The position of the axon initial segment assembly site can be predicted from the shape of the neuron

Synopsis

Neurons (nerve cells) show a high level of cellular polarisation that is critical to their function, with an information- receiving somatodendritic and an information propagating axonal compartment. The mechanism by which this critical asymmetry is established is unknown. In vitro, newly plated neurons are symmetric, characterised by a spherical cell that develops multiple non-differentiated (nascent) cell extensions (neurites). Within days in culture, one of the nascent neurites starts to grow rapidly and differentiates into the axon. It has been shown that axonal differentiation can be driven solely by cell-intrinsic mechanisms. The Axon Initial Segment (AIS) in neurons has two major functions: [1] it is the site of action potential generation and [2] it controls the diffusion and transport of molecules and organelles from the somatodendritic into the axonal compartment to establish and maintain neuronal polarity.

I will show that the position of the AIS in three to five day old cultured hippocampal neurons can be accurately predicted based only on the shape of the cell. This prediction is made by considering the eigenfunctions of the Laplacian operator solved over the geometry of the cell. The AIS position coincides with the nodal line of the first harmonic of the operator. This result appears to be robust over our analysed 214 neurons, including examples with large soma-AIS gaps and pseudo-unipolar morphologies.The observation of the AIS position is constant with localisation via a reaction-diffusion system with a Turing instability. This is the same type of mechanism that is responsible for the localisation of the division plane via the Min system in E. coli. The identification and characterisation of such a system is an ongoing project.