Synchronized and Desynchronized Dynamics Observed from Physical Models of the Vocal and Ventricular Folds

The ventricular folds, located superiorly to the vocal folds, do not usually vibrate during normal phonations. It has been shown, however, that they do vibrate together with the vocal folds under special circumstances such as voice pathology and singing voice. Towards understanding the effect of the ventricular fold oscillations on the vocal fold oscillations, the present study developed a synthetic model that takes into account anatomical features of the human ventricular folds. The synthetic model is made of flexible silicone compounds with material properties comparable to those of human ventricular fold tissues. In our experiment, an air-flow was injected into the vocal and ventricular fold models. As the distance between the left and right ventricular folds was reduced, the ventricular folds started to co-vibrate with the vocal folds. Depending upon the distance, various oscillation patterns of the vocal-ventricular folds were observed, e.g., synchronized dynamics with 1:1 or 1:2 frequency ratio and desynchronized chaotic dynamics. The observed chaotic dynamics might be related to voice pathology induced by the ventricular phonation. A computational model was further presented to elucidate the experimental findings.

Twin vocal folds as a novel evolutionary adaptation for vocal communications in lemurs

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.

Nonlinear dynamics and chaos in a vocal-ventricular fold system

In humans, ventricular folds are located superiorly to the vocal folds. Under special circumstances such as voice pathology or singing, they vibrate together with the vocal folds to contribute to the production of voice. In the present study, experimental data measured from physical models of the vocal and ventricular folds were analyzed in the light of nonlinear dynamics. The physical models provide a useful experimental framework to study the biomechanics of human vocalizations. Of particular interest in this experiment are co-oscillations of the vocal and ventricular folds, occasionally accompanied by irregular dynamics. We show that such a system can be regarded as two coupled oscillators, which give rise to various cooperative behaviors such as synchronized oscillations with a 1:1 or 1:2 frequency ratio and desynchronized oscillations with torus or chaos. The insight gained from the view of nonlinear dynamics should be of significant use for the diagnosis of voice pathologies, such as ventricular fold dysphonia.

Ventricular fold oscillations lower the vocal pitch in rhesus macaques

We carried out ex vivo and in vivo experiments to explore the functional role of the ventricular folds in sound production in macaques. In the ex vivo experiments, 29 recordings out of 67 showed that the ventricular folds co-oscillated with the vocal folds. Transitions from normal vocal fold oscillations to vocal-ventricular fold co-oscillations as well as chaotic irregular oscillations were also observed. The in vivo experiments indicated that the vocal-ventricular fold co-oscillations were also observed in two macaque individuals. In both ex vivo and in vivo experiments, the vocal-ventricular fold co-oscillations significantly lowered the fundamental frequency. A mathematical model revealed that the lowering of the fundamental frequency was caused by a low oscillation frequency inherent in the ventricular folds, which entrained the vocal folds to their low-frequency oscillations. From a physiological standpoint, the macaques may utilize the ventricular fold oscillations more frequently than humans. The advantages as well as disadvantages of using the ventricular folds as an additional vocal repertory are discussed.

Dynamic System Coupling in Voice Production

Voice is a major means of communication for humans, non-human mammals and many other vertebrates like birds and anurans. The physical and physiological principles of voice production are described by two theories: the MyoElastic-AeroDynamic (MEAD) theory and the Source-Filter Theory (SFT). While MEAD employs a multiphysics approach to understand the motor control and dynamics of self-sustained vibration of vocal folds or analogous tissues, SFT predominantly uses acoustics to understand spectral changes of the source via linear propagation through the vocal tract. Because the two theories focus on different aspects of voice production, they are often applied distinctly in specific areas of science and engineering. Here, we argue that the MEAD and the SFT are linked integral aspects of a holistic theory of voice production, describing a dynamically coupled system. The aim of this manuscript is to provide a comprehensive review of both the MEAD and the source-filter theory with its nonlinear extension, the latter of which suggests a number of conceptual similarities to sound production in brass instruments. We discuss the application of both theories to voice production of humans as well as of animals. An appraisal of voice production in the light of non-linear dynamics supports the notion that voice production can best be described with a systems view, considering coupled systems rather than isolated contributions of individual sub-systems.

Anticipating the occurrence and type of critical transitions

Critical transition can occur in many real-world systems. The ability to forecast the occurrence of transition is of major interest in a range of contexts. Various early warning signals (EWSs) have been developed to anticipate the coming critical transition or distinguish types of transition. However, no effective method allows to establish practical threshold indicating the condition when the critical transition is most likely to occur. Here, we introduce a powerful EWS, named dynamical eigenvalue (DEV), that is rooted in bifurcation theory of dynamical systems to estimate the dominant eigenvalue of the system. Theoretically, the absolute value of DEV approaches 1 when the system approaches bifurcation, while its position in the complex plane indicates the type of transition. We demonstrate the efficacy of the DEV approach in model systems with known bifurcation types and also test the DEV approach on various critical transitions in real-world systems.

