A modularity based spectral method for simultaneous community and anti-community detection

In a graph or complex network, communities and anti-communities are node sets whose modularity attains extremely large values, positive and negative, respectively. We consider the simultaneous detection of communities and anti-communities, by looking at spectral methods based on various matrix-based definitions of the modularity of a vertex set. Invariant subspaces associated to extreme eigenvalues of these matrices provide indications on the presence of both kinds of modular structure in the network. The localization of the relevant invariant subspaces can be estimated by looking at particular matrix angles based on Frobenius inner products

SNr astrocytes display spontaneous calcium activity that is partly dependent on neuronal activity.

<p>(<b>A</b>) Fluo-4 loaded cells in the SNr area of a rat sagittal acute slice. Only small cells (astrocytes, less than 10 µm in diameter) were loaded. GABAergic and dopaminergic neurons (with cell bodies from 20 to 40 µm in diameter <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0041793#pone.0041793-Mailly1" target="_blank">[70]</a>) were not labelled in most cases. (<b>B</b>) Distribution of active (red frames) and non active (white frames) ROIs within the slice shown in A. (<b>C</b>) Example of typical fluorescence variations recorded in four SNr astrocytes. (<b>D</b>) Raster plot of fluorescence peaks detected in active ROIs described in B. (<b>E</b>) Example of the cumulative progress of the proportion of active astrocytes during recording over 5, 10, 15, 20, 25 and 30 minutes. (<b>F</b>) Effect of 500 nM TTX (<i>n</i> = 13 slices; <i>p</i><0.001) or 2 µM thapsigargin (Thapsi, <i>n</i> = 7 slices; <i>p</i><0.001) on the spontaneous calcium activity of astrocytes in the SNr.</p

SNr astrocytes AMPA, mGlu and GABA_A receptors are involved in calcium spontaneous activity.

<p>(<b>A</b>) Example of two typical fluorescence variation profiles recorded in SNr astrocytes when 100 µM glutamate was perfused in the bath. (<b>B</b>) Histogram of the percentage of loaded SNr astrocytes responding to the application of 100 µM glutamate (<i>n</i> = 15) and the effect of 500 nM TTX (<i>n</i> = 12; <i>p</i> = 0.317), 10 µM CNQX (<i>n</i> = 8; <i>p</i><0.001), 100 µM LAP-3 (<i>n</i> = 11; <i>p</i> = 0.005), 50 µM AP-5 (<i>n</i> = 4; <i>p</i> = 0.453) or a cocktail containing 10 µM CNQX+100 µM LAP-3+50 µM AP-5 (<i>n</i> = 4; <i>p</i> = 0.001) on this glutamate-induced effect. (<b>C</b>) Typical fluorescence variations recorded in a SNr astrocyte when 20 µM GABA was perfused in the bath. (<b>D</b>) Histogram of the percentage of loaded SNr astrocytes responding to the application of 20 µM GABA (<i>n</i> = 18) and the effect of 500 nM TTX (<i>n</i> = 7; <i>p</i> = 0.215), 20 µM BMI (<i>n</i> = 7; <i>p</i> = 0.02) or 100 µM saclofen (<i>n</i> = 8; <i>p</i> = 0.948) on this GABA-induced effect. (<b>E</b>) Typical fluorescence variations recorded in two SNr astrocytes before and after incubation with a cocktail containing 10 µM CNQX+100 µM LAP-3+50 µM AP-5. (<b>F</b>) Histogram showing the effect of a cocktail containing 10 µM CNQX+100 µM LAP-3+50 µM AP-5 (<i>n</i> = 10; <i>p</i><0.001) or 20 µM BMI (<i>n</i> = 7; <i>p</i> = 0.003) on the spontaneous calcium activity of astrocytes in the SNr. The inhibitory effect is normalized with respect to control residual activity. *, <i>p</i><0.05; **, <i>p</i><0.01 and ***, <i>p</i><0.001.</p

Additional file 2: of TRPA1 channels promote astrocytic Ca2+ hyperactivity and synaptic dysfunction mediated by oligomeric forms of amyloid-β peptide

Characterization of Fluo-4-loaded cells in the stratum radiatum of mouse coronal slice. (a) Confocal image of Fluo-4-loaded (cyan) and SR101-labeled (magenta) cells in the CA1 stratum radiatum. Merged image showing the proportion of loaded astrocytes (white), confirming that most of the loaded cells are astrocytes. One hour before slicing, animals were iv injected with SR101 as described previously [51]. Vessels are only labeled with SR101 (white arrow). (b) Z-stack projections of confocal images of a patched astrocyte loaded with Fluo-4 (cyan) and SR101 (magenta). Merged image showing the Fluo-4 diffusion in the whole astrocytic territory. (c) Example of a passive whole-cell current recorded in a stratum radiatum astrocyte. Cell was held at −70 mV and 10 mV hyper- and depolarizing voltage steps of 80 ms duration were applied (−110 to +80 mV). (TIFF 1907 kb

Characterization of SNr cell populations and Fluo-4 loaded cells.

