Autonomous Oscillations Research Articles

Два связанных квазипериодических генератора, возбуждаемых гармоническим сигналом

A system of two dissipatively coupled generators, which can exhibit autonomous quasiperiodic oscillations, excited by a harmonic signal, is studied. Lyapunov charts are presented that reveal the regimes of invariant tori of different dimensions and chaos. Phase portraits in stroboscopic section and double Poincare section are presented. The coexistence of different regimes, in particular, the bifurcations of invariant tori, is discussed.

Robust in-phase synchronization in repressor-based coupled gene oscillators

Abstract Inside living cells, proteins or mRNA can show oscillations even without a periodic driving force. Such genetic oscillations are precise timekeepers for cell-cycle regulations, pattern formation during embryonic development in higher animals, and daily cycle maintenance in most organisms. The synchronization between oscillations in adjacent cells happens via intercellular coupling, which is essential for periodic segmentation formation in vertebrates and other biological processes. While molecular mechanisms of generating sustained oscillations are quite well understood, how do simple intercellular coupling produces robust synchronizations are still poorly understood? To address this question, we investigate two models of coupled gene oscillators - activator-based coupled oscillators (ACO) and repressor-based coupled oscillators (RCO) models. In our study, a single autonomous oscillator (that operates in a single cell) is based on a negative feedback, which is delayed by intracellular dynamics of an intermediate species. For the ACO model (RCO), the repressor protein of one cell activates (represses) the production of another protein in the neighbouring cell after a intercellular time delay. We investigate the coupled models in the presence of intrinsic noise due to the inherent stochasticity of the biochemical reactions. We analyze the collective oscillations from stochastic trajectories in the presence and absence of explicit coupling delay and make careful comparison between two models. Our results show no clear synchronizations in the ACO model when the coupling time delay is zero. However, a non-zero coupling delay can lead to anti-phase synchronizations in ACO. Interestingly, the RCO model shows robust in-phase synchronizations in the presence and absence of the coupling time delay. Our results suggest that the naturally occurring intercellular couplings might be based on repression rather than activation where in-phase synchronization is crucial.

Analysis of Steady-State Oscillations in an Autonomous Oscillator under Multi-Frequency Excitation

The analysis of the behavior of an oscillator under multi-frequency excitation is considered in the paper. The investigation is based on the phase macromodel. The paper shows that three steady-state modes can exist in oscillator under multi-frequency excitation. The synchronized (locked) mode can be defined as the coincidence of the oscillator fundamentals with the excitation fundamentals in the region of sufficiently large excitation magnitude. The unsynchronized (unlocked) mode exists outside the synchronized region and its spectrum contains additional intrinsic fundamental besides the excitation ones. Singular points mode in some isolated points outside the synchronized region is characterized by the equality of the number of the oscillator fundamentals with the number of the excitation fundamentals. Performed numerical experiments confirmed the appearance of bifurcation points while transition of oscillator into the synchronization mode. The existence of singular points outside the synchronization region and their isolated character was also experimentally demonstrated. The problems of finding a steady-state solution of the phase equation of an excited oscillator by the Harmonic Balance (HB) method are considered. It is shown that main difficulties are connected with the presence of linear term in the steady-state solution. A transformation is proposed to provide the formation of HB equations for the phase micromodel in a standard form. Additional difficulties of HB simulations of synchronized oscillator phase equations are discussed.

In silico Determination of Some Conditions Leading to Glycolytic Oscillations and Their Interference With Some Other Processes in E. coli Cells.

