Autonomous Oscillations Research Articles

CSIG-11. TUMOR-CELL INTRINSIC CALCIUM OSCILLATIONS DRIVE BRAIN METASTASIS

Abstract Calcium is a ubiquitous secondary messenger which regulates many cellular processes. Recently, we have shown that a subpopulation of glioblastoma cells can intrinsically generate calcium oscillations which drive proliferative signalling. Here, we set out to investigate whether such cancer cell autonomous oscillations are also present in secondary brain tumours. Employing longitudinal intravital two-photon microscopy in awake mice, we demonstrate that brain metastases of melanoma and lung cancer exhibit spontaneous calcium oscillations in vivo along the metastatic cascade. These oscillations are already observed during intravascular arrest and in in vitro monocultures, suggesting a tumour-cell intrinsic origin. We developed a fully automatic image analysis pipeline to accurately quantify calcium oscillations both in vivo and in vitro. Mathematical modelling of cytosolic and ER calcium stores can predict stable calcium oscillations with similar frequency and peak characteristics as those experimentally observed. We discovered that these oscillations are tightly regulated by an interplay of calcium-induced calcium release and store-operated calcium entry (SOCE). Similarly, SOCE-related ion channels are enriched in tissue from human melanoma brain metastases compared to healthy brain controls and calcium activity can also be observed ex vivo in patient-derived brain metastasis resections. Finally, by correlating calcium activity and EdU incorporation we discovered that the presence of calcium oscillations predicts their proliferative potential in vitro. Importantly, by intravital two-photon microscopy we show that calcium activity correlates with metastasis size in preclinical models, suggesting a potential new therapeutic angle from which to target brain metastases.

Photochemically Triggered and Autonomous Oscillatory pH-Modulated Transient Assembly/Disassembly of DNA Microdroplet Coacervates.

The assembly of pH-responsive DNA-based, phase-separated microdroplets (MDs) coacervates, consisting of frameworks composed of Y-shaped nucleic acid modules crosslinked by pH-responsive strands, is introduced. The phase-separated MDs reveal dynamic pH-stimulated switchable or oscillatory transient depletion and reformation. In one system, a photoisomerizable merocyanine/spiropyran photoacid is used for the light-induced pH switchable modulation of the reaction medium between the values pH=6.0-4.4. The dynamic transient photochemically-induced switchable depletion/reformation of phase-separated MDs, follows the rhythm of pH changes in solution. In a second system, the Landolt oscillatory reaction mixture pH 7.5→4.2→7.5 is applied to stimulate the oscillatory depletion/reformation of the MDs. The autonomous dynamic oscillation of the assembly/disassembly of the MDs follows the oscillating pH rhythm of the reaction medium.

Photochemically Triggered and Autonomous Oscillatory pH‐Modulated Transient Assembly/Disassembly of DNA Microdroplet Coacervates

AbstractThe assembly of pH‐responsive DNA‐based, phase‐separated microdroplets (MDs) coacervates, consisting of frameworks composed of Y‐shaped nucleic acid modules crosslinked by pH‐responsive strands, is introduced. The phase‐separated MDs reveal dynamic pH‐stimulated switchable or oscillatory transient depletion and reformation. In one system, a photoisomerizable merocyanine/spiropyran photoacid is used for the light‐induced pH switchable modulation of the reaction medium between the values pH=6.0–4.4. The dynamic transient photochemically‐induced switchable depletion/reformation of phase‐separated MDs, follows the rhythm of pH changes in solution. In a second system, the Landolt oscillatory reaction mixture pH 7.5→4.2→7.5 is applied to stimulate the oscillatory depletion/reformation of the MDs. The autonomous dynamic oscillation of the assembly/disassembly of the MDs follows the oscillating pH rhythm of the reaction medium.

