Autonomous Oscillations Research Articles

Strong biological correlations as a cause of autonomous oscillations in epidemics.

We consider the impact of strong biological correlations on the epidemic process. The biological correlations mean the influence of the environment on the individual state of immunity of the infected person. Accounting for the correlations turns the traditional SIRS model into the 3D Lotka-Volterra model, the parameters of which are uniquely determined by the parameters of the original SIRS model. The measure of the biological correlations in the epidemic is the correlation strength parameter [Formula: see text], where [Formula: see text] and [Formula: see text] are the duration of the infectious period of the disease and the duration of immunity, respectively, both measured in years. If the epidemic is highly correlated ([Formula: see text]), then after the first epidemic outbreak, subsequent oscillations occur, the period [Formula: see text] of which is less than one year. The example is the COVID-19 pandemic. If the epidemic is weakly correlated ([Formula: see text]), the period [Formula: see text] of the oscillations is more than one year. Then in the presence of regular annual outbreaks the oscillations do not have time to manifest themselves. The examples are the ordinary flu annual epidemics. In the absence of the annual epidemic factor, the oscillations can exist and persist regardless of the [Formula: see text] value. The examples are the measles epidemics. The 3D Lotka-Volterra model makes it possible to predict the period [Formula: see text] of the future oscillations based on two known clinical parameters-[Formula: see text] and [Formula: see text]. This period turns out to be equal to 2π multiplied by the geometric mean of the duration of the infectious period of the disease [Formula: see text] and the duration of immunity [Formula: see text]. The adequacy of the 3D Lotka-Volterra model is supported by examples of the 2017-2019 annual flu epidemics and the 2020-2022 COVID-19 epidemic in Israel, as well as the succession of measles epidemics in the UK between 1940 and 1970.

Regulation of Pol II Pausing during Daily Gene Transcription in Mouse Liver.

Cell autonomous circadian oscillation is present in central and various peripheral tissues. The intrinsic tissue clock and various extrinsic cues drive gene expression rhythms. Transcription regulation is thought to be the main driving force for gene rhythms. However, how transcription rhythms arise remains to be fully characterized due to the fact that transcription is regulated at multiple steps. In particular, Pol II recruitment, pause release, and premature transcription termination are critical regulatory steps that determine the status of Pol II pausing and transcription output near the transcription start site (TSS) of the promoter. Recently, we showed that Pol II pausing exhibits genome-wide changes during daily transcription in mouse liver. In this article, we review historical as well as recent findings on the regulation of transcription rhythms by the circadian clock and other transcription factors, and the potential limitations of those results in explaining rhythmic transcription at the TSS. We then discuss our results on the genome-wide characteristics of daily changes in Pol II pausing, the possible regulatory mechanisms involved, and their relevance to future research on circadian transcription regulation.

A cryogenic sapphire resonator oscillator with 10−16 mid-term fractional frequency stability

We report in this Letter the outstanding frequency stability performance of an autonomous cryogenic sapphire oscillator (CSO) presenting a flicker frequency noise floor below 2×10−16 near 1000 s of integration time and a long-term Allan deviation limited by a random walk process of ∼1×10−18τ. The frequency stability qualification at this level called for the implementation of sophisticated instrumentation associated with ultra-stable frequency references. This result is technologically sound as it demonstrates the potentiality of the CSO technology. From the physical point of view, it sets an upper limit to the ultimate noise floor of the cryogenic microwave resonator that is competitive to that of the ultra-stable optical Fabry–Pérot cavities.

Функциональное формирование нейроморфного резервуарного вычислительного элемента на базе мемристивного метаматериала

A neural network structure is designed based on the ability of a certain class of calculators to recombine internal resources in order to produce neuromorphic elements to solve applied problems. This approach is rooted in a composite material with controlled local conductivity to form volumetric inhomogeneities capable of responding to and influencing external electrostatic effects. Such compounds aggregate into stable clusters suitable for modelling the processes that occur during information processing in natural neuronal entities. The use of conductive transitions between substrate-formed neuromorphic clusters as a learning structure makes it possible to increase the reliability of the neural network system. Long-term, non-volatile storage of information about the elements of the training sample in variable structures is possible. The basic approach to information conversion is to manage the electrostatic influence as it passes through the layered structures formed. The response to the input is not formed by propagating the signal through conductive elements with variable conductivity, but by passing the energy impact through a limited volume of metamaterial. Thus, a massively parallel processing of information can be achieved with the implementation of a mechanism for combining the opinions of independent neural network clusters that influence the final decision. Furthermore, this method of spreading effects in such an environment greatly simplifies the process of adding elements to the neural network. The lack of direct electrical interconnection facilitates the easy addition of new computational elements without significant rearrangement of the conductive media. Networks of this type are capable of significant growth without loss of experience. The input conversion process using modified delta coding prevents premature wear and tear on reconfigurable network elements. The manner in which information is presented and the manner in which neural network computing is organised enabled the creation of limited autonomous oscillations within the volume of the calculator to maintain circulating memory and the ability to gradually accumulate network experience for its subsequent recording in configurable elements. The identified features resulted in the application of this kind of calculators in the task of developing radio frequency management plans for the organisation of stable communication in a complex electromagnetic environment.

