Synchronizing a multicellular system by external input: an artificial control strategy

MOTIVATION: Although there are significant advances on elucidating the collective behaviors on biological organisms in recent years, the essential mechanisms by which the collective rhythms arise remain to be fully understood, and further how to synchronize multicellular networks by artificial control strategy has not yet been well explored. RESULTS: A control strategy is developed to synchronize gene regulatory networks in a multicellular system when spontaneous synchronization cannot be achieved. We first construct an impulsive control system to model the process of periodically injecting coupling substances with constant or random impulsive control amounts into the common extracellular medium, and further study its effects on the dynamics of individual cells. We derive the threshold of synchronization induced by the periodic substance input. Therefore, we can synchronize the multicellular network to a specific collective behavior by changing the frequency and amplitude of the periodic stimuli. Moreover, a two-stage scheme is proposed to facilitate the synchronization in this paper. We show that the presence of the external input may also initiate different dynamics. The multicellular network of coupled repressilators is used to show the effectiveness of the proposed method. The results not only provide a perspective to understand the interactions between external stimuli and intrinsic physiological rhythms, but also may lead to development of realistic artificial control strategy and medical therapy. AVAILABILITY: CONTACT: aihara@sat.t.u-tokyo.ac.jp.     

Intercellular calcium signalling in cultured renal epithelia: a theoretical study of synchronization mode and pacemaker activity

We investigate a two-dimensional lattice model representation of intercellular Ca²⁺ signalling in a population of epithelial cells coupled by gap junctions. The model is based on and compared with Ca²⁺ imaging data from globally bradykinin-stimulated MDCK-I (Madin-Darby canine kidney)-I cell layers. We study large-scale synchronization of relevance to our laboratory experiments. The system is found to express a wealth of dynamics, including quasiperiodic, chaotic and multiply-periodic behaviour for intermediate couplings. We take a particular interest in understanding the role of pacemaker cells in the synchronization process. It has been hypothesized that a few highly hormone-sensitive cells control the collective frequency of oscillation, which is close to the natural frequencies (without coupling) of these cells. The model behaviour is consistent with the conjectures of the pacemaker cell hypothesis near the critical coupling where the cells lock onto a single frequency. However, the simulations predict that the frequency in globally connected systems decreases with increasing coupling. It is found that a pacemaker is not defined by its natural frequency alone, but that other intrinsic or local factors must be considered. Inclusion of partly sensitized cells that do not oscillate autonomously in the cell layer increases the coupling necessary for global synchronization. For not excessively high coupling, these cells oscillate irregularly and with distinctive lower frequencies. In summary, the present study shows that the frequency of synchronized oscillations is not dictated by one or few fast-responding cells. The collective frequency is the result of a two-way communication between the phase-advanced pacemaker and its environment.     

Spontaneous synchronization of coupled circadian oscillators

In mammals, the circadian pacemaker, which controls daily rhythms, is located in the suprachiasmatic nucleus (SCN). Circadian oscillations are generated in individual SCN neurons by a molecular regulatory network. Cells oscillate with periods ranging from 20 to 28 h, but at the tissue level, SCN neurons display significant synchrony, suggesting a robust intercellular coupling in which neurotransmitters are assumed to play a crucial role. We present a dynamical model for the coupling of a population of circadian oscillators in the SCN. The cellular oscillator, a three-variable model, describes the core negative feedback loop of the circadian clock. The coupling mechanism is incorporated through the global level of neurotransmitter concentration. Global coupling is efficient to synchronize a population of 10,000 cells. Synchronized cells can be entrained by a 24-h light-dark cycle. Simulations of the interaction between two populations representing two regions of the SCN show that the driven population can be phase-leading. Experimentally testable predictions are: 1), phases of individual cells are governed by their intrinsic periods; and 2), efficient synchronization is achieved when the average neurotransmitter concentration would dampen individual oscillators. However, due to the global neurotransmitter oscillation, cells are effectively synchronized.     

Cardiac and respiratory patterns synchronize between persons during choir singing

Dyadic and collective activities requiring temporally coordinated action are likely to be associated with cardiac and respiratory patterns that synchronize within and between people. However, the extent and functional significance of cardiac and respiratory between-person couplings have not been investigated thus far. Here, we report interpersonal oscillatory couplings among eleven singers and one conductor engaged in choir singing. We find that: (a) phase synchronization both in respiration and heart rate variability increase significantly during singing relative to a rest condition; (b) phase synchronization is higher when singing in unison than when singing pieces with multiple voice parts; (c) directed coupling measures are consistent with the presence of causal effects of the conductor on the singers at high modulation frequencies; (d) the different voices of the choir are reflected in network analyses of cardiac and respiratory activity based on graph theory. Our results suggest that oscillatory coupling of cardiac and respiratory patterns provide a physiological basis for interpersonal action coordination.     

