On high moments of strongly diluted large Wigner random matrices

We consider a dilute version of the Wigner ensemble of nxn random matrices $H$ and study the asymptotic behavior of their moments $M_{2s}$ in the limit of infinite $n$, $s$ and $\rho$, where $\rho$ is the dilution parameter. We show that in the asymptotic regime of the strong dilution, the moments $M_{2s}$ with $s=\chi\rho$ depend on the second and the fourth moments of the random entries $H_{ij}$ and do not depend on other even moments of $H_{ij}$. This fact can be regarded as an evidence of a new type of the universal behavior of the local eigenvalue distribution of strongly dilute random matrices at the border of the limiting spectrum. As a by-product of the proof, we describe a new kind of Catalan-type numbers related with the tree-type walks.Comment: 43 pages (version four: misprints corrected, discussion added, other minor modifications

Risky business for a juvenile marine predator? Testing the influence of foraging strategies on size and growth rate under natural conditions

Mechanisms driving selection of body size and growth rate in wild marine vertebrates are poorly understood, thus limiting knowledge of their fitness costs at ecological, physiological and genetic scales. Here, we indirectly tested whether selection for size-related traits of juvenile sharks that inhabit a nursery hosting two dichotomous habitats, protected mangroves (low predation risk) and exposed seagrass beds (high predation risk), is influenced by their foraging behaviour. Juvenile sharks displayed a continuum of foraging strategies between mangrove and seagrass areas, with some individuals preferentially feeding in one habitat over another. Foraging habitat was correlated with growth rate, whereby slower growing, smaller individuals fed predominantly in sheltered mangroves, whereas larger, faster growing animals fed over exposed seagrass. Concomitantly, tracked juveniles undertook variable movement behaviours across both the low and high predation risk habitat. These data provide supporting evidence for the hypothesis that directional selection favouring smaller size and slower growth rate, both heritable traits in this shark population, may be driven by variability in foraging behaviour and predation risk. Such evolutionary pathways may be critical to adaptation within predator-driven marine ecosystems

Development and characterization of thirteen microsatellite markers for the Fiscal Flycatcher (Sigelus silens) for use in phylogeographic and landscape genetics research

The Fiscal Flycatcher, Sigelus silens, is the only representative of a monotypic genus, endemic to Southern Africa, and may represent two cryptic species. Here we describe the development of thirteen microsatellite markers, and characterize polymorphism for each one. We found that all but one of our 13 loci were highly variable, each having five or more alleles. This suggests that these markers will have high variability across the species range and will be of utility in understanding the extent of gene flow among populations

Burst-Time-Dependent Plasticity Robustly Guides ON/OFF Segregation in the Lateral Geniculate Nucleus

Spontaneous retinal activity (known as “waves”) remodels synaptic connectivity to the lateral geniculate nucleus (LGN) during development. Analysis of retinal waves recorded with multielectrode arrays in mouse suggested that a cue for the segregation of functionally distinct (ON and OFF) retinal ganglion cells (RGCs) in the LGN may be a desynchronization in their firing, where ON cells precede OFF cells by one second. Using the recorded retinal waves as input, with two different modeling approaches we explore timing-based plasticity rules for the evolution of synaptic weights to identify key features underlying ON/OFF segregation. First, we analytically derive a linear model for the evolution of ON and OFF weights, to understand how synaptic plasticity rules extract input firing properties to guide segregation. Second, we simulate postsynaptic activity with a nonlinear integrate-and-fire model to compare findings with the linear model. We find that spike-time-dependent plasticity, which modifies synaptic weights based on millisecond-long timing and order of pre- and postsynaptic spikes, fails to segregate ON and OFF retinal inputs in the absence of normalization. Implementing homeostatic mechanisms results in segregation, but only with carefully-tuned parameters. Furthermore, extending spike integration timescales to match the second-long input correlation timescales always leads to ON segregation because ON cells fire before OFF cells. We show that burst-time-dependent plasticity can robustly guide ON/OFF segregation in the LGN without normalization, by integrating pre- and postsynaptic bursts irrespective of their firing order and over second-long timescales. We predict that an LGN neuron will become ON- or OFF-responsive based on a local competition of the firing patterns of neighboring RGCs connecting to it. Finally, we demonstrate consistency with ON/OFF segregation in ferret, despite differences in the firing properties of retinal waves. Our model suggests that diverse input statistics of retinal waves can be robustly interpreted by a burst-based rule, which underlies retinogeniculate plasticity across different species

Null Mutations in EphB Receptors Decrease Sharpness of Frequency Tuning in Primary Auditory Cortex

Primary auditory cortex (A1) exhibits a tonotopic representation of characteristic frequency (CF). The receptive field properties of A1 neurons emerge from a combination of thalamic inputs and intracortical connections. However, the mechanisms that guide growth of these inputs during development and shape receptive field properties remain largely unknown. We previously showed that Eph family proteins help establish tonotopy in the auditory brainstem. Moreover, other studies have shown that these proteins shape topography in visual and somatosensory cortices. Here, we examined the contribution of Eph proteins to cortical organization of CF, response thresholds and sharpness of frequency tuning. We examined mice with null mutations in EphB2 and EphB3, as these mice show significant changes in auditory brainstem connectivity. We mapped A1 using local field potential recordings in adult EphB2−/−;EphB3−/− and EphB3−/− mice, and in a central A1 location inserted a 16-channel probe to measure tone-evoked current-source density (CSD) profiles. Based on the shortest-latency current sink in the middle layers, which reflects putative thalamocortical input, we determined frequency receptive fields and sharpness of tuning (Q20) for each recording site. While both mutant mouse lines demonstrated increasing CF values from posterior to anterior A1 similar to wild type mice, we found that the double mutant mice had significantly lower Q20 values than either EphB3−/− mice or wild type mice, indicating broader tuning. In addition, we found that the double mutants had significantly higher CF thresholds and longer onset latency at threshold than mice with wild type EphB2. These results demonstrate that EphB receptors influence auditory cortical responses, and suggest that EphB signaling has multiple functions in auditory system development

