Synchronizing genetic oscillators by signaling molecules

The authors examine collective rhythms in a general multicell system with both linearly diffusive and nondiffusive couplings. The effect of coupling on synchronization through intercellular signaling in a population of Escherichia coli cells is studied. In particular, a synchronization solution is given through the auxiliary individual system for 2 types of couplings. The sufficient conditions for the global synchronization of such a coupled system are derived based on the Lyapunov function method. The authors show that an appropriate design of the coupling and the inner-linking matrix can ensure global synchronization of the coupled synthetic biological system. Moreover, they demonstrate that the dynamics of an individual cell with coupling and without coupling may be qualitatively different; one is oscillatory, and the other is steady state. The change from a nonoscillatory state to an oscillatory one is induced by appropriate coupling, which also entrains all cells to synchronization. These results establish not only a theoretical foundation but also a quantitative basis for understanding the essential cooperative dynamics, such as collective rhythms or synchronization, in a population of cells.     

Synchronized oscillations in the visual cortex — a synergetic model

We present an oscillator network model for the synchronization of oscillatory neuronal activity underlying visual processing. The single neuron is modeled by means of a limit cycle oscillator with an eigenfrequency corresponding to visual stimulation. The eigenfrequency may be time dependent. The mutual coupling strengths are unsymmetrical and activity dependent, and they scatter within the network. Synchronized clusters (groups) of neurons emerge in the network due to the visual stimulation. The different clusters correspond to different visual stimuli. There is no limitation of the number of stimuli. Distinct clusters do not perturb each other, although the coupling strength between all model neurons is of the same order of magnitude. Our analysis is not restricted to weak coupling strength. The scatter of the couplings causes shifts of the cluster frequencies. The model's behavior is compared with the experimental findings. The coupling mechanism is extended in order to model the influence of bicucullin upon the neural network. We additionally investigate repulsive couplings, which lead to constant phase differences between clusters of the same frequency. Finally, we consider the problem of selective attention from the viewpoint of our model.     

Synchronized oscillations in the visual cortex — a synergetic model

 We present an oscillator network model for the synchronization of oscillatory neuronal activity underlying visual processing. The single neuron is modeled by means of a limit cycle oscillator with an eigenfrequency corresponding to visual stimulation. The eigenfrequency may be time dependent. The mutual coupling strengths are unsymmetrical and activity dependent, and they scatter within the network. Synchronized clusters (groups) of neurons emerge in the network due to the visual stimulation. The different clusters correspond to different visual stimuli. There is no limitation of the number of stimuli. Distinct clusters do not perturb each other, although the coupling strength between all model neurons is of the same order of magnitude. Our analysis is not restricted to weak coupling strength. The scatter of the couplings causes shifts of the cluster frequencies. The model’s behavior is compared with the experimental findings. The coupling mechanism is extended in order to model the influence of bicucullin upon the neural network. We additionally investigate repulsive couplings, which lead to constant phase differences between clusters of the same frequency. Finally, we consider the problem of selective attention from the viewpoint of our model. Received: 15 February 1995/Accepted in revised form: 18 July 1995     

Analysis and modeling of time-variant amplitude–frequency couplings of and between oscillations of EEG bursts

Low-frequency (0.5-2.5 Hz) and individually defined high-frequency (7-11 or 8-12 Hz; 11-15 or 14-18 Hz) oscillatory components of the electroencephalogram (EEG) burst activity derived from thiopental-induced burst-suppression patterns (BSP) were investigated in seven sedated patients (17-26 years old) with severe head injury. The predominant high-frequency burst oscillations (>7 Hz) were detected for each patient by means of time-variant amplitude spectrum analysis. Thereafter, the instantaneous envelope (IE) and the instantaneous frequency (IF) were computed for these low- and high-frequency bands to quantify amplitude-frequency dependencies (envelope-envelope, envelope-frequency, and frequency-frequency correlations). Time-variant phase-locking, phase synchronization, and quadratic phase couplings are associated with the observed amplitude-frequency characteristics. Additionally, these time-variant analyses were carried out for modeled burst patterns. Coupled Duffing oscillators were adapted to each EEG burst and by means of these models data-based burst simulations were generated. Results are: (1) strong envelope-envelope correlations (IE courses) can be demonstrated; (2) it can be shown that a rise of the IE is associated with an increase of the IF (only for the frequency bands 0.5-2.5 and 7-11 or 8-12 Hz); (3) the rise characteristics of all individually averaged envelope-frequency courses (IE-IF) are strongly correlated; (4) for the 7-11 or 8-12 Hz oscillation these associations are weaker and the variation between the time courses of the patients is higher; (5) for both frequency ranges a quantitative amplitude-frequency dependency can be shown because higher IE peak maxima are accompanied by stronger IF changes; (6) the time range of significant phase-locking within the 7-11 or 8-12 Hz frequency bands and of the strongest quadratic phase couplings (between 0.5-2.5 and 7-11 or 8-12 Hz) is between 0 and 1,000 ms; (7) all phase coupling characteristics of the modeled bursts accord well with the corresponding characteristics of the measured EEG burst data. All amplitude-frequency dependencies and phase locking/coupling properties described here are known from and can be discussed using coupled Duffing oscillators which are characterized by autoresonance properties.     

