Quantification of degeneracy in biological systems for characterization of functional interactions between modules

Degeneracy measures in biologically plausible random Boolean networks

Background

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.

Results

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.

Conclusions

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.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12859-022-04601-5.

Entropy, mutual information, and systematic measures of structured spiking neural networks

The aim of this paper is to investigate various information-theoretic measures, including entropy, mutual information, and some systematic measures that are based on mutual information, for a class of structured spiking neuronal networks. In order to analyze and compute these information-theoretic measures for large networks, we coarse-grained the data by ignoring the order of spikes that fall into the same small time bin. The resultant coarse-grained entropy mainly captures the information contained in the rhythm produced by a local population of the network. We first show that these information theoretical measures are well-defined and computable by proving stochastic stability and the law of large numbers. Then we use three neuronal network examples, from simple to complex, to investigate these information-theoretic measures. Several analytical and computational results about properties of these information-theoretic measures are given.

Degeneracy allows for both apparent homogeneity and diversification in populations

Trait diversity - the substrate for natural selection - is necessary for adaptation through selection, particularly in populations faced with environmental changes that diminish population fitness. In habitats that remain unchanged for many generations, stabilizing selection maximizes exploitation of resources by reducing trait diversity to a narrow optimal range. One might expect that such ostensibly homogeneous populations would have a reduced potential for heritable adaptive responses when faced with fitness-reducing environmental changes. However, field studies have documented populations that, even after long periods of evolutionary stasis, can still rapidly evolve in response to changed environmental conditions. We argue that degeneracy, the ability of diverse population elements to function similarly, can satisfy both the current need to maximize fitness and the future need for diversity. Degenerate ensembles appear functionally redundant in certain environmental contexts and functionally diverse in others. We propose that genetic variation not contributing to the observed range of phenotypes in a current population, also known as cryptic genetic variation (CGV), is a specific case of degeneracy. We argue that CGV, which gradually accumulates in static populations in stable environments, reveals hidden trait differences when environments change. By allowing CGV accumulation, static populations prepare themselves for future rapid adaptations to environmental novelty. A greater appreciation of degeneracy's role in resolving the inherent tension between current stabilizing selection and future directional selection has implications in conservation biology and may be applied in social and technological systems to maximize current performance while strengthening the potential for future changes.