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.     

Modulation of synchrony without changes in firing rates

It was often reported and suggested that the synchronization of spikes can occur without changes in the firing rate. However, few theoretical studies have tested its mechanistic validity. In the present study, we investigate whether changes in synaptic weights can induce an independent modulation of synchrony while the firing rate remains constant. We study this question at the level of both single neurons and neuronal populations using network simulations of conductance based integrate-and-fire neurons. The network consists of a single layer that includes local excitatory and inhibitory recurrent connections, as well as long-range excitatory projections targeting both classes of neurons. Each neuron in the network receives external input consisting of uncorrelated Poisson spike trains. We find that increasing this external input leads to a linear increase of activity in the network, as well␣as an increase in the peak frequency of oscillation. In␣contrast, balanced changes of the synaptic weight of␣excitatory long-range projections for both classes of postsynaptic neurons modulate the degree of synchronization without altering the firing rate. These results demonstrate that, in a simple network, synchronization and firing rate can be modulated independently, and thus, may be used as independent coding dimensions. Electronic supplementary material  The online version of this article (doi: ) contains supplementary material, which is available to authorized users.     

Robust synchronization analysis in nonlinear stochastic cellular networks with time-varying delays, intracellular perturbations and intercellular noise

Naturally, a cellular network consisted of a large amount of interacting cells is complex. These cells have to be synchronized in order to emerge their phenomena for some biological purposes. However, the inherently stochastic intra and intercellular interactions are noisy and delayed from biochemical processes. In this study, a robust synchronization scheme is proposed for a nonlinear stochastic time-delay coupled cellular network (TdCCN) in spite of the time-varying process delay and intracellular parameter perturbations. Furthermore, a nonlinear stochastic noise filtering ability is also investigated for this synchronized TdCCN against stochastic intercellular and environmental disturbances. Since it is very difficult to solve a robust synchronization problem with the Hamilton-Jacobi inequality (HJI) matrix, a linear matrix inequality (LMI) is employed to solve this problem via the help of a global linearization method. Through this robust synchronization analysis, we can gain a more systemic insight into not only the robust synchronizability but also the noise filtering ability of TdCCN under time-varying process delays, intracellular perturbations and intercellular disturbances. The measures of robustness and noise filtering ability of a synchronized TdCCN have potential application to the designs of neuron transmitters, on-time mass production of biochemical molecules, and synthetic biology. Finally, a benchmark of robust synchronization design in Escherichia coli repressilators is given to confirm the effectiveness of the proposed methods.     

Maintaining synchronization by decentralized feedback control in time delay neural networks with parameter uncertainties

A decentralized feedback control scheme is proposed to synchronize linearly coupled identical neural networks with time-varying delay and parameter uncertainties. Sufficient condition for synchronization is developed by carefully investigating the uncertain nonlinear synchronization error dynamics in this article. A procedure for designing a decentralized synchronization controller is proposed using linear matrix inequality (LMI) technique. The designed controller can drive the synchronization error to zero and overcome disruption caused by system uncertainty and external disturbance.     

Nonlinear dynamics and information processing in pacemaker neurons

The paper treats some nonlinear dynamic phenomena in oscillatory activity of a single nerve cell. Based on experiments with CNS bursting pacemaker neurons ofHelix pomatia snail, a mathematical model was studied. The model demonstrates the majority of experimentally observable phenomena and allows one to investigate the role of its separate components. The phenomena demonstrated by model neuron (chaotic behavior, bistability, and sensitivity to parameter variations, initial conditions, and stimuli) may be relevant to information processing in nerve cells. The complexity of [Ca²⁺] _in −V phase diagrams of initial conditions depends on parameters. Transient synaptic impulse produces stable parameter-independent changes in activity of model neuron. These results indicate that a single bursting neuron can work in the neuronal ensemble as a dynamic switch. The sensitivity of this switch is regulated by a neurotransmitter.     

Network effects of glutamate on neuronal activity in the medial septum/diagonal band complex in vitro

Inter-neuronal interactions within the medial septum/diagonal band complex (MSDB) are of great interest as this region is believed to be the hippocampal theta rhythm pacemaker. However, the role of glutamatergic system in functioning of the septal cells is yet unclear. Here, we demonstrate for the first time the effects of glutamate in physiological concentration (1 microM) on the MSDB neuronal spontaneous and evoked activities in vitro. These effects (activation of 70% and inhibition of 30% of responsive neurons) differed in pacemaker and non-pacemaker cells. Pacemaker cells were always activated under glutamate, whereas non-pacemaker neurons could be either activated or inhibited. Indeed, in the burst pacemakers, glutamate increased the frequency of rhythmic activity. In a total MSDB neuron population, in 30% of neurons glutamate applications modified responses to the electrical stimulation by unifying the temporal parameters of neuron responses. Along with the increase in the theta-burst frequency, this indicates that the glutamatergic system is involved in the process ofintraseptal synchronization. Obtained data shed light on the role ofglutamatergic system in septal neuron interactions and broaden our understanding of theta oscillation mechanisms in the septo-hippocampal system.     

