A physical understanding and quantification for the regulation of orexin on sleep.

The orexinergic neurons located in the lateral hypothalamus play a vital role in maintaining wakefulness and regulating sleep stability. Previous research has demonstrated that the absence of orexin (Orx) can trigger narcolepsy, a condition characterized by frequent shifts between wakefulness and sleep. However, the specific mechanisms and temporal patterns through which Orx regulates wakefulness/sleep are not fully understood. In this study, we developed a new model that combines the classical Phillips-Robinson sleep model with the Orx network. Our model incorporates a recently discovered indirect inhibition of Orx on sleep-promoting neurons in the ventrolateral preoptic nucleus. By integrating appropriate physiological parameters, our model successfully replicated the dynamic behavior of normal sleep under the influence of circadian drive and homeostatic processes. Furthermore, our results from the new sleep model unveiled two distinct effects of Orx: excitation of wake-active neurons and inhibition of sleep-active neurons. The excitation effect helps to sustain wakefulness, while the inhibition effect contributes to arousal, consistent with experimental findings [De Luca et al., Nat. Commun. 13, 4163 (2022)]. Moreover, we utilized the theory of potential landscapes to investigate the physical mechanisms underlying the frequent transitions observed in narcolepsy. The topography of the underlying landscape delineated the brain's capacity to transition between different states. Additionally, we examined the impact of Orx on barrier height. Our analysis demonstrated that a reduced level of Orx led to a bistable state with an extremely low threshold, contributing to the development of narcoleptic sleep disorder.

Biphasic amplitude oscillator characterized by distinct dynamics of trough and crest.

Biphasic amplitude dynamics (BAD) of oscillation have been observed in many biological systems. However, the specific topology structure and regulatory mechanisms underlying these biphasic amplitude dynamics remain elusive. Here, we searched all possible two-node circuit topologies and identified the core oscillator that enables robust oscillation. This core oscillator consists of a negative feedback loop between two nodes and a self-positive feedback loop of the input node, which result in the fast and slow dynamics of the two nodes, thereby achieving relaxation oscillation. Landscape theory was employed to study the stochastic dynamics and global stability of the system, allowing us to quantitatively describe the diverse positions and sizes of the Mexican hat. With increasing input strength, the size of the Mexican hat exhibits a gradual increase followed by a subsequent decrease. The self-activation of input node and the negative feedback on input node, which dominate the fast dynamics of the input node, were observed to regulate BAD in a bell-shaped manner. Both deterministic and statistical analysis results reveal that BAD is characterized by the linear and nonlinear dependence of the oscillation trough and crest on the input strength. In addition, combining with computational and theoretical analysis, we addressed that the linear response of trough to input is predominantly governed by the negative feedback, while the nonlinear response of crest is jointly regulated by the negative feedback loop and the self-positive feedback loop within the oscillator. Overall, this study provides a natural and physical basis for comprehending the occurrence of BAD in oscillatory systems, yielding guidance for the design of BAD in synthetic biology applications.

Caspase-1 and Gasdermin D Afford the Optimal Targets with Distinct Switching Strategies in NLRP1b Inflammasome-Induced Cell Death.

Inflammasomes are essential complexes of innate immune system, which form the first line of host defense against pathogens. Mounting evidence accumulates that inflammasome signaling is highly correlated with coronavirus disease 2019 (COVID-19). However, there remains a significant gap in our understanding of the regulatory mechanism of inflammasome signaling. Combining mathematical modeling with experimental analysis of NLRP1b inflammasome signaling, we found that only the expression levels of caspase-1 and GSDMD have the potential to individually switch cell death modes. Reduction of caspase-1 or GSDMD switches cell death from pyroptosis to apoptosis. Caspase-1 and GSDMD present different thresholds and exert distinct pathway choices in switching death modes. Pyroptosis switches to apoptosis with an extremely low threshold level of caspase-1, but with a high threshold of GSDMD. Caspase-1-impaired cells employ ASC-caspase-8-dependent pathway for apoptosis, while GSDMD-impaired cells primarily utilize caspase-1-dependent pathway. Additionally, caspase-1 and GSDMD can severally ignite the cooccurrence of pyroptosis and apoptosis. Landscape topography unravels that the cooccurrence is dramatically different in caspase-1- and GSDMD-impaired cells. Besides pyroptosis state and apoptosis state, a potential new "coexisting" state in single cells is proposed when GSDMD acts as the driving force of the landscape. The "seesaw model" is therefore proposed, which can well describe the death states that are controlled by caspase-1 or GSDMD in single cells. Our study sheds new light on NLRP1b inflammasome signaling and uncovers the switching mechanisms among various death modes, providing potential clues to guide the development of more rational control strategies for diseases.

