Analysis of spatial relationships in three dimensions: tools for the study of nerve cell patterning

Our tools enable the analysis of the spatial relationship between neurons within the central nervous system in 3D, and permit the modeling of these fields based on lattice-like simulations, and on simulations of minimal-distance spacing rules. Here we demonstrate the utility of our analysis methods to discriminate between two different simulated neuronal populations.Together, these tools can be used to reveal the presence of nerve cell patterning and to model its foundation, in turn informing on the potential developmental mechanisms that govern its establishment. Furthermore, in conjunction with analyses of dendritic morphology, they can be used to determine the degree of dendritic coverage within a volume of tissue exhibited by mature nerve cells.Recent advances in developmental neuroscience have revealed how the mechanisms controlling proliferation, fate determination, migration, differentiation, synaptogenesis and cell death each contribute to the establishment of the architecture and connectivity of the mature brain. What has been lacking, however, is an understanding of the determinants of the positioning of neurons in 3D space: what controls the position a neuron will come to occupy within a brain structure relative to other cells in the local environment? In some structures, cells are packed side-by-side and there is no mystery to their spacing; in others, the distance between members of a cell type is often conspicuous, but we know nothing of the constraints imposing this spacing. We do not know, for instance, whether higher-order patterning is present, much like a rough or distorted lattice, or whether such cells are essentially randomly distributed within a volume of tissue, constrained only by the physical size of other cells. We may know quite a bit about the dendritic morphology of individual cells within a region, and can make inferences about the relationship between the morphology of a cell and how a population of those cells should be distributed t