Detecting the dynamical instability of complex time series via partitioned entropy

A method is proposed to detect the dynamical instability of complex time series. We focus on how the partitioned entropy of an initially localized region of the attractor evolves in time and show that its growth rate corresponds to the first Lyapunov exponent. To avoid spurious detection of the dynamical instability, a criterion is further introduced to distinguish chaos from limit cycles or tori. Numerical experiments using prototypical models of chaotic systems demonstrate that the growth rate of the partitioned entropy indeed provides a good estimate of the first Lyapunov exponent. The method is also shown to be robust against observational noise and dynamical noise. Analysis of experimental data measured from a physical model of the vocal folds highlights the practical applicability of the present method to real-world data. Advantages of the present method over conventional methods are also discussed.

Physical modeling of the vocal membranes and their influence on animal voice production

The vocal membrane, i.e., an extended part of the vocal fold, is observed in a wide range of species including bats and primates. A theoretical study [Mergell, Fitch, and Herzel (1999). J. Acoust. Soc. Am. 105(3), 2020-2028] predicted that the vocal membranes can make the animal vocalizations more efficient by lowering the phonation threshold pressure. To examine this prediction, a synthetic model of the vocal membrane was developed, and its oscillation properties were examined. The experiments revealed that the phonation threshold pressure was lower in the vocal membrane model compared to that in a model with no vocal membrane. Chaotic oscillations were observed as well.

Evolutionary loss of complexity in human vocal anatomy as an adaptation for speech

Human speech production obeys the same acoustic principles as vocal production in other animals but has distinctive features: A stable vocal source is filtered by rapidly changing formant frequencies. To understand speech evolution, we examined a wide range of primates, combining observations of phonation with mathematical modeling. We found that source stability relies upon simplifications in laryngeal anatomy, specifically the loss of air sacs and vocal membranes. We conclude that the evolutionary loss of vocal membranes allows human speech to mostly avoid the spontaneous nonlinear phenomena and acoustic chaos common in other primate vocalizations. This loss allows our larynx to produce stable, harmonic-rich phonation, ideally highlighting formant changes that convey most phonetic information. Paradoxically, the increased complexity of human spoken language thus followed simplification of our laryngeal anatomy.

Experimental study on the quasi-steady approximation of glottal flows

To examine the quasi-steady approximation of the glottal flow, widely used in the modeling of vocal fold oscillations, intraglottal pressure distributions were measured in a scaled-up static vocal fold model under time-varying flow conditions. The left and right vocal folds were slightly open and set to a symmetric and oblique configuration with a divergence angle. To realize time-varying flow conditions, the flow rate was sinusoidally modulated with a frequency of 2 and 10 Hz, which correspond to 112.5 and 562.5 Hz, respectively, in real life. Measurements of the intraglottal pressures under both steady and time-varying flows revealed that the pressure profiles of the time-varying flow conditions are non-distinguishable from those of the steady flow conditions as far as they have the same subglottal pressure as an input pressure. The air-jet separation point was also non-distinguishable between the steady and the time-varying flow conditions. Our study therefore suggests that the time-varying glottal flow can be approximated as a series of steady flow states with a matching subglottal pressure in the range of normal vocalization frequencies. Since the glottal closure was not taken into account in the present experiment, our argument is valid except for such a critical situation.

A spatial model of the plant circadian clock reveals design principles for coordinated timing

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.

Experimental Study on Inspiratory Phonation Using Physical Model of the Vocal Folds

In inspiratory phonation, the air is inhaled from the mouth. The inhaled air passes through the glottis towards the lungs, thereby inducing the vocal fold vibrations. Such phonation takes place in various situations such as sighs, laughter, and crying. To characterize the inspiratory phonation, an experimental study was carried out using a physical model of the vocal folds. By reversing the direction of the airflow that passed through the vocal fold model, the inspiratory phonation was experimentally realized and compared with the normal expiratory phonation. Our experiments revealed that the phonation threshold pressures as well as the volume flow rates decreased under the inspiratory condition. Accordingly, the vocal efficiency was increased. The fundamental frequency was also increased under the inspiratory condition. The kymograms showed that phase of the upper edge of the vocal fold advanced that of the lower edge under the inspiratory phonation. A mathematical model of the vocal folds was further constructed to elucidate these experiments. Except for few aspects, our experimental findings are in good agreement with the preceding studies on inspiratory phonation (e.g., reversed propagation of the mucosal waves observed in a singer, increased pitches in human subjects, and use of inspiratory phonation in speech therapy).

Effect of gravity on synchronization of two coupled buoyancy-induced turbulent flames

We study the effect of gravity on the synchronization of two coupled buoyancy-induced turbulent flames by recurrence-based analysis and machine learning. A significant change from nearly complete synchronization in the near field to partial synchronization appears in the far field under low gravity. The synchronized state is gradually lost with increasing gravity level. These results are clearly identified from cross recurrence plots and symbolic recurrence plots and by reservoir computing.

