Mathematical Model of Astrocytic Ion Transport Dynamics Under Brain Ischemia

抄録

The multiple ion transporters on astrocytic membranes maintain ion homeostasis in brain tissue. The gradient of ion concentration under brain ischemia is collapsed because the Na⁺-K⁺, ATPase induces functional deficits by ATP deprivation, which leads to functional dysfunction and induces water entry into the cell. In previous studies, both experimental methods and simulation models have focused on the changes in transport rates by multiple ion transporters during ATP deprivation. Although understanding the kinetics of ion disruption is critical, equations conventionally designed for passive transport are mostly applied to the secondary active transporters, and analyses that fully accommodate their functional characteristics remain limited. In this study, based on the Hodgkin–Huxley equation, a transport rate equation was constructed by incorporating both the potential driven by the electric gradient and that driven by the concentration gradient for each ion, weighted by their respective transition probabilities. Subsequently, the changes in transport rates were analyzed at varying concentrations of ATP and glutamate, pH. As a result, the changes in transport rates for each transporter were successfully quantified in response to intracellular and extracellular environmental conditions. Furthermore, the functional degradation process of the transporters was reproduced, enabling a more quantitative analysis of irreversible loss of ionic homeostasis.