Shaping bursting by electrical coupling and noise

Gap-junctional coupling is an important way of communication between neurons and other excitable cells. Strong electrical coupling synchronizes activity across cell ensembles. Surprisingly, in the presence of noise synchronous oscillations generated by an electrically coupled network may differ qualitatively from the oscillations produced by uncoupled individual cells forming the network. A prominent example of such behavior is the synchronized bursting in islets of Langerhans formed by pancreatic \beta-cells, which in isolation are known to exhibit irregular spiking. At the heart of this intriguing phenomenon lies denoising, a remarkable ability of electrical coupling to diminish the effects of noise acting on individual cells. In this paper, we derive quantitative estimates characterizing denoising in electrically coupled networks of conductance-based models of square wave bursting cells. Our analysis reveals the interplay of the intrinsic properties of the individual cells and network topology and their respective contributions to this important effect. In particular, we show that networks on graphs with large algebraic connectivity or small total effective resistance are better equipped for implementing denoising. As a by-product of the analysis of denoising, we analytically estimate the rate with which trajectories converge to the synchronization subspace and the stability of the latter to random perturbations. These estimates reveal the role of the network topology in synchronization. The analysis is complemented by numerical simulations of electrically coupled conductance-based networks. Taken together, these results explain the mechanisms underlying synchronization and denoising in an important class of biological models

Complex and Adaptive Dynamical Systems: A Primer

An thorough introduction is given at an introductory level to the field of quantitative complex system science, with special emphasis on emergence in dynamical systems based on network topologies. Subjects treated include graph theory and small-world networks, a generic introduction to the concepts of dynamical system theory, random Boolean networks, cellular automata and self-organized criticality, the statistical modeling of Darwinian evolution, synchronization phenomena and an introduction to the theory of cognitive systems. It inludes chapter on Graph Theory and Small-World Networks, Chaos, Bifurcations and Diffusion, Complexity and Information Theory, Random Boolean Networks, Cellular Automata and Self-Organized Criticality, Darwinian evolution, Hypercycles and Game Theory, Synchronization Phenomena and Elements of Cognitive System Theory.Comment: unformatted version of the textbook; published in Springer, Complexity Series (2008, second edition 2010

Synchronization Behavior in Coupled Chemical Oscillators

Synchronization is a collective phenomenon emerging from the interactions of different dynamical systems. Systems with different characteristics adjust their behavior to a common behavior of the group. This collective behavior is observed in many biological, chemical, and physical systems. Examples from different fields include pacemaker heart cells, synchronization of neurons during epilepsy seizures, arrays of microwave oscillators, and robot manipulators. Studies of coupled oscillators have revealed different mechanisms by which discrete oscillators interact and organize to a uniform synchronized state from an incoherent state. The discovery of a new type of synchronization state, called the chimera state has further broadened the field of synchronization. A chimera state is made up of coexisting subpopulations of oscillators, each with same coupling structure, but with one exhibiting synchronous behavior and the other asynchronous behavior. The phenomena has been the focus of much theoretical and experimental research in the past decade. In this thesis, experimental and simulation studies of chimera states in populations of coupled chemical oscillators will be described and their relation to other synchronization states will be characterized. Experiments were carried out with the photosensitive Belousov-Zhabotinsky (BZ) chemical oscillators and a light feedback scheme. The dimensionless two-variable Zhabotinsky-Buchholtz-Kiyatin-Epstein (ZBKE) model of the BZ chemical system was used in simulations.;A two-group coupling model, which splits the oscillators into two subpopulations, was used in the first part of the study. The subpopulations are globally coupled, both within and between the subpopulations. The coupling of every oscillator with members of the other subpopulation is weaker than the coupling with members of its own subpopulation. In-phase, out-of-phase, and phase-cluster synchronized states, as well as the chimera state, were found in both experiments and simulations. The probability of finding a chimera state decreases with increasing intra-group coupling strength. The study also revealed that heterogeneity in the frequencies of the oscillators in the system decreases the lifetime of a chimera. This was evidenced by the collapse of the chimera state to a synchronized state in both experiments and simulations with heterogeneous oscillators.;Synchronized and mixed-state behaviors are observed in populations of nonlocally coupled chemical oscillators in a ring configuration. With nonlocal coupling, the nearest neighbors are strongly coupled and the coupling strength decreases exponentially with distance. Experimental studies show stable chimera states, phase cluster states and phase waves coexisting with unsychronized groups of oscillators. These are spontaneously formed from quasi-random initial phase distributions in the experiments and random initial phase distributions in simulations. Simulations with homogeneous and heterogeneous oscillators revealed that a finite spread of frequencies increases the probability of initiating a synchronized group, leading to chimera states. The effects of group size and coupling strength on chimera states, phase waves, phase clusters, and traveling waves are discussed. Complex behaviors in coexisting states were analyzed, consisting of periodic phase slips with identical oscillators and periodic switching with nonidentical oscillators. Fourier transform analysis was used to distinguish between states exhibiting high periodicity and chimera states, which show similar average behavior

E-I balance emerges naturally from continuous Hebbian learning in autonomous neural networks.

