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

Abstract

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. 2/57Dendritic constancy Cuntz et al. Abstract 1Reducing neuronal size results in less cell membrane and therefore lower input conductance. 2 Smaller neurons are thus more excitable as seen in their voltage responses to current injections 3 in the soma. However, the impact of a neuron's size and shape on its voltage responses to 4 synaptic activation in dendrites is much less understood. Here we use analytical cable theory 5 to predict voltage responses to distributed synaptic inputs and show that these are entirely 6 independent of dendritic length. For a given synaptic density, a neuron's response depends 7 only on the average dendritic diameter and its intrinsic conductivity. These results remain 8 true for the entire range of possible dendritic morphologies irrespective of any particular 9 arborisation complexity. Also, spiking models result in morphology invariant numbers of 10 action potentials that encode the percentage of active synapses. Interestingly, in contrast to 11 spike rate, spike times do depend on dendrite morphology. In summary, a neuron's excitability 12 in response to synaptic inputs is not affected by total dendrite length. It rather provides a 13 homeostatic input-output relation that specialised synapse distributions, local non-linearities 14 in the dendrites and synaptic plasticity can modulate. Our work reveals a new fundamental 15 principle of dendritic constancy that has consequences for the overall computation in neural 16 circuits. 17

Dendritic normalisation improves learning in sparsely connected artificial neural networks

“…Cuntz et al (2019) [ 23 ] have shown that neuronal excitability in response to distributed synaptic input is invariant of size. This invariance is exact for a homogeneous passive cable and holds approximately for realistic heterogeneities in dendritic diameter, topology, input dynamics, and active properties.…”

Dendritic normalisation improves learning in sparsely connected artificial neural networks

“…Conversely, larger cells typically have 18 lower input resistances, due to the increased spatial extent and membrane surface area, meaning that larger 19 synaptic currents are necessary to induce the same voltage response and so bring a neuron to threshold (Rall,20 1957; Mainen & Sejnowski, 1996). It has recently been shown by Cuntz et al (2019) that these two phenomena 21 cancel each other exactly: the excitability of neurons receiving distributed excitatory synaptic inputs is largely 22 invariant to changes in size and morphology. In addition, neurons possess several active mechanisms to help 23 maintain firing-rate homeostasis through both synaptic plasticity regulating inputs (Abbott & Nelson, 2000;24 Royer & Paré, 2003) and changes in membrane conductance regulating responses (Gorur-Shandilya et al, 2019).…”

“…We have shown that normalising afferent synaptic weights by their number (L 0 -normalisation), in a manner 168 similar to real neurons (Cuntz et al, 2019), improves the learning performance of sparse artificial neural networks 169 with a variety of different structures. Such dendritic normalisation constrains the weights and expected inputs to 170 be within relatively tight bands, potentially making better use of available neuronal resources.…”

“…Dendrites are able to passively amplify signals selectively 213 based on their timing and direction (Rall, 1962) and actively perform hierarchical computations over branches 214 (Poirazi et al, 2003). Cuntz et al (2019) noted that while mean neuronal firing rates are size-independent, the 215 timing of individual spikes is not necessarily unaffected by morphology. This means that signals encoded by rates 216 are normalised whereas those encoded by spike timing may not be, implying that the two streams of information 217 across the same circuit pathways are differentially affected by changing connectivity.…”

“…we have taken the insights from Cuntz et al (2019) and demonstrated a previously unappreciated way that 228 the structure of dendrites, in particular their properties as leaky core conductors receiving distributed inputs, 229…”