Phase locking induces scale-free topologies in networks of coupled oscillators

An initial unsynchronized ensemble of networking phase oscillators is further subjected to a growing process where a set of forcing oscillators, each one of them following the dynamics of a frequency pacemaker, are added to the pristine graph. Linking rules based on dynamical criteria are followed in the attachment process to force phase locking of the network with the external pacemaker. We show that the eventual locking occurs in correspondence to the arousal of a scale-free degree distribution in the original graph.     

Role of potassium lateral diffusion in non-synaptic epilepsy: a computational study

An increase of extracellular potassium ion concentration can result in neuronal hyperexcitability, and thus contribute to non-synaptic epileptiform activity. It has been shown that potassium lateral diffusion alone is sufficient for synchronization in the low-calcium epilepsy in-vitro model. However, it is not yet known whether the lateral diffusion can, by itself, induce seizure activity. We hypothesize that spontaneous sustained neuronal activity can be generated by potassium coupling between neurons. To test this hypothesis, neuronal simulations with 2-cell or 4-cell models were used. Each model neuron was embedded in a bath of K+ and surrounded by interstitial space. Interstitial potassium concentration was regulated by both K+-pump and glial buffer mechanisms. Simulations performed with two coupled neurons with parameter values within physiological range show that, without chemical and electrical synapses, potassium lateral diffusion alone can generate and synchronize zero-Ca2+ non-synaptic epileptiform activity. Simulations performed with a network of four zero-Ca2+ CA1 pyramidal neurons modeled in zero-calcium conditions also show that spontaneous sustained activity can propagate by potassium lateral diffusion alone with a velocity of approximately 0.93 mm/sec. This diffusion model used for the simulations is based on physiological parameters, is robust for various kinetics, and is able to reproduce both the spontaneous triplet bursting of non-synaptic activity and speed of propagation in low-Ca2+ non-synaptic epilepsy experiments. These simulations suggest that potassium lateral diffusion can play an important role in the synchronization and generation on non-synaptic epilepsy.     

Washout filter aided mean field feedback desynchronization in an ensemble of globally coupled neural oscillators

We propose an approach for desynchronization in an ensemble of globally coupled neural oscillators. The impact of washout filter aided mean field feedback on population synchronization process is investigated. By blocking the Hopf bifurcation of the mean field, the controller desynchronizes the ensemble. The technique is generally demand-controlled. It is robust and can be easily implemented practically. We suggest it for effective deep brain stimulation in neurological diseases characterized by pathological synchronization.     

Computational approaches to neuronal network analysis

Computational modelling is an approach to neuronal network analysis that can complement experimental approaches. Construction of useful neuron and network models is often complicated by a variety of factors and unknowns, most notably the considerable variability of cellular and synaptic properties and electrical activity characteristics found even in relatively ‘simple’ networks of identifiable neurons. This chapter discusses the consequences of biological variability for network modelling and analysis, describes a way to embrace variability through ensemble modelling and summarizes recent findings obtained experimentally and through ensemble modelling.     

Oscillations and synchrony in a cortical neural network

In this paper, the oscillations and synchronization status of two different network connectivity patterns based on Izhikevich model are studied. One of the connectivity patterns is a randomly connected neuronal network, the other one is a small-world neuronal network. This Izhikevich model is a simple model which can not only reproduce the rich behaviors of biological neurons but also has only two equations and one nonlinear term. Detailed investigations reveal that by varying some key parameters, such as the connection weights of neurons, the external current injection, the noise of intensity and the neuron number, this neuronal network will exhibit various collective behaviors in randomly coupled neuronal network. In addition, we show that by changing the number of nearest neighbor and connection probability in small-world topology can also affect the collective dynamics of neuronal activity. These results may be instructive in understanding the collective dynamics of mammalian cortex.     

