NOISE-INDUCED PATTERN FORMATION AND SYNCHRONIZATION IN A SQUARE-LATTICE NEURONAL NETWORK

Noise-induced complete synchronization and frequency synchronization in coupled spiking and bursting neurons are studied firstly. The effects of noise and coupling are discussed. It is found that bursting neurons are easier to achieve firing synchronization than spiking ones, which means that bursting activities are more important for information transfer in neuronal networks. Secondly, the effects of noise on firing synchronization in a noisy map neuronal network are presented. Noise-induced synchronization and temporal order are investigated by means of the firing rate function and the order index. Firing synchronization and temporal order of excitatory neurons can be greatly enhanced by subthreshold stimuli with resonance frequency. Finally, it is concluded that random perturbations play an important role in firing activities and temporal order in neuronal networks.

Neuron–astrocyte signaling and epilepsy

Synchronous firing is commonly observed in the brain, but its underlying mechanisms and neurobiological meaning remain debated. Most commonly, synchrony is attributed either to electrical coupling by gap junctions or to shared excitatory inputs. In the cerebral cortex and hippocampus, fast-spiking (FS) or somatostatin-containing (SOM) inhibitory interneurons are electrically coupled to same-type neighbors, and each subtype-specific network tends to fire in synchrony. Electrical coupling across subtypes is weak or absent, but SOM-FS and FS-FS pairs are often connected by inhibitory synapses. Theoretical studies suggest that purely inhibitory coupling can also promote synchrony; however, this has not been confirmed experimentally. We recorded from 74 pairs of electrically noncoupled layer 4 interneurons in mouse somatosensory cortex in vitro, and found that tonically depolarized FS-FS and SOM-FS pairs connected by unidirectional or bidirectional inhibitory synapses often fired within 1 ms of each other. Using a novel, jitter-based measure of synchrony, we found that synchrony correlated with inhibitory coupling strength. Importantly, synchrony was resistant to ionotropic glutamate receptors antagonists but was strongly reduced when GABA(A) receptors were blocked, confirming that in our experimental system IPSPs were both necessary and sufficient for synchrony. Submillisecond firing lags emerged in a computer simulation of pairs of spiking neurons, in which the only assumed interaction between neurons was by inhibitory synapses. We conclude that cortical interneurons are capable of synchronizing both within and across subtypes, and that submillisecond coordination of firing can arise by mutual synaptic inhibition alone, with neither shared inputs nor electrical coupling.

In this paper, we study the relaxation time (RT) of the steady-state correlation function in a FitzHugh–Nagumo neural system under the presence of multiplicative and additive white noises and time delay. The noise correlation parameter λ can produce a critical behavior in the RT as functions of the multiplicative noise intensity D, the additive noise intensity Q and the time delay τ. That is, the RT decreases as the noise intensities D and Q increase, and increases as the time delay τ increases below the critical value of λ. However, above the critical value, the RT first increases, reaches a maximum, and then decreases as D, Q and τ increase, i.e. a noise intensity D or Q and a time delay τ exist, at which the time scales of the relaxation process are at their largest. In addition, the additive noise intensity Q can also produce a critical behavior in the RT as a function of λ. The noise correlation parameter λ first increases the RT of processes, then decreases it below the critical value of Q. Above the critical value, λ increases it.

Locomotion towards a goal alters the synchronous firing of neurons recorded simultaneously in the subiculum and nucleus accumbens of rats

Activity-dependent modulation of electrical transmission typically involves Ca2+ influx acting directly on gap junctions or initiating Ca2+-dependent pathways that in turn modulate coupling. We now describe short-term use-dependent facilitation of electrical transmission between bag cell neurons from the hermaphroditic snail, Aplysia californica, that is instead mediated by changes in postsynaptic responsiveness. Bag cell neurons secrete reproductive hormone during a synchronous afterdischarge of action potentials coordinated by electrical coupling. Here, recordings from pairs of coupled bag cell neurons in culture showed that nonjunctional currents influence electrical transmission in a dynamic manner. Under a dual whole cell voltage-clamp, the junctional current was linear and largely voltage-independent, while in current-clamp, the coupling coefficient was similar regardless of the extent of presynaptic hyperpolarization. Moreover, a train stimulus of action potential-like waveforms, in a voltage-clamped presynaptic neuron, elicited electrotonic potentials, in a current-clamped postsynaptic neuron, that facilitated over time when delivered at a frequency approximating the afterdischarge. Junctional current remained constant over the train stimulus, as did postsynaptic voltage-gated Ca2+ current. However, postsynaptic voltage-gated K+ current underwent cumulative inactivation, suggesting that K+ current run-down facilitates the electrotonic potential by boosting the response to successive junctional currents. Accordingly, preventing run-down by blocking postsynaptic K+ channels occluded facilitation. Finally, stimulation of bursts in coupled pairs resulted in synchronous firing, where active neurons could recruit silent partners through short-term use-dependent facilitation. Thus, potentiation of electrical transmission may promote synchrony in bag cell neurons and, by extension, reproductive function.NEW & NOTEWORTHY The understanding of how activity can facilitate electrical transmission is incomplete. We found that electrotonic potentials between electrically coupled neuroendocrine bag cell neurons facilitated in a use-dependent fashion. Rather than changes to the junctional current, facilitation was associated with cumulative inactivation of postsynaptic K+ current, presumably augmenting responsiveness. When made to burst, neurons synchronized their spiking, in part by use-dependent facilitation bringing quiescent cells to the threshold. Facilitation may foster en masse firing and neurosecretion.

