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Study on nonlinear characteristics of two synchronizing uncoupled Hindmarsh-Rose neurons

Wu Ying,Xu Jian-Xue,He Dai-Hai,Jin Wu-Yin,
吴 王莹

物理学报 , 2005,
Abstract: Modulating the current input of two uncoupled Hindmarsh-Rose neurons by using the membrane potential of Hindmarsh-Rose neuron under different initial conditions, the evolution mechanism of synchronization process of the two neurons is revealed by analyzing interspike interval sequences. When periodic stimulation is u sed, the full synchronization is realized in two identical neurons, and the sync hronized response of modulated neurons can be different from the stimulation sig nal; and phase synchronization can be obtained in two neurons with different par ameters:two neurons with small parameter mismatch can be synchronized to the per iodic response different from the stimulation signal, and two neurons with big p arameter mismatch can only be synchronized to the response in phase synchronizat ion with stimulation signal. When chaotic stimulation is used, two systems can o nly be synchronized to the response being in phase synchronization with stimulat ion signal. Obviously, chaotic stimulation is more helpful in encoding and deco ding information. Analyzing the relation between the largest condition Lyapunov exponents and the stimulation strength shows that when the largest condition Lya punov exponents of the two systems are both negative is the necessary condition for synchronization. The chaotic stimulation signal can more easily synchronize two neurons than periodic stimulation signal, implying that the effect of chaoti c stimulation is stronger than periodic one, and the experiments also confirm th is conclusion.
The type II phase resetting curve is optimal for stochastic synchrony  [PDF]
Aushra Abouzeid,Bard Ermentrout
Quantitative Biology , 2009, DOI: 10.1103/PhysRevE.80.011911
Abstract: The phase-resetting curve (PRC) describes the response of a neural oscillator to small perturbations in membrane potential. Its usefulness for predicting the dynamics of weakly coupled deterministic networks has been well characterized. However, the inputs to real neurons may often be more accurately described as barrages of synaptic noise. Effective connectivity between cells may thus arise in the form of correlations between the noisy input streams. We use constrained optimization and perturbation methods to prove that PRC shape determines susceptibility to synchrony among otherwise uncoupled noise-driven neural oscillators. PRCs can be placed into two general categories: Type I PRCs are non-negative while Type II PRCs have a large negative region. Here we show that oscillators with Type II PRCs receiving common noisy input sychronize more readily than those with Type I PRCs.
Mechanisms of Magnetic Stimulation of Central Nervous System Neurons  [PDF]
Tamar Pashut,Shuki Wolfus,Alex Friedman,Michal Lavidor,Izhar Bar-Gad,Yosef Yeshurun,Alon Korngreen
PLOS Computational Biology , 2011, DOI: 10.1371/journal.pcbi.1002022
Abstract: Transcranial magnetic stimulation (TMS) is a stimulation method in which a magnetic coil generates a magnetic field in an area of interest in the brain. This magnetic field induces an electric field that modulates neuronal activity. The spatial distribution of the induced electric field is determined by the geometry and location of the coil relative to the brain. Although TMS has been used for several decades, the biophysical basis underlying the stimulation of neurons in the central nervous system (CNS) is still unknown. To address this problem we developed a numerical scheme enabling us to combine realistic magnetic stimulation (MS) with compartmental modeling of neurons with arbitrary morphology. The induced electric field for each location in space was combined with standard compartmental modeling software to calculate the membrane current generated by the electromagnetic field for each segment of the neuron. In agreement with previous studies, the simulations suggested that peripheral axons were excited by the spatial gradients of the induced electric field. In both peripheral and central neurons, MS amplitude required for action potential generation was inversely proportional to the square of the diameter of the stimulated compartment. Due to the importance of the fiber's diameter, magnetic stimulation of CNS neurons depolarized the soma followed by initiation of an action potential in the initial segment of the axon. Passive dendrites affect this process primarily as current sinks, not sources. The simulations predict that neurons with low current threshold are more susceptible to magnetic stimulation. Moreover, they suggest that MS does not directly trigger dendritic regenerative mechanisms. These insights into the mechanism of MS may be relevant for the design of multi-intensity TMS protocols, may facilitate the construction of magnetic stimulators, and may aid the interpretation of results of TMS of the CNS.
