The Influence of Ca Buffers on Free [Ca] Fluctuations and the Effective Volume of Ca Microdomains

Intracellular calcium (Ca²⁺) plays a significant role in many cell signaling pathways, some of which are localized to spatially restricted microdomains. Ca²⁺ binding proteins (Ca²⁺ buffers) play an important role in regulating Ca²⁺ concentration (Ca²⁺]). Buffers typically slow Ca²⁺] temporal dynamics and increase the effective volume of Ca²⁺ domains. Because fluctuations in Ca²⁺] decrease in proportion to the square-root of a domain’s physical volume, one might conjecture that buffers decrease Ca²⁺] fluctuations and, consequently, mitigate the significance of small domain volume concerning Ca²⁺ signaling. We test this hypothesis through mathematical and computational analysis of idealized buffer-containing domains and their stochastic dynamics during free Ca²⁺ influx with passive exchange of both Ca²⁺ and buffer with bulk concentrations. We derive Langevin equations for the fluctuating dynamics of Ca²⁺ and buffer and use these stochastic differential equations to determine the magnitude of Ca²⁺] 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 Ca²⁺ signaling, we find that mobile and rapid buffers typically increase the magnitude of domain Ca²⁺] fluctuations during periods of Ca²⁺ influx, whereas stationary (immobile) Ca²⁺ buffers do not. Also contrary to expectations, we find that in the absence of Ca²⁺ influx, buffers influence the temporal characteristics, but not the magnitude, of Ca²⁺] fluctuations. We derive an analytical formula describing the influence of rapid Ca²⁺ buffers on Ca²⁺] fluctuations and, importantly, identify the stochastic analog of (deterministic) effective domain volume. Our results demonstrate that Ca²⁺ buffers alter the dynamics of Ca²⁺] fluctuations in a nonintuitive manner. The finding that Ca²⁺ buffers do not suppress intrinsic domain Ca²⁺] fluctuations raises the intriguing question of whether or not Ca²⁺] fluctuations are a physiologically significant aspect of local Ca²⁺ signaling.