Biological Oscillators Research Articles

Determination of Oscillation Periods of Biological Clocks

Periodic motion is of paramount importance in science and engineering. The subject is usually covered in courses related to “waves and vibrations”, and Fourier series are frequently used as a tool of analysis of diverse phenomena. In addition, the discrete Fourier transform (DFT) is a means of signal processing in many fields. In this contribution, the periodic patterns of three different biological oscillators are examined using numerical tools suitable for students in the early stages of chemistry, physics, and engineering-oriented careers. The DFT is used to reveal oscillation periods related to the circadian and the menstrual cycles. The time evolution of the segmentation clock, a molecular oscillator operating at the genetic level in the early stages of embryonic growth of vertebrates, is also analyzed. Aimed at both students and instructors, brief descriptions of the methodologies involved are provided and a critical assessment of the results obtained with either of these techniques is carried out.

Circadian metabolic adaptations to infections.

Circadian clocks are biological oscillators that evolved to coordinate rhythms in behaviour and physiology around the 24-hour day. In mammalian tissues, circadian rhythms and metabolism are highly intertwined. The clock machinery controls rhythmic levels of circulating hormones and metabolites, as well as rate-limiting enzymes catalysing biosynthesis or degradation of macromolecules in metabolic tissues, such control being exerted both at the transcriptional and post-transcriptional level. During infections, major metabolic adaptation occurs in mammalian hosts, at the level of both the single immune cell and the whole organism. Under these circumstances, the rhythmic metabolic needs of the host intersect with those of two other players: the pathogen and the microbiota. These three components cooperate or compete to meet their own metabolic demands across the 24 hours. Here, we review findings describing the circadian regulation of the host response to infection, the circadian metabolic adaptations occurring during host-microbiota-pathogen interactions and how such regulation can influence the immune response of the host and, ultimately, its own survival.This article is part of the Theo Murphy meeting issue 'Circadian rhythms in infection and immunity'.

Mathematical Modeling for Oscillations Driven by Noncoding RNAs.

In this chapter, we first survey strategies for the mathematical modeling of gene regulatory networks for capturing physiologically important dynamics in cells such as oscillations. We focus on models based on ordinary differential equations with various forms of nonlinear functions that describe gene regulations. We next use a small system of a microRNA and its mRNA target to illustrate a recently discovered oscillator driven by noncoding RNAs. This oscillator has unique features that distinguish it from conventional biological oscillators, including the absence of an imposed negative feedback loop and the divergence of the periods. The latter property may serve crucial biological functions for restoring heterogeneity of cell populations on the timescale of days. We describe general requirements for obtaining the limit cycle oscillations in terms of underlying biochemical reactions and kinetic rate constants. We discuss future directions stemming from this minimal, noncoding RNA-based model for gene expression oscillation.

A Compensated Clock: Temperature and Nutritional Compensation Mechanisms Across Circadian Systems.

Circadian rhythms are ∼24-h biological oscillations that enable organisms to anticipate daily environmental cycles, so that they may designate appropriate day/night functions that align with these changes. The molecular clock in animals and fungi consists of a transcription-translation feedback loop, the plant clock is comprised of multiple interlocking feedback-loops, and the cyanobacterial clock is driven by a phosphorylation cycle involving three main proteins. Despite the divergent core clock mechanisms across these systems, all circadian clocks are able to buffer period length against changes in the ambient growth environment, such as temperature and nutrients. This defining capability, termed compensation, is critical to proper timekeeping, yet the underlying mechanism(s) remain elusive. Here we examine the known players in, and the current models for, compensation across five circadian systems. While compensation models across these systems are not yet unified, common themes exist across them, including regulation via temperature-dependent changes in post-translational modifications.