Oscillation behavior driven by processing delay in diffusively coupled inactive systems: Cluster synchronization and multistability.

Couplings involving time delay play a relevant role in the dynamical behavior of complex systems. In this work, we address the effect of processing delay, which is a specific kind of coupling delay, on the steady state of general nonlinear systems and prove that it may drive the system to Hopf bifurcation and, in turn, to a rich oscillatory behavior. Additionally, one may observe multistable states and size-dependent cluster synchronization. We derive the analytic conditions to obtain an oscillatory regime and confirm the result by numerically simulated experiments on different oscillator networks. Our results demonstrate the importance of processing delay for complex systems and pave the way for a better understanding of dynamical control and synchronization in oscillatory networks.

Anormal diffusion enhancement of resonant responses for coupled oscillator networks to weak signals.

The normal diffusion effect is introduced as a new regulating factor into the established diffusive coupling model for bistable oscillator networks. We find that the response of the system to the weak signal is substantially enhanced by the anormal diffusion, which is termed anormal-diffusion-induced resonance. We also reveal that the diffusive coupling-induced transition, which changes the system from a bistable to a monostable state, is of fundamental importance for the occurrence of resonance. The proposed approach is validated using simulation studies and theoretical analyses. Our results suggest that diffusion induced resonance can be more easily observed in nonlinear oscillator networks.

Winfree loop sustained oscillation in two-dimensional excitable lattices: Prediction and realization.

The problem of self-sustained oscillations in excitable complex networks is the central issue under investigation, among which the prediction and the realization of self-sustained oscillations in different kinds of excitable networks are the challenging tasks. In this paper, we extensively investigate the prediction and the realization of a Winfree loop sustained oscillation (WLSO) in two-dimensional (2D) excitable lattices. By analyzing the network structure, the fundamental oscillation source structure (FOSS) of WLSO in a 2D excitable lattice is exposed explicitly. For the suitable combinations of system parameters, the Winfree loop can self-organize on the FOSS to form an oscillation source sustaining the oscillation, and these suitable parameter combinations are predicted by calculating the minimum Winfree loop length and have been further confirmed in numerical simulations. However, the FOSS cannot spontaneously offer the WLSO in 2D excitable lattices in usual cases due to the coupling bidirectionality and the symmetry properties of the lattice. A targeted protection scheme of the oscillation source is proposed by overcoming these two drawbacks. Finally, the WLSO is realized in the 2D excitable lattice successfully.

Perturbation analysis and comparison of network synchronization methods.

In many networked systems, synchronization is important and useful, and how to enhance synchronizability is an interesting problem. Based on the matrix perturbation theory, we analyze five methods of network synchronization enhancement, including the link removal, node removal, dividing hub node, pull control, and pinning control methods, and obtain explicit expressions for eigenvalue changes. By these comparisons, we find that, among all these methods, the pull control method is remarkable, as it can extend the synchronization (coupling strength) region from both the left and right sides, for any controlled node. Extensive simulation results are given to support the accuracy of the perturbation-based analysis.

Spiking patterns of a neuron model to stimulus: Rich dynamics and oxygen's role.

Neuronal spiking patterns, which are of fundamental importance for the understanding of information processing in neural systems, can be generated in response to different stimuli. We here investigate in detail the stimulus-induced spiking patterns in a biologically plausible neuron model in which the oxygen concentration and the dynamical concentrations of potassium, sodium, and chloride are considered. Various types of spiking patterns can be induced by the different external potassium accumulations in response to the stimulus, including two different types of epileptic seizure (SZ) and spreading depression (SD) states, two different mixed states of SD and SZ, SZ state with multi-burst, and tonic firing behaviors. Interestingly, we show that these rich spiking patterns can also be induced by the current stimulus with a low oxygen concentration. Furthermore, we reveal that the stimulus can induce two different phase transitions from the SD state to the SZ state according to the phase transition theory, which results in the different electrical activities. All these findings may provide insight into information processing in neural systems.

Spontaneous Oscillations and Synchronization of Active Droplets on a Water Surface via Marangoni Convection.

Shape-oscillations and synchronization are intriguing phenomena in many biological and physical systems. Here, we report the rhythmic mechanical oscillations and synchronization of aniline oil droplets on a water phase, which is induced by Marangoni convection during transfer of the solute. The repetitive increase and decrease in the surface concentration in the vicinity of the contact line leads to the oscillations of droplets through an imbalance in surface tensions. The nature of the oscillations depends on the diameter of the droplet, the depth of the bulk aqueous phase, and the concentration of the aqueous phase. A numerical simulation reproduces the essential behaviors of active oscillations of a droplet. Droplets sense each other through a surface tension gradient and advection, and hydrodynamic coupling in the bulk solution induces the synchronization of droplet oscillations.

