Neuronal firing patterns, neuromodulators, and cerebral metabolism change across sleep-waking states, and the synaptic release of glutamate is critically involved in these processes. Extrasynaptic glutamate can also affect neural function and may be neurotoxic, but whether and how extracellular glutamate is regulated across sleep-waking states is unclear. To assess the effect of behavioral state on extracellular glutamate at high temporal resolution, we recorded glutamate concentration in prefrontal and motor cortex using fixedpotential amperometry in freely behaving rats. Simultaneously, we recorded local field potentials (LFPs) and electroencephalograms (EEGs) from contralateral cortex. We observed dynamic, progressive changes in the concentration of glutamate that switched direction as a function of behavioral state. Specifically, the concentration of glutamate increased progressively during waking (0.329 Ϯ 0.06%/min) and rapid eye movement (REM) sleep (0.349 Ϯ 0.13%/min). This increase was opposed by a progressive decrease during non-REM (NREM) sleep (0.338 Ϯ 0.06%/min). During a 3 h sleep deprivation period, glutamate concentrations initially exhibited the progressive rise observed during spontaneous waking. As sleep pressure increased, glutamate concentrations ceased to increase and began decreasing despite continuous waking. During NREM sleep, the rate of decrease in glutamate was positively correlated with sleep intensity, as indexed by LFP slow-wave activity. The rate of decrease doubled during recovery sleep after sleep deprivation. Thus, the progressive increase in cortical extrasynaptic glutamate during EEG-activated states is counteracted by a decrease during NREM sleep that is modulated by sleep pressure. These results provide evidence for a long-term homeostasis of extracellular glutamate across sleep-waking states.

We investigate the relationship between the algebra of tensor categories and the topology of framed 3-manifolds. On the one hand, tensor categories with certain algebraic properties determine topological invariants. We prove that fusion categories of nonzero global dimension are 3-dualizable, and therefore provide 3dimensional 3-framed local field theories. We also show that all finite tensor categories are 2-dualizable, and yield categorified 2-dimensional 3-framed local field theories. On the other hand, topological properties of 3-framed manifolds determine algebraic equations among functors of tensor categories. We show that the 1-dimensional loop bordism, which exhibits a single full rotation, acts as the double dual autofunctor of a tensor category. We prove that the 2-dimensional belt-trick bordism, which unravels a double rotation, operates on any finite tensor category, and therefore supplies a trivialization of the quadruple dual. This approach produces a quadruple-dual theorem for suitably dualizable objects in any symmetric monoidal 3-category. There is furthermore a correspondence between algebraic structures on tensor categories and homotopy fixed point structures, which in turn provide structured field theories; we describe the expected connection between pivotal tensor categories and combed fixed point structures, and between spherical tensor categories and oriented fixed point structures.

Background: Shaker codes for a Drosophila voltage-dependent potassium channel. Flies carrying Shaker null or hypomorphic mutations sleep 3-4 h/day instead of 8-14 h/day as their wild-type siblings do. Shaker-like channels are conserved across species but it is unknown whether they affect sleep in mammals. To address this issue, we studied sleep in Kcna2 knockout (KO) mice. Kcna2 codes for Kv1.2, the alpha subunit of a Shaker-like voltage-dependent potassium channel with high expression in the mammalian thalamocortical system.

