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Functional changes in vocal organ morphology and motor control facilitate the evolution of acoustic signal diversity. Although many rodents produce vocalizations in a variety of social contexts, few studies have explored the underlying production mechanisms. Here, we describe mechanisms of audible and ultrasonic vocalizations (USVs) produced by grasshopper mice (genus Onychomys). Grasshopper mice are predatory rodents of the desert that produce both loud, long-distance advertisement calls and USVs in close-distance mating contexts. Using live-animal recording in normal air and heliox, laryngeal and vocal tract morphological investigations, and biomechanical modelling, we found that grasshopper mice employ two distinct vocal production mechanisms. In heliox, changes in higher-harmonic amplitudes of long-distance calls indicate an airflow-induced tissue vibration mechanism, whereas changes in fundamental frequency of USVs support a whistle mechanism. Vocal membranes and a thin lamina propria aid in the production of long-distance calls by increasing glottal efficiency and permitting high frequencies, respectively. In addition, tuning of fundamental frequency to the second resonance of a bell-shaped vocal tract increases call amplitude. Our findings indicate that grasshopper mice can dynamically adjust motor control to suit the social context and have novel morphological adaptations that facilitate long-distance communication.

Proteins KaiA, KaiB and KaiC constitute a biochemical circadian oscillator in the cyanobacterium Synechococcus elongatus . It has been reported kaiA inactivation completely abolishes circadian oscillations. However, we show here that kaiBC promoter activity exhibits a damped, low-amplitude oscillation with a period of approximately 24 h in kaiA -inactivated strains. The damped rhythm resonates with external cycles with a period of 24–26 h, indicating that its natural frequency is similar to that of the circadian clock. Double-mutation experiments reveal that kaiC , kaiB , and sasA (encoding a KaiC-binding histidine kinase) are all required for the damped oscillation. Further analysis suggests that the kaiA -less damped transcriptional rhythm requires KaiB-KaiC complex formation and the transcription-translation feedback loop, but not the KaiC phosphorylation cycle. Our results provide insights into mechanisms that could potentially underlie the diurnal/circadian behaviors observed in other bacterial species that possess kaiB and kaiC homologues but lack a kaiA homologue. Proteins KaiA, KaiB and KaiC constitute a biochemical circadian oscillator in Synechococcus cyanobacteria . Here, Kawamoto et al. show that kaiBC promoter activity exhibits a damped, low-amplitude circadian oscillation in the absence of KaiA, which could explain the circadian rhythms observed in other bacteria that lack a kaiA homologue.

Circadian clocks allow organisms to synchronize their physiological processes to diurnal variations. A phase response curve allows researchers to understand clock entrainment by revealing how signals adjust clock genes differently according to the phase in which they are applied. Comprehensively investigating these curves is difficult, however, because of the cost of measuring them experimentally. Here we demonstrate that fundamental properties of the curve are recoverable from the singularity response, which is easily measured by applying a single stimulus to a cellular network in a desynchronized state (i.e. singularity). We show that the singularity response of Arabidopsis to light/dark and temperature stimuli depends on the properties of the phase response curve for these stimuli. The measured singularity responses not only allow the curves to be precisely reconstructed but also reveal organ-specific properties of the plant circadian clock. The method is not only simple and accurate, but also general and applicable to other coupled oscillator systems as long as the oscillators can be desynchronized. This simplified method may allow the entrainment properties of the circadian clock of both plants and other species in nature. Phase response curves reveal how biological clocks respond to stimuli applied during different circadian phases but can be costly to produce. Here Masuda et al. show that phase response curves for plants can be reconstructed by monitoring how a desynchronized population responds to a single stimulus.

Individual plant cells possess a genetic network, the circadian clock, that times internal processes to the day‐night cycle. Mathematical models of the clock are typically either “whole‐plant” that ignore tissue or cell type‐specific clock behavior, or “phase‐only” that do not include molecular components. To address the complex spatial coordination observed in experiments, here we implemented a clock network model on a template of a seedling. In our model, the sensitivity to light varies across the plant, and cells communicate their timing via local or long‐distance sharing of clock components, causing their rhythms to couple. We found that both varied light sensitivity and long‐distance coupling could generate period differences between organs, while local coupling was required to generate the spatial waves of clock gene expression observed experimentally. We then examined our model under noisy light‐dark cycles and found that local coupling minimized timing errors caused by the noise while allowing each plant region to maintain a different clock phase. Thus, local sensitivity to environmental inputs combined with local coupling enables flexible yet robust circadian timing. Synopsis A spatial molecular model is developed to understand the design principles of plant clock coordination. The model shows that local cell‐to‐cell coupling combined with varied environmental signaling allows robust, yet flexible, timing. A spatial molecular model of the plant circadian clock provides a framework for understanding timing across cellular, organ, and whole‐plant scales. Varied sensing of the environment by cells can explain the period differences observed within plants in experiments. Local cell‐to‐cell communication drives spatial waves of gene expression whereas long‐distance communication can create period differences between organs. Under noisy light‐dark conditions, local cell‐to‐cell communication improves timing accuracy yet allows regional phase differences to persist. Graphical Abstract A spatial molecular model is developed to understand the design principles of plant clock coordination. The model shows that local cell‐to‐cell coupling combined with varied environmental signaling allows robust, yet flexible, timing.

