On calcium-buffer dynamics within the excess buffer regime

In intracellular calcium signaling, calcium buffers has been recognized for their role in reshaping and localizing the calcium concentration profile in the vicinity of the channel, as well as reducing the effective diffusion of free calcium. In the presence of an excess of endogenous or exogenous buffers, linearization of the reaction-diffusion system describing the calcium-buffer dynamics has been instrumental in understanding the extent of the microdomain formation and in quantifying the apparent diffusion of the free calcium. In these linearized models, the conclusions are usually drawn from the steady-state solutions upon the opening of the channel. In this work, using the joint Laplace-Fourier method, we give an explicit integral transient solution, as well as, the long-time asymptotic behavior of the linearized calcium-buffer dynamics. The results confirm and emphasize the long stated intuitions on the diffusive character of the calcium-buffer dynamics. Numerical validations of our analytical results will be discussed.