A regularity index for dendrites - local statistics of a neuron's input space.

Neurons collect their inputs from other neurons by sending out arborized dendritic structures. However, the relationship between the shape of dendrites and the precise organization of synaptic inputs in the neural tissue remains unclear. Inputs could be distributed in tight clusters, entirely randomly or else in a regular grid-like manner. Here, we analyze dendritic branching structures using a regularity index R, based on average nearest neighbor distances between branch and termination points, characterizing their spatial distribution. We find that the distributions of these points depend strongly on cell types, indicating possible fundamental differences in synaptic input organization. Moreover, R is independent of cell size and we find that it is only weakly correlated with other branching statistics, suggesting that it might reflect features of dendritic morphology that are not captured by commonly studied branching statistics. We then use morphological models based on optimal wiring principles to study the relation between input distributions and dendritic branching structures. Using our models, we find that branch point distributions correlate more closely with the input distributions while termination points in dendrites are generally spread out more randomly with a close to uniform distribution. We validate these model predictions with connectome data. Finally, we find that in spatial input distributions with increasing regularity, characteristic scaling relationships between branching features are altered significantly. In summary, we conclude that local statistics of input distributions and dendrite morphology depend on each other leading to potentially cell type specific branching features.

Three-dimensional spatial modeling of spines along dendritic networks in human cortical pyramidal neurons.

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.

Wiring Economy of Pyramidal Cells in the Juvenile Rat Somatosensory Cortex.

Ever since Cajal hypothesized that the structure of neurons is designed in such a way as to save space, time and matter, numerous researchers have analyzed wiring properties at different scales of brain organization. Here we test the hypothesis that individual pyramidal cells, the most abundant type of neuron in the cerebral cortex, optimize brain connectivity in terms of wiring length. In this study, we analyze the neuronal wiring of complete basal arborizations of pyramidal neurons in layer II, III, IV, Va, Vb and VI of the hindlimb somatosensory cortical region of postnatal day 14 rats. For each cell, we search for the optimal basal arborization and compare its length with the length of the real dendritic structure. Here the optimal arborization is defined as the arborization that has the shortest total wiring length provided that all neuron bifurcations are respected and the extent of the dendritic arborizations remain unchanged. We use graph theory and evolutionary computation techniques to search for the minimal wiring arborizations. Despite morphological differences between pyramidal neurons located in different cortical layers, we found that the neuronal wiring is near-optimal in all cases (the biggest difference between the shortest synthetic wiring found for a dendritic arborization and the length of its real wiring was less than 5%). We found, however, that the real neuronal wiring was significantly closer to the best solution found in layers II, III and IV. Our studies show that the wiring economy of cortical neurons is related not to the type of neurons or their morphological complexities but to general wiring economy principles.

Dendritic and Axonal Wiring Optimization of Cortical GABAergic Interneurons.

The way in which a neuronal tree expands plays an important role in its functional and computational characteristics. We aimed to study the existence of an optimal neuronal design for different types of cortical GABAergic neurons. To do this, we hypothesized that both the axonal and dendritic trees of individual neurons optimize brain connectivity in terms of wiring length. We took the branching points of real three-dimensional neuronal reconstructions of the axonal and dendritic trees of different types of cortical interneurons and searched for the minimal wiring arborization structure that respects the branching points. We compared the minimal wiring arborization with real axonal and dendritic trees. We tested this optimization problem using a new approach based on graph theory and evolutionary computation techniques. We concluded that neuronal wiring is near-optimal in most of the tested neurons, although the wiring length of dendritic trees is generally nearer to the optimum. Therefore, wiring economy is related to the way in which neuronal arborizations grow irrespective of the marked differences in the morphology of the examined interneurons.

Three-dimensional distribution of cortical synapses: a replicated point pattern-based analysis.

The biggest problem when analyzing the brain is that its synaptic connections are extremely complex. Generally, the billions of neurons making up the brain exchange information through two types of highly specialized structures: chemical synapses (the vast majority) and so-called gap junctions (a substrate of one class of electrical synapse). Here we are interested in exploring the three-dimensional spatial distribution of chemical synapses in the cerebral cortex. Recent research has showed that the three-dimensional spatial distribution of synapses in layer III of the neocortex can be modeled by a random sequential adsorption (RSA) point process, i.e., synapses are distributed in space almost randomly, with the only constraint that they cannot overlap. In this study we hypothesize that RSA processes can also explain the distribution of synapses in all cortical layers. We also investigate whether there are differences in both the synaptic density and spatial distribution of synapses between layers. Using combined focused ion beam milling and scanning electron microscopy (FIB/SEM), we obtained three-dimensional samples from the six layers of the rat somatosensory cortex and identified and reconstructed the synaptic junctions. A total volume of tissue of approximately 4500µm(3) and around 4000 synapses from three different animals were analyzed. Different samples, layers and/or animals were aggregated and compared using RSA replicated spatial point processes. The results showed no significant differences in the synaptic distribution across the different rats used in the study. We found that RSA processes described the spatial distribution of synapses in all samples of each layer. We also found that the synaptic distribution in layers II to VI conforms to a common underlying RSA process with different densities per layer. Interestingly, the results showed that synapses in layer I had a slightly different spatial distribution from the other layers.

Random positions of dendritic spines in human cerebral cortex.

Dendritic spines establish most excitatory synapses in the brain and are located in Purkinje cell's dendrites along helical paths, perhaps maximizing the probability to contact different axons. To test whether spine helixes also occur in neocortex, we reconstructed >500 dendritic segments from adult human cortex obtained from autopsies. With Fourier analysis and spatial statistics, we analyzed spine position along apical and basal dendrites of layer 3 pyramidal neurons from frontal, temporal, and cingulate cortex. Although we occasionally detected helical positioning, for the great majority of dendrites we could not reject the null hypothesis of spatial randomness in spine locations, either in apical or basal dendrites, in neurons of different cortical areas or among spines of different volumes and lengths. We conclude that in adult human neocortex spine positions are mostly random. We discuss the relevance of these results for spine formation and plasticity and their functional impact for cortical circuits.