Decompositions of complete tripartite graphs into triangles with an edge attached

Let K(r, s, t) denote the complete tripartite graph with partite sets of size r, s and t, where r less than or equal to s less than or equal to t. Let D be the graph consisting of a triangle with an edge attached. We show that K(r, s, t) may be decomposed into copies of D if and only if 4 divides rs + st + rt and t less than or equal to 3rs/(r + s).

Bright tripartite entanglement in triply concurrent parametric oscillation

We show that an optical parametric oscillator based on three concurrent chi((2)) nonlinearities can produce, above threshold, bright output beams of macroscopic intensities which exhibit strong tripartite continuous-variable entanglement. We also show that there are two ways that the system can exhibit a three-mode form of the Einstein-Podolsky-Rosen paradox, and calculate the extracavity fluctuation spectra that may be measured to verify our predictions.

Continuous variable tripartite entanglement and Einstein-Podolsky-Rosen correlations from triple nonlinearities

We compare theoretically the tripartite entanglement available from the use of three concurrent x(2) nonlinearities and three independent squeezed states mixed on beamsplitters, using an appropriate version of the van Loock-Furusawa inequalities. We also define three-mode generalizations of the Einstein-Podolsky-Rosen paradox which are an alternative for demonstrating the inseparability of the density matrix.

Continuous variable tripartite entanglement from twin nonlinearities

In this work, we analyse and compare the continuous variable tripartite entanglement available from the use of two concurrent or cascaded X (2) nonlinearities. We examine both idealized travelling-wave models and more experimentally realistic intracavity models, showing that tripartite entangled outputs are readily producible. These may be a useful resource for applications such as quantum cryptography and teleportation.

Ca2+-activated K+(BK) channel inactivation contributes to spike broadening during repetitive firing in the rat lateral amygdala

In many neurons, trains of action potentials show frequency-dependent broadening. This broadening results from the voltage-dependent inactivation of K+ currents that contribute to action potential repolarisation. In different neuronal cell types these K+ currents have been shown to be either slowly inactivating delayed rectifier type currents or rapidly inactivating A-type voltage-gated K+ currents. Recent findings show that inactivation of a Ca2+-dependent K+ current, mediated by large conductance BK-type channels, also contributes to spike broadening. Here, using whole-cell recordings in acute slices, we examine spike broadening in lateral amygdala projection neurons. Spike broadening is frequency dependent and is reversed by brief hyperpolarisations. This broadening is reduced by blockade of voltage-gated Ca2+ channels and BK channels. In contrast, broadening is not blocked by high concentrations of 4-aminopyridine (4-AP) or alpha-dendrotoxin. We conclude that while inactivation of BK-type Ca2+-activated K+ channels contributes to spike broadening in lateral amygdala neurons, inactivation of another as yet unidentified outward current also plays a role.

Neuromuscular synapses mediate motor axon branching and motoneuron survival during the embryonic period of programmed cell death

The embryonic period of motoneuron programmed cell death (PCD) is marked by transient motor axon branching, but the role of neuromuscular synapses in regulating motoneuron number and axonal branching is not known. Here, we test whether neuromuscular synapses are required for the quantitative association between reduced skeletal muscle contraction, increased motor neurite branching, and increased motoneuron survival. We achieved this by comparing agrin and rapsyn mutant mice that lack acetylcholine receptor (AChR) clusters. There were significant reductions in nerve-evoked skeletal muscle contraction, increases in intramuscular axonal branching, and increases in spinal motoneuron survival in agrin and rapsyn mutant mice compared with their wild-type littermates at embryonic day 18.5 (E18.5). The maximum nerve-evoked skeletal muscle contraction was reduced a further 17% in agrin mutants than in rapsyn mutants. This correlated to an increase in motor axon branch extension and number that was 38% more in agrin mutants than in rapsyn mutants. This suggests that specializations of the neuromuscular synapse that ensure efficient synaptic transmission and muscle contraction are also vital mediators of motor axon branching. However, these increases in motor axon branching did not correlate with increases in motoneuron survival when comparing agrin and rapsyn mutants. Thus, agrin-induced synaptic specializations are required for skeletal muscle to effectively control motoneuron numbers during embryonic development. (C) 2003 Elsevier Science (USA). All rights reserved.

The LFA-1-associated molecule PTA-1 (CD226) on T cells forms a dynamic molecular complex with protein 4.1G and human discs large

Clustering of the T cell integrin, LFA-1, at specialized regions of intercellular contact initiates integrin-mediated adhesion and downstream signaling, events that are necessary for a successful immunological response. But how clustering is achieved and sustained is not known. Here we establish that an LFA-1-associated molecule, PTA-1, is localized to membrane rafts and binds the carboxyl-terminal domain of isoforms of the actin-binding protein 4.1G. Protein 4.1 is known to associate with the membrane-associated guanylate kinase homologue, human discs large. We show that the carboxyl-terminal peptide of PTA-1 also can bind human discs large and that the presence or absence of this peptide greatly influences binding between PTA-1 and different isoforms of 4.1G. T cell stimulation with phorbol ester or PTA-1 cross-linking induces PTA-1 and 4.1G to associate tightly with the cytoskeleton, and the PTA-1 from such activated cells now can bind to the amino-terminal region of 4.1G. We propose that these dynamic associations provide the structural basis for a regulated molecular adhesive complex that serves to cluster and transport LFA-1 and associated molecules.