Real-Time Observation for Dynamic Oscillation during the Self-Assembly and Clearance of Aβ42.

The dynamic oscillation implicated in structural heterogeneity during the self-assembly of amyloid peptide 1-42 (Aβ42) may play a crucial role in eliciting cellular responses. We developed a real-time monitoring platform to observe an oscillatory non-equilibrium interaction that dominated the Aβ42 clearance by neuronal cells during interplay with an oscillator (lipopolysaccharide, LPS). Molecular dynamics studies indicated that the electrostatic and hydrophobic segments of LPS involved in the temporary heteromolecular association and slightly decelerated the intrinsic thermally-induced protein dynamics of Aβ42. A bait-specific intervention strategy could temporarily slow down the self-propagation of Aβ42 to extend the lifetime of autonomous oscillation and augment the Aβ42 clearance of neuronal cells. The lifetime increment of dynamic oscillation shows a bait concentration-dependent manner to reflect the non-equilibrium binding strength. This relationship may serve as a drug-screening predictor for Alzheimer's disease drug discovery.

Circadian rhythm of PERIOD2::LUCIFERASE expression in the trigeminal ganglion of mice.

The trigeminal nerve conveys delicate sensations such as warmth, pain, and tactile pressure in the oral and facial regions, and most trigeminal afferent cell bodies are located in the trigeminal ganglion. Our previous study has shown that sensations in trigeminal nerve innervated areas, specifically in the maxillofacial region, exhibit diurnal variation and that sensitivity changes time-dependently. In this study, we aimed to clarify the rhythm of expression of clock gene in the trigeminal ganglion of mice to elucidate the mechanism of circadian regulation in the same area. Immunohistochemistry examined the expression of the PER2 protein in the suprachiasmatic nucleus and trigeminal ganglion of wild-type mice. To measure gene expression as bioluminescence, PERIOD2::LUCIFERASE knock-in (PER2::LUC) mice were used. Unilateral trigeminal ganglion and brain sections including the suprachiasmatic nucleus were incubated ex vivo. Bioluminescence levels were then measured using a highly sensitive photodetector. The same experiments were then conducted with Cry1 gene-deficient (Cry1-/- ) or Cry2 gene-deficient (Cry2-/- ) mice. In the trigeminal ganglion, immunohistochemistry localized PER2 protein expression within the neuronal cell body. Mouse trigeminal ganglion ex vivo tissues showed distinct circadian oscillations in PER2::LUC levels in all genotypes, wild-type, Cry1-/- , and Cry2-/- . The period was shorter in the trigeminal ganglion than in the suprachiasmatic nucleus; it was shorter in Cry1-/- and longer in Cry2-/- mice than in the wild-type mice. The expression of Per2 in neurons of the trigeminal ganglion in ex vivo culture and the oscillation in a distinct circadian rhythm suggests that the trigeminal ganglion is responsible for the relay of sensory inputs and temporal gating through autonomous circadian oscillations.

Ribozyme-mediated RNA synthesis and replication in a model Hadean microenvironment

Enzyme-catalyzed replication of nucleic acid sequences is a prerequisite for the survival and evolution of biological entities. Before the advent of protein synthesis, genetic information was most likely stored in and replicated by RNA. However, experimental systems for sustained RNA-dependent RNA-replication are difficult to realise, in part due to the high thermodynamic stability of duplex products and the low chemical stability of catalytic RNAs. Using a derivative of a group I intron as a model for an RNA replicase, we show that heated air-water interfaces that are exposed to a plausible CO2-rich atmosphere enable sense and antisense RNA replication as well as template-dependent synthesis and catalysis of a functional ribozyme in a one-pot reaction. Both reactions are driven by autonomous oscillations in salt concentrations and pH, resulting from precipitation of acidified dew droplets, which transiently destabilise RNA duplexes. Our results suggest that an abundant Hadean microenvironment may have promoted both replication and synthesis of functional RNAs.