Role of the endothelium on arterial vasomotion

It is well-known that cyclic variations of the vascular diameter, a phenomenon called vasomotion, are induced by synchronous calcium oscillations of smooth muscle cells (SMCs). However, the role of the endothelium on vasomotion is unclear. Some experimental studies claim that the endothelium is necessary for synchronization and vasomotion, whereas others report rhythmic contractions in the absence of an intact endothelium. Moreover, endothelium-derived factors have been shown to abolish vasomotion by desynchronizing the calcium signals in SMCs. By modeling the calcium dynamics of a population of SMCs coupled to a population of endothelial cells, we analyze the effects of an SMC vasoconstrictor stimulation on endothelial cells and the feedback of endothelium-derived factors. Our results show that the endothelium essentially decreases the SMCs calcium level and may move the SMCs from a steady state to an oscillatory domain, and vice versa. In the oscillatory domain, a population of coupled SMCs exhibits synchronous calcium oscillations. Outside the oscillatory domain, the coupled SMCs present only irregular calcium flashings arising from noise modeling stochastic opening of channels. Our findings provide explanations for the published contradictory experimental observations.     

Noise-Induced Coherence in Multicellular Circadian Clocks

In higher organisms, circadian rhythms are generated by a multicellular genetic clock that is entrained very efficiently to the 24-h light-dark cycle. Most studies done so far of these circadian oscillators have considered a perfectly periodic driving by light, in the form of either a square wave or a sinusoidal modulation. However, in natural conditions, organisms are subject to nonnegligible fluctuations in the light level all through the daily cycle. In this article, we investigate how the interplay between light fluctuations and intercellular coupling affects the dynamics of the collective rhythm in a large ensemble of nonidentical, globally coupled cellular clocks modeled as Goodwin oscillators. On the basis of experimental considerations, we assume an inverse dependence of the cell-cell coupling strength on the light intensity, in such a way that the larger the light intensity, the weaker the coupling. Our results show a noise-induced rhythm generation for constant light intensities at which the clock is arrhythmic in the noise-free case. Importantly, the rhythm shows a resonancelike phenomenon as a function of the noise intensity. Such improved coherence can be only observed at the level of the overt rhythm and not at the level of the individual oscillators, thus suggesting a cooperative effect of noise, coupling, and the emerging synchronization between the oscillators.     

Multiple factors influence calcium synchronization in arterial vasomotion

The intercellular synchronization of spontaneous calcium (Ca(2+)) oscillations in individual smooth muscle cells is a prerequisite for vasomotion. A detailed mathematical model of Ca(2+) dynamics in rat mesenteric arteries shows that a number of synchronizing and desynchronizing pathways may be involved. In particular, Ca(2+)-dependent phospholipase C, the intercellular diffusion of inositol trisphosphate (IP(3), and to a lesser extent Ca(2+)), IP(3) receptors, diacylglycerol-activated nonselective cation channels, and Ca(2+)-activated chloride channels can contribute to synchronization, whereas large-conductance Ca(2+)-activated potassium channels have a desynchronizing effect. Depending on the contractile state and agonist concentrations, different pathways become predominant, and can be revealed by carefully inhibiting the oscillatory component of their total activity. The phase shift between the Ca(2+) and membrane potential oscillations can change, and thus electrical coupling through gap junctions can mediate either synchronization or desynchronization. The effect of the endothelium is highly variable because it can simultaneously enhance the intercellular coupling and affect multiple smooth muscle cell components. Here, we outline a system of increased complexity and propose potential synchronization mechanisms that need to be experimentally tested.     

