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Fig. 4 | The Journal of Mathematical Neuroscience

Fig. 4

From: What Is Required for Neuronal Calcium Waves? A Numerical Parameter Study

Fig. 4

Threshold ER radius for eliciting stable calcium waves. For any tested combination of RyR channel density and dendrite radius, there exists a threshold ER radius above which stable calcium waves can be elicited. Overall, the threshold ER radius increases with increasing dendrite radius (since there is more space that the released calcium can diffuse into, which reduces the effective near-ER-membrane concentration) and decreasing RyR density (indicating that the ability to sustain a stable calcium wave scales with the rate of calcium release from the ER). (A) Threshold ER radius as a function of RyR channel density in the ER membrane. The lower four traces, corresponding to the lower dendrite radii, exhibit similar quasi-hyperbolic behavior, scaled by the dendrite radius. They can be fitted by a functional description that assumes instant radial distribution of released calcium in the small radial range from ER to plasma membrane, cf. “Empirical threshold laws”. The upper traces, corresponding to larger dendrites, show two separate regimes: Separated to the left, where the distance between ER and plasma membrane is small, they converge towards a limit trace to the right, where the two membranes are far away from each other. This convergence can be attributed to wave propagation that is faster than radial diffusion to the plasma membrane, cf. again “Empirical threshold laws”. (B) Threshold ER radius as a function of dendrite radius (like A, but projected onto perpendicular plane). While the traces are approximately linear in a small dendrite regime, they reach a limit threshold for larger dendrites. No such limit is reached for the lowest RyR density tested. This is due to calcium buffering in the cytosol. Thus, ER size does not need to be increased proportionally with dendrite radius. Neurons could therefore ensure stable calcium waves, even within larger dendrites, where intracellular space is occupied by other organelles

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