The balanced tensor product M ⊗ A N of two modules over an algebra A is the vector space corepresenting A-balanced bilinear maps out of the product M × N . The balanced tensor product M C N of two module categories over a monoidal linear category C is the linear category corepresenting C-balanced right-exact bilinear functors out of the product category M × N . We show that the balanced tensor product can be realized as a category of bimodule objects in C, provided the monoidal linear category is finite and rigid.Tensor categories are a higher dimensional analogue of algebras. Just as modules and bimodules play a key role in the theory of algebras, the analogous notions of module categories and bimodule categories play a key role in the study of tensor categories (as pioneered by Ostrik [Ost03]). One of the key constructions in the theory of modules and bimodules is the relative tensor product M ⊗ A N . As first recognized by Tambara [Tam01], a similarly important role is played by the balanced tensor product of module categories over a monoidal category M C N (for example, see [Müg03, ENO10, JL09, GS12b, GS12a, DNO13, FSV13]). For C = Vect, this agrees with Deligne's [Del90] tensor product K L of finite linear categories. Etingof, Nikshych, and Ostrik [ENO10] established the existence of a balanced tensor product M C N of finite semisimple module categories over a fusion category, and Davydov and Nikshych [DN13, §2.7] outlined how to generalize this construction to module categories over a finite tensor category. 1 We give a new construction of the balanced tensor product over a finite tensor category as a category of bimodule objects.Recall that the balanced tensor product M ⊗ A N of modules is, by definition, the vector space corepresenting A-balanced bilinear functions out of M × N . In other words, giving a map M ⊗ A N → X is the same as giving a billinear map f : M × N → X with the property that f (ma, n) = f (m, an). If the balanced tensor product exists, it is certainly unique (up to unique isomorphism), but the universal property does not guarantee existence. Instead existence is typically established by an explicit construction as a quotient of a free abelian group on the product M ×N . We now describe the balanced tensor product M C N of module categories over a tensor category. Again this should be universal for certain bilinear functors, however when passing from algebras to tensor categories, the analogue of the equality f (ma, n) = f (m, an) is a natural system of isomorphisms η m,a,n : F(m ⊗ a, n) → F(m, a ⊗ n) satisfying some natural coherence properties. A bilinear functor F together with a natural coherent system of isomorphisms η m,a,n is called a C-balanced functor. Thus the balanced tensor product M C N is defined to be the linear category corepresenting C-balanced right-exact bilinear functors out of M × N . In other words, giving a right-exact functor M C N → X is the same as giving a right-exact bilinear functor M × N → X together with isomorphisms η m,a,n : F(m ⊗ a, n) → F(m, a ⊗ n) sa...

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Intraperitoneal injection of an unmodified antisense peptide nucleic acid (PNA) complementary to mRNA of the rat neurotensin (NT) receptor (NTR1) was demonstrated by a gel shift assay to be present in brain, thus indicating that the PNA had in fact crossed the blood-brain barrier. An i.p. injection of this antisense PNA specifically inhibited the hypothermic and antinociceptive activities of NT microinjected into brain. These results were associated with a reduction in binding sites for NT both in brain and the small intestine. Additionally, the sense-NTR1 PNA, targeted to DNA, microinjected directly into the brain specifically reduced mRNA levels by 50% and caused a loss of response to NT. To demonstrate the specificity of changes in behavioral, binding, and mRNA studies, animals treated with NTR1 PNA were tested for behavioral responses to morphine and their mu receptor levels were determined. Both were found to be unaffected in these NTR1 PNA-treated animals. The effects of both the antisense and sense PNAs were completely reversible. This work provides evidence that any antisense strategy targeted to brain proteins can work through i.p. delivery by crossing the normal blood-brain barrier. Equally important was that an antigene strategy, the sense PNA, was shown in vivo to be a potentially effective therapeutic treatment.Peptide nucleic acids (PNAs), a new type of DNA analog ( Fig. 1), hold great promise as antisense or antigene drugs, because they are electrically neutral oligomers that are stable against nucleases and proteases, bind independently of salt concentration to their complementary nucleic acids, and have higher affinity for nucleic acids than do DNA͞DNA duplexes (1, 2). Additionally, PNA͞DNA duplexes are much more gene specific, because they are less tolerant of mismatches than are DNA͞DNA duplexes (3). Initial enthusiasm for their use as antisense or antigene drugs was dampened by the fact that these molecules pass poorly into cells (4, 5). Our laboratory reported that unmodified (carrier-free) PNAs, on their direct injection into rat brain, enter neuronal cells and inhibit protein synthesis in a gene-specific manner (6).To determine both the mechanism of action of PNAs and whether PNAs could pass the blood-brain barrier (BBB), brain neurotensin (NT) receptors (NTR1) again were targeted. After a single i.p. injection of antisense PNA to NTR1 (targeted to mRNA) behavioral and physiological responses to NT (antinociception and hypothermia) were specifically and almost completely lost. These results were accompanied by specific reductions in receptor sites as determined by radioligand binding assays. However, there were no changes in mRNA levels. A sensitive assay developed to detect the amount of PNAs in tissue (gel shift assay) confirmed the presence of PNA in brain after i.p. injection. Therefore, these results provided evidence that any antisense strategy targeted to brain proteins can work by i.p. delivery and by crossing the normal (i.e., not compromised by malignancy) BBB. Also, of ...