Paradoxical phase response of gamma rhythms facilitates their entrainment in heterogeneous networks

The synchronization of different γ-rhythms arising in different brain areas has been implicated in various cognitive functions. Here, we focus on the effect of the ubiquitous neuronal heterogeneity on the synchronization of ING (interneuronal network gamma) and PING (pyramidal-interneuronal network gamma) rhythms. The synchronization properties of rhythms depends on the response of their collective phase to external input. We therefore determine the macroscopic phase-response curve for finite-amplitude perturbations (fmPRC) of ING- and PING-rhythms in all-to-all coupled networks comprised of linear (IF) or quadratic (QIF) integrate-and-fire neurons. For the QIF networks we complement the direct simulations with the adjoint method to determine the infinitesimal macroscopic PRC (imPRC) within the exact mean-field theory. We show that the intrinsic neuronal heterogeneity can qualitatively modify the fmPRC and the imPRC. Both PRCs can be biphasic and change sign (type II), even though the phase-response curve for the individual neurons is strictly non-negative (type I). Thus, for ING rhythms, say, external inhibition to the inhibitory cells can, in fact, advance the collective oscillation of the network, even though the same inhibition would lead to a delay when applied to uncoupled neurons. This paradoxical advance arises when the external inhibition modifies the internal dynamics of the network by reducing the number of spikes of inhibitory neurons; the advance resulting from this disinhibition outweighs the immediate delay caused by the external inhibition. These results explain how intrinsic heterogeneity allows ING- and PING-rhythms to become synchronized with a periodic forcing or another rhythm for a wider range in the mismatch of their frequencies. Our results identify a potential function of neuronal heterogeneity in the synchronization of coupled γ-rhythms, which may play a role in neural information transfer via communication through coherence.     

Synchronization in a model of two inferior olive cells with variable electrotonic coupling

Synchronization was assessed in a model describing the dynamics of two inferior olive cells coupled electrotonically via gap junctions and surrounded with inhibitory synaptic terminals (modeled from first-order kinetics) that can block this coupling. Depending on the parameters, the system gives rise to various synchronization regimes: 1:1, 1:2, spike “time binding” etc. Even small changes of coupling parameters (coupling strength and decoupling delay) can quite significantly affect the regimes of synchronization between interacting neurons. In some cases, because of collective dynamics the activity of one cell is suppressed while the other cell remains active.     

Collective Cell Movement Promotes Synchronization of Coupled Genetic Oscillators

Collective cell movement is a crucial component of embryonic development. Intercellular interactions regulate collective cell movement by allowing cells to transfer information. A key question is how collective cell movement itself influences information flow produced in tissues by intercellular interactions. Here, we study the effect of collective cell movement on the synchronization of locally coupled genetic oscillators. This study is motivated by the segmentation clock in zebrafish somitogenesis, where short-range correlated movement of cells has been observed. We describe the segmentation clock tissue by a Voronoi diagram, cell movement by the force balance of self-propelled and repulsive forces between cells, the dynamics of the direction of self-propelled motion, and the synchronization of genetic oscillators by locally coupled phase oscillators. We find that movement with a correlation length of about 2 ∼ 3 cell diameters is optimal for the synchronization of coupled oscillators. Quantification of cell mixing reveals that this short-range correlation of cell movement allows cells to exchange neighbors most efficiently. Moreover, short-range correlated movement strongly destabilizes nonuniform spatial phase patterns, further promoting global synchronization. Our theoretical results suggest that collective cell movement may enhance the synchronization of the segmentation clock in zebrafish somitogenesis. More generally, collective cell movement may promote information flow in tissues by enhancing cell mixing and destabilizing spurious patterns.     

Collective Cell Movement Promotes Synchronization of Coupled Genetic Oscillators

Collective cell movement is a crucial component of embryonic development. Intercellular interactions regulate collective cell movement by allowing cells to transfer information. A key question is how collective cell movement itself influences information flow produced in tissues by intercellular interactions. Here, we study the effect of collective cell movement on the synchronization of locally coupled genetic oscillators. This study is motivated by the segmentation clock in zebrafish somitogenesis, where short-range correlated movement of cells has been observed. We describe the segmentation clock tissue by a Voronoi diagram, cell movement by the force balance of self-propelled and repulsive forces between cells, the dynamics of the direction of self-propelled motion, and the synchronization of genetic oscillators by locally coupled phase oscillators. We find that movement with a correlation length of about 2 ∼ 3 cell diameters is optimal for the synchronization of coupled oscillators. Quantification of cell mixing reveals that this short-range correlation of cell movement allows cells to exchange neighbors most efficiently. Moreover, short-range correlated movement strongly destabilizes nonuniform spatial phase patterns, further promoting global synchronization. Our theoretical results suggest that collective cell movement may enhance the synchronization of the segmentation clock in zebrafish somitogenesis. More generally, collective cell movement may promote information flow in tissues by enhancing cell mixing and destabilizing spurious patterns.     

