Topological graph description of multicellular dynamics based on vertex model
Topological graph description of multicellular dynamics based on vertex model
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DOI：
10.1016/j.jtbi.2017.10.023
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发表时间：
2018-01-21
影响因子：
2
通讯作者：
Okuda, Satoru
中科院分区：
文献类型：
--
作者：
Hashimoto, Atsushi;Nagao, Atsuki;Okuda, Satoru
顶点模型通常是探索多细胞动力学生物学见解的强大工具。在这些模型中，多细胞结构用网络表示，并通过拓扑操作动态地重新排列。值得注意的是，网络的拓扑动力学对于保证模型的结果及其生物学意义是重要的。然而，目前尚不清楚的是，多细胞拓扑动力学的整个模式是否可以通过模型中的一组算子准确地表达出来。令人惊讶的是，顶点模型在没有任何数学验证的情况下已经经验性地使用了几十年。在这项研究中，我们提出了一个严格的二/三维（2D/3D）顶点模型来描述多细胞拓扑动力学。为此，我们从图论的角度对几种类型的顶点模型进行了分类。在分类的基础上，数学分析揭示了几个条件，使我们能够准确地应用算子而不产生拓扑误差。在这些条件下，算子可以完全表达多细胞拓扑动力学的整个模式。根据这些结果，我们提出了可以应用于一般多细胞动力学的严格的2D/3D顶点模型，并澄清了几个要点来验证从以前的模型中得到的结果。(C) 2017 Elsevier Ltd.版权所有。
Vertex models are generally powerful tools for exploring biological insights into multicellular dynamics. In these models, a multicellular structure is represented by a network, which is dynamically rearranged using topological operations. Remarkably, the topological dynamics of the network are important in guaranteeing the results from the models and their biological implications. However, it remains unclear whether the entire pattern of multicellular topological dynamics can be accurately expressed by a set of operators in the models. Surprisingly, vertex models have been empirically used for several decades without any mathematical verification. In this study, we propose a rigorous two-/three-dimensional (2D/3D) vertex model to describe multicellular topological dynamics. To do this, we classify several types of vertex models from a graph-theoretic perspective. Based on the classification, mathematical analyses reveal several conditions that enable us to apply the operators accurately without topological errors. Under these conditions, the operators can completely express the entire pattern of multicellular topological dynamics. From these results, we newly propose rigorous 2D/3D vertex models that can be applied to general multicellular dynamics, and we clarify several points to verify the results obtained from previous models. (C) 2017 Elsevier Ltd. All rights reserved.