Linearizabiliy and Lax representations for cubic autonomous and non-autonomous nonlinear oscillators

In this work we consider a family of cubic, with respect to the first derivative, second-order ordinary differential equations. We study linearizability conditions for this family of equations via generalized nonlocal transformations. We construct linearizability criteria in the explicit form for some particular cases of these transformations. We show that each linearizable equation admits a quadratic rational first integral. Moreover, we demonstrate that generalized nonlocal transformations under certain conditions preserve Lax integrability for equations from the considered family. Consequently, we find that any linearizable equation from the considered family possesses a Lax representation. This provides a connection between two different approaches for studying integrability and demonstrates that the Lax technique can be effectively applied to finding and classifying dissipative integrable autonomous and non-autonomous nonlinear oscillators. We illustrate our results by several examples of linearizable equations, including a non-autonomous generalization of the Rayleigh–Duffing oscillator, a family of chemical oscillators and a generalized Duffing–Van der Pol oscillator.

Light‐Fueled Nonequilibrium and Adaptable Hydrogels for Highly Tunable Autonomous Self‐Oscillating Functions

AbstractNonequilibrium oscillation fueled by dissipating chemical energy is ubiquitous in living systems for realizing a broad range of complex functions. The design of synthetic materials that can mimic their biological counterparts in the production of dissipative structures and autonomous oscillations is of great interest but remains challenging. Here, a series of environmentally adaptable hydrogels functionalized with photoswitchable spiropyran derivatives that display a tunable equilibrium‐shifting capability, thus endowing those hydrogels with a high degree of freedom and flexibility is reported. Such nonequilibrium hydrogels are able to responsively adapt their shapes under constant light illumination due to asymmetric deswelling, which in turn generates self‐shadowing and consequently creates autonomous self‐oscillating behaviors through a negative feedback process. Diverse oscillation modes including bending, twisting, and snap‐through buckling with tunable frequency and amplitude are widely observed in three different molecular systems. Density functional theory calculations and finite element simulations further demonstrated the robustness of such a photoadaptable self‐oscillation mechanism. This study provides a useful molecular design strategy for construction of highly adaptable hydrogels with potential applications in self‐sustained soft robots and autonomous devices.

FPGA implementation, controls and synchronization of autonomous Josephson junction jerk oscillator

This paper reports the field programmable gate array (FPGA) implementation of an autonomous Josephson junction jerk oscillator (AJJJO) and the investigated coexisting and chaotic attractors besteered, with different synchronization achieved. AJJJO displays bistability, megastability, and coexistence between limit cycle and self-excited chaotic attractors, which is validated by the FPGA implementation. The elimination of chaotic dynamics exhibited by AJJJO was done by using a double single controller via numerical simulations. The coexisting attractors between limit cycle and self-excited chaotic attractors are destroyed and besteered to the wanted path via the linear augmentation control method. Moreover, controllers are employed to achieve the difference synchronization of three identical coupled chaotic AJJJOs resulting from various starting conditions. Finally, numerical simulations of three identical coupled chaotic AJJJOs indicate the effectiveness of the difference synchronization.

Systematic analysis of negative and positive feedback loops for robustness and temperature compensation in circadian rhythms

Temperature compensation and robustness to biological noise are two key characteristics of the circadian clock. These features allow the circadian pacemaker to maintain a steady oscillation in a wide range of environmental conditions. The presence of a time-delayed negative feedback loop in the regulatory network generates autonomous circadian oscillations in eukaryotic systems. In comparison, the circadian clock of cyanobacteria is controlled by a strong positive feedback loop. Positive feedback loops with substrate depletion can also generate oscillations, inspiring other circadian clock models. What makes a circadian oscillatory network robust to extrinsic noise is unclear. We investigated four basic circadian oscillators with negative, positive, and combinations of positive and negative feedback loops to explore network features necessary for circadian clock resilience. We discovered that the negative feedback loop system performs the best in compensating temperature changes. We also show that a positive feedback loop can reduce extrinsic noise in periods of circadian oscillators, while intrinsic noise is reduced by negative feedback loops.

Expression pattern of circadian rhythm-related genes and its potential relationship with miRNAs activity in endometrial cancer.

