Rufino Ferreira Ana S, Arcak Murat
Department of Electrical Engineering & Computer Sciences, University of California, Berkeley, CA.
SIAM J Appl Dyn Syst. 2013;12(4):2012-2031. doi: 10.1137/130910142. Epub 2013 Dec 17.
We analyze spatial patterns on networks of cells where adjacent cells inhibit each other through contact signaling. We represent the network as a graph where each vertex represents the dynamics of identical individual cells and where graph edges represent cell-to-cell signaling. To predict steady-state patterns we find equitable partitions of the graph vertices and assign them into disjoint classes. We then use results from monotone systems theory to prove the existence of patterns that are structured in such a way that all the cells in the same class have the same final fate. To study the stability properties of these patterns, we rely on the graph partition to perform a block decomposition of the system. Then, to guarantee stability, we provide a small-gain type criterion that depends on the input-output properties of each cell in the reduced system. Finally, we discuss pattern formation in stochastic models. With the help of a modal decomposition we show that noise can enhance the parameter region where patterning occurs.
我们分析细胞网络中的空间模式，其中相邻细胞通过接触信号相互抑制。我们将网络表示为一个图，其中每个顶点代表相同个体细胞的动态，图的边代表细胞间信号传导。为了预测稳态模式，我们找到图顶点的公平划分并将它们分配到不相交的类别中。然后，我们使用单调系统理论的结果来证明存在这样一种结构的模式，即同一类中的所有细胞具有相同的最终命运。为了研究这些模式的稳定性特性，我们依靠图划分对系统进行块分解。然后，为了保证稳定性，我们提供了一个小增益类型的准则，该准则取决于简化系统中每个细胞的输入输出特性。最后，我们讨论随机模型中的模式形成。借助模态分解，我们表明噪声可以扩大发生模式形成的参数区域。