Electrotonic Coupling between Pyramidal Neurons in the Neocortex

Electrotonic couplings (i.e., electrical synapses or gap junctions) are fundamental to neuronal synchronization, and thus essential for many physiological functions and pathological disorders. Interneuron electrical synapses have been studied intensively. Although studies on electrotonic couplings between pyramidal cells (PCs) are emerging, particularly in the hippocampus, evidence is still rare in the neocortex. The electrotonic coupling of PCs in the neocortex is therefore largely unknown in terms of electrophysiological, anatomical and synaptological properties. Using multiple patch-clamp recording with differential interference contrast infrared videomicroscopy (IR-DIC) visualization, histochemical staining, and 3D-computer reconstruction, electrotonic coupling was recorded between close PCs, mainly in the medial prefrontal cortex as well as in the visual cortical regions of ferrets and rats. Compared with interneuron gap junctions, these electrotonic couplings were characterized by several special features. The recording probability of an electrotonic coupling between PCs is extremely low; but the junctional conductance is notably high, permitting the direct transmission of action potentials (APs) and even tonic firing between coupled neurons. AP firing is therefore perfectly synchronized between coupled PCs; Postjunctional APs and spikelets alternate following slight changes of membrane potentials; Postjunctional spikelets, especially at high frequencies, are summated and ultimately reach AP-threshold to fire. These properties of pyramidal electrotonic couplings largely fill the needs, as predicted by simulation studies, for the synchronization of a neuronal assembly. It is therefore suggested that the electrotonic coupling of PCs plays a unique role in the generation of neuronal synchronization in the neocortex.     

Synchronous Ca(2+) oscillation emerges from voltage fluctuations of Ca(2+) stores

Synchronous Ca(2+) oscillation occurs in various cell types to regulate cellular functions. However, the mechanism for synchronization of Ca(2+) increases between cells remains unclear. Recently, synchronous oscillatory changes in the membrane potential of internal Ca(2+) stores were recorded using an organelle-specific voltage-sensitive dye [Yamashita et al. (2006) FEBS J273, 3585-3597], and an electrical coupling model of the synchronization of store potentials and Ca(2+) releases has been proposed [Yamashita (2006) FEBS Lett580, 4979-4983]. This model is based on capacitative coupling, by which transient voltage changes can be synchronized, but oscillatory slow potentials cannot be communicated. Another candidate mechanism is synchronization of action potentials and ensuing Ca(2+) influx through voltage-dependent Ca channels. The present study addresses the question of whether Ca(2+) increases are synchronized by action potentials, and how oscillatory store potentials are synchronized across the cells. Electrophysiological and Ca(2+)-sensitive fluorescence measurements in early embryonic chick retina showed that synchronous Ca(2+) oscillation was caused by releases of Ca(2+) from Ca(2+) stores without any evidence of action potentials in retinal neuroepithelial cells or newborn neurons. High-speed fluorescence measurement of store membrane potential surprisingly revealed that the synchronous oscillatory changes in the store potential were periodic repeats of a burst of high-frequency voltage fluctuations. The burst coincided with a Ca(2+) increase. The present study suggests that synchronization of Ca(2+) release is mediated by the high-frequency fluctuation in the store potential. Close apposition of the store membrane and plasma membrane in an epithelial structure would allow capacitative coupling across the cells.     

