Date Published: June 29, 2017
Publisher: Public Library of Science
Author(s): Laura Anton-Sanchez, Pedro Larrañaga, Ruth Benavides-Piccione, Isabel Fernaud-Espinosa, Javier DeFelipe, Concha Bielza, Manuel S. Malmierca.
We modeled spine distribution along the dendritic networks of pyramidal neurons in both basal and apical dendrites. To do this, we applied network spatial analysis because spines can only lie on the dendritic shaft. We expanded the existing 2D computational techniques for spatial analysis along networks to perform a 3D network spatial analysis. We analyzed five detailed reconstructions of adult human pyramidal neurons of the temporal cortex with a total of more than 32,000 spines. We confirmed that there is a spatial variation in spine density that is dependent on the distance to the cell body in all dendrites. Considering the dendritic arborizations of each pyramidal cell as a group of instances of the same observation (the neuron), we used replicated point patterns together with network spatial analysis for the first time to search for significant differences in the spine distribution of basal dendrites between different cells and between all the basal and apical dendrites. To do this, we used a recent variant of Ripley’s K function defined to work along networks. The results showed that there were no significant differences in spine distribution along basal arbors of the same neuron and along basal arbors of different pyramidal neurons. This suggests that dendritic spine distribution in basal dendritic arbors adheres to common rules. However, we did find significant differences in spine distribution along basal versus apical networks. Therefore, not only do apical and basal dendritic arborizations have distinct morphologies but they also obey different rules of spine distribution. Specifically, the results suggested that spines are more clustered along apical than in basal dendrites. Collectively, the results further highlighted that synaptic input information processing is different between these two dendritic domains.
Many types of real-world events are constrained by networks, such as stores located alongside streets, traffic accidents on roads, street crime sites, etc. These events are called network events. Network spatial analysis refers to statistical and computational methods for analyzing events occurring on or along networks. Most of these methods have been developed by Okabe and collaborators  and include techniques similar to the methods used in traditional spatial analysis but taking into account the network topology. The main difference from traditional spatial analysis using Euclidean distances is that network spatial analysis measures shortest path distances. Shortest path distances are much harder to calculate because they require network topology management. If traditional spatial analysis assuming a plane with Euclidean distances  is applied to network events, then we are likely to draw false conclusions due to short-range clustering (due to the concentration of events, for example, on a road) and/or long-range regularity (for example, due to the separation of different roads).
Table 1 shows some important characteristics of the apical dendrites of each of the five analyzed pyramidal neurons: number of spines, total length of the network, average number of points per unit length in the network, circumradius and number of branching points (complexity measure of the dendritic tree). Table 2 shows the same information for basal dendrites, grouped according to the pyramidal neuron to which they belong. Apical dendrites are clearly more complex than basal dendrites, as a comparison of the mean number of characteristics shown in Tables 1 and 2 patently shows. While the mean number of spines in apical dendrites is 2845, it is 1074 in basal dendrites. The mean length is also much greater in apical than in basal arborizations: 2497.25 μm and 951.85 μm, respectively. The same applies to the mean number of branching points (20 in apical networks vs 6 in basal networks).
We analyzed the spatial distribution of spines along both basal and apical dendritic networks of human pyramidal neurons. To do this, we used network spatial analysis, implementing methods to analyze 3D linear networks for the first time. We studied whether there were differences in the spatial distribution of spines between different pyramidal neurons and between basal and apical dendrites, using replicated point patterns in conjunction with network spatial analysis. To do this, we took advantage of the geometrically corrected K function in order to compare the corrected K functions obtained from different point patterns in different networks .