Equivariant Lefschetz maps for simplicial complexes and smooth manifolds

Let X be a locally compact space with a continuous proper action of a locally compact group G. Assuming that X satisfies a certain kind of duality in equivariant bivariant Kasparov theory, we can enrich the classical construction of Lefschetz numbers to equivariant K-homology classes. We compute the Lefschetz invariants for self-maps of finite-dimensional simplicial complexes and of self-maps of smooth manifolds. The resulting invariants are independent of the extra structure used to compute them. Since smooth manifolds can be triangulated, we get two formulas for the same Lefschetz invariant in these cases. The resulting identity is closely related to the equivariant Lefschetz Fixed Point Theorem of Luck and Rosenberg.Comment: Minor revisions, affecting some theorem number

Rodents and humans are able to detect the odour of L-Lactate.

This is the final version of the article. Available from PLoS via the DOI in this record.L-Lactate (LL) is an essential cellular metabolite which can be used to generate energy. In addition, accumulating evidence suggests that LL is used for inter-cellular signalling. Some LL-sensitive receptors have been identified but we recently proposed that there may be yet another unknown G-protein coupled receptor (GPCR) sensitive to LL in the brain. Olfactory receptors (ORs) represent the largest family of GPCRs and some of them are expressed outside the olfactory system, including brain, making them interesting candidates for non-olfactory LL signalling. One of the "ectopically" expressed ORs, Olfr78 in mice (Olr59 in rats and OR51E2 in humans), reportedly can be activated by LL. This implies that both rodents and humans should be able to detect the LL odour. Surprisingly, this has never been demonstrated. Here we show that mice can detect the odour of LL in odour detection and habituation-dishabituation tasks, and discriminate it from peppermint and vanilla odours. Behaviour of the Olfr78 null mice and wildtype mice in odour detection task was not different, indicating that rodents are equipped with more than one LL-sensitive OR. Rats were also able to use the smell of LL as a cue in an odour-reward associative learning task. When presented to humans, more than 90% of participants detected a smell of LL in solution. Interestingly, LL was perceived differently than acetate or propionate-LL was preferentially reported as a pleasant sweet scent while acetate and propionate were perceived as repulsive sour/acid smells. Subjective perception of LL smell was different in men and women. Taken together, our data demonstrate that both rodents and humans are able to detect the odour of LL. Moreover, in mice, LL perception is not purely mediated by Olfr78. Discovery of further LL-sensitive OR might shed the light on their contribution to LL signalling in the body.This work was supported by BBSRC: BB/L019396/1, BB/K009192/1; and MRC MR/L020661/1. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript

Expression of Microbial Enzymes in Mammalian Astrocytes to Modulate Lactate Release

Astrocytes support and modulate neuronal activity through the release of L-lactate. The suggested roles of astrocytic lactate in the brain encompass an expanding range of vital functions, including central control of respiration and cardiovascular performance, learning, memory, executive behaviour and regulation of mood. Studying the effects of astrocytic lactate requires tools that limit the release of lactate selectively from astrocytes. Here, we report the validation in vitro of novel molecular constructs derived from enzymes originally found in bacteria, that when expressed in astrocytes, interfere with lactate handling. When lactate 2-monooxygenase derived from M. smegmatis was specifically expressed in astrocytes, it reduced intracellular lactate pools as well as lactate release upon stimulation. D-lactate dehydrogenase derived from L. bulgaricus diverts pyruvate towards D-lactate production and release by astrocytes, which may affect signalling properties of lactate in the brain. Together with lactate oxidase, which we have previously described, this set of transgenic tools can be employed to better understand astrocytic lactate release and its role in the regulation of neuronal activity in different behavioural contexts

Equivariant comparison of quantum homogeneous spaces

We prove the deformation invariance of the quantum homogeneous spaces of the q-deformation of simply connected simple compact Lie groups over the Poisson-Lie quantum subgroups, in the equivariant KK-theory with respect to the translation action by maximal tori. This extends a result of Neshveyev-Tuset to the equivariant setting. As applications, we prove the ring isomorphism of the K-group of Gq with respect to the coproduct of C(Gq), and an analogue of the Borsuk-Ulam theorem for quantum spheres.Comment: 21 page

Some Remarks on Group Bundles and C*-dynamical systems

We introduce the notion of fibred action of a group bundle on a C(X)-algebra. By using such a notion, a characterization in terms of induced C*-bundles is given for C*-dynamical systems such that the relative commutant of the fixed-point algebra is minimal (i.e., it is generated by the centre of the given C*-algebra and the centre of the fixed-point algebra). A class of examples in the setting of the Cuntz algebra is given, and connections with superselection structures with nontrivial centre are discussed.Comment: 22 pages; to appear on Comm. Math. Phy

The Baum-Connes Conjecture via Localisation of Categories

We redefine the Baum-Connes assembly map using simplicial approximation in the equivariant Kasparov category. This new interpretation is ideal for studying functorial properties and gives analogues of the assembly maps for all equivariant homology theories, not just for the K-theory of the crossed product. We extend many of the known techniques for proving the Baum-Connes conjecture to this more general setting

Glio- and neuroprotection by prosaposin is mediated by orphan G-protein coupled receptors GPR37L1 and GPR37

