Abstract

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, 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. 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 the robust and adaptive responses required for unforeseen challenges. Such entangled networks function for sloppy and unreliable responses with low Hill coefficient reactions for the expression of each gene. 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, the appropriate response to unforeseen challenges, allowing for functional outputs, is achieved as many genes exhibit similar dynamic expression responses, irrespective of inputs, as confirmed by applying dynamic time warping and dynamic mode decomposition. As complex entangled networks are common in gene regulatory networks and global gene expression responses are observed in microbial experiments, the present results provide a novel design principle for cellular networks.

Highlights

  • Living organisms generally respond appropriately to environmental changes by adapting their internal states to the new conditions

  • 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 to how cells make adaptive responses and provide a different design principle for cellular networks

  • As described in Ref. [21], three types of networks evolved depending on the sensitivity β of the gene expression dynamics: direct connections evolved for large β and intermediate yT, and feed-forward networks having side paths (FF-network type) evolved for large β and large yT

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Summary

INTRODUCTION

Living organisms generally respond appropriately to environmental changes by adapting their internal states to the new conditions. In addition to simple direct or feed-forward networks, we have uncovered another type of entangled network consisting of many components, which can generate an appropriate input-output relationship as a cooperative response of many genes [21]. This cooperative response emerges when each gene expression is sloppy, that is, with a low Hill coefficient as observed in a real GRN [22,23,24,25]. We explore whether this class of networks achieves capacity in noise robustness and AUCs higher than that of traditional direct or feed-forward networks

MODELS
Gene expression dynamics
Selection process
Three types of networks
Quantitative analysis of entanglement
Noise robustness
Mutational robustness
Tolerance to erroneous input
Resemblance of response dynamics between evolutionary and unforeseen inputs
D: F: F: C
Dynamic mode decomposition of response dynamics
DISCUSSION
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