormal neuronal circuits that cause abnormal behavior

Neurofilament depletion improves microtubule dynamics via modulation of Stat3/stathmin signaling

In neurons, microtubules form a dense array within axons, and the stability and function of this microtubule network is modulated by neurofilaments. Accumulation of neurofilaments has been observed in several forms of neurodegenerative diseases, but the mechanisms how elevated neurofilament levels destabilize axons are unknown so far. Here, we show that increased neurofilament expression in motor nerves of pmn mutant mice, a model of motoneuron disease, causes disturbed microtubule dynamics. The disease is caused by a point mutation in the tubulin-specific chaperone E (Tbce) gene, leading to an exchange of the most C-terminal amino acid tryptophan to glycine. As a consequence, the TBCE protein becomes instable which then results in destabilization of axonal microtubules and defects in axonal transport, in particular in motoneurons. Depletion of neurofilament increases the number and regrowth of microtubules in pmn mutant motoneurons and restores axon elongation. This effect is mediated by interaction of neurofilament with the stathmin complex. Accumulating neurofilaments associate with stathmin in axons of pmn mutant motoneurons. Depletion of neurofilament by Nefl knockout increases Stat3-stathmin interaction and stabilizes the microtubules in pmn mutant motoneurons. Consequently, counteracting enhanced neurofilament expression improves axonal maintenance and prolongs survival of pmn mutant mice. We propose that this mechanism could also be relevant for other neurodegenerative diseases in which neurofilament accumulation and loss of microtubules are prominent features