Structure-Function Discrepancy: Inhomogeneity and Delays in Synchronized Neural Networks

The discrepancy between structural and functional connectivity in neural systems forms the challenge in understanding general brain functioning. To pinpoint a mapping between structure and function, we investigated the effects of (in)homogeneity in coupling structure and delays on synchronization behavior in networks of oscillatory neural masses by deriving the phase dynamics of these generic networks. For homogeneous delays, the structural coupling matrix is largely preserved in the coupling between phases, resulting in clustered stationary phase distributions. Accordingly, we found only a small number of synchronized groups in the network. Distributed delays, by contrast, introduce inhomogeneity in the phase coupling so that clustered stationary phase distributions no longer exist. The effect of distributed delays mimicked that of structural inhomogeneity. Hence, we argue that phase (de-)synchronization patterns caused by inhomogeneous coupling cannot be distinguished from those caused by distributed delays, at least not by the naked eye. The here-derived analytical expression for the effective coupling between phases as a function of structural coupling constitutes a direct relationship between structural and functional connectivity. Structural connectivity constrains synchronizability that may be modified by the delay distribution. This explains why structural and functional connectivity bear much resemblance albeit not a one-to-one correspondence. We illustrate this in the context of resting-state activity, using the anatomical connectivity structure reported by Hagmann and others.     

Synchronization study in ring-like and grid-like neuronal networks

In this paper, we study the synchronization status of both two gap-junction coupled neurons and neuronal network with two different network connectivity patterns. One of the network connectivity patterns is a ring-like neuronal network, which only considers nearest-neighbor neurons. The other is a grid-like neuronal network, with all nearest neighbor couplings. We show that by varying some key parameters, such as the coupling strength and the external current injection, the neuronal network will exhibit various patterns of firing synchronization. Different types of firing synchronization are diagnosed by means of a mean field potential, a bifurcation diagram, a correlation coefficient and the ISI-distance method. Numerical simulations demonstrate that the synchronization status of multiple neurons is much dependent on the network patters, when the number of neurons is the same. It is also demonstrated that the synchronization status of two coupled neurons is similar with the grid-like neuronal network, but differs radically from that of the ring-like neuronal network. These results may be instructive in understanding synchronization transitions in neuronal systems.     

Switching Dynamics in an Interpersonal Competition Brings about “Deadlock” Synchronization of Players

In competitive sport game behavior, certain interpersonal patterns of movement coordination evolve even though each individual player only intends to exert their own strategy to win. To investigate this interpersonal pattern formation process, we asked pairs of naïve participants to engage in a play-tag game in which they had to remove a tag fastened to their partner''s hip. Relative phase analysis of the players'' step towards-away velocities indicated that anti-phase synchronization evolved across 10 repetitions of the game. We clarified evolution of this synchronization process using a dynamical model with an attractor (at relative phase) and a repeller (at relative phase) and discuss the self-organized nature of model and its ability to embody general solution for martial art interpersonal coordination.     

AVPR1A and SLC6A4 polymorphisms in choral singers and non-musicians: a gene association study

Amateur choral singing is a common pastime and worthy of study, possibly conferring benefits to health and social behaviour. Participants might be expected to possess musical ability and share some behavioural characteristics. Polymorphisms in genes concerned with serotonergic neurotransmission are associated with both behaviour and musical aptitude. Those investigated previously include the variable number tandem repeats RS1, RS3 and AVR in the AVPR1A (arginine vasopressin receptor 1a) gene and STin2 in the SLC6A4 (solute carrier family 6 [neurotransmitter transporter, serotonin], member 4) gene, as well as the SLC6A4 promoter region polymorphism, 5-HTTLPR. We conducted a genetic association study on 523 participants to establish whether alleles at these polymorphisms occur more commonly in choral singers than in those not regularly participating in organised musical activity (non-musicians). We also analysed tagging single nucleotide polymorphisms (SNPs) for AVPR1A and SLC6A4 to determine whether other variants in these genes were associated with singer/non-musician status. At the STin2 polymorphism, overall association with singer/non-musician status was evident at P = 0.006. The 9-repeat (P = 0.04) and 12-repeat (P = 0.04) alleles were more common in singers and the 10-repeat allele less so (P = 0.009). Odds ratios were 0.73 (95% CI 0.57-0.94) for the 10-repeat allele and 2.47 (95% CI 0.88-6.94) for the rarer 9-repeat allele. No overall association was detected at P<0.05 between any other polymorphism and singer/non-musician status. Our null findings with respect to RS3, RS1 and AVR, polymorphisms associated with musical ability by other authors, suggest that choir membership may depend partly on factors other than musical ability. In a related musical project involving one participating choir, a new 40-part unaccompanied choral work, "Allele", was composed and broadcast on national radio. In the piece, each singer's part incorporated their personal RS3 genotype.     

