Presynaptic Activity-dependent calcium dynamics in cytosol & ER, and a brief proposal for a morphodynamic model of growth cone motility

Understanding the mechanisms regulating Ca2+ concentrations in the presynapse is crucial for synaptic function. The endoplasmic reticulum (ER) acts as a finite calcium store and can modulate calcium signals involved in presynaptic neurotransmitter release. While computational studies have shed light on the spatiotemporal dynamics of calcium in dendritic spines, the distribution of channels along synaptic and ER membranes and their modulation of calcium dynamics remain unclear. We investigated the influence of calcium exchange in different spatial compartments and the dynamics of calcium concentration in the cytosol and ER, revealing the impact of ER calcium on cytosolic calcium in response to action potentials. Additionally, cytosolic calcium plays a crucial role in growth cone motility, transducing guidance cues to the cytoskeleton and generating morphological changes. Understanding calcium's interaction with the growth cone cytoskeleton is key to understanding circuit formation and plasticity. We developed two separate models: a space-time-resolved 3D reaction-diffusion partial differential equation (PDE) model describing calcium dynamics, interactions, and exchange in presynaptic boutons, emphasizing calcium influx through voltage-dependent calcium channels (VDCC) and the distribution of calcium channels and pumps in the ER membrane; and a neuronal growth model based on 3D reaction-diffusion-convection PDEs describing the dynamics of tubulin, MAP-2, and calcium. The plasmatic membrane is a free interface defined by the level set method, and the dynamics of the components determine the kinetics of membrane movement. For both models, we used unstructured surface and volume networks, discretized the PDEs with vertex-centered finite volumes, and solved the resulting systems on parallel clusters. Our simulations elucidate how the axonal ER contributes to presynaptic calcium levels and provide insight into calcium-dependent morphodynamics.