The aim of this work is to study the possibility of the existence of multistability near the boundary of noise-induced synchronization in chaotic continuous and discrete systems. Ensembles of uncoupled Lorenz systems and logistic maps being under influence of a common source of white noise have been chosen as an object under study. Methods. The noise-induced synchronization regime detection has been performed by means of direct comparison of the system states being under influence of the common noise source and by calculation of the synchronization error. To determine the presence of multistability near the boundary of this regime, the multistability measure has been calculated and its dependence on the noise intensity has been obtained. In addition, for fixed moments of time, the basins of attraction of the synchronous and asynchronous regimes have been received for one of the systems driven by noise for fixed initial conditions of the other system. The result of the work is a proof of the presence of multistability near the boundary of noise-induced synchronization. Conclusion. It is shown that the regime of intermittent noise-induced synchronization, as well as the regime of intermittent generalized synchronization, is characterized by multistability, which manifests itself in this case as the existence in the same time interval of the synchronous behavior in one pair of systems being under influence of a common noise source, whereas in the other pair the asynchronous behavior is observed. The found effect is typical for both flow systems and discrete maps being under influence of a common noise source. It can find an application in the information and telecommunication systems for improvement the methods for secure information transmission based on the phenomenon of chaotic synchronization.

The input nucleus of the basal ganglia, the striatum, processes cortical inputs in two output streams, called the direct and indirect pathways. Medium Spiny Neurons (MSNs) that express dopamine D1 receptors constitute the direct pathway (D1 MSNs) and MSNs that express dopamine D2 receptors constitute the indirect pathway (D2 MSNs). The two populations of MSNs differ in their intrinsic excitability with D2 MSNs more responsive to somatic current injection [1]. Inhibitory circuits of the striatal network, including feedback inhibition from other MSNs and feedforward inhibition from fast-spiking interneurons (FSIs), modulate this excitability [2,3] to produce balanced firing in response to synaptic input [4]. During dopamine depletion, there is an imbalance in the firing activity and cortico-striatal plasticity between D1 and D2 MSNs, and increased correlation is observed in output structures such as the globus pallidus. Thus, both dopamine and GABA play crucial roles in modulating the activity and properties of these neurons to produce the desired output of the striatum. This study uses computational modeling to investigate the contribution of intrinsic channels and network interactions in modulating the activity and correlation of the striatal network. The network constitutes multi-compartmental models of 500 D1 MSNs, 500 D2 MSNs and 49 FSIs simulated using GENESIS simulation software. The MSNs receive inhibitory input from the other MSNs in the network and from the FSI network. The FSIs are connected to each other by chemical synapses and gap junctions. Similar to experiments, the model D2 MSNs are more excitable than D1 MSNs in response to current injection [1]. Despite this difference, both types of MSNs have similar firing frequencies and latency to spike during up-states in response to synaptic inputs. Removal of either FSI input, or gap junctions between the FSIs, disrupts the balance of firing between D1 and D2 MSNs. In addition, L-type calcium channels are important for balanced firing as blocking these channels or making their conductance equal in D1 and D2 MSNs also disrupts balance of firing. Correlation among MSN is measured in response to a range of cortical input correlation, both in the control and dopamine depleted condition. Simulations reveal that cortical synchrony produces very little increase in striatal synchrony under control conditions, but significantly enhances striatal synchrony in the dopamine depleted condition. This suggests that some of the synchrony in the output structures of the basal ganglia may be caused by enhanced synchrony in the striatum.

The mossy fiber-granule cell-parallel fiber system conveys proprioceptive and corollary discharge information to principal cells in cerebellum-like systems. In the dorsal cochlear nucleus (DCN), Golgi cells inhibit granule cells and thus regulate information transfer along the mossy fiber-granule cell-parallel fiber pathway. Whereas excitatory synaptic inputs to Golgi cells are well understood, inhibitory and electrical synaptic inputs to Golgi cells have not been examined. Using paired recordings in a mouse brain slice preparation, we find that Golgi cells of the cochlear nucleus reliably form electrical synapses onto one another. Golgi cells were only rarely electrically coupled to superficial stellate cells, which form a separate network of electrically coupled interneurons in the DCN. Spikelets had a biphasic effect on the excitability of postjunctional Golgi cells, with a brief excitatory phase and a prolonged inhibitory phase due to the propagation of the prejunctional afterhyperpolarization through gap junctions. Golgi cells and stellate cells made weak inhibitory chemical synapses onto Golgi cells with low probability. Electrical synapses are therefore the predominant form of synaptic communication between auditory Golgi cells. We propose that electrical synapses between Golgi cells may function to regulate the synchrony of Golgi cell firing when electrically coupled Golgi cells receive temporally correlated excitatory synaptic input.

