Chaos should occur often in gene regulatory networks (GRNs) which have been widely described by nonlinear coupled ordinary differential equations, if their dimensions are no less than 3. It is therefore puzzling that chaos has never been reported in GRNs in nature and is also extremely rare in models of GRNs. On the other hand, the topic of motifs has attracted great attention in studying biological networks, and network motifs are suggested to be elementary building blocks that carry out some key functions in the network. In this paper, chaotic motifs (subnetworks with chaos) in GRNs are systematically investigated. The conclusion is that: (i) chaos can only appear through competitions between different oscillatory modes with rivaling intensities. Conditions required for chaotic GRNs are found to be very strict, which make chaotic GRNs extremely rare. (ii) Chaotic motifs are explored as the simplest few-node structures capable of producing chaos, and serve as the intrinsic source of chaos of random few-node GRNs. Several optimal motifs causing chaos with atypically high probability are figured out. (iii) Moreover, we discovered that a number of special oscillators can never produce chaos. These structures bring some advantages on rhythmic functions and may help us understand the robustness of diverse biological rhythms. (iv) The methods of dominant phase-advanced driving (DPAD) and DPAD time fraction are proposed to quantitatively identify chaotic motifs and to explain the origin of chaotic behaviors in GRNs.

During a public health crisis, the provision and dissemination of health-related information are important for the relevant authorities to keep the public informed. By using different types of message framing, the authorities can effectively guide and persuade people to adopt health-related behaviors (such as vaccination). In this study, a web-based experiment using a 2 × 2 (message framing: gain framing versus loss framing) × (message presentation: narrative versus non-narrative) design was conducted to investigate the effects of different message frames on vaccination promotion. In total, 298 college students were recruited to participate in this study. The results suggest that, for message framing, loss-framed (vs. gain-framed) messages lead to higher intentions to get vaccinated. Furthermore, compared with non-narrative messages, narrative messages are more persuasive in promoting vaccination behavior. However, the interaction effect between gain–loss message framing and narrative framing is not significant. Additionally, perceived severity, perceived benefits, and perceived costs mediate the effect of narrative framing on behavioral intentions. In other words, compared with non-narrative messages, narrative messages lead to higher levels of perceived severity and perceived benefits, and a lower level of perceived costs, which in turn increase intentions to get vaccinated. This paper provides insightful implications for both researchers and practitioners.

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A gold-catalyzed asymmetric intermolecular [3 + 2]-cycloaddition of γ-1-ethoxyethoxy-propiolate and aldehydes by using the chiral ligand 5a or 5b is developed, which provides facile access to highly substituted 2,5-dihydrofurans in up to 84% yield with up to 97% ee.