  Calcium is an ubiquitous second messenger that triggers a plethora of key
physiological responses. The events are initiated in micro- or nano-sized
compartments and determined by the complex interactions with calcium-binding
proteins and mechanisms of calcium clearance. Local calcium increases in the
vicinity of single channels represent an essentially non-linear
reaction-diffusion problem that have been analysed previously using various
linearized approximations. I revisited the problem of stationary patterns that
can be generated by the point calcium source in the presence of buffer and
obtained new explicit solutions. Main results of the analysis of the calcium
buffering are supplemented with pertinent derivations and discussion of
respective mathematical problems in Appendices. I show that for small calcium
influx the calcium gradients around established around channel lumen have
quasi-exponential form. For bigger fluxes, when the buffer is saturated, the
model predicts periodic patterns. The transition between the two regimes depend
on the capacity of buffer and its mobility. Theoretical predictions were
examined using a model one-dimensional system. For sufficiently big fluxes the
oscillatory calcium patterns were observed. Theoretical and experimental
results are discussed in terms of their possible physiological implications.