Experimental study of vocal-ventricular fold oscillations in voice production

Ventricular folds are located in the supraglottal region above the vocal folds. Although the ventricular folds do not vibrate under normal vocalizations, they vibrate under certain conditions, e.g., throat singing or ventricular fold dysphonia. In throat singing, the ventricular folds vibrate at the same frequency as (or at integer ratios of) the vocal fold vibration frequency. In ventricular fold dysphonia, on the other hand, the ventricular folds interfere with the vocal folds, giving rise to a hoarse voice. In the present study, the synthetic larynx model was utilized to examine the vocal-ventricular fold oscillations. Our experiments revealed that the vocal and ventricular folds can co-oscillate at the same frequency with an out-of-phase relation. Compared to the control condition, under which no ventricular folds exist, the phonation threshold pressure was increased in the presence of the ventricular folds. Acoustic analysis indicated that jitter was reduced and vocal efficiency was increased by the ventricular folds. Distance between the vocal and ventricular folds did not alter these oscillation properties. A computational model was further simulated to elucidate the mechanism underlying the observed vocal-ventricular fold oscillations. It has been suggested that out-of-phase oscillations of the vocal and ventricular folds are important for sustaining periodic laryngeal vibrations.

Effect of Ventricular Folds on Vocalization Fundamental Frequency in Domestic Pigs (Sus scrofa domesticus)

This study investigates the effect of the ventricular folds on fundamental frequency (f_o) in the voice production of domestic pigs (Sus scrofa domesticus). The excised larynges of six subadult pigs were phonated in two preparation stages, with the ventricular folds present (PS1) and removed (PS2). Vocal fold resonances were tested with a laser vibrometer, and a four-mass computational model was created. Highly significant f_o differences were found between PS1 and PS2 (means at 93.7 and 409.3 Hz, respectively). Two tissue resonances were found at 115 Hz and 250-290 Hz. The computational model had unique solutions for abducted and adducted ventricular folds at about 150 and 400 Hz, roughly matching the f_o measured ex vivo for PS1 and PS2. The differing f_o encountered across preparation stages PS1 and PS2 is explained by distinct activation of either a high or a low eigenfrequency mode, depending on the engagement of the ventricular folds. The inability of the investigated larynges to vibrate at frequencies below 250 Hz in PS2 suggests that in vivo low-frequency calls of domestic pigs (pre-eminently grunts) are likely produced with engaged ventricular folds. Allometric comparison suggests that the special, mechanically coupled "double oscillator" has evolved to prevent signaling disadvantages. Given these traits, the porcine larynx might - apart from special applications relating to the involvement of ventricular folds - not be an ideal candidate for emulating human voice production in excised larynx experimentation.

Modeling circadian regulation of ovulation timing: age-related disruption of estrous cyclicity

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.

Bright light improves sleep in patients with Parkinson's disease: possible role of circadian restoration

Parkinson’s disease (PD) is one of the most common neurodegenerative disorders. Among the most common manifestations of PD are sleep problems, which are coupled with the adverse effects of dopaminergic therapies (DT). A non-pharmacological solution for these sleep problems has been sought to avoid additional pharmacological intervention. Here, we show that bright light therapy (BLT) is effective for improving sleep in Japanese PD patients receiving DT. Furthermore, experimental evaluation of peripheral clock gene expression rhythms revealed that most PD patients receiving DT who experienced improved sleep following BLT showed a circadian phase shift, indicating the existence of a correlation between circadian modulation and sleep improvement. Conversely, this result indicates that sleep problems in PD patients receiving DT may arise at least in part as a result of circadian dysfunction. Indeed, we found that chronic dopaminergic stimulation induced a rapid attenuation of autonomous oscillations of clock gene expression in ex vivo cultured mouse suprachiasmatic nucleus (SCN) at the single neuron level. In conclusion, BLT is a promising medical treatment for improving sleep in PD patients receiving DT. This BLT-induced improvement may be due to the restoration of circadian function.

Damped circadian oscillation in the absence of KaiA in Synechococcus

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.

Conceptual Models of Entrainment, Jet Lag, and Seasonality

Understanding entrainment of circadian rhythms is a central goal of chronobiology. Many factors, such as period, amplitude, Zeitgeber strength, and daylength, govern entrainment ranges and phases of entrainment. We have tested whether simple amplitude-phase models can provide insight into the control of entrainment phases. Using global optimization, we derived conceptual models with just three free parameters (period, amplitude, and relaxation rate) that reproduce known phenotypic features of vertebrate clocks: phase response curves (PRCs) with relatively small phase shifts, fast re-entrainment after jet lag, and seasonal variability to track light onset or offset. Since optimization found multiple sets of model parameters, we could study this model ensemble to gain insight into the underlying design principles. We found complex associations between model parameters and entrainment features. Arnold onions of representative models visualize strong dependencies of entrainment on periods, relative Zeitgeber strength, and photoperiods. Our results support the use of oscillator theory as a framework for understanding the entrainment of circadian clocks.

A practical method for estimating coupling functions in complex dynamical systems

A foremost challenge in modern network science is the inverse problem of reconstruction (inference) of coupling equations and network topology from the measurements of the network dynamics. Of particular interest are the methods that can operate on real (empirical) data without interfering with the system. One such earlier attempt (Tokuda et al. 2007 Phys. Rev. Lett. 99, 064101. (doi:10.1103/PhysRevLett.99.064101)) was a method suited for general limit-cycle oscillators, yielding both oscillators' natural frequencies and coupling functions between them (phase equations) from empirically measured time series. The present paper reviews the above method in a way comprehensive to domain-scientists other than physics. It also presents applications of the method to (i) detection of the network connectivity, (ii) inference of the phase sensitivity function, (iii) approximation of the interaction among phase-coherent chaotic oscillators, and (iv) experimental data from a forced Van der Pol electric circuit. This reaffirms the range of applicability of the method for reconstructing coupling functions and makes it accessible to a much wider scientific community. This article is part of the theme issue 'Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences'.

