Saltatory and Continuous Calcium Waves and the Rapid Buffering Approximation

Abstract

Calcium waves propagate inside cells due to a regenerative mechanism known as calcium-induced calcium release. Buffer-mediated calcium diffusion in the cytosol plays a crucial role in the process. However, most models of calcium waves either treat buffers phenomenologically or assume that they are in equilibrium with calcium (the rapid buffering approximation). In this article we address the issue of whether this approximation provides a good description of wave propagation. We first compare the timescales present in the problem, and determine the situations in which the equilibrium hypothesis fails. We then present a series of numerical studies based on the simple fire-diffuse-fire model of wave propagation. We find that the differences between the full and reduced descriptions may lead to errors that are above experimental resolution even for relatively fast buffers in the case of saltatory waves. Conversely, in the case of continuous waves, the approximation may give accurate results even for relatively slow buffers.

Distribution of inositol-1,4,5-trisphosphate receptor isotypes and ryanodine receptor isotypes during maturation of the rat hippocampus

“…Consistent with clustering of InsP 3 R1s, functional studies report "hotspots" of internal Ca 2+ release and "Ca 2+ sparks" in non-neuronal cell types (Cheng et al, 1993;Callamaras et al, 1998;Mak et al, 2001;Dargan and Parker, 2003;Dargan et al, 2004). Computational studies provide additional support for clusters of InsP 3 Rs playing an important role in salutatory propagation of Ca 2+ waves within cells (Dawson et al, 1999;Shuai and Jung, 2003;Strier et al, 2003). Finally, clusters of InsP 3 R1s at dendritic bifurcations are consistent with the observation that internal Ca 2+ release in hippocampal pyramidal cells tends to initiate at branch points (Nakamura et al, 2002).…”

Approximate Analytical Time-Dependent Solutions to Describe Large-Amplitude Local Calcium Transients in the Presence of Buffers

“…We considered a special case of Ca 21 waves that are supported by the Ca 21 -induced Ca 21 release (CICR) from the internal stores (endoplasmic reticulum and/or mitochondria (35)) that have been documented in various cell types. We used a sort of ''diffuse-andfire'' model (16,25), which assumes that at any time only one release channel is open and the activation of neighboring channel occurs only when the [Ca 21 ] level in its vicinity reaches a given threshold.…”

“…Hundreds of articles considered various aspects of the local [Ca 21 ] i signals. Illustrative results include the analysis of the form (4,5) and modeling of the function of micro-and nanodomains (6,7), the measurements of spatial widths of [Ca 21 ] i increases around the single channels (8)(9)(10)(11), the effects of buffers on [Ca 21 ] i oscillations (12,13) and waves (14)(15)(16)(17)(18), and Ca 21 dynamics in the dendritic compartments (19); also included are stochastic spreading and integration of intracellular Ca 21 release (20,21) and the effects of exogenous buffers on [Ca 21 ] i transients (22) and waves (23). These and other studies delivered many important insights on spatiotemporal patterns of Ca 21 within neurons and other cell types that is also summarized in several reviews (1,24,25).…”

Signaling in Small Subcellular Volumes. I. Stochastic and Diffusion Effects on Individual Pathways

“…Many studies have examined pattern formation through interacting chemical reactions (Harrison, 1993). The propagation of chemical waves, especially in calcium signaling, has been simulated and closely related to experiments (Fink et al, 2000;Strier et al, 2003). Recent experimental techniques have begun to open the way for investigation of signaling effects on the scale of cellular microdomains (Rich et al, 2000) and dendritic spines (Sabatini and Svoboda, 2000;Goldberg et al, 2003).…”