Fig. 6

Schematics for deriving empirical threshold laws of wave stability. (A) In a stable wave regime the axial position x, where a cytosolic threshold calcium concentration \(c^{\star }\) is attained near the ER membrane, needs to move by Δx to the right within a given time Δt (defined by the wave velocity). The amount of calcium required to increase the original concentration at \(x + \Delta x\) needs to be released from the ER. (B) In dendrites where the distance between ER and plasma membrane is small (compared to the diffusive range of calcium for time Δt), the iso-concentration surfaces (indicated by blue-to-red sequence of lines) are nearly radially aligned. This means the released calcium is roughly constant in radial direction. (C) In dendrites where the distance between ER and plasma membrane is large (compared to the diffusive range), the iso-concentration manifolds (blue-to-red sequence of lines) are bent backwards in axial direction. Calcium released from the ER only diffuses to an effective radius within the wave propagation time Δt and the wave front does not “sense” the plasma membrane