Noise-induced burst and spike synchronizations in an inhibitory small-world network of subthreshold bursting neurons

We are interested in noise-induced firings of subthreshold neurons which may be used for encoding environmental stimuli. Noise-induced population synchronization was previously studied only for the case of global coupling, unlike the case of subthreshold spiking neurons. Hence, we investigate the effect of complex network architecture on noise-induced synchronization in an inhibitory population of subthreshold bursting Hindmarsh–Rose neurons. For modeling complex synaptic connectivity, we consider the Watts–Strogatz small-world network which interpolates between regular lattice and random network via rewiring, and investigate the effect of small-world connectivity on emergence of noise-induced population synchronization. Thus, noise-induced burst synchronization (synchrony on the slow bursting time scale) and spike synchronization (synchrony on the fast spike time scale) are found to appear in a synchronized region of the J–D plane (J: synaptic inhibition strength and D: noise intensity). As the rewiring probability p is decreased from 1 (random network) to 0 (regular lattice), the region of spike synchronization shrinks rapidly in the J–D plane, while the region of the burst synchronization decreases slowly. We separate the slow bursting and the fast spiking time scales via frequency filtering, and characterize the noise-induced burst and spike synchronizations by employing realistic order parameters and statistical-mechanical measures introduced in our recent work. Thus, the bursting and spiking thresholds for the burst and spike synchronization transitions are determined in terms of the bursting and spiking order parameters, respectively. Furthermore, we also measure the degrees of burst and spike synchronizations in terms of the statistical-mechanical bursting and spiking measures, respectively.     

Frequency-domain order parameters for the burst and spike synchronization transitions of bursting neurons

We are interested in characterization of synchronization transitions of bursting neurons in the frequency domain. Instantaneous population firing rate (IPFR) R(t), which is directly obtained from the raster plot of neural spikes, is often used as a realistic collective quantity describing population activities in both the computational and the experimental neuroscience. For the case of spiking neurons, a realistic time-domain order parameter, based on R(t), was introduced in our recent work to characterize the spike synchronization transition. Unlike the case of spiking neurons, the IPFR R(t) of bursting neurons exhibits population behaviors with both the slow bursting and the fast spiking timescales. For our aim, we decompose the IPFR R(t) into the instantaneous population bursting rate R_b(t) (describing the bursting behavior) and the instantaneous population spike rate R_s(t) (describing the spiking behavior) via frequency filtering, and extend the realistic order parameter to the case of bursting neurons. Thus, we develop the frequency-domain bursting and spiking order parameters which are just the bursting and spiking “coherence factors” β_b and β_s of the bursting and spiking peaks in the power spectral densities of R_b and R_s (i.e., “signal to noise” ratio of the spectral peak height and its relative width). Through calculation of β_b and β_s, we obtain the bursting and spiking thresholds beyond which the burst and spike synchronizations break up, respectively. Consequently, it is shown in explicit examples that the frequency-domain bursting and spiking order parameters may be usefully used for characterization of the bursting and the spiking transitions, respectively.     

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.     

Partial phase synchronization of neural populations due to random Poisson inputs

We show that populations of identical uncoupled neurons exhibit partial phase synchronization when stimulated with independent, random unidirectional current spikes with interspike time intervals drawn from a Poisson distribution. We characterize this partial synchronization using the phase distribution of the population, and consider analytical approximations and numerical simulations of phase-reduced models and the corresponding conductance-based models of typical Type I (Hindmarsh-Rose) and Type II (Hodgkin-Huxley) neurons, showing quantitatively how the extent of the partial phase synchronization depends on the magnitude and mean interspike frequency of the stimulus. Furthermore, we present several simple examples that disprove the notion that phase synchrony must be strongly related to spike synchrony. Instead, the importance of partial phase synchrony is shown to lie in its influence on the response of the population to stimulation, which we illustrate using first spike time histograms.     

Clustering in small networks of excitatory neurons with heterogeneous coupling strengths

Excitatory coupling with a slow rise time destabilizes synchrony between coupled neurons. Thus, the fully synchronous state is usually unstable in networks of excitatory neurons. Phase-clustered states, in which neurons are divided into multiple synchronized clusters, have also been found unstable in numerical studies of excitatory networks in the presence of noise. The question arises as to whether synchrony is possible in networks of neurons coupled through slow, excitatory synapses. In this paper, we show that robust, synchronous clustered states can occur in such networks. The effects of non-uniform distributions of coupling strengths are explored. Conditions for the existence and stability of clustered states are derived analytically. The analysis shows that a multi-cluster state can be stable in excitatory networks if the overall interactions between neurons in different clusters are stabilizing and strong enough to counter-act the destabilizing interactions between neurons within each cluster. When heterogeneity in the coupling strengths strengthens the stabilizing inter-cluster interactions and/or weakens the destabilizing in-cluster interactions, robust clustered states can occur in excitatory networks of all known model neurons. Numerical simulations were carried out to support the analytical results.     

