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Irreversibility, in which a transient perturbation leaves a system in a new state, is an emergent property in systems of interacting entities. This property has well-established implications in statistical physics but remains underexplored in biological networks, especially for bacteria and other prokaryotes whose regulation of gene expression occurs predominantly at the transcriptional level. Focusing on the reconstructed regulatory network ofEscherichia coli, we examine network responses to transient single-gene perturbations. We predict irreversibility in numerous cases and find that the incidence of irreversibility increases with the proximity of the perturbed gene to positive circuits in the network. Comparison with experimental data suggests a connection between the predicted irreversibility to transient perturbations and the evolutionary response to permanent perturbations. 

Neural mechanisms and underlying directionality of signaling among brain regions depend on neural dynamics spanning multiple spatiotemporal scales of population activity. Despite recent advances in multimodal measurements of brain activity, there is no broadly accepted multiscale dynamical models for the collective activity represented in neural signals. Here we introduce a neurobiological-driven deep learning model, termedmultiscale neuraldynamicsneuralordinarydifferentialequation (msDyNODE), to describe multiscale brain communications governing cognition and behavior. We demonstrate that msDyNODE successfully captures multiscale activity using both simulations and electrophysiological experiments. The msDyNODE-derived causal interactions between recording locations and scales not only aligned well with the abstraction of the hierarchical neuroanatomy of the mammalian central nervous system but also exhibited behavioral dependences. This work offers a new approach for mechanistic multiscale studies of neural processes.