Neuron morphological physicality and variability define the non-random structure of connectivity

Connectivity in neuronal networks is characterized by high complexity that is required for the correct function of the circuitry. Our attempts to capture it has thus far been limited to the addition of individual features of complexity to stochastic models, leading to limited insights into its origin. Based on the idea that the morphologies of neurons underlies the network structure, we developed an intuitive explanation for the mechanisms leading to structured, non-random connectivity. While a class of neurons on average innervates its entire surroundings, each individual one can only cover a small part of the space. That part is different for each neuron, but in a way that is not completely random, as it must be spatially continuous due to the physicality of neurites. We tested predictions from our hypothesis successfully in biophysically-detailed models and an electron-microscopic (EM) reconstruction of cortical connectivity. We distilled it into a simple stochastic algorithm that generates networks, which accurately match the EM reconstruction in basic network statistics as well as functionally relevant metrics of complexity. Our work may improve the understanding of the impact of neuron malformations and enable the study of the functional role of non-random network structure in simplified models.