The Arabidopsis circadian clock orchestrates gene regulation across the day/night cycle. Although a multiple feedback loop circuit has been shown to generate the 24-hr rhythm, it remains unclear how robust the clock is in individual cells, or how clock timing is coordinated across the plant. Here we examine clock activity at the single cell level across Arabidopsis seedlings over several days under constant environmental conditions. Our data reveal robust single cell oscillations, albeit desynchronised. In particular, we observe two waves of clock activity; one going down, and one up the root. We also find evidence of cell-to-cell coupling of the clock, especially in the root tip. A simple model shows that cell-to-cell coupling and our measured period differences between cells can generate the observed waves. Our results reveal the spatial structure of the plant clock and suggest that unlike the centralised mammalian clock, the Arabidopsis clock has multiple coordination points.

An approach is presented for extracting phase equations from multivariate time series data recorded from a network of weakly coupled limit cycle oscillators. Our aim is to estimate important properties of the phase equations including natural frequencies and interaction functions between the oscillators. Our approach requires the measurement of an experimental observable of the oscillators; in contrast with previous methods it does not require measurements in isolated single or two-oscillator setups. This noninvasive technique can be advantageous in biological systems, where extraction of few oscillators may be a difficult task. The method is most efficient when data are taken from the nonsynchronized regime. Applicability to experimental systems is demonstrated by using a network of electrochemical oscillators; the obtained phase model is utilized to predict the synchronization diagram of the system.

Voice instabilities were studied using excised human larynx experiments and biomechanical modeling. With a controlled elongation of the vocal folds, the experiments showed registers with chest-like and falsetto-like vibrations. Observed instabilities included abrupt jumps between the two registers exhibiting hysteresis, aphonic episodes, subharmonics, and chaos near the register transitions. In order to model these phenomena, a three-mass model was constructed by adding a third mass on top of the simplified two-mass model. Simulation studies showed that the three-mass model can vibrate in both chest-like and falsetto-like patterns. Variation of tension parameters which mimic activities of laryngeal muscles could induce transitions between both registers. For reduced prephonatory areas and damping constants, extended coexistence of chest and falsetto registers was found, in agreement with experimental data. Subharmonics and deterministic chaos were observed close to transitions between the registers. It is concluded that the abrupt changes between chest and falsetto registers can be understood as shifts in dominance of eigenmodes of the vocal folds.

Animal vocalizations range from almost periodic vocal-fold vibration to completely atonal turbulent noise. Between these two extremes, a variety of nonlinear dynamics such as limit cycles, subharmonics, biphonation, and chaotic episodes have been recently observed. These observations imply possible functional roles of nonlinear dynamics in animal acoustic communication. Nonlinear dynamics may also provide insight into the degree to which detailed features of vocalizations are under close neural control, as opposed to more directly reflecting biomechanical properties of the vibrating vocal folds themselves. So far, nonlinear dynamical structures of animal voices have been mainly studied with spectrograms. In this study, the deterministic versus stochastic (DVS) prediction technique was used to quantify the amount of nonlinearity in three animal vocalizations: macaque screams, piglet screams, and dog barks. Results showed that in vocalizations with pronounced harmonic components (adult macaque screams, certain piglet screams, and dog barks), deterministic nonlinear prediction was clearly more powerful than stochastic linear prediction. The difference, termed low-dimensional nonlinearity measure (LNM), indicates the presence of a low-dimensional attractor. In highly irregular signals such as juvenile macaque screams, piglet screams, and some dog barks, the detectable amount of nonlinearity was comparatively small. Analyzing 120 samples of dog barks, it was further shown that the harmonic-to-noise ratio (HNR) was positively correlated with LNM. It is concluded that nonlinear analysis is primarily useful in animal vocalizations with strong harmonic components (including subharmonics and biphonation) or low-dimensional chaos.