Spontaneous brain activity is characterized in part by a balanced asynchronous chaotic state. Cortical recordings show that excitatory (E) and inhibitory (I) drivings in the E-I balanced state are substantially larger than the overall input. We show that such a state arises naturally in fully adapting networks which are deterministic, autonomously active and not subject to stochastic external or internal drivings. Temporary imbalances between excitatory and inhibitory inputs lead to large but short-lived activity bursts that stabilize irregular dynamics. We simulate autonomous networks of rate-encoding neurons for which all synaptic weights are plastic and subject to a Hebbian plasticity rule, the flux rule, that can be derived from the stationarity principle of statistical learning. Moreover, the average firing rate is regulated individually via a standard homeostatic adaption of the bias of each neuron's input-output non-linear function. Additionally, networks with and without short-term plasticity are considered. E-I balance may arise only when the mean excitatory and inhibitory weights are themselves balanced, modulo the overall activity level. We show that synaptic weight balance, which has been considered hitherto as given, naturally arises in autonomous neural networks when the here considered self-limiting Hebbian synaptic plasticity rule is continuously active

Persistent Cell-Autonomous Circadian Oscillations in Fibroblasts Revealed by Six-Week Single-Cell Imaging of PER2::LUC Bioluminescence

Biological oscillators naturally exhibit stochastic fluctuations in period and amplitude due to the random nature of molecular reactions. Accurately measuring the precision of noisy oscillators and the heterogeneity in period and strength of rhythmicity across a population of cells requires single-cell recordings of sufficient length to fully represent the variability of oscillations. We found persistent, independent circadian oscillations of clock gene expression in 6-week-long bioluminescence recordings of 80 primary fibroblast cells dissociated from PER2::LUC mice and kept in vitro for 6 months. Due to the stochastic nature of rhythmicity, the proportion of cells appearing rhythmic increases with the length of interval examined, with 100% of cells found to be rhythmic when using 3-week windows. Mean period and amplitude are remarkably stable throughout the 6-week recordings, with precision improving over time. For individual cells, precision of period and amplitude are correlated with cell size and rhythm amplitude, but not with period, and period exhibits much less cycle-to-cycle variability (CV 7.3%) than does amplitude (CV 37%). The time series are long enough to distinguish stochastic fluctuations within each cell from differences among cells, and we conclude that the cells do exhibit significant heterogeneity in period and strength of rhythmicity, which we measure using a novel statistical metric. Furthermore, stochastic modeling suggests that these single-cell clocks operate near a Hopf bifurcation, such that intrinsic noise enhances the oscillations by minimizing period variability and sustaining amplitude

Synchronization of spatiotemporal patterns and modeling disease spreading using excitable media

Studies of the photosensitive Belousov-Zhabotinsky (BZ) reaction are reviewed and the essential features of excitable media are described. The synchronization of two distributed Belousov-Zhabotinsky systems is experimentally and theoretically investigated. Symmetric local coupling of the systems is made possible with the use of a video camera-projector scheme. The spatial disorder of the coupled systems, with random initial configurations of spirals, gradually decreases until a final state is attained, which corresponds to a synchronized state with a single spiral in each system. The experimental observations are compared with numerical simulations of two identical Oregonator models with symmetric local coupling, and a systematic study reveals generalized synchronization of spiral waves. Modeling studies on disease spreading have been reviewed. The excitable medium of the photosensitive BZ reaction is used to model disease spreading, with static networks, dynamic networks, and a domain model. The spatiotemporal dynamics of disease spreading in these complex networks with diffusive and non-diffusive connections is characterized. The experimental and numerical studies reveal that disease spreading in these model systems is highly dependent on the non-diffusive connections

Synchronization in complex networks

Synchronization processes in populations of locally interacting elements are in the focus of intense research in physical, biological, chemical, technological and social systems. The many efforts devoted to understand synchronization phenomena in natural systems take now advantage of the recent theory of complex networks. In this review, we report the advances in the comprehension of synchronization phenomena when oscillating elements are constrained to interact in a complex network topology. We also overview the new emergent features coming out from the interplay between the structure and the function of the underlying pattern of connections. Extensive numerical work as well as analytical approaches to the problem are presented. Finally, we review several applications of synchronization in complex networks to different disciplines: biological systems and neuroscience, engineering and computer science, and economy and social sciences.Comment: Final version published in Physics Reports. More information available at http://synchronets.googlepages.com