Nonmodular oscillator and switch based on RNA decay drive regeneration of multimodal gene expression

Periodic gene expression dynamics are key to cell and organism physiology. Studies of oscillatory expression have focused on networks with intuitive regulatory negative feedback loops, leaving unknown whether other common biochemical reactions can produce oscillations. Oscillation and noise have been proposed to support the capacity of mammalian progenitor cells to restore heterogenous, multimodal expression from extreme subpopulations, but underlying networks and specific roles of noise remained elusive. We use mass-action-based models to show that regulated RNA degradation involving as few as two RNA species, applicable to nearly half of human protein-coding genes, can generate sustained oscillations without imposed feedback. Diverging oscillation periods synergize with noise to robustly restore bimodal expression in cell populations. The global bifurcation organizing this divergence relies on an oscillator and bistable switch which cannot be decomposed into two structural modules. Our work reveals surprisingly rich dynamics of post-transcriptional reactions and a potentially widespread mechanism useful for development and regeneration.

Phase-reduction analysis of periodic thermoacoustic oscillations in a Rijke tube

Phase-reduction analysis captures the linear phase dynamics with respect to a limit cycle subjected to weak external forcing. We apply this technique to study the phase dynamics of the self-sustained oscillations produced by a Rijke tube undergoing thermoacoustic instability. Through the phase-reduction formulation, we are able to reduce these dynamics to a scalar equation for the phase, which allows us to efficiently determine the synchronisation properties of the system. For the thermoacoustic system, we find the conditions for which $m:n$ frequency locking occurs, which sheds light on the mechanisms behind asynchronous and synchronous quenching. We also reveal the optimal placement of pressure actuators that provide the most efficient route to synchronisation.

Transcription factor competition facilitates self-sustained oscillations in single gene genetic circuits

Genetic feedback loops can be used by cells as a means to regulate internal processes or keep track of time. It is often thought that, for a genetic circuit to display self-sustained oscillations, a degree of cooperativity is needed in the binding and unbinding of actor species. This cooperativity is usually modeled using a Hill function, regardless of the actual promoter architecture. Moreover, genetic circuits do not operate in isolation and often transcription factors are shared between different promoters. In this work we show how mathematical modelling of genetic feedback loops can be facilitated with a mechanistic fold-change function that takes into account the titration effect caused by competing binding sites for transcription factors. The model shows how the titration effect aids self-sustained oscillations in a minimal genetic feedback loop: a gene that produces its own repressor directly — without cooperative transcription factor binding. The use of delay- differential equations leads to a stability contour that predicts whether a genetic feedback loop will show self-sustained oscillations, even when taking the bursty nature of transcription into account.

Energy fluctuations in recorder pipes during transient sound attacks and steady state sound

The evaluation of temporal and spatial fluctuations of energy using compressible fluid analysis is proposed as an effective method to clarify the fundamental mechanism of the self-sustained oscilla-tions in a actual recorder. The main factors of the self-sustained oscillations are investigated in more detail by evaluating not only the steady state of the sound where the flow field and the sound field are completely coupled, but also the characteristics at the attack transient of the sound before the coupling is established. By analyzing the large energy fluctuations that occur just below the edge of the labium in the attack transient, it was shown that this phenomenon may be one of the main causes of the self-sustained oscillations. And the characteristics of the energy fluctuations and sound power generation during the steady state of the sound are discussed. It was also focused on the energy variations in another region that is near the exit of the windway.

Spatiotemporal model of cellular mechanotransduction via Rho and YAP

How cells sense and respond to mechanical stimuli remains an open question. Recent advances have identified the translocation of Yes-associated protein (YAP) between nucleus and cytoplasm as a central mechanism for sensing mechanical forces and regulating mechanotransduction. We formulate a spatiotemporal model of the mechanotransduction signalling pathway that includes coupling of YAP with the cell force-generation machinery through the Rho family of GTPases. Considering the active and inactive forms of a single Rho protein (GTP/GDP-bound) and of YAP (non-phosphorylated/phosphorylated), we study the cross-talk between cell polarization due to active Rho and YAP activation through its nuclear localization. For fixed mechanical stimuli, our model predicts stationary nuclear-to-cytoplasmic YAP ratios consistent with experimental data at varying adhesive cell area. We further predict damped and even sustained oscillations in the YAP nuclear-to-cytoplasmic ratio by accounting for recently reported positive and negative YAP-Rho feedback. Extending the framework to time-varying mechanical stimuli that simulate cyclic stretching and compression, we show that the YAP nuclear-to-cytoplasmic ratio’s time dependence follows that of the cyclic mechanical stimulus. The model presents one of the first frameworks for understanding spatiotemporal YAP mechanotransduction, providing several predictions of possible YAP localization dynamics, and suggesting new directions for experimental and theoretical studies.

Seasonal Treatment of an Infectious Disease is a Social Driver of Sustained Oscillations in the Disease incidence

We analyze a seasonal $SIR$ model that assumes a periodic treatment rate. Using the Leray-Schauder degree theory, we prove that model shows periodic solutions. This result shows that sustained oscillations in the incidence of the disease are related to the periodic application of a treatment against the disease. So, we can say that the periodic application of treatment can be considered a seasonal driver of the sustained oscillations.