Blood vessel architecture and finite element model.

<p>(A) Scanning electron micrograph of a vascular corrosion cast illustrating the density and complexity of cortical vasculature in the rat. Cortical surface is to the top of the figure. Scale bar: 500 μm. From Merchan-Perez and DeFelipe, unpublished material. See also <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0172368#pone.0172368.s001" target="_blank">S1 Movie</a>. (B) The finite element model represents a cylinder of gray matter traversed from top to bottom by a small blood vessel. The blood vessel is considered to be a hollow cylinder with a diameter of 10 μm. The whole model diameter is 60 μm, and its height is 50 μm. Gray matter is assumed to be a linearly-elastic isotropic material. The body has been meshed into approximately 15,000 constant strain tetrahedral elements.</p

Mean optimality percentages of each cortical layer.

<p>Figures closer to 100% denote that the real neuronal wiring was closer to the shortest solutions found.</p

Box plot of the wiring analysis results for all layers.

<p>All the solutions are equal to or less than 100%, signifying that the solutions found by the optimization algorithm had a length equal to or shorter than the real wiring of the cells. For layers II, III and IV, the real neuronal wiring was closer to the shortest solutions found. Deeper layers had a higher degree of dispersion (steeper spacing between the parts of the box).</p

Mean and standard deviation () of the number of dendritic trees and the number of points of the dendritic point clouds (roots, branching points and terminal points) of the 48 cells of each cortical layer.

<p>Mean and standard deviation () of the number of dendritic trees and the number of points of the dendritic point clouds (roots, branching points and terminal points) of the 48 cells of each cortical layer.</p

Maximum displacement of points during blood vessel contraction or dilation.

<p>To compute these curves, 26 points were used. The first point was located on the maximum deformation point of the vessel wall (at the model mid-plane) and the rest were radially distributed at regular intervals (1 μm) until the external boundary of the model was reached. The maximum displacement of the blood vessel wall was 1 μm from the resting state during contraction (inwards) or dilation (outwards). No displacement in the external boundaries of the model was allowed. (A) Maximum absolute displacement of points at regular time intervals (T = 1 to T = 5) until maximum contraction or dilation of the blood vessel is reached (T = 5). (B) Inter-point distance increment as a percentage of the resting-state distance (1 μm). Points were arranged in the same way as in (A), and the distances between each point and its outward neighbor were recorded at the same time intervals. Since the behavior of the model is symmetric, these increments represent an increase of inter-point distances during blood vessel contraction and a decrease during dilation.</p

Mean wiring length (real vs. optimized).

<p>Mean wiring length (<i>μ</i>m) of the 48 analyzed cells in each cortical layer (red) versus mean wiring length of the shortest arborizations found by our optimization algorithm for each layer (green). The optimization algorithm found an equal or slightly better (shorter) wiring for all the neurons in all the layers. We found the biggest difference with respect to the real wiring in layer Va, where the synthetic wiring was, on average, 2.06% shorter than the real wiring. The smallest difference occured in layer IV, where the optimized wiring was, on average, 1.01% shorter than the real wiring.</p

Developmental expression of potassium channels in cultured hippocampal neurons.

<p>(<u>A</u>) Western blot of Kv1.2, Kv2.2 and Kv7.2 in hippocampal neurons cultured at high density (50,000/cm²) for different intervals (from 1 to 21 DIV) in control conditions. (<u>B</u>) Histograms show Kv1.2, Kv2.2 and Kv7.2 expression normalized to actin when quantified densitometry of Western blots. The data represent the mean ± SE of three independent experiments. Note the delayed onset of Kv1.2 expression as compared with that of Kv2.2 and Kv7.2. (<u>C</u>) Photomicrograph of hippocampal neurons cultured for 6 DIV and double immunostained for Kv7.2 (green) and MAP2 (red). Note the early expression of Kv7.2 in a single process emerging from the cell body (arrows). (<u>D</u>) Histogram shows the percentage (mean ± SE) of neurons expressing Kv7.2 at the AIS at different developmental stages <i>in vitro</i>. Scale bar = 16 µm.</p

AIS Kv channel expression is not dependent on the actin cytoskeleton.

<p>Confocal microscopy photomicrographs show that Kv1.2 (<u>A</u>–<u>F</u>) and Kv2.2 (<u>G</u>–<u>L</u>) accumulation in the AIS is not affected by cytochalasin D. Hippocampal neurons were exposed to DMSO (control, <u>A</u>–<u>C</u>, <u>G</u>–<u>I</u>) or cytochalsin D (5 µM; <u>D</u>–<u>F</u>, <u>J</u>–<u>L</u>) from 15 to 17 DIV, double stained for 14D4 or ankyrin G (blue) and Kv1.2 (red, <u>A</u>–<u>F</u>) or Kv2.2 (red, <u>G</u>–<u>L</u>), and stained with Alexa 488 phalloidin to reveal F-actin. Note the presence of Kv1.2 and Kv2.2 at the AIS in both control and cytochalasin D-treated neurons. Scale bar = 25 µm (<u>A</u>–<u>F</u>) and 30 µm (<u>G</u>–<u>L</u>).</p

Example of one basal dendritic arbor of a pyramidal cell in layer II.

<p>A: Real 3D Neurolucida reconstruction where each dendritic tree is shown in a different color. B: Simplified real dendritic arbor where all connections are drawn as straight lines as we measure the (straight) length between points. C: Example of the identification of the root (black), branching points (brown) and terminal points (blue) of one dendritic tree. D: Point cloud formed by all the roots, branching and terminal points of the six basal dendritic trees. E: Shortest arborization found for the point cloud shown in D.</p

Three-dimensional model of a brain blood vessel and the tissue and synapses that surround it.

<p>The model in (A) and (B) represents a cylinder of brain tissue crossed by a blood vessel from top to bottom. Excitatory (glutamatergic) and inhibitory (GABAergic) synapses have been represented as green and red points, respectively. The cylinder height is 50 μm and its diameter is 60 μm. The diameter of the blood vessel at rest is 10 μm. In (A), the maximum contraction of the central part of the blood vessel has been represented (the diameter decreases to 8 μm). In (B), maximum dilation of the central part of the blood vessel has been represented (the diameter increases to 12 μm). No displacement was allowed at the external boundary of the model. The displacements of the synapses that were randomly distributed within the model are represented in (C) and (D) during maximal contraction, and dilation, respectively. See also <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0172368#pone.0172368.s002" target="_blank">S2</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0172368#pone.0172368.s003" target="_blank">S3</a> Movies.</p