Geometrical factors determining dendritic domain intersection between neurons: a modeling study

Abstract

ABSTRACTOverlap between dendritic trees of neighboring neurons is a defining feature of central nervous systems. Dendritic domains sharing a given locus are arguably more likely to share afferent inputs, and proximity is a requirement for dendro-dendritic communication. Dendritic overlap also differentiates neuronal circuits characterized by redundancy and integration from those characterized by a more specific and selective connectivity. We examined the geometrical factors that affect intersection between pairs of neurons by, specifically, modelling the influence of cell-to-cell distance, and dendritic domain size and shape. We developed MATLAB scripts to determine intersected volume between pairs of three-dimensionally reconstructed neurons using their convex hull (CH) polyhedrons as proxies for dendritic domain. The influence of neuron-to-neuron distance on intersection was not straightforward and reflected the diverse and anisotropic geometry of neurons, and the ostensible displacement of cell bodies from the CH centroid. The influence of size on pair intersection was tested by giving each neuronal CH pair the same (average) volume without modifying their shape. Conversely, the influence of neuronal shape on pair intersection was proved by giving each neuronal pair an average shape without modifying volumes. While both normalization increased intersection, shape averaging was remarkably more effective than size averaging in increasing pair intersection. We conclude that intersection does not only depend on neuron-to-neuron proximity, but critically on neuron-to-neuron differences in size and shape. The results predict that circuits characterized by selective connectivity exhibit greater heterogeneity in size, but especially shape, of their constituent neuronal elements.Author summaryNeurons communicate with each other using specialized domains called axons and dendrites. Throughout the brain, dendrites from adjacent neurons overlap. This dendritic overlap helps neurons to share common input information coming from axons and also permits communication between dendrites themselves. One way to study dendritic overlap is using the geometrical representation of the dendrites ‘field of view’, using simplified three-dimensional geometrical shapes (polyhedrons) called convex hulls. In this computational study, we used these convex hulls to analyze the geometrical factors underlying intersection between neurons. For that, we developed methods to obtain the intersected volume of pairs of convex hulls from neurons, to then independently modify the location, size and shape of convex hulls. We observed high variability in intersected volume, even when the neurons were at a similar distance between each other. Relevantly, we also found that variability in volume, but especially variability in convex hull shape is the main factor that determines the degree of intersection between pairs of neurons. These data suggest that differences in dendritic size, but especially differences in shape between neurons have a strong effect on overlap between neurons, and therefore on the potential for neurons to share input information and communicate with each other.