Novel Approach to Increasing the Amplitude of the Mechanical Oscillations of Self-Oscillating Gels: Introduction of Catalysts Both as Pendant Groups and as Crosslinkers

For the first time, we introduced chemomechanical self-oscillating poly(N-isopropylacrylamide)-based gels containing catalytically active Fe or Ru complexes both as crosslinkers and as pendant groups. All the obtained gels exhibited sustained autonomous oscillations driven by the Belousov–Zhabotinsky reaction within their structure. The Ru complex-based gels also demonstrated pronounced chemomechanical oscillations; they periodically swelled/shrunk when the catalyst was reduced/oxidized. It was found that the combination of catalytically active cross-linking and pendant Ru complexes in the same gel led to a change in the structure of the gel and a significant increase in the amplitude of its mechanical oscillations. The proposed approach allowed for increasing the amplitude of the mechanical oscillations of self-oscillating gels and opened up new possibilities for adjusting their characteristics. We believe that these gels hold potential for the development of soft actuators and systems capable of signal processing through propagating and interacting chemical waves.

Autonomous Motion of Hydrogels Driven by Semi-Interpenetrating Chemical Processing Systems.

Developing artificial autonomous materials is crucial for a deeper understanding of the emergence of life-like behavior. In nature, cells achieve autonomy through chemical processing systems incorporated into soft material-based frameworks. Inspired by natural cells, we herein describe a straightforward methodology for constructing artificial autonomous materials consisting of a polymer-based chemical processing system and a hydrogel-based soft framework. Using a material comprising a hydrogel framework devoid of active components in combination with semi-interpenetrating self-oscillating linear polymers, we discovered that semi-interpenetrating polymer-based chemical processing systems drive the autonomous motion of the hydrogel framework. The material exhibited autonomous volumetric oscillation powered by the Belousov-Zhabotinsky reaction. Furthermore, the autonomous behavior is controllable by changing the content of the chemical processing system incorporated into the hydrogel framework. Our findings shed light on a class of autonomous materials based on polymer-based chemical processing systems with soft frameworks.

An Adaptive Stabilization Scheme for Autonomous System Oscillations

An Adaptive Stabilization Scheme for Autonomous System Oscillations

Co-Complexes-Based Self-Oscillating Gels Driven by the Belousov-Zhabotinsky Reaction.

We report the synthesis of novel cobalt complexes-based catalysts designed for the oscillatory Belousov-Zhabotinsky (BZ) reaction. For the first time, we introduce cobalt complex-based self-oscillating gels that demonstrate autonomous color oscillations within a BZ reagent solution, functioning without the need for any external stimuli. We created acrylamide-based self-oscillating gels containing immobilized tris(2,2'-bipyridine)cobalt(II) or tris(1,10-phenanthroline)cobalt(II) complexes and gels containing covalently bound (5-acrylamido-1,10-phenanthroline)bis(2,2'-bipyridine)cobalt(II), (5-acrylamido-1,10-phenanthroline)bis(1,10-phenanthroline) cobalt(II), or tris(5-acrylamido-1,10-phenanthroline)cobalt(II) complexes. When the BZ reaction takes place within the gels, it results in the observation of moving chemical waves and reversible color changes. We believe that Co-complexes-based self-oscillating gels have potential applications in the design of soft actuators and chemical devices for signal processing.

Autonomous snap oscillator with only one steady state: dynamical probing, controls, pseudo-random number generation and difference synchronization

The theoretical probing, microcontroller implementation, amplitude controls, chaos control, -pseudo-random number generation (PRNG), and difference synchronization of autonomous snap oscillator with only one steady state (ASOOSS) are studied in this paper. The ASOOSS exhibits self-excited complex attractors, periodic oscillations, coexistence of chaotic hidden attractors with a stable steady state, and hidden chaotic attractors. The simulated attractors are endorsed by the microcontroller execution of ASOOSS. Then, the total and partial controls of the amplitude of ASOOSS are demonstrated by using newly inserted parameters. Moreover, the efficacy of the configured single controller in suppressing chaos within ASOOSS is demonstrated through both analytical and numerical analyses. Furthermore, the binary data generated by the ASOOSS-based PRNG successfully passes the NIST 800–22 statistical tests, providing proof of the random nature of the ASOOSS-based PRNG and making it suitable for digital applications based on chaos. Additionally, controllers are devised to enable differential synchronization of three identical coupled chaotic ASOOSS systems. The effectiveness of the differential synchronization approach is validated through numerical simulations of the coupled chaotic ASOOSS systems.