Weak coupling between intracellular feedback loops explains dissociation of clock gene dynamics

Circadian rhythms are generated by interlocked transcriptional-translational negative feedback loops (TTFLs), the molecular process implemented within a cell. The contributions, weighting and balancing between the multiple feedback loops remain debated. Dissociated, free-running dynamics in the expression of distinct clock genes has been described in recent experimental studies that applied various perturbations such as slice preparations, light pulses, jet-lag, and culture medium exchange. In this paper, we provide evidence that this "presumably transient" dissociation of circadian gene expression oscillations may occur at the single-cell level. Conceptual and detailed mechanistic mathematical modeling suggests that such dissociation is due to a weak interaction between multiple feedback loops present within a single cell. The dissociable loops provide insights into underlying mechanisms and general design principles of the molecular circadian clock.

Experimental study on nonlinear source-filter interaction using synthetic vocal fold models

Under certain conditions, e.g., singing voice, the fundamental frequency of the vocal folds can go up and interfere with the formant frequencies. Acoustic feedback from the vocal tract filter to the vocal fold source then becomes strong and non-negligible. An experimental study was presented on such source-filter interaction using three types of synthetic vocal fold models. Asymmetry was also created between the left and right vocal folds. The experiment reproduced various nonlinear phenomena, such as frequency jump and quenching, as reported in humans. Increase in phonation threshold pressure was also observed when resonant frequency of the vocal tract and fundamental frequency of the vocal folds crossed each other. As a combined effect, the phonation threshold pressure was further increased by the left-right asymmetry. Simulation of the asymmetric two-mass model reproduced the experiments to some extent. One of the intriguing findings of this study is the variable strength of the source-filter interaction over different model types. Among the three models, two models were strongly influenced by the vocal tract, while no clear effect of the vocal tract was observed in the other model. This implies that the level of source-filter interaction may vary considerably from one subject to another in humans.

Highly Heterogeneous Excitatory Connections Require Less Amount of Noise to Sustain Firing Activities in Cortical Networks

Cortical networks both in vivo and in vitro sustain asynchronous irregular firings with extremely low frequency. To realize such self-sustained activity in neural network models, balance between excitatory and inhibitory activities is known to be one of the keys. In addition, recent theoretical studies have revealed that another feature commonly observed in cortical networks, i.e., sparse but strong connections and dense weak connections, plays an essential role. The previous studies, however, have not thoroughly considered the cooperative dynamics between a network of such heterogeneous synaptic connections and intrinsic noise. The noise stimuli, representing inherent nature of the neuronal activities, e.g., variability of presynaptic discharges, should be also of significant importance for sustaining the irregular firings in cortical networks. Here, we numerically demonstrate that highly heterogeneous distribution, typically a lognormal type, of excitatory-to-excitatory connections, reduces the amount of noise required to sustain the network firing activities. In the sense that noise consumes an energy resource, the heterogeneous network receiving less amount of noise stimuli is considered to realize an efficient dynamics in cortex. A noise-driven network of bi-modally distributed synapses further shows that many weak and a few very strong synapses are the key feature of the synaptic heterogeneity, supporting the network firing activity.

Reducing the complexity of mathematical models for the plant circadian clock by distributed delays

A major bottleneck in the modelling of biological networks is the parameter explosion problem - the exponential increase in the number of parameters that need to be optimised to data as the size of the model increases. Here, we address this problem in the context of the plant circadian clock by applying the method of distributed delays. We show that using this approach, the system architecture can be simplified efficiently - reducing the number of parameters - whilst still preserving the core mechanistic dynamics of the gene regulatory network. Compared to models with discrete time-delays, which are governed by functional differential equations, the distributed delay models can be converted into sets of equivalent ordinary differential equations, enabling the use of standard methods for numerical integration, and for stability and bifurcation analyses. We demonstrate the efficiency of our modelling approach by applying it to three exemplar mathematical models of the Arabidopsis circadian clock of varying complexity, obtaining significant reductions in complexity in each case. Moreover, we revise one of the most up-to-date Arabidopsis models, updating the regulation of the PRR9 and PRR7 genes by LHY in accordance with recent experimental data. The revised model more accurately reproduces the LHY-induction experiments of core clock genes, compared with the original model. Our work thus shows that the method of distributed delays facilitates the optimisation and reformulation of genetic network models.

