Many complex cellular processes involve major changes in topology and geometry. We have developed a method using topology-based geometric modelling in which the edge labels of an n-dimensional generalized map (a subclass of graphs) represent the relations between neighbouring biological compartments. We illustrate our method using two topological models of the Golgi apparatus. These models can be animated using transformation rules, which depend on geometric and/or biochemical data and which modify both these data and the topology. Both models constitute plausible topological representations of the Golgi apparatus, but only the model based on a recent hypothesis about the Golgi apparatus is fully compatible with data from electron microscopy. Finally, we outline how our method may help biologists to choose between different hypotheses.

中文翻译：

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基于拓扑的复杂生物系统抽象：在高尔基体中的应用。

许多复杂的细胞过程涉及拓扑和几何的重大变化。我们开发了一种使用基于拓扑的几何建模的方法，其中 n 维广义图（图的一个子类）的边缘标签表示相邻生物区室之间的关系。我们使用高尔基体的两个拓扑模型来说明我们的方法。可以使用转换规则对这些模型进行动画处理，转换规则取决于几何和/或生化数据并修改这些数据和拓扑。两种模型都构成了高尔基体的合理拓扑表示，但只有基于最近关于高尔基体的假设的模型才与电子显微镜数据完全兼容。最后，我们概述了我们的方法如何帮助生物学家在不同的假设之间进行选择。