Autonomous three-dimensional oscillator with two and four wings attractors embedded in the microcontroller: analysis, amplitude controls, random number generator, and image encryption application

Robust chaotic systems offer unpredictability, complex dynamics, noise-like properties, efficient bifurcation behavior, and the ability to model real-world phenomena, making them valuable in diverse scientific and engineering applications. This paper details on the dynamical appraisal, amplitude controls, microcontroller execution, Random number generator (RNG) of an autonomous three-dimensional (3D) oscillator with two and four wings attractors (ATDOTFWA), and its image encryption application. Thanks to the Routh-Hurwitz criteria, five steady states found in the ATDOTFWA are classified as stable or unstable, depending on its two control parameters. During the numerical simulations employing the Runge–Kutta scheme, the ATDOTFWA exhibit a wide range of dynamic behaviors, including no oscillations, Hopf bifurcation, limit cycle, five distinct presentations of two wings chaotic structures, monostable and bistable two wings chaotic structures, bistable and monostable regular oscillations, chaotic bursting characteristics, coexistence of period-2-oscillations and four wings chaotic structure, and four wings chaotic attractor which were validated experimentally by the microcontroller implementation. The total and partial controls of the amplitude are achieved in the ATDOTFWA. A RNG is designed based on the ATDOTFWA, and the generated random numbers are successfully tested using the ENT and NIST 800–22 statistical test suites, demonstrating the reliability of the ATDOTFWA-based RNG. This reliability is further confirmed through the application of the ATDOTFWA-based RNG in an efficient and secure image encryption process, where the generated random numbers are used as the encryption key. The effectiveness of the image encryption process is validated through comprehensive cryptanalysis, with an encryption time of 0.1923 s for a 512×512 image, an average normalized pixel change rate (NPCR) of 99.6126%, an average unified average changing intensity (UACI) of 33.4578%, and an average information entropy of 7.9994.

Human primary cells can tell body time: Dedicated to Steven A. Brown.

The field of chronobiology has advanced significantly since ancient observations of natural rhythms. The intricate molecular architecture of circadian clocks, their hierarchical organization within the mammalian body, and their pivotal roles in organ physiology highlight the complexity and significance of these internal timekeeping mechanisms. In humans, circadian phenotypes exhibit considerable variability among individuals and throughout the individual's lifespan. A fundamental challenge in mechanistic studies of human chronobiology arises from the difficulty of conducting serial sampling from most organs. The concept of studying circadian clocks in vitro relies on the groundbreaking discovery by Ueli Schibler and colleagues that nearly every cell in the body harbours autonomous molecular oscillators. The advent of circadian bioluminescent reporters has provided a new perspective for this approach, enabling high-resolution continuous measurements of cell-autonomous clocks in cultured cells, following in vitro synchronization pulse. The work by Steven A. Brown has provided compelling evidence that clock characteristics assessed in primary mouse and human skin fibroblasts cultured in vitro represent a reliable estimation of internal clock properties in vivo. The in vitro approach for studying molecular human clocks in cultured explants and primary cells, pioneered by Steve Brown, represents an invaluable tool for assessing inter-individual differences in circadian characteristics alongside comprehensive genetic, biochemical and functional analyses. In a broader context, this reliable and minimally invasive approach offers a unique perspective for unravelling the functional inputs and outputs of oscillators operative in nearly any human tissue in physiological contexts and across various pathologies.

Diverse genetic alteration dysregulates neuropeptide and intracellular signalling in the suprachiasmatic nuclei.

