Short Pyridine-Furan Springs Exhibit Bistable Dynamics of Duffing Oscillators

The intensive development of nanodevices acting as two-state systems has motivated the search for nanoscale molecular structures whose dynamics are similar to those of bistable mechanical systems, such as Euler arches and Duffing oscillators. Of particular interest are the molecular structures capable of spontaneous vibrations and stochastic resonance. Recently, oligomeric molecules that were a few nanometers in size and exhibited the bistable dynamics of an Euler arch were identified through molecular dynamics simulations of short fragments of thermo-responsive polymers subject to force loading. In this article, we present molecular dynamics simulations of short pyridine-furan springs a few nanometers in size and demonstrated the bistable dynamics of a Duffing oscillator with thermally-activated spontaneous vibrations and stochastic resonance.

Multi-site enzymes as a mechanism for bistability in reaction networks

Here, we focus on a common class of enzymes that have multiple substrate-binding sites (multi-site enzymes), and analyse their capacity to generate bistable dynamics in the reaction systems that they are embedded in. Using mathematical techniques, we show that the inherent binding and catalysis reactions arising from multiple substrate-enzyme complexes creates a potential for bistable dynamics in a reaction system. We construct a generic model of an enzyme with n substrate binding sites and derive an analytical solution for the steady state concentration of all enzyme-substrate complexes. By studying these expressions, we obtain a mechanistic understanding for bistability and derive parameter combinations that guarantee bistability and show how changing specific enzyme kinetic parameters and enzyme levels can lead to bistability in reaction systems involving mjulti-site enzymes. Thus, the presented findings provide a biochemical and mathematical basis for predicting and engineering bistability in multi-site enzymes.

Global analysis of a juvenile-adult model for cannibalistic species

Cannibalism is a life trait occurring in a wide variety of species. To describe the population dynamics of cannibalistic species, we develop a stage-structured population model in which adults prey on juveniles with a Holling type I functional response. We make a rigorous analysis of the global dynamics in the model. The results of theoretical analysis show that the model has no boundary equilibrium other than the extinction one since juveniles and adults are cooperative (adults reproduce juveniles and juveniles grow into adults). Under certain conditions, the model has multiple interior equilibria and exhibits several types of bistable dynamics, in which different initial densities of juveniles and adults produce different long-term outcomes.

Stress granules display bistable dynamics modulated by Cdk

Stress granules (SGs) are conserved biomolecular condensates that originate in response to many stress conditions. These membraneless organelles contain nontranslating mRNAs and a diverse subproteome, but our knowledge of their regulation and functional relevance is still incipient. Here, we describe a mutual-inhibition interplay between SGs and Cdc28, the budding yeast Cdk. Among Cdc28 interactors acting as negative modulators of Start, we have identified Whi8, an RNA-binding protein that localizes to SGs and recruits the mRNA of CLN3, the most upstream G1 cyclin, for efficient translation inhibition and Cdk inactivation under stress. However, Whi8 also contributes to recruiting Cdc28 to SGs, where it acts to promote their dissolution. As predicted by a mutual-inhibition framework, the SG constitutes a bistable system that is modulated by Cdk. Since mammalian cells display a homologous mechanism, we propose that the opposing functions of specific mRNA-binding proteins and Cdk’s subjugate SG dynamics to a conserved hysteretic switch.

Bistable and oscillatory dynamics of Nicholson's blowflies equation with Allee effect

<p style='text-indent:20px;'>The bistable dynamics of a modified Nicholson's blowflies delay differential equation with Allee effect is analyzed. The stability and basins of attraction of multiple equilibria are studied by using Lyapunov-LaSalle invariance principle. The existence of multiple periodic solutions are shown using local and global Hopf bifurcations near positive equilibria, and these solutions generate long transient oscillatory patterns and asymptotic stable oscillatory patterns.</p>

Noise-induced properties of active dendrites

Dendrites play an essential role in the integration of highly fluctuating input into neurons across all nervous systems. Nevertheless, they are often studied under the conditions where inputs to dendrites are sparse. Up to date, the dynamic properties of active dendrites facing in-vivo-like fluctuating input remains elusive. In this paper, we uncover fundamentally new dynamics in a canonical model of a dendritic compartment with active calcium channels, receiving in-vivo-like fluctuating input. We show in-vivo-like noise induces non-monotonic or bistable dynamics in the input-output relation of a dendritic compartment, both of which are absent in a noiseless condition. Our analysis shows that the timescales of the activation gating variable of the dendritic calcium dynamics determine noise-induced spontaneous order in the system. Noise can induce non-monotonicity or bistability with fast or slow calcium activation respectively. We characterize these noise-induced phenomena and their influence on the input-output relation. Furthermore, we show that timescales of the emerging stochastic bistable dynamics go far beyond a deterministic system due to stochastic switching between the solutions. Our results reveal that noise contributes to sustained dendritic nonlinearities, and it could be considered a principal component of the dendritic input integration strategies.