Hamiltonian reductions of free particles under polar actions of compact Lie groups

Classical and quantum Hamiltonian reductions of free geodesic systems of complete Riemannian manifolds are investigated. The reduced systems are described under the assumption that the underlying compact symmetry group acts in a polar manner in the sense that there exist regularly embedded, closed, connected submanifolds meeting all orbits orthogonally in the configuration space. Hyperpolar actions on Lie groups and on symmetric spaces lead to families of integrable systems of spin Calogero-Sutherland type.Comment: 15 pages, minor correction and updated references in v

On extending actions of groups

Problems of dense and closed extension of actions of compact transformation groups are solved. The method developed in the paper is applied to problems of extension of equivariant maps and of construction of equivariant compactifications

Quantization of Midisuperspace Models

We give a comprehensive review of the quantization of midisuperspace models. Though the main focus of the paper is on quantum aspects, we also provide an introduction to several classical points related to the definition of these models. We cover some important issues, in particular, the use of the principle of symmetric criticality as a very useful tool to obtain the required Hamiltonian formulations. Two main types of reductions are discussed: those involving metrics with two Killing vector fields and spherically symmetric models. We also review the more general models obtained by coupling matter fields to these systems. Throughout the paper we give separate discussions for standard quantizations using geometrodynamical variables and those relying on loop quantum gravity inspired methods.Comment: To appear in Living Review in Relativit

Interrogating and Predicting Tolerated Sequence Diversity in Protein Folds: Application to E. elaterium Trypsin Inhibitor-II Cystine-Knot Miniprotein

Cystine-knot miniproteins (knottins) are promising molecular scaffolds for protein engineering applications. Members of the knottin family have multiple loops capable of displaying conformationally constrained polypeptides for molecular recognition. While previous studies have illustrated the potential of engineering knottins with modified loop sequences, a thorough exploration into the tolerated loop lengths and sequence space of a knottin scaffold has not been performed. In this work, we used the Ecballium elaterium trypsin inhibitor II (EETI) as a model member of the knottin family and constructed libraries of EETI loop-substituted variants with diversity in both amino acid sequence and loop length. Using yeast surface display, we isolated properly folded EETI loop-substituted clones and applied sequence analysis tools to assess the tolerated diversity of both amino acid sequence and loop length. In addition, we used covariance analysis to study the relationships between individual positions in the substituted loops, based on the expectation that correlated amino acid substitutions will occur between interacting residue pairs. We then used the results of our sequence and covariance analyses to successfully predict loop sequences that facilitated proper folding of the knottin when substituted into EETI loop 3. The sequence trends we observed in properly folded EETI loop-substituted clones will be useful for guiding future protein engineering efforts with this knottin scaffold. Furthermore, our findings demonstrate that the combination of directed evolution with sequence and covariance analyses can be a powerful tool for rational protein engineering

Astrocytes convert network excitation to tonic inhibition of neurons

<p>Abstract</p> <p>Background</p> <p>Glutamate and γ-aminobutyric acid (GABA) transporters play important roles in balancing excitatory and inhibitory signals in the brain. Increasing evidence suggest that they may act concertedly to regulate extracellular levels of the neurotransmitters.</p> <p>Results</p> <p>Here we present evidence that glutamate uptake-induced release of GABA from astrocytes has a direct impact on the excitability of pyramidal neurons in the hippocampus. We demonstrate that GABA, synthesized from the polyamine putrescine, is released from astrocytes by the reverse action of glial GABA transporter (GAT) subtypes GAT-2 or GAT-3. GABA release can be prevented by blocking glutamate uptake with the non-transportable inhibitor DHK, confirming that it is the glutamate transporter activity that triggers the reversal of GABA transporters, conceivably by elevating the intracellular Na⁺concentration in astrocytes. The released GABA significantly contributes to the tonic inhibition of neurons in a network activity-dependent manner. Blockade of the Glu/GABA exchange mechanism increases the duration of seizure-like events in the low-[Mg²⁺] <it>in vitro </it>model of epilepsy. Under <it>in vivo </it>conditions the increased GABA release modulates the power of gamma range oscillation in the CA1 region, suggesting that the Glu/GABA exchange mechanism is also functioning in the intact hippocampus under physiological conditions.</p> <p>Conclusions</p> <p>The results suggest the existence of a novel molecular mechanism by which astrocytes transform glutamat<it>ergic </it>excitation into GABA<it>ergic </it>inhibition providing an adjustable, <it>in situ </it>negative feedback on the excitability of neurons.</p