In mammals, intrinsic 24 h or circadian rhythms are primarily generated by the suprachiasmatic nuclei (SCN). Rhythmic daily changes in the transcriptome and proteome of SCN cells are controlled by interlocking transcription-translation feedback loops (TTFLs) of core clock genes and their proteins. SCN cells function as autonomous circadian oscillators, which synchronize through intercellular neuropeptide signalling. Physiological and behavioural rhythms can be severely disrupted by genetic modification of a diverse range of genes and proteins in the SCN. With the advent of next generation sequencing, there is unprecedented information on the molecular profile of the SCN and how it is affected by genetically targeted alteration. However, whether the expression of some genes is more readily affected by genetic alteration of the SCN is unclear. Here, using publicly available datasets from recent RNA-seq assessments of the SCN from genetically altered and control mice, we evaluated whether there are commonalities in transcriptome dysregulation. This was completed for four different phases across the 24 h cycle and was augmented by Gene Ontology Molecular Function (GO:MF) and promoter analysis. Common differentially expressed genes (DEGs) and/or enriched GO:MF terms included signalling molecules, their receptors, and core clock components. Finally, examination of the JASPAR database indicated that E-box and CRE elements in the promoter regions of several commonly dysregulated genes. From this analysis, we identify differential expression of genes coding for molecules involved in SCN intra- and intercellular signalling as a potential cause of abnormal circadian rhythms.

Autonomous and Self-sustained Circadian Oscillators Displayed in Human Primary Parathyroid Cell Culture Drive Parathormone Secretion

Abstract Background Most cells in our body possess circadian oscillators controlling diurnal rhythmicity of body metabolism. The role of molecular clocks in regulating the function and disfunction of human parathyroid gland (PG), responsible for calcium homeostasis, has not been unraveled. Hyperparathyroidism is a common endocrine pathology, characterized by an unadapted PTH secretion to calcium levels. Aims Here we aimed at characterizing molecular makeup of circadian clocks in human primary parathyroid cell culture (HPPCC), and at establishing differential transcriptional patterns of normal and pathological PGs. Methods RNA extracted from normal, adenomatous, and hyperplastic PG tissues was subjected to RNA sequencing (RNAseq) analysis. The rim of normal PG tissue was dissected from parathyroid adenoma specimens based on the higher autofluorescence intensity assessed by the near infra-red imaging. HPPCCs were established from adenomatous and hyperplastic PG biopsies. Efficient circadian clock disruption was achieved in HPPCCs by small interfering RNA-mediated knockdown of CLOCK. The functionality of circadian clock machinery was assessed by continuous recording of circadian bioluminescence introduced via lentivectors and paralleled with around-the-clock measurement of PTH secretion using perfusion system. Results The RNAseq analyses revealed transcriptional signatures that distinguished between pathological and normal PGs, and among adenomatous and hyperplastic PGs. We report, for the first time, robust anti-phasic circadian rhythmicity of Per2-luciferase and Bmal1-luciferase reporters in HPPCCs synchronized in vitro. Strikingly, we observed circadian rhythmicity of PTH secretion by parathyroid adenoma cells. Moreover, clock disruption in PG adenoma cells has an impact on transcription of functional genes. Conclusion Our data indicate presence of cell-autonomous molecular clock in human PG cells paralleled with circadian rhythmic PTH secretion and provide large-scale transcriptional pattern of parathyroid adenoma and hyperplastic tissues.

The Existence of Li–Yorke Chaos in a Discrete-Time Glycolytic Oscillator Model

This paper investigates an autonomous discrete-time glycolytic oscillator model with a unique positive equilibrium point which exhibits chaos in the sense of Li–Yorke in a certain region of the parameters. We use Marotto’s theorem to prove the existence of chaos by finding a snap-back repeller. The illustration of the results is presented by using numerical simulations.

