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Reducing neuronal size results in less cell membrane and therefore lower input conductance. Smaller neurons are thus more excitable as seen in their voltage responses to current injections in the soma. However, the impact of a neuron’s size and shape on its voltage responses to synaptic activation in dendrites is much less understood. Here we use analytical cable theory to predict voltage responses to distributed synaptic inputs and show that these are entirely independent of dendritic length. For a given synaptic density, a neuron’s response depends only on the average dendritic diameter and its intrinsic conductivity. These results remain true for the entire range of possible dendritic morphologies irrespective of any particular arborisation complexity. Also, spiking models result in morphology invariant numbers of action potentials that encode the percentage of active synapses. Interestingly, in contrast to spike rate, spike times do depend on dendrite morphology. In summary, a neuron’s excitability in response to synaptic inputs is not affected by total dendrite length. It rather provides a homeostatic input-output relation that specialised synapse distributions, local non-linearities in the dendrites and synaptic plasticity can modulate. Our work reveals a new fundamental principle of dendritic constancy that has consequences for the overall computation in neural circuits.
Borders and edges are salient and behaviourally relevant features for navigating the environment. The brain forms dedicated neural representations of environmental boundaries, which are assumed to serve as a reference for spatial coding. Here we expand this border coding network to include the retrosplenial cortex (RSC) in which we identified neurons that increase their firing near all boundaries of an arena. RSC border cells specifically encode walls, but not objects, and maintain their tuning in the absence of direct sensory detection. Unlike border cells in the medial entorhinal cortex (MEC), RSC border cells are sensitive to the animal’s direction to nearby walls located contralateral to the recorded hemisphere. Pharmacogenetic inactivation of MEC led to a disruption of RSC border coding, but not vice versa, indicating network directionality. Together these data shed light on how information about distance and direction of boundaries is generated in the brain for guiding navigation behaviour.