The circadian clock is an autonomous oscillator that controls key aspects of cell physiology, including metabolism, transcriptional state, and cell signaling. Disturbances of circadian rhythms lead to disruption of cell and tissue homeostasis, which promotes carcinogenesis. The aim of the study was to determine the expression of circadian rhythm-related genes in endometrial cancer and to select miRNAs involved in the regulation of their expression. 50 endometrial tissue samples were collected from patients who underwent hysterectomy: 40 diagnosed with endometrial cancer and 10 without cancer. Expression profile of circadian rhythm-related genes was evaluated using microarrays and validated with RT-qPCR. MicroRNA expression was assessed using microarrays. Then mirTAR tool was used to identify miRNAs involved in the expression regulation of circadian rhythm-related genes. CLOCK expression is disrupted in endometrial cancer, which may be due to miR-15b, miR-331-3p and miR-200a overexpression. Elevated NPAS2 and CSNK1D levels may be associated with miR-432 silencing. In addition, high miR-874 and miR-200a expression may be potentially responsible for the reduction of PER3 level. Change of CLOCK, CSNK1D, NPAS2 and PER3 expression may suggest that circadian rhythms are disrupted in endometrial cancer. A possible mechanism of the observed changes may be related to miRNAs activity.

Infinite coexisting attractors in an autonomous hyperchaotic megastable oscillator and linear quadratic regulator-based control and synchronization

Infinite coexisting attractors in an autonomous hyperchaotic megastable oscillator and linear quadratic regulator-based control and synchronization

Marangoni- vs. buoyancy-driven flows: competition for spatio-temporal oscillations in A + B → C systems.

The emergence of self-organized behaviors such as spatio-temporal oscillations is well-known for complex reactions involving nonlinear chemical or thermal feedback. Recently, it was shown that local oscillations of the chemical species concentration can be induced under isothermal batch conditions for simple bimolecular A + B → C reactions, provided they are actively coupled with hydrodynamics. When two reactants A and B, initially separated in space, react upon diffusive contact, damped spatio-temporal oscillations could develop when the surface tension increases sufficiently in the reaction zone. Additionally, if the density decreases, the coupling of both surface tension- and buoyancy-driven contributions to the flow can further sustain this oscillatory instability. Here, we investigate the opposite case of a reaction inducing a localized decrease in surface tension and an increase in density in the reacting zones. In this case, the competition arising from the two antagonistic flows is needed to create oscillatory dynamics, i.e., no oscillations are observed for pure chemically driven Marangoni flows. We study numerically these scenarios in a 2-dimensional system and show how they are controlled by the following key parameters: (i) ΔM and ΔR governing the surface tension and density variation during the reaction, respectively, (ii) the layer thickness of the system, and (iii) its lateral length. This work is a further step toward inducing and controlling chemical oscillations in simple reactions.

Dynamics of Three Coupled Generators of Quasi-periodic Oscillations

The dynamics of three coupled generators capable of demonstrating autonomous quasi-periodic oscillations is studied. The complex structure of the Lyapunov charts of the system is discussed, which reveals invariant tori of different dimensions, quasi-periodic bifurcations of tori, and Arnold’s resonant web based on tori of different dimensions. Cases of different types of tuning of individual generators (periodic oscillations, quasi-periodic oscillations) are considered. A detailed numerical bifurcation analysis of the equilibrium state and limit cycles, which form a complex picture of dynamic regimes, is carried out.Common features and differences compared to the case of three coupled van der Pol oscillators are discussed.

Circadian rhythms and cancer.

Circadian rhythms are autonomous oscillators developed by the molecular circadian clock, essential for coordinating internal time with the external environment in a 24-h daily cycle. In mammals, this circadian clock system plays a major role in all physiological processes and severely affects human health. The regulation of the circadian clock extends beyond the clock genes to involve several clock-controlled genes. Hence, the aberrant expression of these clock genes leads to the downregulation of important targets that control the cell cycle and the ability to undergo apoptosis. This may lead to genomic instability and promotes carcinogenesis. Alteration in the clock genes and their modulation is recognized as a new approach for the development of effective treatment against several diseases, including cancer. Until now, there has been a lack of understanding of circadian rhythms and cancer disease. For that, this chapter aims to represent the core components of circadian rhythms and their function in cancer pathogenesis and progression. In addition, the clinical impacts, current clock drugs, and potential therapeutic targets have been discussed.