Mathematical modeling of temperature-induced circadian rhythms

The central circadian pacemaker in the suprachiasmatic nuclei (SCN) aligns the phase and period of autonomous molecular oscillators in peripheral cells to daily light/dark cycles via physiological, neuronal, hormonal, and metabolic signals. Among different entrainment factors, temperature entrainment has been proposed as an essential alternative for inducing and sustaining circadian rhythms in vitro. While the synchronization mechanisms for hormones such as glucocorticoids have been widely studied, little is known about the crucial role of body temperature as a systemic cue. In this work, we develop a semi-mechanistic mathematical model describing the entrainment of peripheral clocks to temperature rhythms. The model incorporates a temperature sensing-transduction cascade involving a heat shock transcription factor-1 (HSF1) and heat shock response (HSR) pathway to simulate the entrainment of clock genes. The model is used to investigate the mammalian temperature entrainment and synchronization of cells subject to temperature oscillations of different amplitudes and magnitudes and examine the effects of transitioning between temperature schedules. Our computational analyses of the system’s dynamic responses reveal that 1) individual cells gradually synchronize to the rhythmic temperature signal by resetting their intrinsic phases to achieve coherent dynamics while oscillations are abolished in the absence of temperature rhythmicity; 2) alterations in the amplitude and period of temperature rhythms impact the peripheral synchronization behavior; 3) personalized synchronization strategies allow for differential, adaptive responses to temperature rhythms. Our results demonstrate that temperature can be a potent entrainer of circadian rhythms. Therefore, in vitro systems subjected to temperature modulation can serve as a potential tool for studying the adjustment or disruption of circadian rhythms.

Trained recurrent neural networks develop phase-locked limit cycles in a working memory task.

Neural oscillations are ubiquitously observed in many brain areas. One proposed functional role of these oscillations is that they serve as an internal clock, or 'frame of reference'. Information can be encoded by the timing of neural activity relative to the phase of such oscillations. In line with this hypothesis, there have been multiple empirical observations of such phase codes in the brain. Here we ask: What kind of neural dynamics support phase coding of information with neural oscillations? We tackled this question by analyzing recurrent neural networks (RNNs) that were trained on a working memory task. The networks were given access to an external reference oscillation and tasked to produce an oscillation, such that the phase difference between the reference and output oscillation maintains the identity of transient stimuli. We found that networks converged to stable oscillatory dynamics. Reverse engineering these networks revealed that each phase-coded memory corresponds to a separate limit cycle attractor. We characterized how the stability of the attractor dynamics depends on both reference oscillation amplitude and frequency, properties that can be experimentally observed. To understand the connectivity structures that underlie these dynamics, we showed that trained networks can be described as two phase-coupled oscillators. Using this insight, we condensed our trained networks to a reduced model consisting of two functional modules: One that generates an oscillation and one that implements a coupling function between the internal oscillation and external reference. In summary, by reverse engineering the dynamics and connectivity of trained RNNs, we propose a mechanism by which neural networks can harness reference oscillations for working memory. Specifically, we propose that a phase-coding network generates autonomous oscillations which it couples to an external reference oscillation in a multi-stable fashion.

Multi-parametric optimization for controlling bifurcation structures

Bifurcations organize the dynamics of many natural and engineered systems. They induce qualitative and quantitative changes to a system’s dynamics, which can have catastrophic consequences if ignored during design. In this paper, we propose a general computational method to control the local bifurcations of dynamical systems by optimizing design parameters. We define an objective functional that enforces the appearance of local bifurcation points at targeted locations or even encourages their disappearance. The methodology is an efficient alternative to bifurcation tracking techniques capable of handling many design parameters ( > 10 2 ). The method is demonstrated on a Duffing oscillator featuring a hardening cubic nonlinearity and an autonomous van der Pol-Duffing oscillator coupled to a nonlinear tuned vibration absorber. The finite-element model of a clamped-free Euler–Bernoulli beam, coupled with a reduced-order modelling technique, is also used to show the extension to the shape optimization of more complicated structures. Results demonstrate that several local bifurcations of various types can be handled simultaneously by the bifurcation control framework, with both parameter and state target values.