Changes to peptide structure, not concentration, contribute to expansion of the lowest avidity cytotoxic T lymphocytes

The efficient in vitro expansion of antigen-specific CD8(+) cytotoxic T lymphocytes (CTL) for use in adoptive immunotherapy represents an important clinical goal. Furthermore, the avidity of expanded CTL populations often correlates closely with clinical outcome. In our study, high-avidity CTL lines could be expanded ex vivo from an antigen-primed animal using low peptide concentration, and intermediate peptide concentrations favored the generation of lower avidity CTL. Further increases in peptide concentration during culture inhibited the expansion of all peptide-specific CD8(+) cells. In contrast, a single amino acid variant peptide efficiently generated functional CTL populations at high or low peptide concentration, which responded to wild-type epitope with the lowest average avidity seen in this study. We propose that for some peptides, the efficient generation of low-avidity CTL responses will be favored by stimulation with altered peptide rather than high concentrations of wild-type epitope. In addition, some variant peptides designed to have improved binding to major histocompatibility complex class I may reduce rather than enhance the functional avidity for the wild-type peptide of ex vivo-expanded CTL. These observations are relevant to in vitro expansion of CTL for immunotherapy and strategies to elicit regulatory or therapeutic immunity to neo-self-antigen when central tolerance has eliminated high-avidity, cognate T cells.

Critical fluctuations and entanglement in the nondegenerate parametric oscillator

We present a fully quantum mechanical treatment of the nondegenerate optical parametric oscillator both below and near threshold. This is a nonequilibrium quantum system with a critical point phase transition, that is also known to exhibit strong yet easily observed squeezing and quantum entanglement. Our treatment makes use of the positive P representation and goes beyond the usual linearized theory. We compare our analytical results with numerical simulations and find excellent agreement. We also carry out a detailed comparison of our results with those obtained from stochastic electrodynamics, a theory obtained by truncating the equation of motion for the Wigner function, with a view to locating regions of agreement and disagreement between the two. We calculate commonly used measures of quantum behavior including entanglement, squeezing, and Einstein-Podolsky-Rosen (EPR) correlations as well as higher order tripartite correlations, and show how these are modified as the critical point is approached. These results are compared with those obtained using two degenerate parametric oscillators, and we find that in the near-critical region the nondegenerate oscillator has stronger EPR correlations. In general, the critical fluctuations represent an ultimate limit to the possible entanglement that can be achieved in a nondegenerate parametric oscillator.

Glycinergic and GABAergic synaptic activity differentially regulate motoneuron survival and skeletal muscle innervation

GABAergic and glycinergic synaptic transmission is proposed to promote the maturation and refinement of the developing CNS. Here we provide morphological and functional evidence that glycinergic and GABAergic synapses control motoneuron development in a region-specific manner during programmed cell death. In gephyrin-deficient mice that lack all postsynaptic glycine receptor and some GABA(A) receptor clusters, there was increased spontaneous respiratory motor activity, reduced respiratory motoneuron survival, and decreased innervation of the diaphragm. In contrast, limb-innervating motoneurons showed decreased spontaneous activity, increased survival, and increased innervation of their target muscles. Both GABA and glycine increased limb-innervating motoneuron activity and decreased respiratory motoneuron activity in wild-type mice, but only glycine responses were abolished in gephyrin-deficient mice. Our results provide genetic evidence that the development of glycinergic and GABAergic synaptic inputs onto motoneurons plays an important role in the survival, axonal branching, and spontaneous activity of motoneurons in developing mammalian embryos.

Correlation of non-uniform protein expression with variation in transmitter release probability

The strength of synaptic transmission is highly variable between different synapses. The present study examined some factors that may contribute to this variation in the strength of neurotransmission in sympathetic varicosities of the mouse vas deferens. Transmitter release was measured using a focal macropatch electrode placed over pairs of visualised varicosities. By regulating the calcium concentration of the solutions inside the recording electrode and in the bath independently of each other, transmitter release was restricted to one or two surface varicosities at each recording site. Using this technique, transmitter release probability was shown to be highly variable, even between adjacent varicosities on single axon branches. Very little variation was observed in the calcium influx following single impulse nerve stimulation between adjacent Oregon Green BAPTA-1 loaded varicosities. However, the staining intensities of three vesicular proteins, SV2, synaptophysin, and synaptotagmin 1, showed considerable variation between adjacent varicosities on single axon branches. This variation in staining intensity may be partly explained by variation in the density of synaptic vesicles. However, double staining experiments using two vesicular antigens showed some varicosities staining for one vesicular antigen, but not for the second, suggesting that the expression of these release machinery proteins is regulated locally within the varicosities. The results of the present study strengthen suggestions that synaptic strength is at least in part, regulated by variation in the expression of vesicular proteins. (C) 2004 Wiley-Liss, Inc.