Autonomous oscillations of species levels in the glycolysis express the self-control of this essential cellular pathway belonging to the central carbon metabolism (CCM), and this phenomenon takes place in a large number of bacteria. Oscillations of glycolytic intermediates in living cells occur according to the environmental conditions and to the cell characteristics, especially the adenosine triphosphate (ATP) recovery system. Determining the conditions that lead to the occurrence and maintenance of the glycolytic oscillations can present immediate practical applications. Such a model-based analysis allows in silico (model-based) design of genetically modified microorganisms (GMO) with certain characteristics of interest for the biosynthesis industry, medicine, etc. Based on our kinetic model validated in previous works, this paper aims to in silico identify operating parameters and cell factors leading to the occurrence of stable glycolytic oscillations in the Escherichia coli cells. As long as most of the glycolytic intermediates are involved in various cellular metabolic pathways belonging to the CCM, evaluation of the dynamics and average level of its intermediates is of high importance for further applicative analyses. As an example, by using a lumped kinetic model for tryptophan (TRP) synthesis from literature, and its own kinetic model for the oscillatory glycolysis, this paper highlights the influence of glycolytic oscillations on the oscillatory TRP synthesis through the PEP (phosphoenolpyruvate) glycolytic node shared by the two oscillatory processes. The numerical analysis allows further TRP production maximization in a fed-batch bioreactor (FBR).

Computationally enhanced quantitative phase microscopy reveals autonomous oscillations in mammalian cell growth

The fine balance of growth and division is a fundamental property of the physiology of cells, and one of the least understood. Its study has been thwarted by difficulties in the accurate measurement of cell size and the even greater challenges of measuring growth of a single cell over time. We address these limitations by demonstrating a computationally enhanced methodology for quantitative phase microscopy for adherent cells, using improved image processing algorithms and automated cell-tracking software. Accuracy has been improved more than twofold and this improvement is sufficient to establish the dynamics of cell growth and adherence to simple growth laws. It is also sufficient to reveal unknown features of cell growth, previously unmeasurable. With these methodological and analytical improvements, in several cell lines we document a remarkable oscillation in growth rate, occurring throughout the cell cycle, coupled to cell division or birth yet independent of cell cycle progression. We expect that further exploration with this advanced tool will provide a better understanding of growth rate regulation in mammalian cells.

Inkjet-Printed Electronics on Paper for RF Identification (RFID) and Sensing

The newly developed research area of inkjet-printed radio frequency (RF) electronics on cellulose-based and synthetic paper substrates is introduced in this paper. This review paper presents the electrical properties of the paper substrates, the printed silver nanoparticle-based thin films, the dielectric layers, and the catalyst-based metallization process. Numerous inkjet-printed microwave passive/ative systems on paper, such as a printed radio frequency identification (RFID) tag, an RFID-enabled sensor utilizing carbon nanotubes (CNTs), a substrate-integrated waveguide (SIW), fully printed vias, an autonomous solar-powered beacon oscillator (active antenna), and artificial magnetic conductors (AMC), are discussed. The reported technology could potentially act as the foundation for true “green” low-cost scalable wireless topologies for autonomous Internet-of-Things (IoT), bio-monitoring, and “smart skin” applications.

A Simple Approach for Dealing with Autonomous Conservative Oscillator under Initial Velocity

The current study is involved to analytical solution of nonlinear oscillators under initial velocity. By using energy conservation principle, system initial condition converts to condition which oscillator’s velocity become zero. When oscillator’s speed is zero and placed out of movement’s origin, the relation between frequency and amplitude could be extracted. By paying attention to energy conservation principle and relation between the initial velocity and amplitude, the frequency-amplitude relation is extended to frequency-initial velocity relationship. In order to demonstrate the effectiveness of proposed method, Duffing oscillator with cubic nonlinearity and oscillator with discontinuity are considered. Comparison of results with numerical solution shows good agreement. The proposed method is simple and efficient enough to achieve the analytical approximation of nonlinear autonomous conservative oscillator with initial velocity.

Study of Autonomous Conservative Oscillator Using an Improved Perturbation Method

In a recent article \cite{manimegalai2019}, Aboodh transform based homotopy perturbation method ($AT$) has been found to produce approximate analytical solutions in a simple way but with better accuracy in comparison to those obtained from some of the established approximation methods \cite{mehdipour2010application,nofal2013analytical} for some physically relevant anharmonic oscillators such as autonomous conservative oscillator (ACO). In the present article, expansion of frequency ($\omega$) and an auxiliary parameter ($h$) are incorporated in the framework of the homotopy perturbation method (HPM) to improve the accuracy by retaining its simplicity. Laplace transform is used to make the calculation simpler. This improved HPM ($LH$) is simple but provides highly accurate results for ACO in comparison to those obtained from $AT$. The error in the values of frequency and displacement calculated using the $LH$ is found to be one or two order of magnitude less than those obtained from $AT$ for the considered parameter sets.