The circadian system has been regarded as a limit cycle oscillator constructed by the integrated interaction of clock genes and proteins. Here, we investigated a mammalian circadian oscillation geometrically before and after a perturbation. We detected the singular point and transition from a type 1 to type 0 phase response curve (PRC) and determined the embedding dimension to show how many variables are needed to describe the limit cycle oscillation and relaxation process after a perturbation. As a perturbation, forskolin (FK) was administered to Rat-1 cells expressing the Per2::luc gene. By broadly and finely changing the phase and strength of the perturbation, we detected the transition of the PRC from type 1 to type 0 and a possible singular transition point, the property of which agreed quite well with our numerical simulation of the noisy Goodwin model, a simple yet canonical model for the transcription-translation feedback loop of the core clock genes. Furthermore, we estimated the embedding dimension of the limit cycle before and after the perturbation. The trajectory of the limit cycle was embedded in two dimensions but with the perturbation of the state point moved out of the trajectory, the relaxation process was generally embedded in higher dimensions. The average number of embedding dimensions at each dose of FK increased as the FK dose increased but most of the relaxation process was generally embedded within four dimensions. These findings support the existence of a circadian limit cycle oscillator in mammalian cells and suggest that a small number of variables determine the relaxation process after a perturbation.

Circadian clocks are autonomous oscillators driving daily rhythms in physiology and behavior. In mammals, a network of coupled neurons in the suprachiasmatic nucleus (SCN) is entrained to environmental light-dark cycles and orchestrates the timing of peripheral organs. In each neuron, transcriptional feedbacks generate noisy oscillations. Coupling mediated by neuropeptides such as VIP and AVP lends precision and robustness to circadian rhythms. The detailed coupling mechanisms between SCN neurons are debated. We analyze organotypic SCN slices from neonatal and adult mice in wild-type and multiple knockout conditions. Different degrees of rhythmicity are quantified by pixel-level analysis of bioluminescence data. We use empirical orthogonal functions (EOFs) to characterize spatio-temporal patterns. Simulations of coupled stochastic single cell oscillators can reproduce the diversity of observed patterns. Our combination of data analysis and modeling provides deeper insight into the enormous complexity of the data: (1) Neonatal slices are typically stronger oscillators than adult slices pointing to developmental changes of coupling. (2) Wild-type slices are completely synchronized and exhibit specific spatio-temporal patterns of phases. (3) Some slices of Cry double knockouts obey impaired synchrony that can lead to co-existing rhythms (\"splitting\"). (4) The loss of VIP-coupling leads to desynchronized rhythms with few residual local clusters. Additional information was extracted from co-culturing slices with rhythmic neonatal wild-type SCNs. These co-culturing experiments were simulated using external forcing terms representing VIP and AVP signaling. The rescue of rhythmicity via co-culturing lead to surprising results, since a cocktail of AVP-antagonists improved synchrony. Our modeling suggests that these counter-intuitive observations are pointing to an antagonistic action of VIP and AVP coupling. Our systematic theoretical and experimental study shows that dual coupling mechanisms can explain the astonishing complexity of spatio-temporal patterns in SCN slices.