Coherency of circadian rhythms in the SCN is governed by the interplay of two coupling factors

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 mammalian circadian clock is orchestrated by a network of coupled neurons. Brain slice preparations allow the analysis of coupling mechanisms mediated by neuropeptides. From bioluminescence recordings, we extract single cell characteristics such as period, amplitude and damping rate. Our data-based stochastic network model involves local coupling between cells and additional external forcing. Available experimental data guide our simulations with two distinct coupling and forcing mechanisms representing the neuropeptides VIP and AVP. We compare our simulations with experiments from neonatal and adult wild-type brain slices and multiple knockouts. Furthermore, we study co–culturing of slices with synchronized neonatal wild-type slices. The extreme complexity of the spatio-temporal patterns is quantified using empirical orthogonal functions (EOFs). The experimental reduction of AVP coupling leads to surprising observations. In double knockouts, inhibition of AVP signaling can improve synchrony, whereas, in triple knockouts, coherency is reduced. Our network modeling shows that these counter-intuitive observations can be explained by an antagonistic action of VIP and AVP signaling. The agreement of experiments and simulations suggests that quite complex spatio-temporal patterns can appear as emergent properties of oscillator networks with dual coupling mechanisms.

Photic phase-response curves for cycling female mice

The photic entrainment system is critical for the internal circadian clock to be synchronized by external time cues. In nocturnal rodents, exposure to light during the early subjective night causes a phase delay, whereas it causes a phase advance during the late subjective night. This is represented by a phase-response curve (PRC). The PRC of females has not been well studied due to their estrous cycles. Our aim in this study was to understand the characteristics of photic entrainment in female cycling rodents and identify differences in photic entrainment among the stages of the estrous cycle. To establish two types of PRC, immediate PRC (iPRC) and steady state PRC (ssPRC), in each stage of the estrous cycle, we recorded circadian rhythms of wheel running activity, applying a 15-min light pulse to cycling female mice in constant darkness. In the iPRC, which was evaluated on the next day of the light pulse, the amount of phase shift in the diestrus was larger than that in the metestrus stage at circadian time (CT) 2. Similarly, the amount of phase shift in metestrus was larger than that in proestrus at CT 10. In the ssPRC, which was evaluated after completion of a new steady state, no significant estrous variations in the amount of photic phase shifts were detected for any CTs. Although these results indicate that the intrinsic photic entrainment system is not influenced by the estrous cycle, it may affect photoreception and cause sudden behavioral changes.

Coordination of robust single cell rhythms in the Arabidopsis circadian clock via spatial waves of gene expression

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.

Synchronization of two coupled turbulent fires

We numerically study the scale-free nature of a buoyancy-induced turbulent fire and synchronization of two coupled turbulent fires. A scale-free structure is detected in weighted networks between vortices, while its lifetime obeys a clear power law, indicating intermittent appearances, disappearances, and reappearances of the scale-free property. A significant decrease in the distance between the two fire sources gives rise to a synchronized state in the near field dominated by the unstable motion of transverse vortex rings. The synchronized state vanishes in the far field forming well-developed turbulent plumes, regardless of the distance between the two fire sources.

Characterization and detection of thermoacoustic combustion oscillations based on statistical complexity and complex-network theory

We present an experimental study on the characterization of dynamic behavior of flow velocity field during thermoacoustic combustion oscillations in a turbulent confined combustor from the viewpoints of statistical complexity and complex-network theory, involving detection of a precursor of thermoacoustic combustion oscillations. The multiscale complexity-entropy causality plane clearly shows the possible presence of two dynamics, noisy periodic oscillations and noisy chaos, in the shear layer regions (1) between the outer recirculation region in the dump plate and a recirculation flow in the wake of the centerbody and (2) between the outer recirculation region in the dump plate and a vortex breakdown bubble away from the centerbody. The vertex strength in the turbulence network and the community structure of the vorticity field can identify the vortical interactions during thermoacoustic combustion oscillations. Sequential horizontal visibility graph motifs are useful for capturing a precursor of themoacoustic combustion oscillations.

Salt-inducible kinase 3 regulates the mammalian circadian clock by destabilizing PER2 protein

Salt-inducible kinase 3 (SIK3) plays a crucial role in various aspects of metabolism. In the course of investigating metabolic defects in Sik3-deficient mice (Sik3^-/-), we observed that circadian rhythmicity of the metabolisms was phase-delayed. Sik3^-/- mice also exhibited other circadian abnormalities, including lengthening of the period, impaired entrainment to the light-dark cycle, phase variation in locomotor activities, and aberrant physiological rhythms. Ex vivo suprachiasmatic nucleus slices from Sik3^-/- mice exhibited destabilized and desynchronized molecular rhythms among individual neurons. In cultured cells, Sik3-knockdown resulted in abnormal bioluminescence rhythms. Expression levels of PER2, a clock protein, were elevated in Sik3-knockdown cells but down-regulated in Sik3-overexpressing cells, which could be attributed to a phosphorylation-dependent decrease in PER2 protein stability. This was further confirmed by PER2 accumulation in the Sik3^-/- fibroblasts and liver. Collectively, SIK3 plays key roles in circadian rhythms by facilitating phosphorylation-dependent PER2 destabilization, either directly or indirectly.

Nonlinear dynamics of a buoyancy-induced turbulent fire

We conduct a numerical study on the dynamic behavior of a buoyancy-induced turbulent fire from the viewpoints of symbolic dynamics, complex networks, and statistical complexity. Here, we consider two classes of entropies: the permutation entropy and network entropy in ε-recurrence networks, both of which evaluate the degree of randomness in the underlying dynamics. These entropies enable us to capture the significant changes in the dynamic behavior of flow velocity fluctuations. The possible presence of two important dynamics, low-dimensional deterministic chaos in the near field dominated by the motion of large-scale vortices and high-dimensional chaos in the far field forming a well-developed turbulent plume, is clearly identified by the multiscale complexity-entropy causality plane.

