Ca2+ spiral waves in a spatially discrete and random medium

College of Science, China University of Mining and Technology, 221008 Xuzhou, China.
Biophysics of Structure and Mechanism (Impact Factor: 2.22). 08/2009; 38(8):1061-8. DOI: 10.1007/s00249-009-0509-y
Source: PubMed


It is well known that the spatial distribution of the calcium ion channels in the endoplasmic reticulum is discrete. We study the Ca(2+) spiral pattern formation based on a model in which ion channels are discretely and randomly distributed. Numerical simulations are performed on different types of media with the Ca(2+) release sites uniformly distributed, discretely and uniformly arranged, or discretely and randomly arranged. The comparisons among the different media show that random distribution is necessary for spontaneous initiation of Ca(2+) spiral waves, and the discrete and random distribution is of significance for spiral waves under physiologically reasonable conditions. The period and velocity of spiral waves are also calculated, and they are not prominently changed by varying the type of medium.

Download full-text


Available from: Jun Tang, Oct 06, 2015
11 Reads
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Based on a modified 2D cardiac tissue model, the spiral-wave dynamics is numerically studied. The diversity in the cardiac tissue is considered by letting the value of a dynamical parameter Gaussian distributed. It is found that, comparing to the dynamical parameter I0 of the model, the spiral waves in the cardiac tissue are much robust to the diversity. Only strong diversity can destroy the spiral waves. It is intriguing that although the weak diversity can not suppress the spiral, it can induce the transition of spiral tips between different types.
    EPL (Europhysics Letters) 01/2012; 97(2):28003. DOI:10.1209/0295-5075/97/28003 · 2.10 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: The inositol 1,4,5-trisphosphate (IP(3)) receptor is a Ca(2+) channel located in the endoplasmic reticulum and is regulated by IP(3) and Ca(2+). This channel is critical to calcium signaling in cell types as varied as neurons and pancreatic beta cells to mast cells. De Young and Keizer (1992) created an eight-state, nine-variable model of the IP(3) receptor. In their model, they accounted for three binding sites, a site for IP(3), activating Ca(2+), and deactivating Ca(2+). The receptor is only open if IP(3) and activating Ca(2+) is bound. Li and Rinzel followed up this paper in 1994 by introducing a reduction that made it into a two variable system. A recent publication by Rossi et al. (2009) studied the effect of introducing IP(3)-like molecules, referred to as partial agonists (PA), into the cell to determine the structure-function relationship between IP(3) and its receptor. Initial results suggest a competitive model, where IP(3) and PA fight for the same binding site. We extend the original eight-state model to a 12-state model in order to illustrate this competition, and perform a similar reduction to that of Li and Rinzel in the first modeling study we are aware of considering PA effect on an IP(3) receptor. Using this reduction we solve for the equilibrium open probability for calcium release in the model. We replicate graphs provided by the Rossi paper, and find that optimizing the subunit affinities for IP(3) and PA yields a good fit to the data. We plug our extended reduced model into a full cell model, in order to analyze the effects PA have on whole cell properties specifically the propagation of calcium waves in two dimensions. We conclude that PA creates qualitatively different calcium dynamics than would simply reducing IP(3), but that effectively PA can act as an IP(3) knockdown.
    Journal of Theoretical Biology 06/2012; 310:97-104. DOI:10.1016/j.jtbi.2012.06.011 · 2.12 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: The cytosolic calcium system is inhomogenous because of the discrete and random distribution of ion channels on the ER membrane. It is well known that the spiral tip can be pinned by the heterogenous area, and the field can detach the spiral from the heterogeneity. We use the adventive field to counteract the attractive force exerting on the calcium spiral wave by the heterogeneity, then the strength of the adventive field is used to quantify the attractive force indirectly. Two factors determining the attractive force are studied. It is found that: (1) the attractive force sharply increases with size of the heterogeneity for small-size heterogeneity, whereas the force increases to a saturated value for large-size heterogeneity; (2) for large-size heterogeneity, the force almost remains constant unless the level of the heterogeneity vanishes, the force decreases to zero linearly and sharply, and for small-size heterogeneity, the force decreases successively with the level of the heterogeneity. Furthermore, it is found that the forces exist only when the spiral tip is very close to the heterogenous area. Our study may shed some light on the control or suppression of the calcium spiral wave.
    Chinese Physics Letters 11/2013; 30(11). DOI:10.1088/0256-307X/30/11/118701 · 0.95 Impact Factor
Show more