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.Author summary: Dendritic tree structures of nerve cells are built to optimally collect inputs from other cells in the circuit. By looking at how regularly the branch and termination points of dendrites are distributed, we find characteristic differences between cell types that correlate little with other traditional branching statistics and affect their scaling properties. Using computational models based on optimal wiring principles, we then show that termination points of dendrites generally spread more randomly than the inputs that they receive while branch points follow more closely the underlying input organization. Existing connectome data validate these predictions indicating the importance of our findings for large scale neural circuit analysis.