Multicellularity enriches the entrainment of Arabidopsis circadian clock

The phase response curve (PRC) of the circadian clock provides one of the most significant indices for anticipating entrainment of outer cycles, despite the difficulty of making precise PRC determinations in experiments. We characterized the PRC of the Arabidopsisthaliana circadian clock on the basis of its phase-locking property to variable periodic pulse perturbations. Experiments revealed that the PRC changed remarkably from continuous to discontinuous fashion, depending on the oscillation amplitude. Our hypothesis of amplitude-dependent adaptability to outer cycles was successfully clarified by elucidation of this transition of PRC as a change in the collective response of the circadian oscillator network. These findings provide an essential criterion against which to evaluate the precision of PRC measurement and an advanced understanding of the adaptability of plant circadian systems to environmental conditions.

Potential contribution of tandem circadian enhancers to nonlinear oscillations in clock gene expression

Limit-cycle oscillations require the presence of nonlinear processes. Although mathematical studies have long suggested that multiple nonlinear processes are required for autonomous circadian oscillation in clock gene expression, the underlying mechanism remains controversial. Here we show experimentally that cell-autonomous circadian transcription of a mammalian clock gene requires a functionally interdependent tandem E-box motif; the lack of either of the two E-boxes results in arrhythmic transcription. Although previous studies indicated the role of the tandem motifs in increasing circadian amplitude, enhancing amplitude does not explain the mechanism for limit-cycle oscillations in transcription. In this study, mathematical analysis suggests that the interdependent behavior of enhancer elements including not only E-boxes but also ROR response elements might contribute to limit-cycle oscillations by increasing transcriptional nonlinearity. As expected, introduction of the interdependence of circadian enhancer elements into mathematical models resulted in autonomous transcriptional oscillation with low Hill coefficients. Together these findings suggest that interdependent tandem enhancer motifs on multiple clock genes might cooperatively enhance nonlinearity in the whole circadian feedback system, which would lead to limit-cycle oscillations in clock gene expression.

Effect of level difference between left and right vocal folds on phonation: Physical experiment and theoretical study

As an alternative factor to produce asymmetry between left and right vocal folds, the present study focuses on level difference, which is defined as the distance between the upper surfaces of the bilateral vocal folds in the inferior-superior direction. Physical models of the vocal folds were utilized to study the effect of the level difference on the phonation threshold pressure. A vocal tract model was also attached to the vocal fold model. For two types of different models, experiments revealed that the phonation threshold pressure tended to increase as the level difference was extended. Based upon a small amplitude approximation of the vocal fold oscillations, a theoretical formula was derived for the phonation threshold pressure. This theory agrees with the experiments, especially when the phase difference between the left and right vocal folds is not extensive. Furthermore, an asymmetric two-mass model was simulated with a level difference to validate the experiments as well as the theory. The primary conclusion is that the level difference has a potential effect on voice production especially for patients with an extended level of vertical difference in the vocal folds, which might be taken into account for the diagnosis of voice disorders.

Grasshopper mice employ distinct vocal production mechanisms in different social contexts

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.

Transition of phase response properties and singularity in the circadian limit cycle of cultured cells

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.

Effective Suppression of Pathological Synchronization in Cortical Networks by Highly Heterogeneous Distribution of Inhibitory Connections

Even without external random input, cortical networks in vivo sustain asynchronous irregular firing with low firing rate. In addition to detailed balance between excitatory and inhibitory activities, recent theoretical studies have revealed that another feature commonly observed in cortical networks, i.e., long-tailed distribution of excitatory synapses implying coexistence of many weak and a few extremely strong excitatory synapses, plays an essential role in realizing the self-sustained activity in recurrent networks of biologically plausible spiking neurons. The previous studies, however, have not considered highly non-random features of the synaptic connectivity, namely, bidirectional connections between cortical neurons are more common than expected by chance and strengths of synapses are positively correlated between pre- and postsynaptic neurons. The positive correlation of synaptic connections may destabilize asynchronous activity of networks with the long-tailed synaptic distribution and induce pathological synchronized firing among neurons. It remains unclear how the cortical network avoids such pathological synchronization. Here, we demonstrate that introduction of the correlated connections indeed gives rise to synchronized firings in a cortical network model with the long-tailed distribution. By using a simplified feed-forward network model of spiking neurons, we clarify the underlying mechanism of the synchronization. We then show that the synchronization can be efficiently suppressed by highly heterogeneous distribution, typically a lognormal distribution, of inhibitory-to-excitatory connection strengths in a recurrent network model of cortical neurons.