Polyglot entrainment for higher dimensional neuronal models

The entrainment of biological oscillators is a classic problem in the field of dynamical systems and synchronization. This paper explores a novel type of entrainment mechanism referred to as polyglot entrainment [Khan et al., “The emergence of polyglot entrainment responses to periodic inputs in vicinities of Hopf bifurcations in slow–fast systems,” Chaos 32, 063137 (2022)] (multiple disconnected 1:1 regions for a range of forcing amplitude) for higher dimensional nonlinear systems. Polyglot entrainment has been recently explored only in two-dimensional slow–fast models in the vicinity of Hopf bifurcations (HBs). Heading toward generality, in this research, we investigate the phenomenon of polyglot entrainment in higher-dimensional conductance-based models including the four-dimensional Hodgkin-Huxley model and its reduced three-dimensional version. We utilize dynamical systems tools to uncover the mechanism of entrainment and geometric structure of the null surfaces to explore the conditions for the existence of polyglot entrainment in these models. In light of our findings, in the vicinity of HB, when an unforced system acts as a damped oscillator and the fixed point is located near a cubic-like manifold, polyglot entrainment is observed.

Synchronization of E. coli Bacteria Moving in Coupled Microwells.

Synchronization plays a crucial role in the dynamics of living organisms. Uncovering the mechanism behind it requires an understanding of individual biological oscillators and the coupling forces between them. Here, a single-cell assay is developed that studies rhythmic behavior in the motility of E.coli cells that can be mutually synchronized. Circular microcavities are used to isolate E.coli cells that swim along the cavity wall, resulting in self-sustained oscillations. Connecting these cavities by microchannels yields synchronization patterns with phase slips. It is demonstrated that the coordinated movement observed in coupled E.coli oscillators follows mathematical rules of synchronization which is used to quantify the coupling strength. These findings advance the understanding of motility in confinement, and open up new opportunities for engineering networks of coupled oscillators in microbial activematter.

Extrinsic fluctuations in the p53 cycle.

Fluctuations are inherent to biological systems, arising from the stochastic nature of molecular interactions, and influence various aspects of system behavior, stability, and robustness. These fluctuations can be categorized as intrinsic, stemming from the system's inherent structure and dynamics, and extrinsic, arising from external factors, such as temperature variations. Understanding the interplay between these fluctuations is crucial for obtaining a comprehensive understanding of biological phenomena. However, studying these effects poses significant computational challenges. In this study, we used an underexplored methodology to analyze the effect of extrinsic fluctuations in stochastic systems using ordinary differential equations instead of solving the master equation with stochastic parameters. By incorporating temperature fluctuations into reaction rates, we explored the impact of extrinsic factors on system dynamics. We constructed a master equation and calculated the equations for the dynamics of the first two moments, offering computational efficiency compared with directly solving the chemical master equation. We applied this approach to analyze a biological oscillator, focusing on the p53 model and its response to temperature-induced extrinsic fluctuations. Our findings underscore the impact of extrinsic fluctuations on the nature of oscillations in biological systems, with alterations in oscillatory behavior depending on the characteristics of extrinsic fluctuations. We observed an increased oscillation amplitude and frequency of the p53 concentration cycle. This study provides valuable insights into the effects of extrinsic fluctuations on biological oscillations and highlights the importance of considering them in more complex systems to prevent unwanted scenarios related to health issues.

Plausible, robust biological oscillations through allelic buffering

Biological oscillators can specify time- and dose-dependent functions via dedicated control of their oscillatory dynamics. However, how biological oscillators, which recurrently activate noisy biochemical processes, achieve robust oscillations remains unclear. Here, we characterize the long-term oscillations of p53 and its negative feedback regulator Mdm2 in single cells after DNA damage. Whereas p53 oscillates regularly, Mdm2 from a single MDM2 allele exhibits random unresponsiveness to ∼9% of p53 pulses. Using allelic-specific imaging of MDM2 activity, we show that MDM2 alleles buffer each other to maintain p53 pulse amplitude. Removal of MDM2 allelic buffering cripples the robustness of p53 amplitude, thereby elevating p21 levels and cell-cycle arrest. In silico simulations support that allelic buffering enhances the robustness of biological oscillators and broadens their plausible biochemical space. Our findings show how allelic buffering ensures robust p53 oscillations, highlighting the potential importance of allelic buffering for the emergence of robust biological oscillators during evolution. A record of this paper's transparent peer review process is included in the supplemental information.