On the geometric and analytical properties of the anharmonic oscillator

Here we consider the anharmonic oscillator that is a dynamical system given by yxx+δyn=0. We demonstrate that to this equation corresponds a new example of a superintegrable two-dimensional metric with a linear and a transcendental first integrals. Moreover, we show that for particular values of n the transcendental first integral degenerates into a polynomial one, which provides an example of a superintegrable metric with additional polynomial first integral of an arbitrary even degree. We also discuss a general procedure of how to construct a superintegrable metric with one linear first integral from an autonomous nonlinear oscillator that is cubic with respect to the first derivative. We classify all cubic oscillators that can be used in this construction. Furthermore, we study the Liénard equations that are equivalent to the anharmonic oscillator with respect to the point transformations. We show that there are nontrivial examples of the Liénard equations that belong to this equivalence class, like the generalized Duffing oscillator or the generalized Duffing–Van der Pol oscillator.

Dynamical investigation and FPGA implementation of a new Heartbeat model based on the Barrio-Varea-Aragon-Maini oscillator

This paper is devoted to the investigation of the nonlinear dynamics of a heartbeat model. The model is based on three coupled nonlinear autonomous oscillators representing the three automatism centres of the physical heart; each of these automatism centres is represented by an autonomous Barrio-Varea-Aragon-Maini (BVAM) oscillator model. Our study includes theoretical and experimental investigations. The theoretical part consists of the analysis of fixed point(s), bifurcations, Hamiltonian energy, hysteretic behaviour and coexisting attractors. The experimental investigation includes the discretization of the mathematical model followed by its synthesis and implementation under the Vivado 2017.4 platform and its simulation and its physical implementation on the Nexys-4 Artix-7 xc7a-100T FPGA trainer board. Two R-2R network digital-to-analog converters are built to visualise the practical results on a digital storage oscilloscope; a perfect correlation is observed between the theoretical, numerical and experimental results.

A dual-clock-driven model of lymphatic muscle cell pacemaking to emulate knock-out of Ano1 or IP3R.

Lymphatic system defects are involved in a wide range of diseases, including obesity, cardiovascular disease, and neurological disorders, such as Alzheimer's disease. Fluid return through the lymphatic vascular system is primarily provided by contractions of muscle cells in the walls of lymphatic vessels, which are in turn driven by electrochemical oscillations that cause rhythmic action potentials and associated surges in intracellular calcium ion concentration. There is an incomplete understanding of the mechanisms involved in these repeated events, restricting the development of pharmacological treatments for dysfunction. Previously, we proposed a model where autonomous oscillations in the membrane potential (M-clock) drove passive oscillations in the calcium concentration (C-clock). In this paper, to model more accurately what is known about the underlying physiology, we extend this model to the case where the M-clock and the C-clock oscillators are both active but coupled together, thus both driving the action potentials. This extension results from modifications to the model's description of the IP3 receptor, a key C-clock mechanism. The synchronised dual-driving clock behaviour enables the model to match IP3 receptor knock-out data, thus resolving an issue with previous models. We also use phase-plane analysis to explain the mechanisms of coupling of the dual clocks. The model has the potential to help determine mechanisms and find targets for pharmacological treatment of some causes of lymphoedema.

Cooling the optical-spin driven limit cycle oscillations of a levitated gyroscope

Birefringent microspheres, trapped in vacuum and set into rotation by circularly polarised light, demonstrate remarkably stable translational motion. This is in marked contrast to isotropic particles in similar conditions. Here we demonstrate that this stability is obtained because the fast rotation of these birefringent spheres reduces the effect of azimuthal spin forces created by the inhomogeneous optical spin of circularly polarised light. At reduced pressures, the unique profile of these rotationally averaged, effective azimuthal forces results in the formation of nano-scale limit cycles. We demonstrate feedback cooling of these non-equilibrium oscillators, resulting in effective temperatures on the order of a milliKelvin. The principles we elaborate here can inform the design of high-stability rotors carrying enhanced centripetal loads or result in more efficient cooling schemes for autonomous limit cycle oscillations. Ultimately, this latter development could provide experimental access to non-equilibrium quantum effects within the mesoscopic regime.