Coupling Controls the Synchrony of Clock Cells in Development and Knockouts

In mammals, a network of coupled neurons within the hypothalamus coordinates physiological rhythms with daily changes in the environment. In each neuron, delayed negative transcriptional feedbacks generate oscillations, albeit noisy and unreliable ones. Coupling mediated by diffusible neuropeptides lends precision and robustness to circadian rhythms. The double knockout of Cryptochrome Cry turns adult mice arrhythmic. But, remarkably, double knockout neonates continue to show robust oscillation much like wild-type neonates and appear to lose rhythmicity with development. We study quantitatively dispersed neurons and brain slices from wild-type and Cry double knockout mice to understand the links between single cell rhythmicity and intercellular coupling. We quantify oscillator properties of dispersed cells using nonlinear regression and study bifurcations diagrams of network models. We find that varying just three parameters-oscillator strength, strength of coupling, and timing of coupling-can reproduce experimentally observed features. In particular, modeling reveals that minor changes in timing of coupling can destroy synchronization as observed in adult slices from knockout mice.

Phase response of the Arabidopsis thaliana circadian clock to light pulses of different wavelengths

Light is known as one of the most powerful environmental time cues for the circadian system. The quality of light is characterized by its intensity and wavelength. We examined how the phase response of Arabidopsis thaliana depends on the wavelength of the stimulus light and the type of light perturbation. Using transgenic A. thaliana expressing a luciferase gene, we monitored the rhythm of the bioluminescence signal. We stimulated the plants under constant red light using 3 light perturbation treatments: (1) increasing the red light intensity, (2) turning on a blue light while turning off the red light, and (3) turning on a blue light while keeping the red light on. To examine the phase response properties, we generated a phase transition curve (PTC), which plots the phase after the perturbation as a function of the phase before the perturbation. To evaluate the effect of the 3 light perturbation treatments, we simulated PTCs using a mathematical model of the plant circadian clock and fitted the simulated PTCs to the experimentally measured PTCs. Among the 3 treatments, perturbation (3) provided the strongest stimulus. The results indicate that the color of the stimulus light and the type of pulse administration affect the phase response in a complex manner. Moreover, the results suggest the involvement of interaction between red and blue light signaling pathways in resetting of the plant circadian clock.

An extended mathematical model for reproducing the phase response of Arabidopsis thaliana under various light conditions

Experimental studies showed that light qualities such as color and strength influence the phase response properties of plant circadian systems. These effects, however, have yet to be properly addressed in theoretical models of plant circadian systems. To fill this gap, the present paper develops a mathematical model of a plant circadian clock that takes into account the intensity and wavelength of the input light. Based on experimental knowledge, we model three photoreceptors, Phytochrome A, Phytochrome B, and Cryptochrome 1, which respond to red and/or blue light, in Arabidopsis thaliana. The three photoreceptors are incorporated into a standard mathematical model of the plant system, in which activator and repressor genes form a single feedback loop. The model capability is examined by a phase response curve (PRC), which plots the phase shifts elicited by the light perturbation as a function of the perturbation phase. Numerical experiments demonstrate that the extended model reproduces the essential features of the PRCs measured experimentally under various light conditions. Particularly, unlike conventional models, the model generates the inherent shape of the PRC under dark pulse stimuli. The outcome of our modeling approach may motivate future theoretical and experimental studies of plant circadian rhythms.

The source-filter theory of whistle-like calls in marmosets: Acoustic analysis and simulation of helium-modulated voices

Whistle-like high-pitched "phee" calls are often used as long-distance vocal advertisements by small-bodied marmosets and tamarins in the dense forests of South America. While the source-filter theory proposes that vibration of the vocal fold is modified independently from the resonance of the supralaryngeal vocal tract (SVT) in human speech, a source-filter coupling that constrains the vibration frequency to SVT resonance effectively produces loud tonal sounds in some musical instruments. Here, a combined approach of acoustic analyses and simulation with helium-modulated voices was used to show that phee calls are produced principally with the same mechanism as in human speech. The animal keeps the fundamental frequency (f0) close to the first formant (F1) of the SVT, to amplify f0. Although f0 and F1 are primarily independent, the degree of their tuning can be strengthened further by a flexible source-filter interaction, the variable strength of which depends upon the cross-sectional area of the laryngeal cavity. The results highlight the evolutionary antiquity and universality of the source-filter model in primates, but the study can also explore the diversification of vocal physiology, including source-filter interaction and its anatomical basis in non-human primates.

Segmental Bayesian estimation of gap-junctional and inhibitory conductance of inferior olive neurons from spike trains with complicated dynamics

The inverse problem for estimating model parameters from brain spike data is an ill-posed problem because of a huge mismatch in the system complexity between the model and the brain as well as its non-stationary dynamics, and needs a stochastic approach that finds the most likely solution among many possible solutions. In the present study, we developed a segmental Bayesian method to estimate the two parameters of interest, the gap-junctional (gc ) and inhibitory conductance (gi ) from inferior olive spike data. Feature vectors were estimated for the spike data in a segment-wise fashion to compensate for the non-stationary firing dynamics. Hierarchical Bayesian estimation was conducted to estimate the gc and gi for every spike segment using a forward model constructed in the principal component analysis (PCA) space of the feature vectors, and to merge the segmental estimates into single estimates for every neuron. The segmental Bayesian estimation gave smaller fitting errors than the conventional Bayesian inference, which finds the estimates once across the entire spike data, or the minimum error method, which directly finds the closest match in the PCA space. The segmental Bayesian inference has the potential to overcome the problem of non-stationary dynamics and resolve the ill-posedness of the inverse problem because of the mismatch between the model and the brain under the constraints based, and it is a useful tool to evaluate parameters of interest for neuroscience from experimental spike train data.