A Model for Cross-Cultural Reciprocal Interactions through Mass Media

We investigate the problem of cross-cultural interactions through mass media in a model where two populations of social agents, each with its own internal dynamics, get information about each other through reciprocal global interactions. As the agent dynamics, we employ Axelrod''s model for social influence. The global interaction fields correspond to the statistical mode of the states of the agents and represent mass media messages on the cultural trend originating in each population. Several phases are found in the collective behavior of either population depending on parameter values: two homogeneous phases, one having the state of the global field acting on that population, and the other consisting of a state different from that reached by the applied global field; and a disordered phase. In addition, the system displays nontrivial effects: (i) the emergence of a largest minority group of appreciable size sharing a state different from that of the applied global field; (ii) the appearance of localized ordered states for some values of parameters when the entire system is observed, consisting of one population in a homogeneous state and the other in a disordered state. This last situation can be considered as a social analogue to a chimera state arising in globally coupled populations of oscillators.     

Coupling-induced synchronization in multicellular circadian oscillators of mammals

In mammals, circadian rhythms are controlled by the neurons located in the suprachiasmatic nucleus (SCN) of the hypothalamus. Each neuron in the SCN contains an autonomous molecular clock. The fundamental question is how the individual cellular oscillators, expressing a wide range of periods, interact and assemble to achieve phase synchronization. Most of the studies carried out so far emphasize the crucial role of the periodicity imposed by the light-dark cycle in neuronal synchronization. However, in natural conditions, the interaction between the SCN neurons is non-negligible and coupling between cells in the SCN is achieved partly by neurotransmitters. In this paper, we use a model of nonidentical, globally coupled cellular clocks considered as Goodwin oscillators. We mainly study the synchronization induced by coupling from an analytical way. Our results show that the role of the coupling is to enhance the synchronization to the external forcing. The conclusion of this paper can help us better understand the mechanism of circadian rhythm.     

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.     

Experimental Study of the Irrational Phase Synchronization of Coupled Nonidentical Mechanical Metronomes

It has recently been observed in numerical simulations that the phases of two coupled nonlinear oscillators can become locked into an irrational ratio, exhibiting the phenomenon of irrational phase synchronization (IPS) [Phys. Rev. E 69, 056228 (2004)]. Here, using two coupled nonidentical periodic mechanical metronomes, we revisit this interesting phenomenon through experimental studies. It is demonstrated that under suitable couplings, the phases of the metronomes indeed can become locked into irrational ratios. Numerical simulations confirm the experimental observations and also reveal that in the IPS state, the system dynamics are chaotic. Our studies provide a solid step toward further studies of IPS.     

Gβ Regulates Coupling between Actin Oscillators for Cell Polarity and Directional Migration

For directional movement, eukaryotic cells depend on the proper organization of their actin cytoskeleton. This engine of motility is made up of highly dynamic nonequilibrium actin structures such as flashes, oscillations, and traveling waves. In Dictyostelium, oscillatory actin foci interact with signals such as Ras and phosphatidylinositol 3,4,5-trisphosphate (PIP₃) to form protrusions. However, how signaling cues tame actin dynamics to produce a pseudopod and guide cellular motility is a critical open question in eukaryotic chemotaxis. Here, we demonstrate that the strength of coupling between individual actin oscillators controls cell polarization and directional movement. We implement an inducible sequestration system to inactivate the heterotrimeric G protein subunit Gβ and find that this acute perturbation triggers persistent, high-amplitude cortical oscillations of F-actin. Actin oscillators that are normally weakly coupled to one another in wild-type cells become strongly synchronized following acute inactivation of Gβ. This global coupling impairs sensing of internal cues during spontaneous polarization and sensing of external cues during directional motility. A simple mathematical model of coupled actin oscillators reveals the importance of appropriate coupling strength for chemotaxis: moderate coupling can increase sensitivity to noisy inputs. Taken together, our data suggest that Gβ regulates the strength of coupling between actin oscillators for efficient polarity and directional migration. As these observations are only possible following acute inhibition of Gβ and are masked by slow compensation in genetic knockouts, our work also shows that acute loss-of-function approaches can complement and extend the reach of classical genetics in Dictyostelium and likely other systems as well.