nAdder: A scale-space approach for the 3D analysis of neuronal traces

Tridimensional microscopy and algorithms for automated segmentation and tracing are revolutionizing neuroscience through the generation of growing libraries of neuron reconstructions. Innovative computational methods are needed to analyze these neuronal traces. In particular, means to characterize the geometric properties of traced neurites along their trajectory have been lacking. Here, we propose a local tridimensional (3D) scale metric derived from differential geometry, measuring for each point of a curve the characteristic length where it is fully 3D as opposed to being embedded in a 2D plane or 1D line. The larger this metric is and the more complex the local 3D loops and turns of the curve are. Available through the GeNePy3D open-source Python quantitative geometry library (https://genepy3d.gitlab.io), this approach termed nAdder offers new means of describing and comparing axonal and dendritic arbors. We validate this metric on simulated and real traces. By reanalysing a published zebrafish larva whole brain dataset, we show its ability to characterize different population of commissural axons, distinguish afferent connections to a target region and differentiate portions of axons and dendrites according to their behavior, shedding new light on the stereotypical nature of neurites’ local geometry.Auhor summary: To study how brain circuits are formed and function, one can extract neuron traces, i.e. the precise path that neuron arbors take in the brain to connect to other neurons. New techniques enable to do so with increasingly higher throughput, up to every single neuron with so called ‘connectomic’ approaches. Up to now, the geometry of those traces has not been a focus of study and has mainly been analysed in bulk/on average. Here, we propose to quantitatively analyse the local 3D geometry of the curves that comprise neuron arbors. We introduce an algorithm that determines whether a locally-defined curve is best fit to a line, a plane or a 3D structure. We use it to compute a single number at each point of the trace, termed local 3D scale, that measures the characteristic size of the local 3D structure: the larger this local 3D scale metric, the more the neuron’s curve meanders in 3D locally. We reanalyse published neuronal traces to demonstrate that our local geometry approach enables to better characterize a neuron’s morphology, with direct relevance to understanding its development and function. The local 3D scale metric will be useful in all neuroscience research that works with neuronal traces, bringing a new, geometric layer of information.