The food-borne carcinogenic 2-amino-1-methyl-6-phenylimidazo[4,5-b]pyridine (PhIP) disrupts circadian rhythms and ameliorated by pterostilbene (PSB) in Caenorhabditis elegans.

The food-borne 2-amino-1-methyl-6-phenylimidazo[4,5-b]pyridine (PhIP) is a potential human carcinogen abundant in cooked meat. While circadian rhythms are crucial biological oscillations, the negative impact of PhIP on circadian systems and the potential of mitigation remain underexplored. We investigated the effects of PhIP on circadian rhythms and the mitigating effects of the phytochemical antioxidant pterostilbene (PSB) in Caenorhabditis elegans. We show that exposure to 10μM PhIP disrupts the 24-h circadian rhythms of C. elegans, an effect mitigated by co-exposure to 100μM PSB. In addition, PhIP-induced circadian disruption can be linked to defective oxidative stress resistance, which is associated with the DAF-16/FOXO pathway and is modulated by PSB. Molecular docking suggested that PhIP and PSB bind similarly to DAF-16. Moreover, 10μM PhIP abolished the rhythmic expression of the core clock gene prdx-2, which is restored by 100μM PSB. Findings from this study provide novel insight of how food-borne contaminant like PhIP may contribute to the disruption of circadian rhythms and suggest potential for PSB to mitigate these effects in higher organisms.

Optimising 4D imaging of fast-oscillating structures using X-ray microtomography with retrospective gating

Imaging the internal architecture of fast-vibrating structures at micrometer scale and kilohertz frequencies poses great challenges for numerous applications, including the study of biological oscillators, mechanical testing of materials, and process engineering. Over the past decade, X-ray microtomography with retrospective gating has shown very promising advances in meeting these challenges. However, breakthroughs are still expected in acquisition and reconstruction procedures to keep improving the spatiotemporal resolution, and study the mechanics of fast-vibrating multiscale structures. Thereby, this works aims to improve this imaging technique by minimising streaking and motion blur artefacts through the optimisation of experimental parameters. For that purpose, we have coupled a numerical approach relying on tomography simulation with vibrating particles with known and ideal 3D geometry (micro-spheres or fibres) with experimental campaigns. These were carried out on soft composites, imaged in synchrotron X-ray beamlines while oscillating up to 400 Hz, thanks to a custom-developed vibromechanical device. This approach yields homogeneous angular sampling of projections and gives reliable predictions of image quality degradation due to motion blur. By overcoming several technical and scientific barriers limiting the feasibility and reproducibility of such investigations, we provide guidelines to enhance gated-CT 4D imaging for the analysis of heterogeneous, high-frequency oscillating materials.

From resonance to chaos by modulating spatiotemporal patterns through a synthetic optogenetic oscillator

Oscillations are a recurrent phenomenon in biological systems across scales, but deciphering their fundamental principles is very challenging. Here, we tackle this challenge by redesigning the wellcharacterised synthetic oscillator known as “repressilator” in Escherichia coli and controlling it using optogenetics, creating the “optoscillator”. Bacterial colonies manifest oscillations as spatial ring patterns. When we apply periodic light pulses, the optoscillator behaves as a forced oscillator and we systematically investigate the properties of the rings under various light conditions. Combining experiments with mathematical modeling, we demonstrate that this simple oscillatory circuit can generate complex dynamics that are transformed into distinct spatial patterns. We report the observation of synchronisation, resonance, subharmonic resonance and period doubling. Furthermore, we present evidence of a chaotic regime. This work highlights the intricate spatiotemporal patterns accessible by synthetic oscillators and underscores the potential of our approach in revealing fundamental principles of biological oscillations.