<p>(<b>A</b>) NeuN staining (green) labels few cells within SNr. Nuclei are identified by TO-PRO staining (blue). Merged image showing the proportion of neurons within the SNr (right panel). (<b>B</b>) Two-photon multistack (40 slices at 2 µm spacing) mosaic reconstruction of SNr astrocytes and vessels in an acute brain slice 2 h after sulforhodamine 101 (10 mg/ml) intravenous injection (100 µl/50 g body weight). Antero-posterior (AP) and medio-lateral (ML) orientations are shown in the upper right part of the figure. (<b>C</b>) Bi-photon imaging of sulforhodamine 101 (red) and Hoescht 33342 (blue) in the SNr. Merged image showing the proportion of astrocytes within the SNr (right panel). (<b>D</b>) Representative confocal images of SR101-labeled (red) and Fluo-4-loaded (green) cells in the SNr of a sagittal acute slice of rat brain. Merged image showing sulforhodamine 101 and Fluo-4 staining within the SNr, confirming that most of the loaded cells are astrocytes.</p

Additional file 7: of TRPA1 channels promote astrocytic Ca2+ hyperactivity and synaptic dysfunction mediated by oligomeric forms of amyloid-β peptide

TRPA1 channels expression is located in thick GFAP-positive processes and in adjacent thin processes lacking GFAP staining. 3D–recontsruct of astrocytic processes objectivized by GFAP staining (magenta) showing that TRPA1 channels (green) expression went over in contiguous processes excluding GFAP staining. Scale bar: 50 nm. (ZIP 1736 kb

3D morphological analysis of the astrocytic network after iv injection of SRB.

<p><b>A</b>) A multistacks mosaic acquired in the somatosensory area of a coronal acute brain slice (P17 rat). The region of interest (ROI; white rectangle) shows colored astrocytes detected using ImageJ plugins. Each color corresponds to single astrocytes cell body. Scale bar = 150 µm. <b>B</b>) Frequency histogram showing of astrocyte densities as a function of cortical depth calculated from the ROI described above. Depth was divided in 15 bins with 100 µm increments. <b>C</b>) Frequency histogram of normalized astrocytes radial densities in the cortical layer 1 and <b>E</b>) in layers 2/3. <b>D</b>) TPLSM images showing astrocytes in the cortical layer 1 and <b>F</b>) in layers 2/3. Scale bar = 25 µm.</p

Comparison of two <i>in vivo</i> methods for astrocytes staining (P21 rat).

<p>TPLSM images acquired: <b>A_1–3</b>) 30 minutes after SRB (20 mg/kg) intravenous injection and <b>B_1–3</b>) 5 minutes after SR101 application (100 µM) on the cortical surface. (<b>A₁</b>) and (<b>B₁</b>) Images were taken at 100 µm below the pia.mater (<b>A₂</b>) and (<b>B₂</b>) Images were taken at 250 µm below the surface of the cortex. (<b>A₃</b>) and (<b>B₃</b>) show a 3D reconstruction (V3D) using the entire stack of images. Scale bar = 50 µm.</p

Rearrangement of the astroglial network in a mouse model of mesiotemporal lobe epilepsy.

<p><b>A–B</b>) Bright field microscopy imaging (Nikon Multizoom AZ100, France) of acute hippocampal slices from adult mice 2 weeks after a unilateral intrahippocampal kainate injection. <b>A</b>) Contralateral non-injected hippocampus. <b>B</b>) Ipsilateral hippocampus. Note the absence of CA1/CA3 areas and the enlargement of the dentate gyrus. <b>C–D</b>) TPLSM imaging of regions indicated by white squares on (A) and (B) images, respectively, after iv injection of SR101. Scale bar = 50 µm. <b>E</b>) Column scatters representation showing the distribution of astrocytes cell body volumes at both sides of the hippocampus. The bar corresponds to the mean value.</p

Sulforhodamine stained cells are only astrocytes.

<p><b>A</b>) Two-photon excitation spectra of SRB and SR101 shows the possibility to excite one dye without exciting the other. Z-projection (standard-deviation) of a 100 µm stack acquired on an acute coronal brain slice of rat somatosensory cortex (P23) after iv injection of SRB/SR101 mix (1∶1) and FITC-dextran to stain vasculature. The left merged image was acquired with an 800 nm laser excitation wavelength, corresponding to SRB (orange) and FITC-dextran (green) emissions. The central merged image was acquired with a 900 nm laser excitation wavelength, corresponding to SR101 (red) and FITC-dextran (green) emissions. The right panel shows a merge of SRB, SR101 and FITC-dextran (pink corresponds to SRB and SR101 colocalization). Scale bar = 50 µm. <b>B</b>) Z-projection (standard-deviation) of two-photon microscopy images of cortical brain slices from GFAP-GFP transgenic mouse (P37) 2 h after iv injection of SRB. Left image shows SRB staining (red), central image shows GFAP-GFP expression (green) and right panel is a merge of left and central images with double-stained cells appearing in yellow. <b>C</b>) Z-projection (standard-deviation) of TPLSM images of cortical brain slices from a P18 rat. Left image: SRB astrocytes staining after iv injection (red), central image: slice immunostained with S100B antibody (green). Right panel is a merge of left and central images with double-stained cells appearing in yellow. <b>D</b>) Merge images of SRB-stained slices (red) secondarily immunostained with NG2 antibody (green, left panel), or NeuN antibody (green, central panel), or CD11b antibody (green, right panel). Arrowheads show NG2 cells or microglial cells which are not SRB-stained. Scale bar = 20 µm.</p