This is the author accepted manuscript. Available on open access from Wiley via the DOI in this recordDiscovery of neuroprotective pathways is one of the major priorities for neuroscience. Astrocytes are the natural neuroprotectors and it is likely that brain resilience can be enhanced by mobilising their protective potential. Among G-protein coupled receptors expressed by astrocytes, two highly related receptors, GPR37L1 and GPR37, are of particular interest. Previous studies suggested that these receptors are activated by a peptide Saposin C and its neuroactive fragments (such as prosaptide TX14), which were demonstrated to be neuroprotective in various animal models by several groups. However, pairing of Saposin C or prosaptides with GPR37L1/GPR37 has been challenged and presently GPR37L1/GPR37 have regained their orphan status. Here we demonstrate that in their natural habitat, astrocytes, these receptors mediate a range of effects of TX14, including protection from oxidative stress. The Saposin C/GPR37L1/GPR37 pathway is also involved in the neuroprotective effect of astrocytes on neurons subjected to oxidative stress. The action of TX14 is at least partially mediated by Gi-proteins and the cAMP-PKA axis. On the other hand, when recombinant GPR37L1 or GPR37 are expressed in HEK293 cells, they are not functional and do not respond to TX14, which explains unsuccessful attempts to confirm the ligand-receptor pairing. Therefore this study identifies GPR37L1/GPR37 as the receptors for TX14, and, by extension of Saposin C, and paves the way for the development of neuroprotective therapeutics acting via these receptors.Biotechnology and Biological Sciences Research CouncilMedical Research Council (MRC

Cardioprotection evoked by remote ischaemic preconditioning is critically dependent on the activity of vagal pre-ganglionic neurones

AIMS: Innate mechanisms of inter-organ protection underlie the phenomenon of remote ischaemic preconditioning (RPc) in which episode(s) of ischaemia and reperfusion in tissues remote from the heart reduce myocardial ischaemia/reperfusion injury. The uncertainty surrounding the mechanism(s) underlying RPc centres on whether humoral factor(s) produced during ischaemia/reperfusion of remote tissue and released into the systemic circulation mediate RPc, or whether a neural signal is required. While these two hypotheses may not be incompatible, one approach to clarify the potential role of a neural pathway requires targeted disruption or activation of discrete central nervous substrate(s). METHODS AND RESULTS: Using a rat model of myocardial ischaemia/reperfusion injury in combination with viral gene transfer, pharmaco-, and optogenetics, we tested the hypothesis that RPc cardioprotection depends on the activity of vagal pre-ganglionic neurones and consequently an intact parasympathetic drive. For cell-specific silencing or activation, neurones of the brainstem dorsal motor nucleus of the vagus nerve (DVMN) were targeted using viral vectors to express a Drosophila allatostatin receptor (AlstR) or light-sensitive fast channelrhodopsin variant (ChIEF), respectively. RPc cardioprotection, elicited by ischaemia/reperfusion of the limbs, was abolished when DVMN neurones transduced to express AlstR were silenced by selective ligand allatostatin or in conditions of systemic muscarinic receptor blockade with atropine. In the absence of remote ischaemia/reperfusion, optogenetic activation of DVMN neurones transduced to express ChIEF reduced infarct size, mimicking the effect of RPc. CONCLUSION: These data indicate a crucial dependence of RPc cardioprotection against ischaemia/reperfusion injury upon the activity of a distinct population of vagal pre-ganglionic neurones

Piano Studio Recital, September 24, 2019

Carter Campbell, from the studio of Professor Kasparov Andrei S. Johnson, from the studio of Professor Lutsyshyn Joel Sanford, from the studio of Professor Toomey Robert Stahl, from the studio of Professor Rayd

Astrocytes modulate baroreflex sensitivity at the level of the nucleus of the solitary tract

Maintenance of cardiorespiratory homeostasis depends on autonomic reflexes controlled by neuronal circuits of the brainstem. The neurophysiology and neuroanatomy of these reflex pathways are well understood, however, the mechanisms and functional significance of autonomic circuit modulation by glial cells remain largely unknown. In experiments conducted in male laboratory rats we show that astrocytes of the nucleus tractus solitarii (NTS), the brain area that receives and integrates sensory information from the heart and blood vessels, respond to incoming afferent inputs with [Ca2+]i elevations. Astroglial [Ca2+]i responses are triggered by transmitters released by vagal afferents, glutamate acting at AMPA receptors and 5-HT acting at 5-HT2A receptors. In conscious freely behaving animals blockade of Ca2+-dependent vesicular mechanisms in NTS astrocytes by virally driven expression of a dominant-negative SNARE protein (dnSNARE) increased baroreflex sensitivity by 70% (p<0.001). The effect of compromised astroglial function was specific to the NTS as expression of dnSNARE in astrocytes of the ventrolateral brainstem had no effect. ATP considered the principle gliotransmitter and is released by vesicular mechanisms affected by dnSNARE expression. Consistent with this hypothesis, in anesthetized rats, activation P2Y1 purinoceptors in the NTS decreased baroreflex gain by 40% (p=0.031), while blockade of P2Y1 receptors increased baroreflex gain by 57% (p=0.018). These results suggest that glutamate and 5-HT released by NTS afferent terminals trigger Ca2+-dependent astroglial release of ATP to modulate baroreflex sensitivity via P2Y1 receptors. These data add to the growing body of evidence supporting an active role of astrocytes in the brain information processing