Bubble-free System for Belousov-Zhabotinsky Gels

The chemical energy from the Belousov-Zhabotinsky (BZ) reaction powers autonomous mechanical oscillations in BZ gels. One drawback is that the process produces carbon dioxide bubbles, making length...

A chaotic circuit based on a physical memristor

Abstract The memristor is a fundamental two-terminal electrical component unique in that it possesses the properties of non-linearity and memory, which are pervasive across natural systems. It has been proven to be in principle a viable substrate for novel dynamical systems showing chaotic behavior, but the recourse to abstract, idealized mathematical non-linearities throughout the existing literature hinders practical realization using physical devices. In this work, we realize a fully autonomous chaotic oscillator circuit based on self-directed channel memristors. Its architecture comprises two feedback loops, a linear one and a non-linear one involving the memristor. Low-dimensional chaotic dynamics are readily obtained experimentally using tungsten-based as well as carbon-based physical devices, despite their non-idealities. A mathematical model of the circuit, revealing further interesting non-linear features such as bifurcations without parameters, is also offered.

Bright light improves sleep in patients with Parkinson\u2019s disease: possible role of circadian restoration

Parkinson’s disease (PD) is one of the most common neurodegenerative disorders. Among the most common manifestations of PD are sleep problems, which are coupled with the adverse effects of dopaminergic therapies (DT). A non-pharmacological solution for these sleep problems has been sought to avoid additional pharmacological intervention. Here, we show that bright light therapy (BLT) is effective for improving sleep in Japanese PD patients receiving DT. Furthermore, experimental evaluation of peripheral clock gene expression rhythms revealed that most PD patients receiving DT who experienced improved sleep following BLT showed a circadian phase shift, indicating the existence of a correlation between circadian modulation and sleep improvement. Conversely, this result indicates that sleep problems in PD patients receiving DT may arise at least in part as a result of circadian dysfunction. Indeed, we found that chronic dopaminergic stimulation induced a rapid attenuation of autonomous oscillations of clock gene expression in ex vivo cultured mouse suprachiasmatic nucleus (SCN) at the single neuron level. In conclusion, BLT is a promising medical treatment for improving sleep in PD patients receiving DT. This BLT-induced improvement may be due to the restoration of circadian function.

Timekeeping in the hindbrain: a multi-oscillatory circadian centre in the mouse dorsal vagal complex

Metabolic and cardiovascular processes controlled by the hindbrain exhibit 24 h rhythms, but the extent to which the hindbrain possesses endogenous circadian timekeeping is unresolved. Here we provide compelling evidence that genetic, neuronal, and vascular activities of the brainstem’s dorsal vagal complex are subject to intrinsic circadian control with a crucial role for the connection between its components in regulating their rhythmic properties. Robust 24 h variation in clock gene expression in vivo and neuronal firing ex vivo were observed in the area postrema (AP) and nucleus of the solitary tract (NTS), together with enhanced nocturnal responsiveness to metabolic cues. Unexpectedly, we also find functional and molecular evidence for increased penetration of blood borne molecules into the NTS at night. Our findings reveal that the hindbrain houses a local network complex of neuronal and non-neuronal autonomous circadian oscillators, with clear implications for understanding local temporal control of physiology in the brainstem.

Solitary phase waves in a chain of autonomous oscillators.

In the present paper, we study phase waves of self-sustained oscillators with a nearest-neighbor dispersive coupling on an infinite lattice. To analyze the underlying dynamics, we approximate the lattice with a quasi-continuum (QC). The resulting partial differential model is then further reduced to the Gardner equation, which predicts many properties of the underlying solitary structures. Using an iterative procedure on the original lattice equations, we determine the shapes of solitary waves, kinks, and the flat-like solitons that we refer to as flatons. Direct numerical experiments reveal that the interaction of solitons and flatons on the lattice is notably clean. All in all, we find that both the QC and the Gardner equation predict remarkably well the discrete patterns and their dynamics.

