# Impact on backpropagation of the spatial heterogeneity of sodium channel kinetics in the axon initial segment

## TL;DR

This study shows how the location of sodium channels in neurons affects how signals travel back into the cell, which could influence learning and development.

## Contribution

The paper reveals how spatial distribution of sodium channel subtypes in the AIS differentially impacts backpropagation under somatic and axonal stimulation.

## Key findings

- Proximal clustering of right-shifted sodium channels enhances backpropagation during axonal stimulation.
- Somatic stimulation leads to impaired backpropagation due to higher activation thresholds of right-shifted channels.
- Developmental changes in sodium channel distribution affect both activation and availability kinetics.

## Abstract

In a variety of neurons, action potentials (APs) initiate at the proximal axon, within a region called the axon initial segment (AIS), which has a high density of voltage-gated sodium channels (NaVs) on its membrane. In pyramidal neurons, the proximal AIS has been reported to exhibit a higher proportion of NaVs with gating properties that are “right-shifted” to more depolarized voltages, compared to the distal AIS. Further, recent experiments have revealed that as neurons develop, the spatial distribution of NaV subtypes along the AIS can change substantially, suggesting that neurons tune their excitability by modifying said distribution. When neurons are stimulated axonally, computational modelling has shown that this spatial separation of gating properties in the AIS enhances the backpropagation of APs into the dendrites. In contrast, in the more natural scenario of somatic stimulation, our simulations show that the same distribution can impede backpropagation, suggesting that the choice of orthodromic versus antidromic stimulation can bias or even invert experimental findings regarding the role of NaV subtypes in the AIS. We implemented a range of hypothetical NaV distributions in the AIS of three multicompartmental pyramidal cell models and investigated the precise kinetic mechanisms underlying such effects, as the spatial distribution of NaV subtypes is varied. With axonal stimulation, proximal NaV
availability dominates, such that concentrating right-shifted NaVs in the proximal AIS promotes backpropagation. However, with somatic stimulation, the models are insensitive to availability kinetics. Instead, the higher activation threshold of right-shifted NaVs in the AIS impedes backpropagation. Therefore, recently observed developmental changes to the spatial separation and relative proportions of NaV1.2 and NaV1.6 in the AIS differentially impact activation and availability. The observed effects on backpropagation, and potentially learning via its putative role in synaptic plasticity (e.g. through spike-timing-dependent plasticity), are opposite for orthodromic versus antidromic stimulation, which should inform hypotheses about the impact of the developmentally regulated subcellular localization of these NaV subtypes.

Neurons use sodium ion currents, controlled by a neuron’s voltage, to trigger signals called action potentials (APs). These APs typically result from synaptic input from other neurons onto the dendrites and soma. An AP is generated at the axon initial segment (AIS) just beyond the soma. From there, it travels down the axon to other cells, but can also propagate “backwards” into the soma and dendrites. This “backpropagation” allows the neuron to compare the timing of outgoing and incoming signals at synapses where input was received, a feedback process that modifies its connections to other neurons (spike-timing-dependent synaptic plasticity) which is a mechanism for learning. It is puzzling that in many neurons, sodium ion channels come in two types: high-voltage threshold channels clustered near the soma where the AIS begins, and low-voltage ones further away towards the axon. This separation changes in the early development of the animal, which raises the question of its role in backpropagation. We constructed detailed mathematical models to explore how separation affects backpropagation. Separation either impedes or enhances backpropagation, depending on whether the AP results from input to the soma or dendrites or, less typically, input received in the axon. This is explained by the different effects the separation has on two key kinetic processes that govern sodium currents.