Spatiotemporal dynamics in excitable homogeneous random networks composed of periodically self-sustained oscillation.

The collective behaviors of networks are often dependent on the network connections and bifurcation parameters, also the local kinetics plays an important role in contributing the consensus of coupled oscillators. In this paper, we systematically investigate the influence of network structures and system parameters on the spatiotemporal dynamics in excitable homogeneous random networks (EHRNs) composed of periodically self-sustained oscillation (PSO). By using the dominant phase-advanced driving (DPAD) method, the one-dimensional (1D) Winfree loop is exposed as the oscillation source supporting the PSO, and the accurate wave propagation pathways from the oscillation source to the whole network are uncovered. Then, an order parameter is introduced to quantitatively study the influence of network structures and system parameters on the spatiotemporal dynamics of PSO in EHRNs. Distinct results induced by the network structures and the system parameters are observed. Importantly, the corresponding mechanisms are revealed. PSO influenced by the network structures are induced not only by the change of average path length (APL) of network, but also by the invasion of 1D Winfree loop from the outside linking nodes. Moreover, PSO influenced by the system parameters are determined by the excitation threshold and the minimum 1D Winfree loop. Finally, we confirmed that the excitation threshold and the minimum 1D Winfree loop determined PSO will degenerate as the system size is expanded.

Insensitivity of synchronization to network structure in chaotic pendulum systems with time-delay coupling.

It has been generally believed that both time delay and network structure could play a crucial role in determining collective dynamical behaviors in complex systems. In this work, we study the influence of coupling strength, time delay, and network topology on synchronization behavior in delay-coupled networks of chaotic pendulums. Interestingly, we find that the threshold value of the coupling strength for complete synchronization in such networks strongly depends on the time delay in the coupling, but appears to be insensitive to the network structure. This lack of sensitivity was numerically tested in several typical regular networks, such as different locally and globally coupled ones as well as in several complex networks, such as small-world and scale-free networks. Furthermore, we find that the emergence of a synchronous periodic state induced by time delay is of key importance for the complete synchronization.

Effect of Dynamic Interaction between microRNA and Transcription Factor on Gene Expression.

MicroRNAs (miRNAs) are endogenous noncoding RNAs which participate in diverse biological processes in animals and plants. They are known to join together with transcription factors and downstream gene, forming a complex and highly interconnected regulatory network. To recognize a few overrepresented motifs which are expected to perform important elementary regulatory functions, we constructed a computational model of miRNA-mediated feedforward loops (FFLs) in which a transcription factor (TF) regulates miRNA and targets gene. Based on the different dynamic interactions between miRNA and TF on gene expression, four possible structural topologies of FFLs with two gate functions (AND gate and OR gate) are introduced. We studied the dynamic behaviors of these different motifs. Furthermore, the relationship between the response time and maximal activation velocity of miRNA was investigated. We found that the curve of response time shows nonmonotonic behavior in Co1 loop with OR gate. This may help us to infer the mechanism of miRNA binding to the promoter region. At last we investigated the influence of important parameters on the dynamic response of system. We identified that the stationary levels of target gene in all loops were insensitive to the initial value of miRNA.

An Algorithm for Finding the Singleton Attractors and Pre-Images in Strong-Inhibition Boolean Networks.

The detection of the singleton attractors is of great significance for the systematic study of genetic regulatory network. In this paper, we design an algorithm to compute the singleton attractors and pre-images of the strong-inhibition Boolean networks which is a biophysically plausible gene model. Our algorithm can not only identify accurately the singleton attractors, but also find easily the pre-images of the network. Based on extensive computational experiments, we show that the computational time of the algorithm is proportional to the number of the singleton attractors, which indicates the algorithm has much advantage in finding the singleton attractors for the networks with high average degree and less inhibitory interactions. Our algorithm may shed light on understanding the function and structure of the strong-inhibition Boolean networks.

Resonance induced by a spatially periodic force in the reaction-diffusion system.

The stimulus-dynamic response is an important topic in physics. In this work, we study the dynamics in the reaction-diffusion system subjected to a weak signal and a spatially periodic force. We find that the response of the system to the weak signal is enhanced largely by the spatially periodic force, which is termed spatially periodic-force-induced resonance. In particular, the response becomes stronger when the spatial frequency is chosen such that the system synchronizes with spatially periodic force. This combinative behavior, i.e., the spatially periodic-force-induced resonance and the spatial-synchronization-enhanced resonance, is of great interest and may shed light on our understanding of the dynamics of nonlinear systems subjected to spatially periodic force in responding to a weak signal.

