Center for Complex Systems and Brain Sciences, Florida Atlantic University, Boca Raton, FL, USA.
The Brain Institute, Florida Atlantic University, Jupiter, FL, 33431, USA.
BMC Bioinformatics. 2022 Feb 14;23(1):71. doi: 10.1186/s12859-022-04601-5.
Degeneracy-the ability of structurally different elements to perform similar functions-is a property of many biological systems. Highly degenerate systems show resilience to perturbations and damage because the system can compensate for compromised function due to reconfiguration of the underlying network dynamics. Degeneracy thus suggests how biological systems can thrive despite changes to internal and external demands. Although degeneracy is a feature of network topologies and seems to be implicated in a wide variety of biological processes, research on degeneracy in biological networks is mostly limited to weighted networks. In this study, we test an information theoretic definition of degeneracy on random Boolean networks, frequently used to model gene regulatory networks. Random Boolean networks are discrete dynamical systems with binary connectivity and thus, these networks are well-suited for tracing information flow and the causal effects. By generating networks with random binary wiring diagrams, we test the effects of systematic lesioning of connections and perturbations of the network nodes on the degeneracy measure.
Our analysis shows that degeneracy, on average, is the highest in networks in which ~ 20% of the connections are lesioned while 50% of the nodes are perturbed. Moreover, our results for the networks with no lesions and the fully-lesioned networks are comparable to the degeneracy measures from weighted networks, thus we show that the degeneracy measure is applicable to different networks.
Such a generalized applicability implies that degeneracy measures may be a useful tool for investigating a wide range of biological networks and, therefore, can be used to make predictions about the variety of systems' ability to recover function.
简并性——结构不同的元素能够执行相似功能的能力——是许多生物系统的特性。高度简并的系统对扰动和损伤具有弹性，因为系统可以通过重新配置基础网络动态来补偿功能受损。因此，简并性表明了生物系统如何能够在内部和外部需求变化的情况下茁壮成长。尽管简并性是网络拓扑结构的一个特征，并且似乎与广泛的生物过程有关，但对生物网络中的简并性的研究大多仅限于加权网络。在这项研究中，我们在随机布尔网络上测试了简并性的信息论定义，随机布尔网络常用于模拟基因调控网络。随机布尔网络是具有二进制连接的离散动力系统，因此，这些网络非常适合追踪信息流和因果效应。通过生成具有随机二进制布线图的网络，我们测试了连接的系统损伤和网络节点的扰动对简并性度量的影响。
我们的分析表明，在连接损伤率约为 20%而节点扰动率为 50%的网络中，平均简并性最高。此外，我们对无损伤和完全损伤网络的结果与加权网络的简并性度量相当，因此我们表明简并性度量适用于不同的网络。
这种广义适用性意味着简并性度量可能是研究广泛的生物网络的有用工具，因此可以用于预测各种系统恢复功能的能力。