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.     

Statistical-mechanical measure of stochastic spiking coherence in a population of inhibitory subthreshold neurons

By varying the noise intensity, we study stochastic spiking coherence (i.e., collective coherence between noise-induced neural spikings) in an inhibitory population of subthreshold neurons (which cannot fire spontaneously without noise). This stochastic spiking coherence may be well visualized in the raster plot of neural spikes. For a coherent case, partially-occupied "stripes" (composed of spikes and indicating collective coherence) are formed in the raster plot. This partial occupation occurs due to "stochastic spike skipping" which is well shown in the multi-peaked interspike interval histogram. The main purpose of our work is to quantitatively measure the degree of stochastic spiking coherence seen in the raster plot. We introduce a new spike-based coherence measure M ( s ) by considering the occupation pattern and the pacing pattern of spikes in the stripes. In particular, the pacing degree between spikes is determined in a statistical-mechanical way by quantifying the average contribution of (microscopic) individual spikes to the (macroscopic) ensemble-averaged global potential. This "statistical-mechanical" measure M ( s ) is in contrast to the conventional measures such as the "thermodynamic" order parameter (which concerns the time-averaged fluctuations of the macroscopic global potential), the "microscopic" correlation-based measure (based on the cross-correlation between the microscopic individual potentials), and the measures of precise spike timing (based on the peri-stimulus time histogram). In terms of M ( s ), we quantitatively characterize the stochastic spiking coherence, and find that M ( s ) reflects the degree of collective spiking coherence seen in the raster plot very well. Hence, the "statistical-mechanical" spike-based measure M ( s ) may be used usefully to quantify the degree of stochastic spiking coherence in a statistical-mechanical way.     

GAD and GABA in an enriched population of cultured GABAergic neurons from rat cerebral cortex

To study various aspects of GABAergic metabolism in an easily accessible system, dissociated cells from postnatal rat cerebral cortex were cultured in a serum-based medium and characterized morphologically and biochemically. The majority (70–90%) of the neurons were GABAergic as determined by three double-labeling procedures. The specific activity of glutamine synthetase in the cultures was 4–5% of the levels in rat astrocyte cultures and intact rat brain, indicating that glia were a minor component. The developmental increase of GABA levels preceded the increase of GAD activity in both immunocytochemical and biochemical experiments. GABA turnover rates also increased with culture age and were 20–30% of GAD activity. Four anti-GAD antibodies, which recognize GAD subunits with differing molecular masses to varying degrees, were used to stain cultured neurons and make immunoblots. Immunoblots showed that the neurons contained two major subunits of GAD which differed in mass by 2 kDa. All four antibodies immunostained both neuronal perikarya and neurites but one antibody, which on the immunoblots predominantly labeled the GAD protein with the lower molecular weight, showed a somewhat more pronounced punctate staining, possibly indicating a principal localization to neurites.     

Age-associated reduction of nuclear shape dynamics in excitatory neurons of the visual cortex

Neurons decline in their functionality over time, and age-related neuronal alterations are associated with phenotypes of neurodegenerative diseases. In nonneural tissues, an infolded nuclear shape has been proposed as a hallmark of aged cells and neurons with infolded nuclei have also been reported to be associated with neuronal activity. Here, we performed time-lapse imaging in the visual cortex of Nex-Cre;SUN1-GFP mice. Nuclear infolding was observed within 10 min of stimulation in young nuclei, while the aged nuclei were already infolded pre-stimulation and showed reduced dynamics of the morphology. In young nuclei, the depletion of the stimuli restored the nucleus to a spherical shape and reduced the dynamic behavior, suggesting that nuclear infolding is a reversible process. We also found the aged nucleus to be stiffer than the young one, further relating to the age-associated loss of nuclear shape dynamics. We reveal temporal changes in the nuclear shape upon external stimulation and observe that these morphological dynamics decrease with age.     

