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

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

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

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

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

3D morphology-based clustering and simulation of human pyramidal cell dendritic spines

<div><p>The dendritic spines of pyramidal neurons are the targets of most excitatory synapses in the cerebral cortex. They have a wide variety of morphologies, and their morphology appears to be critical from the functional point of view. To further characterize dendritic spine geometry, we used in this paper over 7,000 individually 3D reconstructed dendritic spines from human cortical pyramidal neurons to group dendritic spines using model-based clustering. This approach uncovered six separate groups of human dendritic spines. To better understand the differences between these groups, the discriminative characteristics of each group were identified as a set of rules. Model-based clustering was also useful for simulating accurate 3D virtual representations of spines that matched the morphological definitions of each cluster. This mathematical approach could provide a useful tool for theoretical predictions on the functional features of human pyramidal neurons based on the morphology of dendritic spines.</p></div

Example of one of the analyzed pyramidal neurons.

<p>(a) Confocal microscopy image of an intracellularly injected layer III pyramidal neuron of the human temporal cortex (Neuron 1 in Tables <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0180400#pone.0180400.t001" target="_blank">1</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0180400#pone.0180400.t002" target="_blank">2</a>), visualized in 3D from high-resolution confocal stacks of images. (b) 3D reconstruction of the complete morphology of the cell shown in (a). (c) 3D reconstruction of the same neuron showing the apical dendrite in red and the four reconstructed basal dendrites in blue, green, orange and purple. We use the blue basal tree in (c) throughout the manuscript to illustrate the analysis performed. Scale bar (in (b)): 50 <i>μ</i>m.</p

Model-based clustering representation and interpretation.

<p><b>(A)</b> Graph showing the resulting BIC values depending on the number of clusters. Results are shown in a range from two to ten clusters. The model that achieved the highest BIC value had six clusters. <b>(B)</b> Representative examples of dendritic spines with a <i>p</i>* = 1 (highest membership probability) from the six different clusters. <b>(C)</b> 2D projection of the 6D probability distributions representing the membership probability of each spine to each cluster according to classical multidimensional scaling. Spines were colored combining cluster colors according to their probabilities of membership to each cluster. <b>(D)</b> The absolute value of the logarithm of the total variance for each cluster, i.e., |log₁₀det(<b>Σ</b>_<i>i</i>)|, where <b>Σ</b>_<i>i</i> is the variance-covariance matrix of cluster <i>i</i>. It is a value that summarizes the heterogeneity of morphologies within a cluster.</p

Simulation of 3D dendritic spines.

<p><b>(A)</b> Skeleton built from the set of features computed according to the multiresolution Reeb graph. <b>(B)</b> Generation of the surface between two ellipses through the triangulation of the region. <b>(C)</b> Three-dimensional representation of a spine. Once all the regions of the spine have been triangulated, the spine is a closed mesh used to visualize an artificial spine. <b>(D)</b> Improved spine representation. Loop’s subdivision algorithm yields a smoother and more accurate version of the artificial spine. <b>(E)</b> Examples of simulated spines for each cluster.</p

Results for Pearson’s <i>χ</i>² test checking if the distribution of each cluster is independent of its dendritic compartment, age and combination of both.

<p>Results for Pearson’s <i>χ</i>² test checking if the distribution of each cluster is independent of its dendritic compartment, age and combination of both.</p