Measures of degeneracy and redundancy in biological networks
Measures of degeneracy and redundancy in biological networks
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DOI：
10.1073/pnas.96.6.3257
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发表时间：
1999-03-16
影响因子：
11.1
通讯作者：
Edelman, GM
中科院分区：
文献类型：
--
作者：
Tononi, G;Sporns, O;Edelman, GM
简并性，即结构不同的元素执行相同功能的能力，是从基因到神经网络再到进化本身的许多生物系统的突出特性。由于结构上不同的元素在不同的环境中可能会产生不同的输出，因此简并应该与冗余区分开来，当相同的功能由相同的元素执行时会出现冗余。然而，由于结构和功能之间的区别含糊不清，并且缺乏理论处理，这两个概念经常被混为一谈。通过使用信息理论的概念，我们在这里开发的功能措施的退化和冗余的系统相对于一组输出。这些措施有助于区分简并的概念，从冗余，使其操作上有用的。通过计算机模拟的神经系统不同的连接，我们表明，退化是低的系统中，每个元素独立影响输出和冗余系统中，许多元素可以影响输出以类似的方式，但没有独立的影响。相比之下，对于许多不同元素可以以类似的方式影响输出并且同时可以具有独立影响的系统，简并性很高。我们证明，已被选定为退化的网络具有高的复杂性值，一个系统的子集之间的平均互信息的措施。这些措施有望有助于表征和理解生物网络的功能鲁棒性和适应性。
Degeneracy, the ability of elements that are structurally different to perform the same function, is a prominent property of many biological systems ranging from genes to neural networks to evolution itself. Because structurally different elements mag produce different outputs in different contexts, degeneracy should be distinguished from redundancy, which occurs when the same function is performed by identical elements. However, because of ambiguities in the distinction between structure and function and because of the lack of a theoretical treatment, these two notions often are conflated. By using information theoretical concepts, we develop here functional measures of the degeneracy and redundancy of a system with respect to a set of outputs. These measures help to distinguish the concept of degeneracy from that of redundancy and make it operationally useful. Through computer simulations of neural systems differing in connectivity, we show that degeneracy is low both for systems in which each element affects the output independently and for redundant systems in which many elements can affect the output in a similar way but do not have independent effects. By contrast, degeneracy is high for systems in which many different elements can affect the output in a similar way and at the same time can have independent effects. We demonstrate that networks that have been selected for degeneracy have high values of complexity, a measure of the average mutual information between the subsets of a system. These measures promise to be useful in characterizing and understanding the functional robustness and adaptability of biological networks.