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Modeling Intracellular Calcium Waves and Sparks

  • Gregory D. Smith
  • John E. Pearson
  • Joel E. Keizer
Chapter
Part of the Interdisciplinary Applied Mathematics book series (IAM, volume 20)

Abstract

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.

Keywords

Endoplasmic Reticulum Wave Model Release Site Wave Phenomenon Heteroclinic Orbit 
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Suggestions for Further Reading

  1. Simulation of the fertilization calcium wave in Xenopus laevis eggs, John Wagner, Yue Xian Li, John Pearson, Joel Keizer. Modeling study of the fertilization Ca2+ wave that suggests inhomogeneities in the Ca2+ release properties near the plasma membrane are required to explain the shape and speed of these waves (Wagner et al. 1998).Google Scholar
  2. Diffusion of inositol 1,4,5-trisphosphate but not Ca2+is necessary for a class of inositol 1,4,5-trisphosphate-induced Ca2+waves, Saleet Jafri and Joel Keizer. A modeling study of kinematic IP3-mediated Ca2+ waves (Jafri and Keizer 1994).Google Scholar
  3. Mathematical Biology, James D. Murray. Advanced mathematical treatment of biological wave phenomena (Murray 1989).Google Scholar
  4. Propagation of waves in an excitable medium with discrete release sites, James Keener. Mathematical analysis of wave propagation in inhomogeneous bistable media (Keener 2000).Google Scholar
  5. Fire-diffuse-fire model of dynamics of intracellular calcium waves, Silvia Ponce-Dawson, Joel Keizer, John Pearson. The fire-diffuse-fire model is analyzed to illuminate the differences between continuous and saltatory Ca2+ wave propagation (Ponce-Dawson et al. 1999).Google Scholar
  6. Asymptotic analysis buffered Ca2+diffusion near a point source, Greg Smith, Longxiang Dai, Robert Miura, and Arthur Sherman. Details the rapid and excess buffer approximations appropriate for modeling the steady-state Ca2+ and buffer profiles of localized Ca2+ elevations (Smith et al. 2001).Google Scholar
  7. Modeling local and global Ca2+signals using reaction-diffusion equations, Greg Smith. This book chapter provides more discussion on the effect of buffers on propagating Ca2+ waves as well as simulations utilizing the rapid buffering approximation outside the low-affinity limit (Smith 2001).Google Scholar

Copyright information

© Springer-Verlag New York, Inc. 2002

Authors and Affiliations

  • Gregory D. Smith
  • John E. Pearson
  • Joel E. Keizer

There are no affiliations available

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