A coupled model between circadian, cell-cycle, and redox rhythms reveals their regulation of oxidative stress

Most organisms possess three biological oscillators, circadian clock, cell cycle, and redox rhythm, which are autonomous but interact each other. However, whether their interactions and autonomy are beneficial for organisms remains unclear. Here, we modeled a coupled oscillator system where each oscillator affected the phase of the other oscillators. We found that multiple types of coupling prevent a high H2O2 level in cells at M phase. Consequently, we hypothesized a high H2O2 sensitivity at the M phase and found that moderate coupling reduced cell damage due to oxidative stress by generating appropriate phase relationships between three rhythms, whereas strong coupling resulted in an elevated cell damage by increasing the average H2O2 level and disrupted the cell cycle. Furthermore, the multicellularity model revealed that phase variations among cells confer flexibility in synchronization with environments at the expense of adaptability to the optimal environment. Thus, both autonomy and synchrony among the oscillators are important for coordinating their phase relationships to minimize oxidative stress, and couplings balance them depending on environments.

Biological Rhythms Generated by a Single Activator-Repressor Loop with Inhomogeneity and Diffusion.

Common models of circadian rhythms are typically constructed as compartmental reactions of well-mixed biochemicals, incorporating a negative-feedback loop consisting of several intermediate reaction steps essentially required to produce oscillations. Spatial transport of each reactant is often represented as an extra compartmental reaction step. Contrary to this traditional understanding, in this Letter we demonstrate that a single activation-repression biochemical reaction pair is sufficient to generate sustained oscillations if the sites of both reactions are spatially separated and molecular transport is mediated by diffusion. Our proposed scenario represents the simplest configuration in terms of the participating chemical reactions and offers a conceptual basis for understanding biological oscillations and inspiring invitro assays aimed at constructing minimal clocks.

Resilience of the slow component in timescale-separated synchronized oscillators.

Physiological networks are usually made of a large number of biological oscillators evolving on a multitude of different timescales. Phase oscillators are particularly useful in the modelling of the synchronization dynamics of such systems. If the coupling is strong enough compared to the heterogeneity of the internal parameters, synchronized states might emerge where phase oscillators start to behave coherently. Here, we focus on the case where synchronized oscillators are divided into a fast and a slow component so that the two subsets evolve on separated timescales. We assess the resilience of the slow component by, first, reducing the dynamics of the fast one using Mori-Zwanzig formalism. Second, we evaluate the variance of the phase deviations when the oscillators in the two components are subject to noise with possibly distinct correlation times. From the general expression for the variance, we consider specific network structures and show how the noise transmission between the fast and slow components is affected. Interestingly, we find that oscillators that are among the most robust when there is only a single timescale, might become the most vulnerable when the system undergoes a timescale separation. We also find that layered networks seem to be insensitive to such timescale separations.

Emergent Synchronous Volumetric Oscillation in Hierarchically Structured Self-Oscillating Gel Clusters.

Emergent properties accompanying synchronization among oscillators are vital characteristics in biological systems. Belousov-Zhabotinsky (BZ) oscillators are an artificial model to study the emergence and synchronization in life. This research represents a self-oscillating gel system with clusterable properties to experimentally examine synchronous and emergent properties at a fundamental hierarchical level. Incorporating acrylic acid (AAc) moieties within the gel network facilitates cluster formation through hydrogen bonding in an acidic BZ substrate solution. Upon clustering, both homogeneous and heterogeneous gel assemblies─ranging from double to quadruple clusters─exhibit increased and synchronized periods and amplitudes during the BZ reaction. Notably, in heterogeneous clusters, gel units with initially short periods and small volumetric amplitudes display a significant increase, aligning with the lonfger periods and larger amplitudes of other elements within the cluster, an emergent property. This research can pave the way for a better understanding of synchronous and emergent properties in biological oscillators such as cardiomyocytes.

