The influence of Ca²⁺ buffers on free [Ca²⁺] fluctuations and the effective volume of Ca²⁺ microdomains

Intracellular calcium (Ca(2+)) plays a significant role in many cell signaling pathways, some of which are localized to spatially restricted microdomains. Ca(2+) binding proteins (Ca(2+) buffers) play an important role in regulating Ca(2+) concentration ([Ca(2+)]). Buffers typically slow [Ca(2+)] temporal dynamics and increase the effective volume of Ca(2+) domains. Because fluctuations in [Ca(2+)] decrease in proportion to the square-root of a domain's physical volume, one might conjecture that buffers decrease [Ca(2+)] fluctuations and, consequently, mitigate the significance of small domain volume concerning Ca(2+) signaling. We test this hypothesis through mathematical and computational analysis of idealized buffer-containing domains and their stochastic dynamics during free Ca(2+) influx with passive exchange of both Ca(2+) and buffer with bulk concentrations. We derive Langevin equations for the fluctuating dynamics of Ca(2+) and buffer and use these stochastic differential equations to determine the magnitude of [Ca(2+)] fluctuations for different buffer parameters (e.g., dissociation constant and concentration). In marked contrast to expectations based on a naive application of the principle of effective volume as employed in deterministic models of Ca(2+) signaling, we find that mobile and rapid buffers typically increase the magnitude of domain [Ca(2+)] fluctuations during periods of Ca(2+) influx, whereas stationary (immobile) Ca(2+) buffers do not. Also contrary to expectations, we find that in the absence of Ca(2+) influx, buffers influence the temporal characteristics, but not the magnitude, of [Ca(2+)] fluctuations. We derive an analytical formula describing the influence of rapid Ca(2+) buffers on [Ca(2+)] fluctuations and, importantly, identify the stochastic analog of (deterministic) effective domain volume. Our results demonstrate that Ca(2+) buffers alter the dynamics of [Ca(2+)] fluctuations in a nonintuitive manner. The finding that Ca(2+) buffers do not suppress intrinsic domain [Ca(2+)] fluctuations raises the intriguing question of whether or not [Ca(2+)] fluctuations are a physiologically significant aspect of local Ca(2+) signaling.