While experimental and theoretical studies have established the prevalence of rhythmic behaviour at all levels of biological organization, less common is the coexistence between multiple oscillatory regimes (multi-rhythmicity), which has been predicted by a variety of models for biological oscillators. The phenomenon of multi-rhythmicity involves, most commonly, the coexistence between two (birhythmicity) or three (trirhythmicity) distinct regimes of self-sustained oscillations. Birhythmicity has been observed experimentally in a few chemical reactions and in biological examples pertaining to cardiac cell physiology, neurobiology, human voice patterns and ecology. The present study consists of two parts. We first review the mechanisms underlying multi-rhythmicity in models for biochemical and cellular oscillations in which the phenomenon was investigated over the years. In the second part, we focus on the coupling of the cell cycle and the circadian clock and show how an additional source of multi-rhythmicity arises from the bidirectional coupling of these two cellular oscillators. Upon bidirectional coupling, the two oscillatory networks generally synchronize in a unique manner characterized by a single, common period. In some conditions, however, the two oscillators may synchronize in two or three different ways characterized by distinct waveforms and periods. We refer to this type of multi-rhythmicity as ‘multi-synchronization’.

Circadian clocks control the physiological and behavioral rhythms to adapt to the environment with a period of ~24 h. However, the influences and mechanisms of the extreme light/dark cycles on the circadian clock remain unclear. We showed that, in Neurospora crassa, both the growth and the microconidia production contribute to adaptation in LD12:12 (12 h light/12 h dark, periodically). Mathematical modeling and experiments demonstrate that in short LD cycles, the expression of the core clock protein FREQUENCY was entrained to the LD cycles when LD > 3:3 while it free ran when T ≤ LD3:3. The conidial rhythmicity can resonate with a series of different LD conditions. Moreover, we demonstrate that the existence of unknown blue light photoreceptor(s) and the circadian clock might promote the conidiation rhythms that resonate with the environment. The ubiquitin E3 ligase FWD-1 and the previously described CRY-dependent oscillator system were implicated in regulating conidiation under short LD conditions. These findings shed new light on the resonance of Neurospora circadian clock and conidiation rhythms to short LD cycles, which may benefit the understandings of both the basic regulatory aspects of circadian clock and the adaptation of physiological rhythms to the extreme conditions.

Antibiotic treatment is widely used for gastrointestinal diseases, often leading to drug resistance. However, the underlying mechanisms of drug resistance remain unclear. Mathematical modeling provides a powerful tool to explore the dynamics of antibiotic resistance, yet few models have considered the effect of biological noise, which originates from microscopic interactions between bacteria. In this study, we constructed a stochastic model based on the chemical master equations to investigate how stochastic noise influences the development of antibiotic resistance. Our simulations demonstrated that antibiotic resistance developed stepwise: while effective antibiotic treatments maintained the host’s total pathogen numbers at healthy levels, the compositional balance shifted significantly through progressive increases in resistant pathogen proportions. Stochastic noise further amplified this shift and accelerated resistance by exacerbating post-treatment changes in the sensitive-to-resistant pathogen ratio. Finally, we found that the presence of coupling between different microbial communities can delay the onset of resistance and might even prevent its development. These results highlight noise’s critical role in resistance development and suggest enhancing microbial interactions as a potential mitigation strategy.

In response to a light stimulus, the mammalian circadian clock first dramatically increases the expression of Per1 mRNA, and then drops to a baseline even when light persists. This phenomenon is known as light adaptation, which has been experimentally proven to be related to the CRTC1-SIK1 pathway in suprachiasmatic nucleus (SCN). However, the role of this light adaptation in the circadian rhythm remains to be elucidated. To reveal the in-depth function of light adaptation and the underlying dynamics, we proposed a mathematical model for the CRTC1-SIK1 network and coupled it to a mammalian circadian model. The simulation result proved that the light adaptation is achieved by the self-inhibition of the CRTC1/CREB complex. Also, consistently with experimental observations, this adaptation mechanism can limit the phase response to short-term light stimulus, and it also restricts the rate of the phase shift in a jet lag protocol to avoid overly rapid re-entrainment. More importantly, this light adaptation is predicted to prevent the singularity behavior in the cell population, which represents the abolishment of circadian rhythmicity due to desynchronization of oscillating cells. Furthermore, it has been shown to provide refractoriness to successive stimuli with short gap. Therefore, we concluded that the light adaptation generated by the CRTC1-SIK1 pathway in the SCN provides a robust mechanism, allowing the circadian system to maintain homeostasis in the presence of light perturbations. These results not only give new insights into the dynamics of light adaptation from a computational perspective but also lead us to formulate hypotheses about the related physiological significance.

In this paper, we construct a delayed diffusive model to explore the spatial dynamics of cell cycle in G2/M transition. We first obtain the local stability of the unique positive equilibrium for this model, which is irrelevant to the diffusion. Then, through investigating the delay-induced Hopf bifurcation in this model, we establish the existence of spatially homogeneous and inhomogeneous bifurcating periodic solutions. Applying the normal form and center manifold theorem of functional partial differential equations, we also determine the stability and direction of these bifurcating periodic solutions. Finally, numerical simulations are presented to validate our theoretical results.

The circadian clock is closely linked to glucose regulation, but the dynamical consequences of specific metabolic feedback pathways on core clock regulation remain incompletely understood. In this study, we developed a theoretical metabolic-circadian model incorporating a REV-ERB$\mathrm{\alpha }$-glucagon-glucose feedback pathway. The model extends a previously established mammalian circadian clock framework by introducing glucagon-mediated regulation of blood glucose and glucose-dependent modulation of Rev-erbα transcription. Using this model, we examined how the feedback pathway affects circadian oscillations, the sensitivity of period and amplitude to parameter perturbations, and phase-related responses under light stimulation and light–dark cycles. Simulations of the feedback-related parameters showed that the glucose-to-clock feedback strength had a marked effect on oscillation period and amplitude, motivating a further assessment of whether regular circadian dynamics were preserved under parameter perturbations. We therefore analyzed both one-parameter perturbations and simultaneous perturbations of all model parameters. For one-parameter scans, we quantified not only the oscillatory boundaries but also the period variation and the amplitude variation of Per and Rev-erbα within the oscillatory ranges. For simultaneous all-parameter perturbations, Latin hypercube sampling was used to compare coupled and uncoupled models under bounded perturbation ranges. The coupled model showed a higher fraction of regular circadian oscillations under local perturbations, mainly by reducing the probability of rhythm loss. We further examined phase responses and light–dark entrainment to assess how the feedback affects dynamical properties beyond period and amplitude. In the phase-response analysis, the feedback reduced excessive phase shifts in the model, suggesting a possible phase-response robustness effect in this theoretical framework. These theoretical results suggest that the REV-ERB$\mathrm{\alpha }$-glucagon-glucose feedback pathway may be relevant to circadian regulation under fasting-associated metabolic conditions.