Adaptation controls synchrony and cluster states of coupled threshold-model neurons  [PDF]
Josef Ladenbauer,Judith Lehnert,Hadi Rankoohi,Thomas Dahms,Eckehard Sch?ll,Klaus Obermayer
Physics , 2013, DOI: 10.1103/PhysRevE.88.042713
Abstract: We analyze zero-lag and cluster synchrony of delay-coupled non-smooth dynamical systems by extending the master stability approach, and apply this to networks of adaptive threshold-model neurons. For a homogeneous population of excitatory and inhibitory neurons we find (i) that subthreshold adaptation stabilizes or destabilizes synchrony depending on whether the recurrent synaptic excitatory or inhibitory couplings dominate, and (ii) that synchrony is always unstable for networks with balanced recurrent synaptic inputs. If couplings are not too strong, synchronization properties are similar for very different coupling topologies, i.e., random connections or spatial networks with localized connectivity. We generalize our approach for two subpopulations of neurons with non-identical local dynamics, including bursting, for which activity-based adaptation controls the stability of cluster states, independent of a specific coupling topology.
Spike-Timing Precision and Neuronal Synchrony Are Enhanced by an Interaction between Synaptic Inhibition and Membrane Oscillations in the Amygdala  [PDF]
Steven J. Ryan, David E. Ehrlich, Aaron M. Jasnow, Shabrine Daftary, Teresa E. Madsen, Donald G. Rainnie
PLOS ONE , 2012, DOI: 10.1371/journal.pone.0035320
Abstract: The basolateral complex of the amygdala (BLA) is a critical component of the neural circuit regulating fear learning. During fear learning and recall, the amygdala and other brain regions, including the hippocampus and prefrontal cortex, exhibit phase-locked oscillations in the high delta/low theta frequency band (~2–6 Hz) that have been shown to contribute to the learning process. Network oscillations are commonly generated by inhibitory synaptic input that coordinates action potentials in groups of neurons. In the rat BLA, principal neurons spontaneously receive synchronized, inhibitory input in the form of compound, rhythmic, inhibitory postsynaptic potentials (IPSPs), likely originating from burst-firing parvalbumin interneurons. Here we investigated the role of compound IPSPs in the rat and rhesus macaque BLA in regulating action potential synchrony and spike-timing precision. Furthermore, because principal neurons exhibit intrinsic oscillatory properties and resonance between 4 and 5 Hz, in the same frequency band observed during fear, we investigated whether compound IPSPs and intrinsic oscillations interact to promote rhythmic activity in the BLA at this frequency. Using whole-cell patch clamp in brain slices, we demonstrate that compound IPSPs, which occur spontaneously and are synchronized across principal neurons in both the rat and primate BLA, significantly improve spike-timing precision in BLA principal neurons for a window of ~300 ms following each IPSP. We also show that compound IPSPs coordinate the firing of pairs of BLA principal neurons, and significantly improve spike synchrony for a window of ~130 ms. Compound IPSPs enhance a 5 Hz calcium-dependent membrane potential oscillation (MPO) in these neurons, likely contributing to the improvement in spike-timing precision and synchronization of spiking. Activation of the cAMP-PKA signaling cascade enhanced the MPO, and inhibition of this cascade blocked the MPO. We discuss these results in the context of spike-timing dependent plasticity and modulation by neurotransmitters important for fear learning, such as dopamine.
Information on mean, fluctuation and synchrony conveyed by a population of firing neurons  [PDF]
Hiode Hasegawa
Physics , 2007,
Abstract: A population of firing neurons is expected to carry not only mean firing rate but also its fluctuation and synchrony among neurons. In order to examine this possibility, we have studied responses of neuronal ensembles to three kinds of inputs: mean-, fluctuation- and synchrony-driven inputs. The generalized rate-code model including additive and multiplicative noise (H. Hasegawa, Phys. Rev. E {\bf 75}, 051904 (2007)) has been studied by direct simulations (DSs) and the augmented moment method (AMM) in which equations of motion for mean firing rate, fluctuation and synchrony are derived. Results calculated by the AMM are in good agreement with those by DSs. The independent component analysis (ICA) of our results has shown that mean firing rate, fluctuation (or variability) and synchrony may carry independent information in the population rate-code model. The input-output relation of mean firing rates is shown to have higher sensitivity for larger multiplicative noise, as recently observed in prefrontal cortex. A comparison is made between results obtained by the integrate-and-fire (IF) model and our rate-code model. The relevance of our results to experimentally obtained data is also discussed.
Optogenetic stimulation effectively enhances intrinsically generated network synchrony  [PDF]
Ahmed El Hady,Ghazaleh Afshar,Kai Br?king,Oliver M. Schlüter,Theo Geisel,Fred Wolf
Frontiers in Neural Circuits , 2013, DOI: 10.3389/fncir.2013.00167
Abstract: Synchronized bursting is found in many brain areas and has also been implicated in the pathophysiology of neuropsychiatric disorders such as epilepsy, Parkinson’s disease, and schizophrenia. Despite extensive studies of network burst synchronization, it is insufficiently understood how this type of network wide synchronization can be strengthened, reduced, or even abolished. We combined electrical recording using multi-electrode array with optical stimulation of cultured channelrhodopsin-2 transducted hippocampal neurons to study and manipulate network burst synchronization. We found low frequency photo-stimulation protocols that are sufficient to induce potentiation of network bursting, modifying bursting dynamics, and increasing interneuronal synchronization. Surprisingly, slowly fading-in light stimulation, which substantially delayed and reduced light-driven spiking, was at least as effective in reorganizing network dynamics as much stronger pulsed light stimulation. Our study shows that mild stimulation protocols that do not enforce particular activity patterns onto the network can be highly effective inducers of network-level plasticity.
