Calcium wave propagation in chains of endothelial cells with nonlinear reaction dynamics: Green's function approach
Calcium wave propagation in chains of endothelial cells with nonlinear reaction dynamics: Green's function approach
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DOI：
10.1103/physreve.82.041913
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发表时间：
2010-10-18
影响因子：
2.4
通讯作者：
Vasseur, Jerome O.
中科院分区：
文献类型：
--
作者：
Deymier, Pierre A.;Runge, Keith;Vasseur, Jerome O.
提出了一种基于绿色函数的微扰方法来求解内皮细胞网络中的非线性反应扩散问题。我们专注于一个单一的组件（Ca2+），分段非线性模型的内质网钙动力学和跨膜扩散。非线性反应动力学和线性扩散之间的解耦使得具有非平凡拓扑的细胞网络的绿色函数的扩散部分的计算成为可能。我们验证分析，然后数值计算，我们的方法导致已知的过渡，从传播的钙前失败的传播时，扩散速率相对于反应速率变化。然后，我们推导出的绿色的功能与各种边界条件的半无限链的细胞。我们发现，在半无限链的末端附近的细胞的钙动力学强烈依赖于边界条件。具有吸收边界条件的半无限链的行为，一个简单的多细胞结构模型，其末端与细胞外基质接触，表明末端的细胞和嵌入链内的细胞之间的行为分化。
We present a Green's function-based perturbative approach to solving nonlinear reaction-diffusion problems in networks of endothelial cells. We focus on a single component (Ca2+), piecewise nonlinear model of endoplasmic calcium dynamics and trans-membrane diffusion. The decoupling between nonlinear reaction dynamics and the linear diffusion enables the calculation of the diffusion part of the Green's function for network of cells with nontrivial topologies. We verify analytically and then numerically that our approach leads to the known transition from propagation of calcium front to failure of propagation when the diffusion rate is varied relative to the reaction rates. We then derive the Green's function for a semi-infinite chain of cells with various boundary conditions. We show that the calcium dynamics of cells in the vicinity of the end of the semi-infinite chain is strongly dependent on the boundary conditions. The behavior of the semi-infinite chain with absorbing boundary conditions, a simple model of a multicellular structure with an end in contact with the extracellular matrix, suggests behavioral differentiation between cells at the end and cells embedded within the chain.