298 research outputs found
Differential sensitivity of brainstem vs cortical astrocytes to changes in pH reveals functional regional specialization of astroglia
Astrocytes might function as brain interoceptors capable of detecting different (chemo)sensory modalities and transmitting sensory information to the relevant neural networks controlling vital functions. For example, astrocytes which reside near the ventral surface of the brainstem (central respiratory chemosensitive area) respond to physiological decreases in pH with vigorous elevations in intracellular Ca(2+) and release of ATP. ATP transmits astroglial excitation to the brainstem respiratory network and contributes to adaptive changes in lung ventilation. Here we show that in terms of pH-sensitivity ventral brainstem astrocytes are clearly distinct from astrocytes residing in the cerebral cortex. We monitored vesicular fusion in cultured rat brainstem astrocytes using total internal reflection fluorescence microscopy and found that approximately 35% of them respond to acidification with an increased rate of exocytosis of ATP-containing vesicular compartments. These fusion events require intracellular Ca(2+) signaling and are independent of autocrine ATP actions. In contrast, the rate of vesicular fusion in cultured cortical astrocytes is not affected by changes in pH. Compared to cortical astrocytes, ventral brainstem astrocytes display higher levels of expression of genes encoding proteins associated with ATP vesicular transport and fusion, including vesicle-associated membrane protein-3 and vesicular nucleotide transporter. These results suggest that astrocytes residing in different parts of the rat brain are functionally specialized. In contrast to cortical astrocytes, astrocytes of the brainstem chemosensitive area(s) possess signaling properties which are functionally relevant – they are able to sense changes in pH and respond to acidification with enhanced vesicular release of ATP
Equivariant geometric K-homology for compact Lie group actions
Let G be a compact Lie-group, X a compact G-CW-complex. We define equivariant
geometric K-homology groups K^G_*(X), using an obvious equivariant version of
the (M,E,f)-picture of Baum-Douglas for K-homology. We define explicit natural
transformations to and from equivariant K-homology defined via KK-theory (the
"official" equivariant K-homology groups) and show that these are isomorphism.Comment: 25 pages. v2: some mistakes corrected, more detail added, Michael
Walter as author added. To appear in Abhandlungen aus dem Mathematischen
Seminar der Universit\"at Hambur
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
Operator *-correspondences in analysis and geometry
An operator *-algebra is a non-selfadjoint operator algebra with completely
isometric involution. We show that any operator *-algebra admits a faithful
representation on a Hilbert space in such a way that the involution coincides
with the operator adjoint up to conjugation by a symmetry. We introduce
operator *-correspondences as a general class of inner product modules over
operator *-algebras and prove a similar representation theorem for them. From
this we derive the existence of linking operator *-algebras for operator
*-correspondences. We illustrate the relevance of this class of inner product
modules by providing numerous examples arising from noncommutative geometry.Comment: 31 pages. This work originated from the MFO workshop "Operator spaces
and noncommutative geometry in interaction
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
Uniformization and an Index Theorem for Elliptic Operators Associated with Diffeomorphisms of a Manifold
We consider the index problem for a wide class of nonlocal elliptic operators
on a smooth closed manifold, namely differential operators with shifts induced
by the action of an isometric diffeomorphism. The key to the solution is the
method of uniformization: We assign to the nonlocal problem a
pseudodifferential operator with the same index, acting in sections of an
infinite-dimensional vector bundle on a compact manifold. We then determine the
index in terms of topological invariants of the symbol, using the Atiyah-Singer
index theorem.Comment: 16 pages, no figure
A Short Survey of Noncommutative Geometry
We give a survey of selected topics in noncommutative geometry, with some
emphasis on those directly related to physics, including our recent work with
Dirk Kreimer on renormalization and the Riemann-Hilbert problem. We discuss at
length two issues. The first is the relevance of the paradigm of geometric
space, based on spectral considerations, which is central in the theory. As a
simple illustration of the spectral formulation of geometry in the ordinary
commutative case, we give a polynomial equation for geometries on the four
dimensional sphere with fixed volume. The equation involves an idempotent e,
playing the role of the instanton, and the Dirac operator D. It expresses the
gamma five matrix as the pairing between the operator theoretic chern
characters of e and D. It is of degree five in the idempotent and four in the
Dirac operator which only appears through its commutant with the idempotent. It
determines both the sphere and all its metrics with fixed volume form.
We also show using the noncommutative analogue of the Polyakov action, how to
obtain the noncommutative metric (in spectral form) on the noncommutative tori
from the formal naive metric. We conclude on some questions related to string
theory.Comment: Invited lecture for JMP 2000, 45
Fluxes, Brane Charges and Chern Morphisms of Hyperbolic Geometry
The purpose of this paper is to provide the reader with a collection of
results which can be found in the mathematical literature and to apply them to
hyperbolic spaces that may have a role in physical theories. Specifically we
apply K-theory methods for the calculation of brane charges and RR-fields on
hyperbolic spaces (and orbifolds thereof). It is known that by tensoring
K-groups with the rationals, K-theory can be mapped to rational cohomology by
means of the Chern character isomorphisms. The Chern character allows one to
relate the analytic Dirac index with a topological index, which can be
expressed in terms of cohomological characteristic classes. We obtain explicit
formulas for Chern character, spectral invariants, and the index of a twisted
Dirac operator associated with real hyperbolic spaces. Some notes for a
bivariant version of topological K-theory (KK-theory) with its connection to
the index of the twisted Dirac operator and twisted cohomology of hyperbolic
spaces are given. Finally we concentrate on lower K-groups useful for
description of torsion charges.Comment: 26 pages, no figures, LATEX. To appear in the Classical and Quantum
Gravit
Homology and K--Theory Methods for Classes of Branes Wrapping Nontrivial Cycles
We apply some methods of homology and K-theory to special classes of branes
wrapping homologically nontrivial cycles. We treat the classification of
four-geometries in terms of compact stabilizers (by analogy with Thurston's
classification of three-geometries) and derive the K-amenability of Lie groups
associated with locally symmetric spaces listed in this case. More complicated
examples of T-duality and topology change from fluxes are also considered. We
analyse D-branes and fluxes in type II string theory on with torsion flux and demonstrate in details
the conjectured T-duality to with no flux. In the
simple case of , T-dualizing the circles reduces to
duality between with
flux and with no flux.Comment: 27 pages, tex file, no figure
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