LOCAL PARTIAL DIFFERENTIAL EQUATION DISCOVERY FOR SPATIO-TEMPORAL CALCIUM DYNAMICS IN ASTROCYTE ENDFEET GEOMETRIES

Calcium signals in astrocytes modulate key brain functions, such as synaptic transmission, cognition and behavior (Ahrens et al., CSHPB, 2024). These functions are in part facilitated by gap junctions (GJs), which allow inter-cellular diffusion of molecules below 1.2 kDa and ions. These channels have historically been observed between neighboring astrocytes and contribute to ion and neurotransmitter homeostasis (Mazaud et al., Glia, 2021).
Recently, gap junctions have been observed between processes of the same cell (Benoit et al., Cell, 2025), which suggests that intracellular GJ-coupling might occur. Concomitantly, recent reports suggest that changes in the morphology of astrocytes in pathological conditions might be accompanied by an increase of intracellular GJ density. For example, Gilbert et al. (eLife, 2021) have reported that perivascular astrocytic processes in megalencephalic leukoencephalopathy are deformed, stacked on top of each other, coupled by large GJ plaques.
Similar observations have been made in APP/PS1 Alzheimer's disease mouse models (unpublished data, Murai lab). Here, we leverage a 3D model of diffusion and a machine learning technique named Partial Differential Equation (PDE) discovery to investigate how such restructuring of astrocyte morphology might impact local signaling.
This framework allows studying the impact of gap junction density and spatial organization on calcium diffusion and identifying governing equations of local microdomains, providing an intuitive understanding of the underlying mechanisms (Messenger et al., JCP, 2021).
Together, this work aims to better understand the influence of intracellular GJ coupling on astrocyte microdomain activity and to assess the consequences of its pathological remodeling.