Circadian timing systems, like most physiological processes, cannot escape the effects of aging. With age, humans experience decreased duration and quality of sleep. Aged mice exhibit decreased amplitude and increased fragmentation of the activity rhythm, and lengthened circadian free-running period in both light-dark (LD) and constant dark (DD) conditions. Several studies have shown that aging impacts neural activity rhythms in the central circadian clock in the suprachiasmatic nucleus (SCN). However, evidence for age-related disruption of circadian oscillations of clock genes in the SCN has been equivocal. We hypothesized that daily exposure to LD cycles masks the full impact of aging on molecular rhythms in the SCN. We performed ex vivo bioluminescent imaging of cultured SCN slices of young and aged PER2::luciferase knock-in (PER2::LUC) mice housed under LD or prolonged DD conditions. Under LD conditions, the amplitude of PER2::LUC rhythms differed only slightly between SCN explants from young and aged animals; under DD conditions, the PER2::LUC rhythms of aged animals showed markedly lower amplitudes and longer circadian periods than those of young animals. Recordings of PER2::LUC rhythms in individual SCN cells using an electron multiplying charge-coupled device camera revealed that aged SCN cells showed longer circadian periods and that the rhythms of individual cells rapidly became desynchronized. These data suggest that aging degrades the SCN circadian ensemble, but that recurrent LD cycles mask these effects. We propose that these changes reflect a decline in pacemaker robustness that could increase vulnerability to environmental challenges, and partly explain age-related sleep and circadian disturbances.

Cavities branching off the main vocal tract are ubiquitous in nonhumans. Mammalian air sacs exist in human relatives, including all four great apes, but only a substantially reduced version exists in humans. The present paper focuses on acoustical functions of the air sacs. The hypotheses are investigated on whether the air sacs affect amplitude of utterances and/or position of formants. A multilayer synthetic model of the vocal folds coupled with a vocal tract model was utilized. As an air sac model, four configurations were considered: open and closed uniform tube-like side branches, a rigid cavity, and an inflatable cavity. Results suggest that some air sac configurations can enhance the sound level. Furthermore, an air sac model introduces one or more additional resonance frequencies, shifting formants of the main vocal tract to some extent but not as strongly as previously suggested. In addition, dynamic range of vocalization can be extended by the air sacs. A new finding is also an increased variability of the vocal tract impedance, leading to strong nonlinear source-filter interaction effects. The experiments demonstrated that air-sac-like structures can destabilize the sound source. The results were validated by a transmission line computational model.

Biomechanical modeling and bifurcation theory are applied to study phonation onset and register transition. A four-mass body-cover model with a smooth geometry is introduced to reproduce characteristic features of chest and falsetto registers. Sub- and supraglottal resonances are modeled using a wave-reflection model. Simulations for increasing and decreasing subglottal pressure reveal that the phonation onset exhibits amplitude jumps and hysteresis referring to a subcritical Hopf bifurcation. The onset pressure is reduced due to vocal tract resonances. Hysteresis is observed also for the voice breaks at the chest-falsetto transition. Varying the length of the subglottal resonator has only minor effects on this register transition. Contrarily, supraglottal resonances have a strong effect on the pitch, at which the chest-falsetto transition is found. Experiment of glissando singing shows that the supraglottis has indeed an influence on the register transition.

Plant circadian systems are composed of a large number of self-sustained cellular circadian oscillators. Although the light-dark signal in the natural environment is known to be the most powerful Zeitgeber for the entrainment of cellular oscillators, its effect is too strong to control the plant rhythm into various forms of synchrony. Here, we show that the application of pulse perturbations, i.e., short-term injections of darkness under constant light, provides a novel technique for controlling the synchronized behavior of plant rhythm in Arabidopsis thaliana. By destroying the synchronized cellular activities, circadian singularity was experimentally induced. The present technique is based upon the theory of phase oscillators, which does not require prior knowledge of the detailed dynamics of the plant system but only knowledge of its phase and amplitude responses to the pulse perturbation. Our approach can be applied to diverse problems of controlling biological rhythms in living systems.