Coexisting oscillations and four-scroll chaotic attractors in a pair of coupled memristor-based Duffing oscillators: Theoretical analysis and circuit simulation

We introduce a new four-scroll chaotic system consisting of two autonomous Duffing oscillators with memristive nonlinearity. The memristor emulator consists of a diode bridge and a first-order RC filter. The analytical study of the coupled system shows that it is dissipative, symmetric, and has nine equilibrium points. By using some chaos characterization tools such as bifurcation diagrams, Lyapunov exponent graphs, phase portraits, power spectra, and Poincaré sections, a plethora of dynamical behaviors, such as the period doubling scenario to chaos as well as multistability, are obtained and illustrated. We demonstrate that the system can generate mono-scroll, double-scroll, and four-scroll chaotic attractors according to the coupling parameter. Basins of attraction (illustrating the scenario to four-scroll chaotic attractor) as well as two-parameter Lyapunov diagrams (illustrating the dynamics of the system) are obtained and depicted. To ensure that the new system is implementable, an electronic circuit emulating the model is built and simulated in the PSpice environment.

Autonomous three-dimensional oscillator with five terms: spiking oscillations generation mechanism, microcontroller implementation and controls

This paper presents a report on the microcontroller implementation of an autonomous three-dimensional oscillator with five terms (ATDOFT) and performance analysis based on partial and total amplitude controls. ATDOFT displays periodic spiking behaviors, period-tripling bifurcation to chaos, chaotic spiking attractors, coexisting attractors and bistable attractors. ATDOFT is divided into two subsystems; namely the fast and slow subsystems to investigate the mechanism of the spiking dynamics. Relying on the stability analysis based on the fast subsystem with respect to the slow variable, it is shown that the spiking oscillations present in the ATDOFT arise from the system switching between the unstable state and the stable state of the lone equilibrium point of the fast subsystem. By inserting two controller parameters into the rate equations of the ATDOFT, total and partial amplitude controls are achieved. Finally, the dynamical behaviors found in ATDOFT are validated by the microcontroller implementation.

How clock heterogeneity affects synchronization and can enhance stability.

The production process of integrated electronic circuitry inherently leads to large heterogeneities on the component level. For electronic clock networks this implies detuned intrinsic frequencies and differences in coupling strength and the characteristic time delays associated with signal transmission, processing, and feedback. Using a phase-model description, we study the effects of such component heterogeneity on the dynamical properties of synchronization in networks of mutually delay-coupled Kuramoto oscillators. We test the theory against experimental results and circuit-level simulations in a prototype system of mutually delay-coupled electronic clocks, so-called phase-locked loops. Interestingly, our results show that heterogeneity in the system can actually enhance the stability of synchronized states. That means that beyond the optimizations that can be achieved by tuning homogeneous coupling strengths, time delays, and loop-filter cut-off frequencies, heterogeneities in these system parameters enable much better optimization of perturbation decay rates, stabilization of synchronous states, and tuning of phase differences between the clocks. Our theory enables the design of custom-fit synchronization layers according to the specific requirements and properties of electronic systems, such as operational frequencies, phase relations, and, e.g., transmission delays. These results are not restricted to electronic systems, because signal transmission, processing, and feedback delays are common to networks of spatially distributed and coupled autonomous oscillators.

Planetary sleep medicine: Studying sleep at the individual, population, and planetary level.

Circadian rhythms are a series of endogenous autonomous oscillators that are generated by the molecular circadian clock which coordinates and synchronizes internal time with the external environment in a 24-h daily cycle (that can also be shorter or longer than 24 h). Besides daily rhythms, there exist as well other biological rhythms that have different time scales, including seasonal and annual rhythms. Circadian and other biological rhythms deeply permeate human life, at any level, spanning from the molecular, subcellular, cellular, tissue, and organismal level to environmental exposures, and behavioral lifestyles. Humans are immersed in what has been called the "circadian landscape," with circadian rhythms being highly pervasive and ubiquitous, and affecting every ecosystem on the planet, from plants to insects, fishes, birds, mammals, and other animals. Anthropogenic behaviors have been producing a cascading and compounding series of effects, including detrimental impacts on human health. However, the effects of climate change on sleep have been relatively overlooked. In the present narrative review paper, we wanted to offer a way to re-read/re-think sleep medicine from a planetary health perspective. Climate change, through a complex series of either direct or indirect mechanisms, including (i) pollution- and poor air quality-induced oxygen saturation variability/hypoxia, (ii) changes in light conditions and increases in the nighttime, (iii) fluctuating temperatures, warmer values, and heat due to extreme weather, and (iv) psychological distress imposed by disasters (like floods, wildfires, droughts, hurricanes, and infectious outbreaks by emerging and reemerging pathogens) may contribute to inducing mismatches between internal time and external environment, and disrupting sleep, causing poor sleep quantity and quality and sleep disorders, such as insomnia, and sleep-related breathing issues, among others. Climate change will generate relevant costs and impact more vulnerable populations in underserved areas, thus widening already existing global geographic, age-, sex-, and gender-related inequalities.