Entangled gene regulatory networks with cooperative expression endow robust adaptive responses to unforeseen environmental changes

Living organisms must respond to environmental changes. Generally, accurate and rapid responses are provided by simple, unidirectional networks that connect inputs with outputs. Besides accuracy and speed, however, biological responses should also be robust to environmental or intracellular noise and mutations. Furthermore, cells must also respond to unforeseen environmental changes that have not previously been experienced, to avoid extinction prior to the evolutionary rewiring of their networks, which takes numerous generations. To address the question how cells can make robust adaptation even to unforeseen challenges, we have investigated gene regulatory networks that mutually activate or inhibit, and have demonstrated that complex entangled networks can make appropriate input-output relationships that satisfy such adaptive responses. Such entangled networks function when the expression of each gene shows sloppy and unreliable responses with low Hill coefficient reactions. To compensate for such sloppiness, several detours in the regulatory network exist. By taking advantage of the averaging over such detours, the network shows a higher robustness to environmental and intracellular noise as well as to mutations in the network, when compared to simple unidirectional circuits. Furthermore, it is demonstrated that the appropriate response to unforeseen environmental changes, allowing for functional outputs, is achieved as many genes exhibit similar dynamic expression responses, irrespective of inputs including unforeseen inputs. The similarity of the responses is statistically confirmed by applying dynamic time warping and dynamic mode decomposition methods. As complex entangled networks are commonly observed in the data in gene regulatory networks whereas global gene expression responses are measured in transcriptome analysis in microbial experiments, the present results give an answer how cells make adaptive responses and also provide a novel design principle for cellular networks. Author summary Recent experimental advances have demonstrated that cells often have appropriate, robust responses to environmental changes, including those that have not previously been experienced. It is known that accurate and rapid responses can be achieved by simple unidirectional networks that connect straightforwardly input and outputs. However, such responses were not robust to perturbations. Here we have made numerical evolution of gene regulatory networks with mutual activation and inhibitions, and uncovered that complex entangled networks including many feedforward and feedback paths can make robust input-output responses, when each gene expression is not accurate. Remarkably, they make appropriate responses even to unforeseen environmental changes, as are supported by global, correlated responses across genes that are similar for all input signals. The results explain why cells adopt complex gene regulatory networks and exhibit global expression changes, even though they may not be advantageous in terms of their energy cost or response speed. The present results are consistent with the recent experiments on microbial gene expression changes and network analyses. This investigation provides insights into how cells survive fluctuating and unforeseen unpredictable environmental changes, and gives a universal conceptual framework to go beyond the standard picture based on a combination of network motifs.