Diffusively coupled bursters: Effects of cell heterogeneity

The interaction of a pair of weakly coupled biological bursters is examined. Bursting refers to oscillations in which an observable slowly alternates between phases of relative quiescence and rapid oscillatory behavior. The motivation for this work is to understand the role of electrical coupling in promoting the synchronization of bursting electrical activity (BEA) observed in the β-cells of the islet of Langerhans, which secrete insulin in response to glucose. By studying the coupled fast subsystem of a model of BEA, we focus on the interaction that occurs during the rapid oscillatory phase. Coupling is weak, diffusive and non-scalar. In addition, non-identical oscillators are permitted. Using perturbation methods with the assumption that the uncoupled oscillators are near a Hopf bifurcation, a reduced system of equations is obtained. A detailed bifurcation study of this reduced system reveals a variety of patterns but suggests that asymmetrically phase-locked solutions are the most typical. Finally, the results are applied to the unreduced full bursting system and used to predict the burst pattern for a pair of cells with a given coupling strength and degree of heterogeneity. An erratum to this article is available at .     

Social status and cortisol levels in singing rock hyraxes

Many mammals use acoustic signals to communicate with conspecifics. Rock hyraxes (Procavia capensis) are social mammals whose vocal communication is usually restricted to quiet sounds used between nearby individuals. Loud repetitive warning trills are an exception. In our study site, a third of the adult male hyraxes also produces a rich, complex and loud vocalization we term 'singing'. In this study, we examine whether singers, which are more conspicuous by the act of singing, have higher cortisol (i.e. basal stress; C) levels than non-singers, and whether there is an association between social status and stress hormones in male hyraxes. We show that 'singing' males are different from the general adult male population in that their C levels are higher than those of silent males. Only in singers, C levels are associated with social rank, with dominants showing the highest levels. Singers are also on average older and more dominant than most other sexually mature non-singing males. Further, they copulate more than non-singers, suggesting that singing males may have higher reproductive success. Our results support the ‘stress of domination’ hypothesis and indicate that in the rock hyrax singing may reflect high competitive ability, designating singers as a distinct class of males, unique in their personal attributes and behavior.     

Stability of two cluster solutions in pulse coupled networks of neural oscillators

Phase response curves (PRCs) have been widely used to study synchronization in neural circuits comprised of pacemaking neurons. They describe how the timing of the next spike in a given spontaneously firing neuron is affected by the phase at which an input from another neuron is received. Here we study two reciprocally coupled clusters of pulse coupled oscillatory neurons. The neurons within each cluster are presumed to be identical and identically pulse coupled, but not necessarily identical to those in the other cluster. We investigate a two cluster solution in which all oscillators are synchronized within each cluster, but in which the two clusters are phase locked at nonzero phase with each other. Intuitively, one might expect this solution to be stable only when synchrony within each isolated cluster is stable, but this is not the case. We prove rigorously the stability of the two cluster solution and show how reciprocal coupling can stabilize synchrony within clusters that cannot synchronize in isolation. These stability results for the two cluster solution suggest a mechanism by which reciprocal coupling between brain regions can induce local synchronization via the network feedback loop.     

Temporal Aspects of Singing Interactions among Territorial Ovenbirds (Seiurus aurocapillus)

The temporal aspects of singing interactions among birds have received relatively little attention. To determine if the song delivery of one individual is affected by that of its territorial neighbor, I recorded singing interactions between territorial ovenbirds (Seiurus aurocapillus). Ovenbirds appeared to adopt one of two roles during singing interactions, Type I or Type II singers. Type II singers placed more of their songs immediately after the song of their neighbor than expected. The singing pattern of Type I singers could not be distinguished from a random pattern with respect to their neighbor's songs. In each observed pair of interacting birds, one individual was a Type I singer and one was a Type II singer. Although there was some intra-individual variation, most birds maintained the same role with each of their recorded territorial neighbors. Variation occurred between the two study sites in the extent that individuals overlapped the songs of their neighbors. Song overlap was common at one site, but occurred as, or less, often than expected at the other site.     

