A theoretical investigation of the recruitment of sodium channels to the Axon Initial Segment (AIS) in neurons

Abstract

The axon initial segment (AIS) in neurons plays a vital role in initiating action potentials, primarily due to the high density of voltage-gated sodium (Nav) channels concentrated in this region. These Nav channels contain multiple serine residues that mediate their recruitment to the AIS through interactions with ankyrin-G (AnkG). AnkG plays a pivotal role in neurogenerative diseases such as Alzheimer’s, and it is important to understand the dynamics of its interactions with other proteins. In this paper, we develop a theoretical approach to understand the roles of two AIS proteins—casein kinase 2 (CK2) and AnkG—in facilitating Nav channel recruitment to the AIS membrane by firstly modelling the CK2 phosphorylation of Nav and then the binding of AnkG to phosphorylated Nav. Given the structure of Nav, we develop a conceptual model for the mathematical models based on well-defined macro- and micro- states of Nav that participate in elementary reactions simultaneously. The results of the models are discussed in graphical manner to unravel the complexity associated with the AIS dynamics and the dependence of associated kinetic coefficients.