The molecular phylogeny of eph receptors and ephrin ligands

<p>Abstract</p> <p>Background</p> <p>The tissue distributions and functions of Eph receptors and their ephrin ligands have been well studied, however less is known about their evolutionary history. We have undertaken a phylogenetic analysis of Eph receptors and ephrins from a number of invertebrate and vertebrate species.</p> <p>Results</p> <p>Our findings indicate that Eph receptors form three major clades: one comprised of non-chordate and cephalochordate Eph receptors, a second comprised of urochordate Eph receptors, and a third comprised of vertebrate Eph receptors. Ephrins, on the other hand, fall into either a clade made up of the non-chordate and cephalochordate ephrins plus the urochordate and vertebrate ephrin-Bs or a clade made up of the urochordate and vertebrate ephrin-As.</p> <p>Conclusion</p> <p>We have concluded that Eph receptors and ephrins diverged into A and B-types at different points in their evolutionary history, such that primitive chordates likely possessed an ancestral ephrin-A and an ancestral ephrin-B, but only a single Eph receptor. Furthermore, ephrin-As appear to have arisen in the common ancestor of urochordates and vertebrates, whereas ephrin-Bs have a more ancient bilaterian origin. Ancestral ephrin-B-like ligands had transmembrane domains; as GPI anchors appear to have arisen or been lost at least 3 times.</p

Ephrin-A5 and EphA5 Interaction Induces Synaptogenesis during Early Hippocampal Development

Synaptogenesis is a fundamental step in neuronal development. For spiny glutamatergic synapses in hippocampus and cortex, synaptogenesis involves adhesion of pre and postsynaptic membranes, delivery and anchorage of pre and postsynaptic structures including scaffolds such as PSD-95 and NMDA and AMPA receptors, which are glutamate-gated ion channels, as well as the morphological maturation of spines. Although electrical activity-dependent mechanisms are established regulators of these processes, the mechanisms that function during early development, prior to the onset of electrical activity, are unclear. The Eph receptors and ephrins provide cell contact-dependent pathways that regulate axonal and dendritic development. Members of the ephrin-A family are glycosyl-phosphatidylinositol-anchored to the cell surface and activate EphA receptors, which are receptor tyrosine kinases.Here we show that ephrin-A5 interaction with the EphA5 receptor following neuron-neuron contact during early development of hippocampus induces a complex program of synaptogenic events, including expression of functional synaptic NMDA receptor-PSD-95 complexes plus morphological spine maturation and the emergence of electrical activity. The program depends upon voltage-sensitive calcium channel Ca2+ fluxes that activate PKA, CaMKII and PI3 kinase, leading to CREB phosphorylation and a synaptogenic program of gene expression. AMPA receptor subunits, their scaffolds and electrical activity are not induced. Strikingly, in contrast to wild type, stimulation of hippocampal slices from P6 EphA5 receptor functional knockout mice yielded no NMDA receptor currents.These studies suggest that ephrin-A5 and EphA5 signals play a necessary, activity-independent role in the initiation of the early phases of synaptogenesis. The coordinated expression of the NMDAR and PSD-95 induced by eprhin-A5 interaction with EphA5 receptors may be the developmental switch that induces expression of AMPAR and their interacting proteins and the transition to activity-dependent synaptic regulation

Rapid Reversal of Chondroitin Sulfate Proteoglycan Associated Staining in Subcompartments of Mouse Neostriatum during the Emergence of Behaviour

BACKGROUND: The neostriatum, the mouse homologue of the primate caudate/putamen, is the input nucleus for the basal ganglia, receiving both cortical and dopaminergic input to each of its sub-compartments, the striosomes and matrix. The coordinated activation of corticostriatal pathways is considered vital for motor and cognitive abilities, yet the mechanisms which underlie the generation of these circuits are unknown. The early and specific targeting of striatal subcompartments by both corticostriatal and nigrostriatal terminals suggests activity-independent mechanisms, such as axon guidance cues, may play a role in this process. Candidates include the chondroitin sulfate proteoglycan (CSPG) family of glycoproteins which have roles not only in axon guidance, but also in the maturation and stability of neural circuits where they are expressed in lattice-like perineuronal nets (PNNs). METHODOLOGY/PRINCIPAL FINDINGS: The expression of CSPG-associated structures and PNNs with respect to neostriatal subcompartments has been examined qualitatively and quantitatively using double-labelling for Wisteria floribunda agglutinin (WFA), and the mu-opioid receptor (muOR), a marker for striosomes, at six postnatal ages in mice. We find that at the earliest ages (postnatal day (P)4 and P10), WFA-positive clusters overlap preferentially with the striosome compartment. By P14, these clusters disappear. In contrast, PNNs were first seen at P10 and continued to increase in density and spread throughout the caudate/putamen with maturation. Remarkably, the PNNs overlap almost exclusively with the neostriatal matrix. CONCLUSIONS/SIGNIFICANCE: This is the first description of a reversal in the distribution of CSPG associated structures, as well as the emergence and maintenance of PNNs in specific subcompartments of the neostriatum. These results suggest diverse roles for CSPGs in the formation of functional corticostriatal and nigrostriatal connectivity within the striosome and matrix compartments of the developing caudate/putamen