Modelling CK2-dependent phosphorylation and ankyrin-G binding in sodium channel recruitment to the axon initial segment

The axon initial segment (AIS) is essential for action potential initiation due to the high density of voltage-gated sodium (Nav) channels localized in this region. The recruitment of Nav channels to the AIS is mediated by ankyrin-G (AnkG) and regulated by phosphorylation via casein kinase 2 (CK2), yet the dynamic interplay between these processes remains poorly understood. In this study, we develop a mathematical model to investigate the coupled roles of CK2-mediated phosphorylation and AnkG binding in Nav channel recruitment. The model incorporates distinct molecular states of Nav channels and describes their transitions through a system of coupled kinetic equations. Our results show that phosphorylation acts as a regulatory mechanism controlling the availability of AnkG-binding-competent Nav states. The model further reveals nonlinear behaviour in channel recruitment, with phosphorylation kinetics leading to significant variations in Nav localization. Analysis identifies key parameters governing system dynamics, suggesting potential mechanisms by which disruptions in CK2 or AnkG function may contribute to neuronal dysfunction. These findings provide a quantitative framework for understanding AIS assembly and generate testable predictions for experimental studies of Nav channel localization and associated neurological disorders.