Branch point control at malonyl-CoA node: A computational framework to uncover the design principles of an ideal genetic-metabolic switch

Living organism is an intelligent system coded by hierarchically-organized information to perform precisely-controlled biological functions. Biophysical models are important tools to uncover the design rules underlying complex genetic-metabolic circuit interactions. Based on a previously engineered synthetic malonyl-CoA switch (Xu et al., PNAS, 2014), we have formulated nine differential equations to unravel the design principles underlying an ideal metabolic switch to improve fatty acids production in E. coli. By interrogating the physiologically accessible parameter space, we have determined the optimal controller architecture to configure both the metabolic source pathway and metabolic sink pathway. We determined that low protein degradation rate, medium strength of metabolic inhibitory constant, high metabolic source pathway induction rate, strong binding affinity of the transcriptional activator toward the metabolic source pathway, weak binding affinity of the transcriptional repressor toward the metabolic sink pathway, and a strong cooperative interaction of transcriptional repressor toward metabolic sink pathway benefit the accumulation of the target molecule (fatty acids). The target molecule (fatty acid) production is increased from 50% to 10-folds upon application of the autonomous metabolic switch. With strong metabolic inhibitory constant, the system displays multiple steady states. Stable oscillation of metabolic intermediate is the driving force to allow the system deviate from its equilibrium state and permits bidirectional ON-OFF gene expression control, which autonomously compensates enzyme level for both the metabolic source and metabolic sink pathways. The computational framework may facilitate us to design and engineer predictable genetic-metabolic switches, quest for the optimal controller architecture of the metabolic source/sink pathways, as well as leverage autonomous oscillation as a powerful tool to engineer cell function.

Wielo-oscylatorowa teoria mechanizmu zegara biologicznego ssaków

Cyklicznie zmieniające się warunki środowiska wywoływane obrotowym ruchem Ziemi są niezmiernie ważnym czynnikiem w procesie ewolucyjnym. Dlatego też, organizmy żywe wykształciły mechanizmy zwane zegarami biologicznymi, które pozwalają im nie tylko biernie na nie reagować, ale je przewidywać i adaptować do nich swoje procesy fizjologiczne oraz zachowania okołodobowe. Historycznie, jądra nadskrzyżowaniowe podwzgórza (ang. suprachiasmatic nuclei, SCN) uważane były za główny i jedyny zegar okołodobowy ssaków. Powszechne było przekonanie, że rytmiczna ekspresja genów zegarowych tego jądra i dobowe zmiany jego aktywności elektrycznej kontrolują wszystkie procesy rytmiczne organizmu. Nowe odkrycia kwestionują jednak teorię dominacji jednego oscylatora. Istnieje coraz więcej dowodów potwierdzających obecność i funkcjonowanie neuronalnych i nie-neuronalnych, niezależnych od SCN, endogennych oscylatorów zegara biologicznego, zlokalizowanych w wielu miejscach mózgowia i poza nim. W artykule opisujemy i charakteryzujemy nowo odkryte autonomiczne zegary mózgowia. Przedstawiamy dowody popierające teorię wielo-oscylatorową i jej rolę w zrozumieniu mechanizmu zegara biologicznego, w kontekście powszechności i znaczenia rytmów biologicznych w fizjologii i patologii funkcjonowania organizmu człowieka.

Clb3-centered regulations are recurrent across distinct parameter regions in minimal autonomous cell cycle oscillator designs

Some biological networks exhibit oscillations in their components to convert stimuli to time-dependent responses. The eukaryotic cell cycle is such a case, being governed by waves of cyclin-dependent kinase (cyclin/Cdk) activities that rise and fall with specific timing and guarantee its timely occurrence. Disruption of cyclin/Cdk oscillations could result in dysfunction through reduced cell division. Therefore, it is of interest to capture properties of network designs that exhibit robust oscillations. Here we show that a minimal yeast cell cycle network is able to oscillate autonomously, and that cyclin/Cdk-mediated positive feedback loops (PFLs) and Clb3-centered regulations sustain cyclin/Cdk oscillations, in known and hypothetical network designs. We propose that Clb3-mediated coordination of cyclin/Cdk waves reconciles checkpoint and oscillatory cell cycle models. Considering the evolutionary conservation of the cyclin/Cdk network across eukaryotes, we hypothesize that functional (“healthy”) phenotypes require the capacity to oscillate autonomously whereas dysfunctional (potentially “diseased”) phenotypes may lack this capacity.

