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.