Evaluation of Renal Microhemodynamics Heterogeneity in Different Strains and Sexes of Mice

Addressing the existing gaps in our understanding of sex- and strain-dependent disparities in renal microhemodynamics, this study conducted an investigation into the variations in renal function and related biological oscillators. Using the genetically diverse mouse models BALB/c, C57BL/6, and Kunming, which serve as established proxies for the study of renal pathophysiology, we implemented laser Doppler flowmetry conjoined with wavelet transform analyses to interrogate dynamic renal microcirculation. Creatinine, urea, uric acid, glucose, and cystatin C levels were quantified to investigate potential divergences attributable to sex and genetic lineage. Our findings reveal marked sexual dimorphism in metabolite concentrations, as well as strain-specific variances, particularly in creatinine and cystatin C levels. Through the combination of Mantel tests and Pearson correlation coefficients, we delineated the associations between renal functional metrics and microhemodynamics, uncovering interactions in female BALB/c mice for creatinine and uric acid, and in male C57BL/6 mice for cystatin C. Histopathologic examination confirmed an augmented microvascular density in female mice and elucidating variations in the expression of estrogen receptor β among the strains. These data collectively highlight the influence of both sex and genetic constitution on renal microcirculation, providing an understanding that may inform the etiologic exploration of renal ailments.

A novel approach to synchronizing a biological snap oscillator within a fixed time and expanding the method to various chaotic systems

A novel approach to synchronizing a biological snap oscillator within a fixed time and expanding the method to various chaotic systems

Recent advances in understanding the kidney circadian clock mechanism.

Circadian rhythms are endogenous biological oscillations that regulate various physiological processes in organisms, including kidney function. The kidney plays a vital role in maintaining homeostasis by regulating water and electrolyte balance, blood pressure, and excretion of metabolic waste products, all of which display circadian rhythmicity. For this reason, studying the circadian regulation of the kidney is important, and the time of day is a biological and experimental variable that must be considered. Over the past decade, considerable progress has been made in understanding the molecular mechanisms underlying circadian regulation within the kidney. In this review, the current knowledge regarding circadian rhythms in the kidney is explored, focusing on the molecular clock machinery, circadian control of renal functions, and the impact of disrupted circadian rhythms on kidney health. In addition, parameters that should be considered and future directions are outlined in this review.

Incommensurate fractional-order analysis of a chaotic system based on interaction between dark matter and dark energy with engineering applications

Chaotic systems, characterized by their sensitivity to initial conditions and the presence of deterministic unpredictability, have garnered significant attention in various fields of science and engineering. Researchers have demonstrated a growing interest in recent years in identifying various physical systems as chaotic system, including but not limited to fluid dynamics, electrical circuits, and biological oscillators. In this study, a cosmological chaotic system that portrays the interaction between dark matter and dark energy is examined using incommensurate fractional-order analysis. The effects of incommensurate fractional orders are evaluated by means of phase portraits, bifurcation diagrams and Lyapunov exponents spectra. It is dedicated that wider chaotic regions are observed once the values of these incommensurate fractional orders are changed. Meanwhile, a hidden attractor is found based on the stability analysis and basin of attraction in the incommensurate fractional-order dark matter and dark energy (IFODMDE) chaotic system. These findings highlight the richer dynamic characteristics of the IFODMDE chaotic system. Furthermore, the identified hidden attractor is effectively employed in this study for various engineering applications, including chaos control, random number generator (RNG) design, and image encryption. The analytical results offer a more accurate description of real-world physical phenomena, thanks to the inclusion of incommensurate fractional orders. The application results prove the good randomness of the IFODMDE chaotic system.

Apparent nonlinear damping triggered by quantum fluctuations

Nonlinear damping, the change in damping rate with the amplitude of oscillations plays an important role in many electrical, mechanical and even biological oscillators. In novel technologies such as carbon nanotubes, graphene membranes or superconducting resonators, the origin of nonlinear damping is sometimes unclear. This presents a problem, as the damping rate is a key figure of merit in the application of these systems to extremely precise sensors or quantum computers. Through measurements of a superconducting resonator, we show that from the interplay of quantum fluctuations and the nonlinearity of a Josephson junction emerges a power-dependence in the resonator response which closely resembles nonlinear damping. The phenomenon can be understood and visualized through the flow of quasi-probability in phase space where it reveals itself as dephasing. Crucially, the effect is not restricted to superconducting circuits: we expect that quantum fluctuations or other sources of noise give rise to apparent nonlinear damping in systems with a similar conservative nonlinearity, such as nano-mechanical oscillators or even macroscopic systems.