Potential Mechanisms for Imperfect Synchronization in Parkinsonian Basal Ganglia

Neural activity in the brain of parkinsonian patients is characterized by the intermittently synchronized oscillatory dynamics. This imperfect synchronization, observed in the beta frequency band, is believed to be related to the hypokinetic motor symptoms of the disorder. Our study explores potential mechanisms behind this intermittent synchrony. We study the response of a bursting pallidal neuron to different patterns of synaptic input from subthalamic nucleus (STN) neuron. We show how external globus pallidus (GPe) neuron is sensitive to the phase of the input from the STN cell and can exhibit intermittent phase-locking with the input in the beta band. The temporal properties of this intermittent phase-locking show similarities to the intermittent synchronization observed in experiments. We also study the synchronization of GPe cells to synaptic input from the STN cell with dependence on the dopamine-modulated parameters. Earlier studies showed how the strengthening of dopamine-modulated coupling may lead to transitions from non-synchronized to partially synchronized dynamics, typical in Parkinson''s disease. However, dopamine also affects the cellular properties of neurons. We show how the changes in firing patterns of STN neuron due to the lack of dopamine may lead to transition from a lower to a higher coherent state, roughly matching the synchrony levels observed in basal ganglia in normal and parkinsonian states. The intermittent nature of the neural beta band synchrony in Parkinson''s disease is achieved in the model due to the interplay of the timing of STN input to pallidum and pallidal neuronal dynamics, resulting in sensitivity of pallidal output to the phase of the arriving STN input. Thus the mechanism considered here (the change in firing pattern of subthalamic neurons through the dopamine-induced change of membrane properties) may be one of the potential mechanisms responsible for the generation of the intermittent synchronization observed in Parkinson''s disease.     

A persistent cellular change in a single modulatory neuron contributes to associative long-term memory

Most neuronal models of learning assume that changes in synaptic strength are the main mechanism underlying long-term memory (LTM) formation. However, we show here that a persistent depolarization of membrane potential, a type of cellular change that increases neuronal responsiveness, contributes significantly to a long-lasting associative memory trace. The use of a model invertebrate network with identified neurons and known synaptic connectivity had the advantage that the contribution of this cellular change to memory could be evaluated in a neuron with a known function in the learning circuit. Specifically, we used the well-understood motor circuit underlying molluscan feeding and showed that a key modulatory neuron involved in the initiation of feeding ingestive movements underwent a long-term depolarization following behavioral associative conditioning. This depolarization led to an enhanced single cell and network responsiveness to a previously neutral tactile conditioned stimulus, and the persistence of both matched the time course of behavioral associative memory. The change in the membrane potential of a key modulatory neuron is both sufficient and necessary to initiate a conditioned response in a reduced preparation and underscores its importance for associative LTM.     

Dynamical features of higher-order correlation events: impact on cortical cells

Cortical neurons receive signals from thousands of other neurons. The statistical properties of the input spike trains substantially shape the output response properties of each neuron. Experimental and theoretical investigations have mostly focused on the second order statistical features of the input spike trains (mean firing rates and pairwise correlations). Little is known of how higher order correlations affect the integration and firing behavior of a cell independently of the second order statistics. To address this issue, we simulated the dynamics of a population of 5000 neurons, controlling both their second order and higher-order correlation properties to reflect physiological data. We then used these ensemble dynamics as the input stage to morphologically reconstructed cortical cells (layer 5 pyramidal, layer 4 spiny stellate cell), and to an integrate and fire neuron. Our results show that changes done solely to the higher-order correlation properties of the network’s dynamics significantly affect the response properties of a target neuron, both in terms of output rate and spike timing. Moreover, the neuronal morphology and voltage dependent mechanisms of the target neuron considerably modulate the quantitative aspects of these effects. Finally, we show how these results affect sparseness of neuronal representations, tuning properties, and feature selectivity of cortical cells. An erratum to this article can be found at     

Structure Identification of Uncertain Complex Networks Based on Anticipatory Projective Synchronization

This paper investigates a method to identify uncertain system parameters and unknown topological structure in general complex networks with or without time delay. A complex network, which has uncertain topology and unknown parameters, is designed as a drive network, and a known response complex network with an input controller is designed to identify the drive network. Under the proposed input controller, the drive network and the response network can achieve anticipatory projective synchronization when the system is steady. Lyapunov theorem and Barbǎlat’s lemma guarantee the stability of synchronization manifold between two networks. When the synchronization is achieved, the system parameters and topology in response network can be changed to equal with the parameters and topology in drive network. A numerical example is given to show the effectiveness of the proposed method.     

Optimal Information Transfer in the Cortex through Synchronization

In recent experimental work it has been shown that neuronal interactions are modulated by neuronal synchronization and that this modulation depends on phase shifts in neuronal oscillations. This result suggests that connections in a network can be shaped through synchronization. Here, we test and expand this hypothesis using a model network. We use transfer entropy, an information theoretical measure, to quantify the exchanged information. We show that transferred information depends on the phase relation of the signal, that the amount of exchanged information increases as a function of oscillations in the signal and that the speed of the information transfer increases as a function of synchronization. This implies that synchronization makes information transport more efficient. In summary, our results reinforce the hypothesis that synchronization modulates neuronal interactions and provide further evidence that gamma band synchronization has behavioral relevance.     