Enhanced multiple vibrational resonances by Na+ and K+ dynamics in a neuron model.

Some neuronal receptors perceive external input in the form of hybrid periodic signals. The signal detection may be based on the mechanism of vibrational resonance, in which a system's response to the low frequency signal can become optimal by an appropriate choice of the vibration amplitude of HFS. The vibrational resonance effect is investigated in a neuron model in which the intra- and extra-cellular potassium and sodium concentrations are allowed to evolve temporally, depending on ion currents, Na(+)-K(+) pumps, glial buffering, and ion diffusion. Our results reveal that, compared to the vibrational resonances in the model with constant ion concentrations, the significantly enhanced vibrational multi-resonances can be observed for the single neuron system where the potassium and sodium ion concentrations vary temporally. Thus, in contradiction to a popular view that ion concentrations dynamics play little role in signal detection, we indicate that the neuron's response to an external subthreshold signal can be largely improved by sodium and potassium dynamics.

Time delay induced different synchronization patterns in repulsively coupled chaotic oscillators.

Time delayed coupling plays a crucial role in determining the system's dynamics. We here report that the time delay induces transition from the asynchronous state to the complete synchronization (CS) state in the repulsively coupled chaotic oscillators. In particular, by changing the coupling strength or time delay, various types of synchronous patterns, including CS, antiphase CS, antiphase synchronization (ANS), and phase synchronization, can be generated. In the transition regions between different synchronous patterns, bistable synchronous oscillators can be observed. Furthermore, we show that the time-delay-induced phase flip bifurcation is of key importance for the emergence of CS. All these findings may light on our understanding of neuronal synchronization and information processing in the brain.

The study of amplitude death in globally delay-coupled nonidentical systems based on order parameter expansion.

The method of order parameter expansion is used to study the dynamical behavior in the globally delay-coupled nonidentical systems. Using the Landau-Stuart periodic system and Rössler chaotic oscillator to construct representative systems, the method can identify the boundary curves of amplitude death island analytically in the parameter space of the coupling and time delay. Furthermore, the parameter mismatch (diversity) effect on the size of island is investigated numerically. For the case of coupled chaotic Rössler systems with different timescales, the diversity increases the domain of death island monotonically. However, for the case of delay-coupled Landua-Stuart periodic systems with different frequencies, the average frequency turns out to be a critical role that determines change of size with the increase of diversity.

Frequency-resonance-enhanced vibrational resonance in bistable systems.

The dynamics in an overdamped bistable system subject to the action of two periodic forces (assuming their frequencies are ω and Ω, and amplitudes are A and B, respectively) is studied. For the usual vibrational resonance, the nonmonotonic dependence of signal output of the low frequency ω on the change of B for a fixed Ω, the condition Ω≫ω is always assumed in all previous studies. Here, removing this restriction, we find that a resonant behavior can extensively occur with respect to the changes of both the frequency Ω and amplitude B. Especially, the resonance becomes stronger when Ω is chosen such that it is exactly in frequency resonance with ω. This combinative behavior, called frequency-resonance-enhanced vibrational resonance, is of great interest and may shed an improved light on our understanding of the dynamics of nonlinear systems subject to a biharmonic force.

Signal transmission by vibrational resonance in one-way coupled bistable systems.

Low-frequency signal transmission in one-way coupled bistable systems subject to a high-frequency force is studied. Two cases including the high-frequency force on all sites (case 1) and only on the first site (case 2) are considered. In these two cases, vibrational resonance induced by the high-frequency force can play an active role to effectively improve the signal transmission, and undamped signal transmission can be found in a broad parameter region. The combinative action of injected low-frequency signal, high-frequency driving, and coupling is of importance. Our findings suggest that high-frequency signal could be properly used in low-frequency signal transmission, and especially the implementation of high-frequency force simply on the first site for case 2 is meaningful for its simplicity and high efficiency.

Eliminating delay-induced oscillation death by gradient coupling.

In this work, we investigate gradient coupling effect on oscillation death in a ring of N delay-coupled oscillators. We find that the gradient coupling monotonically reduces the domain of death island in the parameter space of the diffusive coupling and time delay, and thus the death island can be completely eliminated once the gradient coupling strength exceeds a certain threshold, whose value is found to be a constant if N is sufficiently large. For two special cases, a ring with zero gradient coupling and a one-way ring for identical diffusive and gradient couplings, all previous results in the literature are recovered. In particular, for the one-way ring, a size effect of N is discovered, which indicates that under this situation the death can always be eliminated if N is above a critical N(max). All the described results are proved to hold generally in coupled oscillator systems.