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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.

During active somatosensation, neural signals expected from movement of the sensors are suppressed in the cortex, whereas information related to touch is enhanced. This tactile suppression underlies low-noise encoding of relevant tactile features and the brain's ability to make fine tactile discriminations. Layer (L) 4 excitatory neurons in the barrel cortex, the major target of the somatosensory thalamus (VPM), respond to touch, but have low spike rates and low sensitivity to the movement of whiskers. Most neurons in VPM respond to touch and also show an increase in spike rate with whisker movement. Therefore, signals related to self-movement are suppressed in L4. Fast-spiking (FS) interneurons in L4 show similar dynamics to VPM neurons. Stimulation of halorhodopsin in FS interneurons causes a reduction in FS neuron activity and an increase in L4 excitatory neuron activity. This decrease of activity of L4 FS neurons contradicts the "paradoxical effect" predicted in networks stabilized by inhibition and in strongly-coupled networks. To explain these observations, we constructed a model of the L4 circuit, with connectivity constrained by in vitro measurements. The model explores the various synaptic conductance strengths for which L4 FS neurons actively suppress baseline and movement-related activity in layer 4 excitatory neurons. Feedforward inhibition, in concert with recurrent intracortical circuitry, produces tactile suppression. Synaptic delays in feedforward inhibition allow transmission of temporally brief volleys of activity associated with touch. Our model provides a mechanistic explanation of a behavior-related computation implemented by the thalamocortical circuit.