神经元簇的层次性联合编码假设

提出一个新的神经信息编码假设,称为神经元簇的层次性联合编码假设。它不同于祖母细胞假设和Hebb经典细胞群编码模型,但融合了它们的优点,因而可以解释更多的神经生物学实验。     

Fast calcium wave propagation mediated by electrically conducted excitation and boosted by CICR

We have investigated synchronization and propagation of calcium oscillations, mediated by gap junctional excitation transmission. For that purpose we used an experimentally based model of normal rat kidney (NRK) cells, electrically coupled in a one-dimensional configuration (linear strand). Fibroblasts such as NRK cells can form an excitable syncytium and generate spontaneous inositol 1,4,5-trisphosphate (IP(3))-mediated intracellular calcium waves, which may spread over a monolayer culture in a coordinated fashion. An intracellular calcium oscillation in a pacemaker cell causes a membrane depolarization from within that cell via calcium-activated chloride channels, leading to an L-type calcium channel-based action potential (AP) in that cell. This AP is then transmitted to the electrically connected neighbor cell, and the calcium inflow during that transmitted AP triggers a calcium wave in that neighbor cell by opening of IP(3) receptor channels, causing calcium-induced calcium release (CICR). In this way the calcium wave of the pacemaker cell is rapidly propagated by the electrically transmitted AP. Propagation of APs in a strand of cells depends on the number of terminal pacemaker cells, the L-type calcium conductance of the cells, and the electrical coupling between the cells. Our results show that the coupling between IP(3)-mediated calcium oscillations and AP firing provides a robust mechanism for fast propagation of activity across a network of cells, which is representative for many other cell types such as gastrointestinal cells, urethral cells, and pacemaker cells in the heart.     

Weak electric fields detectability in a noisy neural network

We investigate the detectability of weak electric field in a noisy neural network based on Izhikevich neuron model systematically. The neural network is composed of excitatory and inhibitory neurons with similar ratio as that in the mammalian neocortex, and the axonal conduction delays between neurons are also considered. It is found that the noise intensity can modulate the detectability of weak electric field. Stochastic resonance (SR) phenomenon induced by white noise is observed when the weak electric field is added to the network. It is interesting that SR almost disappeared when the connections between neurons are cancelled, suggesting the amplification effects of the neural coupling on the synchronization of neuronal spiking. Furthermore, the network parameters, such as the connection probability, the synaptic coupling strength, the scale of neuron population and the neuron heterogeneity, can also affect the detectability of the weak electric field. Finally, the model sensitivity is studied in detail, and results show that the neural network model has an optimal region for the detectability of weak electric field signal.     

Stochastic models of neuronal dynamics

Cortical activity is the product of interactions among neuronal populations. Macroscopic electrophysiological phenomena are generated by these interactions. In principle, the mechanisms of these interactions afford constraints on biologically plausible models of electrophysiological responses. In other words, the macroscopic features of cortical activity can be modelled in terms of the microscopic behaviour of neurons. An evoked response potential (ERP) is the mean electrical potential measured from an electrode on the scalp, in response to some event. The purpose of this paper is to outline a population density approach to modelling ERPs.We propose a biologically plausible model of neuronal activity that enables the estimation of physiologically meaningful parameters from electrophysiological data. The model encompasses four basic characteristics of neuronal activity and organization: (i) neurons are dynamic units, (ii) driven by stochastic forces, (iii) organized into populations with similar biophysical properties and response characteristics and (iv) multiple populations interact to form functional networks. This leads to a formulation of population dynamics in terms of the Fokker-Planck equation. The solution of this equation is the temporal evolution of a probability density over state-space, representing the distribution of an ensemble of trajectories. Each trajectory corresponds to the changing state of a neuron. Measurements can be modelled by taking expectations over this density, e.g. mean membrane potential, firing rate or energy consumption per neuron. The key motivation behind our approach is that ERPs represent an average response over many neurons. This means it is sufficient to model the probability density over neurons, because this implicitly models their average state. Although the dynamics of each neuron can be highly stochastic, the dynamics of the density is not. This means we can use Bayesian inference and estimation tools that have already been established for deterministic systems. The potential importance of modelling density dynamics (as opposed to more conventional neural mass models) is that they include interactions among the moments of neuronal states (e.g. the mean depolarization may depend on the variance of synaptic currents through nonlinear mechanisms).Here, we formulate a population model, based on biologically informed model-neurons with spike-rate adaptation and synaptic dynamics. Neuronal sub-populations are coupled to form an observation model, with the aim of estimating and making inferences about coupling among sub-populations using real data. We approximate the time-dependent solution of the system using a bi-orthogonal set and first-order perturbation expansion. For didactic purposes, the model is developed first in the context of deterministic input, and then extended to include stochastic effects. The approach is demonstrated using synthetic data, where model parameters are identified using a Bayesian estimation scheme we have described previously.