A general principle of dendritic constancy – a neuron’s size and shape invariant excitability

Abstract 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. In brief We show that realistic neuron models essentially collapse to point neurons when stimulated by randomly distributed inputs instead of by single synapses or current injection in the soma. Highlights A simple equation that predicts voltage in response to distributed synaptic inputs. Responses to distributed and clustered inputs are largely independent of dendritic length. Spike rates in various Hodgkin Huxley (HH) like or Leaky Integrate-and-Fire (LIF) models are largely independent of morphology. Precise spike timing (firing pattern) depends on dendritic morphology. NeuroMorpho.Org database-wide analysis of the relation between dendritic morphology and electrophysiology. Our equations set precise input-output relations in realistic dendrite models.