Interconnected ensembles of biological entities are perhaps some of the most complex systems that modern science has encountered so far. In particular, scientists have concentrated on understanding how the complexity of the interacting structure between different neurons, proteins, or species influences the functioning of their respective systems. It is well established that many biological networks are constructed in a highly hierarchical way with two main properties: short average paths that join two apparently distant nodes (neuronal, species, or protein patches) and a high proportion of nodes in modular aggregations. Although several hypotheses have been proposed so far, still little is known about the relation of the modules with the dynamical activity in such biological systems. Here we show that network modularity is a key ingredient for the formation of self-organizing patterns of functional activity, independently of the topological peculiarities of the structure of the modules. In particular, we propose a self-organizing mechanism which explains the formation of macroscopic spatial patterns, which are homogeneous within modules. This may explain how spontaneous order in biological networks follows their modular structural organization. We test our results on real-world networks to confirm the important role of modularity in creating macroscale patterns.

中文翻译：

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模块化在生物网络自组织动力学中的作用

生物实体的互连集合可能是现代科学迄今为止遇到的一些最复杂的系统。特别是，科学家们专注于了解不同神经元、蛋白质或物种之间相互作用结构的复杂性如何影响其各自系统的功能。众所周知，许多生物网络是以高度分层的方式构建的，具有两个主要特性：连接两个明显相距较远的节点（神经元、物种或蛋白质块）的短平均路径和模块聚合中高比例的节点。尽管到目前为止已经提出了几种假设，但对于模块与此类生物系统中的动态活动之间的关系仍然知之甚少。在这里，我们表明网络模块化是形成功能活动的自组织模式的关键因素，独立于模块结构的拓扑特性。特别是，我们提出了一种自组织机制，它解释了宏观空间模式的形成，这些模式在模块内是同质的。这可以解释生物网络中的自发秩序如何遵循其模块化结构组织。我们在现实世界的网络上测试我们的结果，以确认模块化在创建宏观模式中的重要作用。它们在模块内是同质的。这可以解释生物网络中的自发秩序如何遵循其模块化结构组织。我们在现实世界的网络上测试我们的结果，以确认模块化在创建宏观模式中的重要作用。它们在模块内是同质的。这可以解释生物网络中的自发秩序如何遵循其模块化结构组织。我们在现实世界的网络上测试我们的结果，以确认模块化在创建宏观模式中的重要作用。