Traffic of botulinum toxins A and E in excitatory and inhibitory neurons

Botulinum neurotoxins (BoNTs), proteases specific for the SNARE proteins, are used to study the molecular machinery supporting exocytosis and are used to treat human diseases characterized by cholinergic hyperactivity. The recent extension of the use of BoNTs to central nervous system (CNS) pathologies prompted the study of their traffic in central neurons. We used fluorescent BoNT/A and BoNT/E to study the penetration, the translocation and the catalytic action of these toxins in excitatory and inhibitory neurons. We show that BoNT/A and BoNT/E, besides preferentially inhibiting synaptic vesicle recycling at glutamatergic relative to Gamma-aminobutyric acid (GABA)-ergic neurons, are more efficient in impairing the release of excitatory than inhibitory neurotransmitter from brain synaptosomes. This differential effect does not result from a defective penetration of the toxin in line with the presence of the BoNT/A receptor, synaptic vesicle protein 2 (SV2), in both types of neurons. Interestingly, exogenous expression of SNAP-25 in GABAergic neurons confers sensitivity to BoNT/A. These results indicate that the expression of the toxin substrate, and not the toxin penetration, most likely accounts for the distinct effects of the two neurotoxins at the two types of terminals and support the use of BoNTs for the therapy of CNS diseases caused by the altered activity of selected neuronal populations.     

Dynamics of networks of randomly connected excitatory and inhibitory spiking neurons

Recent advances in the understanding of the dynamics of populations of spiking neurones are reviewed. These studies shed light on how a population of neurones can follow arbitrary variations in input stimuli, how the dynamics of the population depends on the type of noise, and how recurrent connections influence the dynamics. The importance of inhibitory feedback for the generation of irregularity in single cell behaviour is emphasized. Examples of computation that recurrent networks with excitatory and inhibitory cells can perform are then discussed. Maintenance of a network state as an attractor of the system is discussed as a model for working memory function, in both object and spatial modalities. These models can be used to interpret and make predictions about electrophysiological data in the awake monkey.     

The effect of population density on the growth of an animal population

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Contribution from the Department of Fisheries, Kyoto University.

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Contribution from the Entomological Laboratory, Kyoto University, No. 201.     

Pharmacological and functional characterization of excitatory amino acid mediated cytotoxicity in cerebral cortical neurons

The cytotoxic action of the excitatory amino acids (EAAs) glutamate, N-methyl- D-aspartate (NMDA), quisqualate (QA), kainate (KA) and (RS)-2-amino-3(3-hydoxy-5-methylisoxazol-4-yl) propionate (AMPA) was studied in cerebral cortical neurons in culture. The pharmacological profile of these actions was characterized using the NMDA selective antagonist D-(-)-2-amino-5- phosphonopentanoate (APV) and the non-NMDA selective antagonists 6.7- dinitroquinoxaline-2,3-dione (DNQX), 2-amino-3[3-(carboxymethoxy)-5- methylisoxazol-4-yl]-propionate (AMOA) and 2-amino-3-[2-(3-hydroxy-5- methylisoxazol-4-yl)methyl-3-methyl-3-oxoisoxazolin-4-yl] propionate (AMNH). The role of intracellular Ca⁺⁺ homeostasis and cGMP production for development of EAA mediated cytotoxicity was assessed by measurements of changes in [Ca⁺⁺]i using the flourescent Ca⁺⁺ chelator Fluo-3 and in cGMP concentrations using a conventional radioimmune assay. It was found that glutamate toxicity involves both NMDA and non-NMDA receptor activation and that aberrations in Ca⁺⁺ homeostasis brought about by Ca⁺⁺ influx and/or liberation of Ca⁺⁺ from internal stores aare important for development of toxicity. The drug dantrolene which prevents release of Ca⁺⁺ from such stores can prevent toxicity induced by glutamate, NMDA and QA completely but has no effect on KA and AMPA toxicity. Changes in cGMP levels appear to play a role for development of glutamate, NMDA and KA toxicity but does not seem to be involved in that triggered by QA and AMPA.Abbreviations AMNH: (2-amino-3-[2-(3-hydroxy-5-methylisoxazol-4-yl)methyl-5-methyl-3-oxoisoxazolin-4-yl]propionate) - AMOA: (2-amino-3[3-(carboxymethoxy)-5-methylisoxazol-4-yl]propinate) - AMPA: ( (RS) —2-amino-3-(3-hydroxy-5-methylisoxazol-4-yl)propinate) - APV: (D-(-)-2-amino-5-phosphonopentanoate) - DNQX: (6,7-dinitroquinoxaline-2,3-dione) - KA (kinate) - QA (quisqualate)     

