Modeling Intracellular Calcium Waves and Sparks
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In this chapter we shall discuss a variety of intracellular Ca2+ wave phenomena, but always from the perspective that the distance scales of interest are large enough that Ca2+ transport is well-modeled by conservation equations based on a continuum description of matter (recall Chapter 7). Although recent experimental and theoretical work suggests that the macroscopic behavior of propagating Ca2+ waves (e.g., wave speed) may depend in subtle ways on the density and distribution of intracellular Ca2+ release channels, we postpone consideration of intracellular heterogeneities such as clusters of Ca2+ release channels until later in the chapter. This makes sense because both the mathematics and simulation methods used to study nonlinear wave propagation in homogeneous media are simpler than the heterogeneous case. This simplicity should facilitate the development of intuition regarding nonlinear wave propagation. Throughout the chapter a recurring theme will be the manner in which Ca2+ buffers, through their important association with free Ca2+, can influence wave phenomena dependent on diffusion. The chapter concludes with calculations of localized Ca2+ elevations due to intracellular Ca2+ release, i.e., Ca2+ “puffs” or “sparks,” elementary events that sum to produce Ca2+ waves.
KeywordsEndoplasmic Reticulum Wave Model Release Site Wave Phenomenon Heteroclinic Orbit
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