论文标题
2-D中的局部信号隔室结合了散装扩散场：在混合良好的极限下进行群体传感和同步振荡
Localized Signaling Compartments in 2-D Coupled by a Bulk Diffusion Field: Quorum Sensing and Synchronous Oscillations in the Well-Mixed Limit
论文作者
论文摘要
我们为耦合的PDE系统系统分析了振荡不稳定性，该系统模拟了局部隔离的动态活跃信号隔室之间的通信，该信号隔室通过有限的2-D域中的被动细胞外体积扩散场耦合。假定每个信号室将化学物质分泌到细胞外培养基（散装区域）中，并且还可以感觉到该化学物质在其边界周围地区的浓度。来自整个细胞集合产生的散装区域的反馈反过来又改变了每个细胞内的细胞内动力学。在信号隔室是带有小的公共半径$ε\ ll 1 $且批量扩散率渐近较大的圆盘的极限中，使用匹配的渐近分析可将无量纲的PDE-ODE系统降低到具有全球辅助的非线性ODE系统中。对于Sel'kov反应动力学，该动力学和散装扩散场的空间平均水平的这种ODE系统随后用于研究由于全局耦合而触发的细胞动力学中的振荡不稳定性。特别是，ODE上的数值分叉软件用于研究耦合有缺陷的细胞（与其余细胞不同）对一组相同细胞的总体影响。此外，当细胞数量较大时，计算库拉莫托级参数以预测细胞内动力学的相同步程度。还研究了细胞内动力学中集体行为的发作的特征，随着细胞数量的增加，群体感应行为的特征也被研究。我们的分析表明，细胞种群密度起触发的双重作用，然后在细胞内动力学中淬灭同步振荡。
We analyze oscillatory instabilities for a coupled PDE-ODE system modeling the communication between localized spatially segregated dynamically active signaling compartments that are coupled through a passive extracellular bulk diffusion field in a bounded 2-D domain. Each signaling compartment is assumed to secrete a chemical into the extracellular medium (bulk region) and it can also sense the concentration of this chemical in the region around its boundary. This feedback from the bulk region, resulting from the entire collection of cells, in turn modifies the intracellular dynamics within each cell. In the limit where the signaling compartments are circular disks with a small common radius $ε\ll 1$ and where the bulk diffusivity is asymptotically large, a matched asymptotic analysis is used to reduce the dimensionless PDE-ODE system into a nonlinear ODE system with global coupling. For Sel'kov reaction kinetics, this ODE system for the intracellular dynamics and the spatial average of the bulk diffusion field is then used to investigate oscillatory instabilities in the dynamics of the cells that are triggered due to the global coupling. In particular, numerical bifurcation software on the ODEs is used to study the overall effect of coupling defective cells (cells that behave differently from the remaining cells) to a group of identical cells. Moreover, when the number of cells is large, the Kuramoto order parameter is computed to predict the degree of phase synchronization of the intracellular dynamics. Quorum sensing behavior, characterized by the onset of collective behavior in the intracellular dynamics as the number of cells increases above a threshold, is also studied. Our analysis shows that the cell population density plays a dual role of triggering and then quenching synchronous oscillations in the intracellular dynamics.