蛋白激酶A介导慢性压迫背根节神经元的肾上腺素能兴奋反应

本实验在奶节（ＤＲＧ）慢性压迫模型上,采用离体灌流ＤＲＧ和单纤维记录神经元自发放电的方法研究了初级感觉神经元的交感－感觉耦联作用及其细胞内机制。用外源性支甲肾上腺素（ＮＥ,１０μｍｏｌ／Ｌ）浸浴损伤的ＤＲＧ时,在９５个ＤＲＧ神经元中有８５个自发放电的神经元产生明显反应。其中,４４个呈现单纯兴奋效应,２１个表现先兴奋后抑制效应,６个出现兴奋－抑制交替振荡现象,１４个表现抑制效应。ＮＥ对损伤神经元的兴     

Optimal harvesting of an age-structured population

Here we investigate the optimal harvesting of an age-structured population. We use the McKendrick model of population dynamics, and optimize a discounted yield on an infinite time horizon. The harvesting function is allowed to depend arbitrarily on age and time and its magnitude is unconstrained. We obtain, in addition to existence, the qualitative result that an optimal harvesting policy consists of harvesting at no more than three distinct ages.     

光学方法同步记录成群前庭神经节细胞膜电位

目的 :采用电压敏感染料和多位点光学成像系统研究前庭神经节细胞 (vestibularganglioncells ,VGCs)电生理特性。方法 :自新生小鼠内耳分离并培养的VGCs ,用吸光性电压敏感染料RH15 5染色后 ,多个或成群VGCs被同时成像于 16× 16记录单元Photodiodearrays (PDA)光学成像系统。 结果 :用高钾溶液灌流刺激时发现当VGCs膜电位变化时 ,膜表面的光吸收增强 ,光吸收度为 0 .2 3%± 0 .0 8%。并且所记录的光学反应具有波长特性。另外 ,在本实验条件下 ,光损伤和染料的药毒性副作用不明显或者可忽略不计。结论 :光学记录可以同步观测多个和成群VGCs膜电位变化 ,是电生理研究的新方法     

Transient information flow in a network of excitatory and inhibitory model neurons: Role of noise and signal autocorrelation

We investigate the performance of sparsely-connected networks of integrate-and-fire neurons for ultra-short term information processing. We exploit the fact that the population activity of networks with balanced excitation and inhibition can switch from an oscillatory firing regime to a state of asynchronous irregular firing or quiescence depending on the rate of external background spikes. We find that in terms of information buffering the network performs best for a moderate, non-zero, amount of noise. Analogous to the phenomenon of stochastic resonance the performance decreases for higher and lower noise levels. The optimal amount of noise corresponds to the transition zone between a quiescent state and a regime of stochastic dynamics. This provides a potential explanation of the role of non-oscillatory population activity in a simplified model of cortical micro-circuits.     

Maintaining diversity in an artificially propagated population

Populations may suffer unexpected loss or distortion of biodiversity as a consequence of strategies employed in artificial propagation programs. The Trinity River Fish Hatchery may have inadvertently experienced this while attempting to preserve diversity in a return time within a Chinook salmon population. We develop a model for this system and prove that the long-term distribution of return types converges and that it is strongly tied to the management strategy. Given estimates of heritabilities for return type and differential survival rates, an estimate of this long-term distribution can be computed easily.     

Influence of circadian disorder on structures and functions of neurons in hippocampus of mice

Objective: This study explored the effect of circadian disorder on structure and function of neurons in hippocampus of mice. Methods: Forty male ICR mice were randomly divided into rhythm disorder group (RDG) and normal rhythm group (NRG). The RDG was treated with 3 h light/5 h dark and 5 h light/3 h dark light–dark (LD) cycle alternately. The normal rhythm group was treated with 12/12 h LD cycle. Electron microscope was used to detect the mouse hippocampal cell ultrastructure. Morris water maze was used to test mice cognitive function. The brain slice electric physiological techniques were used to detect synapses in the hippocampal Long-term potentiation (LTP) effect. Results: The time of through central area of RDG was less than that of NRG. The axoplasm in anterior-posterior membranes of synapses of RDG was dissolved and synaptic vesicles of RDG were decreased. Conclusion: Circadian rhythm disorder induced by irregular light–dark circle can lead to the structural damage of hippocampal neurons and damage the cognitive function in mice.