  Calcium oscillation is an important calcium homeostasis, imbalance of which
is the key mechanism of initiation and progression of many major diseases. The
formation and maintenance of calcium homeostasis are closely related to the
spatial distribution of calcium channels. In the current paper, a theoretical
framework is established by abstracting the spatial distribution of the calcium
channels as a nonlinear biological complex network with calcium channels as
nodes and Ca$^{2+}$ as edges. A dynamical model for a RyR is adopted to
investigate the effect of spatial distribution on calcium oscillation. The
mean-field model can be well reproduced from the complete graph and dense
Erd\"os-R\'enyi network. The synchronization of RyRs is found important to
generate a global calcium oscillation. The clique graph with a cluster
structure can not produce a global oscillation due to the failure of
synchronization between clusters. A more realistic geometric network is
constructed in a two-dimensional plane based on the experimental information
about the RyR arrangement of clusters and the frequency distribution of cluster
sizes. Different from the clique graph, the global oscillation can be generated
with reasonable parameters on the geometric network. The simulation also
suggests that existence of small clusters and rogue RyR's plays an important
role in the maintenance of global calcium oscillation through keeping
synchronization between large clusters. Such results support the heterogeneous
distribution of RyR's with different-size clusters, which is helpful to
understand recent observations with super resolution nanoscale imaging
techniques. The current theoretical framework can also be extent to investigate
other phenomena in calcium signal transduction.