Diel patterns in singing activity of humpback whales in a winter breeding area in Okinawan (Ryukyuan) waters

Male humpback whales produce complex sounds known as songs during their breeding season. Previous studies have shown diel patterns of song in their breeding areas, but there had been no similar studies in the breeding area around Okinawa, Japan. To study diel patterns of song and the behavior of humpback whales in Okinawa, we conducted 24 hr recording with a fixed hydrophone in 2007, and vessel-based sighting surveys during 2014–2017. Song was monitored for 15 days, with peaks at sunrise and around 2200. Singing activity declined significantly between sunrise and sunset, then increased until 2200. Activity levels at night were higher and more stable than during the day. During 278 days of sighting surveys, 2,551 whales in 1,382 groups were observed. 79 individuals were confirmed as singers, all of which were lone whales. In six cases, singing individuals stopped singing before joining a group or began singing after leaving a group. Previous studies have shown that group size of humpback whales increases through the day. Considering the results from our study and the former studies, the decrease in singing activity as the day progresses may be a result of aggregation increasing, thus reducing the number of lone singers during the day.     

To write better,write better paragraphs

A case of musicogenic epilepsy is reported in which the seizures were precipitated by singing voices. It was found that some singers'' voices were particularly epileptogenic and that some of their songs, but not others, would precipitate a seizure. A study of the "offending" songs and singers did not reveal a common key, chord, harmonic interval, pitch or rhythm, and the emotional feeling or intensity of the music did not seem to be relevant. However, the voices that caused the seizures had a throaty, "metallic" quality. Such a singing voice results from incorrect positioning of the larynx such that it is not allowed to descend fully during singing; consequently, the vowel sounds produced must be manipulated by the lips or jaw to be distinguished. This trait is most common in singers with a low voice range who sing softly and use a microphone. It is not seen in trained operatic or musical theatre singers. The results of repeated testing showed that the seizures in this patient were caused by listening to singers who positioned the larynx incorrectly.     

电突触耦合神经元的相位同步及放电节律的转化

研究了两个参数失配较大情况下,处于不同放电模式的两个电突触耦合Hindmarsh-rose(HR)神经元的相位同步问题,发现在适当耦合强度下可以实现相同步并呈现出复杂的放电节律.利用峰峰间期(Interspikeinterval,ISI)和平均放电频率证实了相同步的发生,给出并分析了不同放电状态的神经元在电突触耦合下实现相同步后的神经放电节律.从相同步的角度显示,神经元同步后呈现簇放电特征或峰放电特征,除与两耦合神经元独自放电模式有关外,还与电突触耦合强度有一定的内在关系.     

Possible involvement of ATP-purinoceptor signalling in the intercellular synchronization of intracellular Ca2+ oscillation in cultured cardiac myocytes

Isolated and cultured neonatal cardiac myocytes contract spontaneously and cyclically. The contraction rhythms of two isolated cardiac myocytes, each of which beats at different frequencies at first, become synchronized after the establishment of mutual contacts, suggesting that mutual entrainment occurs due to electrical and/or mechanical interactions between two myocytes. The intracellular concentration of free Ca(2+) also changes rhythmically in association with the rhythmic contraction of myocytes (Ca(2+) oscillation), and such a Ca(2+) oscillation was also synchronized among cultured cardiac myocytes. In this study, we investigated whether intercellular communication other than via gap junctions was involved in the intercellular synchronization of intracellular Ca(2+) oscillation in spontaneously beating cultured cardiac myocytes. Treatment with either blockers of gap junction channels or an un-coupler of E-C coupling did not affect the intercellular synchronization of Ca(2+) oscillation. In contrast, treatment with a blocker of P2 purinoceptors resulted in the asynchronization of Ca(2+) oscillatory rhythms among cardiac myocytes. The present study suggested that the extracellular ATP-purinoceptor system was responsible for the intercellular synchronization of Ca(2+) oscillation among cardiac myocytes.     

Alteration of phase–phase coupling between theta and gamma rhythms in a depression-model of rats

Alterations in oscillatory brain activity are strongly correlated with cognitive performance in various physiological rhythms, especially the theta and gamma rhythms. In this study, we investigated the coupling relationship of neural activities between thalamus and medial prefrontal cortex (mPFC) by measuring the phase interactions between theta and gamma oscillations in a depression model of rats. The phase synchronization analysis showed that the phase locking at theta rhythm was weakened in depression. Furthermore, theta-gamma phase locking at n:m (1:6) ratio was found between thalamus and mPFC, while it was diminished in depression state. In addition, the analysis of coupling direction based on phase dynamics showed that the unidirectional influence from thalamus to mPFC was diminished in depression state only in theta rhythm, while it was partly recovered after the memantine treatment in a depression model of rats. The results suggest that the effects of depression on cognitive deficits are modulated via profound alterations in phase information transformation of theta rhythm and theta-gamma phase coupling.