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. The cycle of day and night sets the pace for the existence of most life on Earth. In response, many organisms have evolved internal biological clocks which are synchronized with the rhythm of light and dark. Thanks to this ‘circadian clock’, plants and animals can predict the onset of dawn and dusk, and schedule biological processes to specific times of the day. Each cell possesses its own circadian clock, which is formed of a complex network of genes and proteins that get activated along a 24-hour cycle. This raises the question: how do these cells coordinate to create a body clock at the level of the entire organism? In mammals, this synchronisation happens thanks to a structure in the brain, but much less is known about how this occurs in plants. This is partly because few studies exist that focus on measuring the clocks of individual plant cells. Here, Gould, Domijan et al. monitor the circadian clock of single cells in seedlings of a plant called Arabidopsis thaliana across several days and under constant environmental conditions. To do so, they use time-lapse microscopy and genetic methods to see when and where one of the clock’s core genes is switched on. The results show that, at the level of the plant, Arabidopsis has two waves of clock gene expression, one that goes up and one that goes down the root. In addition, the various parts of the plant have slightly different circadian rhythms – for instance, the tip of the root has a faster clock. Robust clock rhythms are also detected in individual cells across the plant. Clocks in neighbouring cells are found to communicate with each other to keep track of time, which might be contributing to this robustness. Mathematical simulations show that, when the individual clocks interact, they generate patterns of clock activity across the plant, which explains the two waves of gene expression in the root. Plant circadian rhythms control traits that are crucial for agriculture, such as growth, yield, disease resistance and flowering time. Understanding, and ultimately controlling, the intricate cogs of these clocks may one day allow scientists to create better performing crops.

The circadian clocks within the hypothalamic–pituitary–gonadal axis control estrous cycles in female rodents. The suprachiasmatic nucleus (SCN), where the central clock is located, generates daily signals to trigger surge release of luteinizing hormone (LH), which in turn induces ovulation. It has been observed in aged rodents that output from the SCN such as neuronal firing activity is declined, and estrous cycles become irregular and finally stop. Circadian clock mutants display accelerated reproductive aging, suggesting the complicated interplay between the circadian system and the endocrine system. To investigate such circadian regulation of estrous cycles, we construct a mathematical model that describes dynamics of key hormones such as LH and of circadian clocks in the SCN and in the ovary, and simulate estrous cycles for various parameter values. Our simulation results demonstrate that reduction of the amplitude of the SCN signal, which is a symptom of aging, makes estrous cycles irregular. We also show that variation in the phase of the SCN signal and changes in the period of ovarian circadian clocks exacerbates the aging effect on estrous cyclicity. Our study suggests that misalignment between the SCN and ovarian circadian oscillations is one of the primary causes of the irregular estrous cycles.

We previously proposed, on theoretical grounds, that the cerebellum must regulate the dimensionality of its neuronal activity during motor learning and control to cope with the low firing frequency of inferior olive neurons, which form one of two major inputs to the cerebellar cortex. Such dimensionality regulation is possible via modulation of electrical coupling through the gap junctions between inferior olive neurons by inhibitory GABAergic synapses. In addition, we previously showed in simulations that intermediate coupling strengths induce chaotic firing of inferior olive neurons and increase their information carrying capacity. However, there is no in vivo experimental data supporting these two theoretical predictions. Here, we computed the levels of synchrony, dimensionality, and chaos of the inferior olive code by analyzing in vivo recordings of Purkinje cell complex spike activity in three different coupling conditions: carbenoxolone (gap junctions blocker), control, and picrotoxin (GABA-A receptor antagonist). To examine the effect of electrical coupling on dimensionality and chaotic dynamics, we first determined the physiological range of effective coupling strengths between inferior olive neurons in the three conditions using a combination of a biophysical network model of the inferior olive and a novel Bayesian model averaging approach. We found that effective coupling co-varied with synchrony and was inversely related to the dimensionality of inferior olive firing dynamics, as measured via a principal component analysis of the spike trains in each condition. Furthermore, for both the model and the data, we found an inverted U-shaped relationship between coupling strengths and complexity entropy, a measure of chaos for spiking neural data. These results are consistent with our hypothesis according to which electrical coupling regulates the dimensionality and the complexity in the inferior olive neurons in order to optimize both motor learning and control of high dimensional motor systems by the cerebellum.

Primates have varied vocal repertoires to communicate with conspecifics and sometimes other species. The larynx has a central role in vocal source generation, where a pair of vocal folds vibrates to modify the air flow. Here, we show that Madagascan lemurs have a unique additional pair of folds in the vestibular region, parallel to the vocal folds. The additional fold has a rigid body of a vocal muscle branch and it is covered by a stratified squamous epithelium, equal to those of the vocal fold. Such anatomical features support the hypothesis that it also vibrates in a manner like the vibrations that occur in the vocal folds. To examine the acoustic function of the two pairs of folds, we made a silicone compound model to demonstrate that they can simultaneously vibrate to lower the fundamental frequency and increase vocal efficiency. Similar acoustic effects are achieved using different features of the larynx for the other primates, e.g., by vibrating multiple sets of ventricular folds in several species and further by an evolutionary modification of enlarged larynx in howler monkeys. Our multidisciplinary approaches found that these functions were acquired through a unique evolutionary adaptation of the twin vocal folds in Madagascan lemurs.