Tononi G, Sporns O, Edelman G M
The Neurosciences Institute, 10640 John J. Hopkins Drive, San Diego, CA 92121, USA.
Proc Natl Acad Sci U S A. 1999 Mar 16;96(6):3257-62. doi: 10.1073/pnas.96.6.3257.
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 may 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.
简并性是指结构不同的元件执行相同功能的能力，它是许多生物系统的一个显著特性，涵盖从基因到神经网络再到进化本身等多个层面。由于结构不同的元件在不同情境下可能产生不同的输出，简并性应与冗余性区分开来，冗余性是指相同的元件执行相同的功能。然而，由于结构与功能之间的区分存在模糊性，且缺乏理论探讨，这两个概念常常被混淆。通过运用信息理论概念，我们在此开发了一个系统相对于一组输出的简并性和冗余性的功能度量。这些度量有助于区分简并性和冗余性的概念，并使其在实际操作中具有实用性。通过对连接性不同的神经系统进行计算机模拟，我们发现，对于每个元件独立影响输出的系统以及许多元件能以相似方式影响输出但不具有独立效应的冗余系统，简并性都较低。相比之下，对于许多不同元件能以相似方式且同时具有独立效应影响输出的系统，简并性较高。我们证明，为简并性而选择的网络具有高复杂性值，复杂性是衡量系统子集之间平均互信息的指标。这些度量有望在表征和理解生物网络的功能稳健性和适应性方面发挥作用。