Recent studies have found gap junctions between striatal fast spiking interneurons (FSN). Gap junctions between neocortical FSNs cause increased synchrony of firing in response to current injection, but the effect of gap junctions in response to synaptic input is unknown. To explore this issue, we built a network model of FSNs. Each FSN connects to 30–40% of its neighbours, as found experimentally, and each FSN in the network is activated by simulated up-state synaptic inputs. Simulation experiments show that the proportion of synchronous spikes in coupled FSNs increases with gap junction conductance. Proximal gap junctions increase the synchronization more than distal gap junctions. During up-states the synchronization effects in FSNs coupled pairwise with proximal gap junctions are small for experimentally estimated gap junction conductances; however, higher order correlations are significantly increased in larger FSN networks.

Chaos synchronization of coupled neurons with gap junctions

Hearing loss, caused by gene mutations and environmental factors, is a common sensory disorder in the human population. In the developed countries, the incidence of congenital hearing loss is estimated at 1 in 1000 births, of which approximately 60% cases are attributed to genetic factors. To date, 59 auditory genes have been identified. Connexin (Cx) belongs to a large gene family, and the products of Cx gene family constitute a gap junction channel responsible for regulation of the physiological and developmental process, involving the exchange of ions and small molecules. Every six Cxs compose a hemichannel (so called as connexon), and then two hemichannel to form an integral gap junction. This study applied cell model to determine the Cx29 and Cx43 gene mutations in the pathogenic mechanisms causing hearing loss. To confirm the localization patterns seen in the immunolabeling assay, HeLa cells were transfected with Cx29 constructs that were directly ‘tagged’ with GFP or DsRed at the C-terminal end of the protein. The results reveal the Cx29WT-EGFP was expressed along apposed cell membranes in the fluorescent localization assay with a continuous staining. In contrast, the p.E269D- EGFP (missense mutation) resulted in the accumulation of the Cx29 mutant protein in the endoplasmic reticulum (ER) rather than in the plasma membrane. Co-expression of Cx29WT and Cx29E269D proteins by a bi-directional tet-on expression system demonstrated that the heteromeric connexon accumulated in the cytoplasm, thereby impairing the formation of the gap junction. Assuming these findings, we suggest that Cx29E269D has a dominant negative effect on the formation of the gap junction. To determine the crucial relationship between wild type Cx43 and three of mutant Cx43 genes( S69P、T326Iand 932 del C) were cloned and their functions were analysed in HeLa cells. Localization assay of WT Cx43 reveals a typical punctuate fluorescence pattern of a gap junction channel between neighboring expression cells. Additionally, immunoblotting analysis of the transfectants confirms the production of mutant proteins, in which their distributions along appositional membranes are determined using immunofluorescent staining procedures. Furthermore, dye transfer assay results demonstrate that gap junctional intercellular communication (GJIC) is less in HeLa cells carrying mutant GJA1 orψGJA1 gene than in WT-expressing cell. In summary, we use molecular biology methods to create the normal and mutant constructs containing Cx29 or Cx43 gene and determine the pathogenic effects of normal and mutant Cx29or Cx43 gene in transfected HeLa cells. Our data reveal the Cx29 and Cx43 gene mutations play causal roles in the pathogenesis of hearing loss.

Impact of multiplexing noise on multilayer networks of bistable maps

Stochastic coherence (SC) and self-induced stochastic resonance (SISR) are two distinct mechanisms of noise-induced coherent motion. For interacting SC and SISR oscillators, we find that whether or not phase synchronization is achieved depends sensitively on the coupling strength and noise intensities. Specifically, in the case of weak coupling, individual oscillators are insensitive to each other, whereas in the case of strong coupling, one fixed oscillator with optimal coherence can be entrained to the other, adjustable oscillator (i.e., its noise intensity is tunable), achieving phase-locking synchronization, as long as the tunable noise intensity is not beyond a threshold; such synchronization is lost otherwise. For an array lattice of SISR oscillators, except for coupling-enhanced coherence similar to that found in the case of coupled SC oscillators, there is an optimal network topology degree (i.e., number of coupled nodes), such that coherence and synchronization are optimally achieved, implying that the system-size resonance found in an ensemble of noise-driven bistable systems can occur in coupled SISR oscillators.

We study the effects of different coupling strengths and network topologies on signal detection in small-world neuronal networks. Research has previously revealed that the ability of detecting subthreshold signals could be significantly enhanced by appropriately fine-tuning the noise intensity. Here we show that the coupling strength and the structure of the underlying network can also lead toward enhanced signal detection. In particular, we show that there are two levels of the coupling strength at which the subthreshold signal can be detected at an appropriate noise intensity and network structure. We also show that the network structure has little impact on signal detection if the coupling is weak. On the other hand, for intermediate coupling strengths, we show that the shorter the average path length, the better the signal detection. Finally, if the coupling is strong, we show that there exists an intermediate average path length at which signal detection becomes optimal.