Santa Fe Institute, Santa Fe, NM 87501, USA.
J R Soc Interface. 2012 Sep 7;9(74):2131-44. doi: 10.1098/rsif.2011.0840. Epub 2012 Feb 29.
A common feature of biological networks is the geometrical property of self-similarity. Molecular regulatory networks through to circulatory systems, nervous systems, social systems and ecological trophic networks show self-similar connectivity at multiple scales. We analyse the relationship between topology and signalling in contrasting classes of such topologies. We find that networks differ in their ability to contain or propagate signals between arbitrary nodes in a network depending on whether they possess branching or loop-like features. Networks also differ in how they respond to noise, such that one allows for greater integration at high noise, and this performance is reversed at low noise. Surprisingly, small-world topologies, with diameters logarithmic in system size, have slower dynamical time scales, and may be less integrated (more modular) than networks with longer path lengths. All of these phenomena are essentially mesoscopic, vanishing in the infinite limit but producing strong effects at sizes and time scales relevant to biology.
生物网络的一个共同特征是自相似性的几何性质。从分子调节网络到循环系统、神经系统、社会系统和生态营养网络，在多个尺度上都表现出自相似的连接性。我们分析了拓扑结构和信号在这些拓扑结构的不同类别之间的关系。我们发现，网络在包含或在网络中任意节点之间传播信号的能力上存在差异，这取决于它们是否具有分支或环形特征。网络在对噪声的响应方式上也存在差异，使得一个网络在高噪声下允许更大的集成，而在低噪声下则相反。令人惊讶的是，具有直径对数系统大小的小世界拓扑结构具有较慢的动态时间尺度，并且可能比具有较长路径长度的网络集成度更低（更模块化）。所有这些现象本质上都是介观的，在无穷大极限下消失，但在与生物学相关的大小和时间尺度上产生强烈的影响。