Multistability Control of Space Magnetization in Hyperjerk Oscillator: A Case Study

Abstract In this paper, multistability control of a 5D autonomous hyperjerk oscillator through linear augmentation scheme is investigated. The space magnetization is characterized by the coexistence of five different stable states including an asymmetric pair of chaotic attractors, an asymmetric pair of period-3 cycle, and a symmetric chaotic attractor for a given/fixed set of parameters. The linear augmentation method is applied here to control, for the first time, five coexisting attractors. Standard Lyapunov exponents, bifurcation diagrams, basins of attraction, and 3D phase portraits are presented as methods to conduct the efficaciousness of the control scheme. The results of the applied methods reveal that the monostable chaotic attractor is obtained through three important crises when varying the coupling strength. In particular, below the first critical value of the coupling strength, five distinct attractors are coexisting. Above that critical value, three and then two chaotic attractors are now coexisting, respectively. While for higher values of the coupling strength, only the symmetric chaotic attractor is viewed in the controlled system. The process of annihilation of coexisting multiple attractors to monostable one is confirmed experimentally. The important results of the controlled hyperjerk system with its unique survived chaotic attractor are suited in applications like secure communications.

Implementación electrónica basada en FPAA del oscilador caótico de Lorenz

Nowadays, chaotic systems are very interesting topics for engineers, physicists and mathematicians because most real physical systems are inherently non-linear in nature. The first electronic implementations of autonomous chaotic oscillators were developed using operational amplifiers and diodes, different references detail implementations of chaotic circuits and systems using analog integrated circuit technology, discrete devices such as FPGA (Field programmable gate arrays), microcontrollers, etc. However, analog implementations suffer the problem of sensitivity of analog component values and digital implementations suffer the problem of degradation due to the reduced number of bits to perform computer arithmetic operations. The systems of differential equations that model the chaotic oscillators require integrators that can be implemented with FPAA's (Field programmable analogue array), in this work electronic implementations are developed that are measured in laboratory conditions to observe experimental chaotic attractors, which will be used in the implementation of random number generators and secure communication systems for image encryption.

Dissipative Self-Assembly of Dynamic Multicompartmentalized Microsystems with Light-Responsive Behaviors

Summary Living cells are compartmentalized systems operating far from thermodynamic equilibrium and consume energy from the environment to carry out their functions. The construction of biomimetic synthetic compartments has both scientific and technological value. Despite many advances, the assembly of synthetic compartments that present nonequilibrium behaviors based on dissipative (or transient) self-assembly remains a grand challenge. Here, we describe the design and synthesis of multicompartmental systems with an active microstructure and complex behaviors. By including an artificial pathway for energy dissipation, we demonstrate the autonomous generation of active polymeric systems using a strategy based on polymerization-induced self-assembly (PISA), driven by chemical fuel. Remarkably, these self-organized synthetic systems exhibit a dynamic change in their multicompartmental structures when exposed to light. This work introduces a strategy toward the design and construction of synthetic compartments with a dynamic structure and also presents pathways to engineer materials with spatially controllable structures and functionalities.

Study of a piezoelectric plate based self-sustained electric and electromechanical oscillator

This work deals with the electrical characterization of a piezoelectric plate and its use to generate self-sustained electrical and mechanical oscillations. An experimental frequency-impedance curve of the piezoelectric plate is obtained leading to the electric equivalent of the piezoelectric plate constituted of a capacitive branch in parallel with many RLC resonant branches. The values of the electric components for each branch are determined using the resonant and anti-resonant frequencies. It is demonstrated theoretically that these branches can be understood in terms of vibration modes of the plate; each of which has its own resonant frequency. It is then demonstrated theoretically and experimentally that putting the piezoelectric plate in series with a resistor presenting a nonlinear I − V characteristics having a negative slope, autonomous oscillations of the Van der Pol type can be observed. A theoretical development has led to the appearance of self-sustained periodic and mixed modes mechanical oscillations of the plate deflection.