  Ca$^{2+}$ plays an important role in cell signal transduction. Its
intracellular propagation is the most basic process of Ca$^{2+}$ signaling,
such as calcium wave and double messenger system. In this work, with both
numerical simulation and mean field ansatz, the 3-dimensional probability
distribution of Ca$^{2+}$, which is read out by phosphorylation, is studied in
two scenarios with boundaries. The coverage of distribution of Ca$^{2+}$ is
found at an order of magnitude of $\mu$m, which is consistent with experimental
observed calcium spike and wave. Our results suggest that the double messenger
system may occur in the ER-PM junction to acquire great efficiency. The buffer
effect of kinase is also discussed by calculating the average position of
phosphorylations and free Ca$^{2+}$. The results are helpful to understand the
mechanism of Ca$^{2+}$ signaling.
