Lemon Greg
School of Mathematics and Statistics, University of Sydney, New South Wales 2006, Australia.
Bull Math Biol. 2004 Jan;66(1):65-90. doi: 10.1016/S0092-8240(03)00074-0.
The propagation of fire-diffuse-fire Ca(2+) waves through a three-dimensional rectangular domain is considered. The domain is infinite in extent in the direction of propagation but with lateral barriers to diffusion which contain Ca(2+) pumps. The Ca(2+) concentration profile due to the firing of a release site (spark) is derived analytically based on the Green's function for the diffusion equation on the domain. The existence, stability and speed of these waves is shown to be critically dependent on the dimensions of the domain and the Ca(2+) pump rate. It is shown that the smaller the dimensions of the region, the lower the Ca(2+) release flux required for wave propagation, and the higher the wave speed. Also it is shown that the region may support multiple Ca(2+) wavefronts of varying wave speed. This model is relevant to subsarcolemmal waves in atrial myocytes (Kockskämper et al., 2001, Biophys. J. 81, 2590-2605), and the results may be of importance in understanding the roles of the endoplasmic/sarcoplasmic reticulum, surface membranes and Ca(2+) pumps in the intracellular Ca(2+) dynamics of cells.
本文考虑了火焰扩散式钙离子波在三维矩形区域中的传播。该区域在传播方向上是无限延伸的,但在横向存在包含钙离子泵的扩散屏障。基于该区域扩散方程的格林函数,通过解析方法推导出了由释放位点(火花)激发所导致的钙离子浓度分布。结果表明,这些波的存在、稳定性和速度严重依赖于区域的尺寸以及钙离子泵的速率。研究发现,区域尺寸越小,波传播所需的钙离子释放通量越低,波速越高。此外,还表明该区域可能支持多个不同波速的钙离子波前。此模型与心房肌细胞中的肌膜下波相关(Kockskämper等人,2001年,《生物物理杂志》81卷,2590 - 2605页),其结果对于理解内质网/肌浆网、表面膜以及钙离子泵在细胞内钙离子动力学中的作用可能具有重要意义。