A bifurcation analysis of calcium buffering

Many mathematical models of calcium oscillations model buffering implicitly by using a rapid buffering approximation. This approximation assumes that separate time scales can be distinguished, with the buffer reactions occurring on a faster time scale than the other calcium fluxes. The rapid buffering approximation is convenient as it reduces the model to a single transport equation for calcium, but buffering is not always so fast. We investigated what happens if such an assumption is made for slower buffers for parameter values typical of both endogenous and exogenous buffers. We found that no qualitative differences are introduced to the bifurcation structure, i.e. there are no anomalous behaviour or artifacts in the dynamics when a rapid buffering approximation is used compared with including buffering explicitly in the model. We found that there exist distinct buffer parameter regions in which either the rapid buffering approximation or an assumption of no buffering could be used. Separating the two regions was a small transition region of buffer parameters for which care needs to be taken in modelling buffers. However, overall, the qualitative behaviour in all three regions was similar.