Functional morphology of the Alligator mississippiensis larynx with implications for vocal production

Sauropsid vocalization is mediated by the syrinx in birds and the larynx in extant reptiles; but whereas avian vocal production has received much attention, the vocal mechanism of basal reptilians is poorly understood. The American alligator (Alligator mississippiensis) displays a large vocal repertoire during mating and in parent–offspring interactions. Although vocal outputs of these behaviors have received some attention, the underlying mechanism of sound production remains speculative. Here, we investigate the laryngeal anatomy of juvenile and adult animals by macroscopic and histological methods. Observations of the cartilaginous framework and associated muscles largely corroborate earlier findings, but one muscle, the cricoarytenoideus, exhibits a heretofore unknown extrinsic insertion that has important implications for effective regulation of vocal fold length and tension. Histological investigation of the larynx revealed a layered vocal fold morphology. The thick lamina propria consists of non-homogenous extracellular matrix containing collagen fibers that are tightly packed below the epithelium but loosely organized deep inside the vocal fold. We found few elastic fibers but comparatively high proportions of hyaluronan. Similar organizational complexity is also seen in mammalian vocal folds and the labia of the avian syrinx: convergent morphologies that suggest analogous mechanisms for sound production. In tensile tests, alligator vocal folds demonstrated a linear stress–strain behavior in the low strain region and nonlinear stress responses at strains larger than 15%, which is similar to mammalian vocal fold tissue. We have integrated morphological and physiological data in a two-mass vocal fold model, providing a systematic description of the possible acoustic space that could be available to an alligator larynx. Mapping actual call production onto possible acoustic space validates the model's predictions.

Estimation of inferior-superior vocal fold kinematics from high-speed stereo endoscopic data in vivo

Despite being an indispensable tool for both researchers and clinicians, traditional endoscopic imaging of the human vocal folds is limited in that it cannot capture their inferior-superior motion. A three-dimensional reconstruction technique using high-speed video imaging of the vocal folds in stereo is explored in an effort to estimate the inferior-superior motion of the medial-most edge of the vocal folds under normal muscle activation in vivo. Traditional stereo-matching algorithms from the field of computer vision are considered and modified to suit the specific challenges of the in vivo application. Inferior-superior motion of the medial vocal fold surface of three healthy speakers is reconstructed over one glottal cycle. The inferior-superior amplitude of the mucosal wave is found to be approximately 13 mm for normal modal voice, reducing to approximately 3 mm for strained falsetto voice, with uncertainty estimated at σ ≈ 2 mm and σ ≈ 1 mm, respectively. Sources of error, and their relative effects on the estimation of the inferior-superior motion, are considered and recommendations are made to improve the technique.

Controlling circadian rhythms by dark-pulse perturbations in Arabidopsis thaliana

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.

Solution to the inverse problem of estimating gap-junctional and inhibitory conductance in inferior olive neurons from spike trains by network model simulation

The inferior olive (IO) possesses synaptic glomeruli, which contain dendritic spines from neighboring neurons and presynaptic terminals, many of which are inhibitory and GABAergic. Gap junctions between the spines electrically couple neighboring neurons whereas the GABAergic synaptic terminals are thought to act to decrease the effectiveness of this coupling. Thus, the glomeruli are thought to be important for determining the oscillatory and synchronized activity displayed by IO neurons. Indeed, the tendency to display such activity patterns is enhanced or reduced by the local administration of the GABA-A receptor blocker picrotoxin (PIX) or the gap junction blocker carbenoxolone (CBX), respectively. We studied the functional roles of the glomeruli by solving the inverse problem of estimating the inhibitory (gi) and gap-junctional conductance (gc) using an IO network model. This model was built upon a prior IO network model, in which the individual neurons consisted of soma and dendritic compartments, by adding a glomerular compartment comprising electrically coupled spines that received inhibitory synapses. The model was used in the forward mode to simulate spike data under PIX and CBX conditions for comparison with experimental data consisting of multi-electrode recordings of complex spikes from arrays of Purkinje cells (complex spikes are generated in a one-to-one manner by IO spikes and thus can substitute for directly measuring IO spike activity). The spatiotemporal firing dynamics of the experimental and simulation spike data were evaluated as feature vectors, including firing rates, local variation, auto-correlogram, cross-correlogram, and minimal distance, and were contracted onto two-dimensional principal component analysis (PCA) space. gc and gi were determined as the solution to the inverse problem such that the simulation and experimental spike data were closely matched in the PCA space. The goodness of the match was confirmed by an analysis of variance (ANOVA) of the PCA scores between the experimental and simulation spike data. In the PIX condition, gi was found to decrease to approximately half its control value. CBX caused an approximately 30% decrease in gc from control levels. These results support the hypothesis that the glomeruli are control points for determining the spatiotemporal characteristics of olivocerebellar activity and thus may shape its ability to convey signals to the cerebellum that may be used for motor learning or motor control purposes.