Subthalamic Nucleus High-Frequency Stimulation Restores Altered Electrophysiological Properties of Cortical Neurons in Parkinsonian Rat  [PDF]
Bertrand Degos, Jean-Michel Deniau, Mario Chavez, Nicolas Maurice
PLOS ONE , 2013, DOI: 10.1371/journal.pone.0083608
Abstract: Electrophysiological recordings performed in parkinsonian patients and animal models have confirmed the occurrence of alterations in firing rate and pattern of basal ganglia neurons, but the outcome of these changes in thalamo-cortical networks remains unclear. Using rats rendered parkinsonian, we investigated, at a cellular level in vivo, the electrophysiological changes induced in the pyramidal cells of the motor cortex by the dopaminergic transmission interruption and further characterized the impact of high-frequency electrical stimulation of the subthalamic nucleus, a procedure alleviating parkinsonian symptoms. We provided evidence that a lesion restricted to the substantia nigra pars compacta resulted in a marked increase in the mean firing rate and bursting pattern of pyramidal neurons of the motor cortex. These alterations were underlain by changes of the electrical membranes properties of pyramidal cells including depolarized resting membrane potential and increased input resistance. The modifications induced by the dopaminergic loss were more pronounced in cortico-striatal than in cortico-subthalamic neurons. Furthermore, subthalamic nucleus high-frequency stimulation applied at parameters alleviating parkinsonian signs regularized the firing pattern of pyramidal cells and restored their electrical membrane properties.
Noisy Galvanic Vestibular Stimulation Modulates the Amplitude of EEG Synchrony Patterns  [PDF]
Diana J. Kim, Vignan Yogendrakumar, Joyce Chiang, Edna Ty, Z. Jane Wang, Martin J. McKeown
PLOS ONE , 2013, DOI: 10.1371/journal.pone.0069055
Abstract: Noisy galvanic vestibular stimulation has been associated with numerous cognitive and behavioural effects, such as enhancement of visual memory in healthy individuals, improvement of visual deficits in stroke patients, as well as possibly improvement of motor function in Parkinson’s disease; yet, the mechanism of action is unclear. Since Parkinson’s and other neuropsychiatric diseases are characterized by maladaptive dynamics of brain rhythms, we investigated whether noisy galvanic vestibular stimulation was associated with measurable changes in EEG oscillatory rhythms within theta (4–7.5 Hz), low alpha (8–10 Hz), high alpha (10.5–12 Hz), beta (13–30 Hz) and gamma (31–50 Hz) bands. We recorded the EEG while simultaneously delivering noisy bilateral, bipolar stimulation at varying intensities of imperceptible currents – at 10, 26, 42, 58, 74 and 90% of sensory threshold – to ten neurologically healthy subjects. Using standard spectral analysis, we investigated the transient aftereffects of noisy stimulation on rhythms. Subsequently, using robust artifact rejection techniques and the Least Absolute Shrinkage Selection Operator regression and cross-validation, we assessed the combinations of channels and power spectral features within each EEG frequency band that were linearly related with stimulus intensity. We show that noisy galvanic vestibular stimulation predominantly leads to a mild suppression of gamma power in lateral regions immediately after stimulation, followed by delayed increase in beta and gamma power in frontal regions approximately 20–25 s after stimulation ceased. Ongoing changes in the power of each oscillatory band throughout frontal, central/parietal, occipital and bilateral electrodes predicted the intensity of galvanic vestibular stimulation in a stimulus-dependent manner, demonstrating linear effects of stimulation on brain rhythms. We propose that modulation of neural oscillations is a potential mechanism for the previously-described cognitive and motor effects of vestibular stimulation, and noisy galvanic vestibular stimulation may provide an additional non-invasive means for neuromodulation of functional brain networks.
In vivo patch-clamp analysis of response properties of rat primary somatosensory cortical neurons responding to noxious stimulation of the facial skin
Mamoru Takeda, Masayuki Takahashi, Masanori Nasu, Shigeji Matsumoto
Molecular Pain , 2010, DOI: 10.1186/1744-8069-6-30
Abstract: In vivo whole-cell current-clamp recordings were performed in rat SI neurons (layers III-IV). Twenty-seven out of 63 neurons were identified in the mechanical receptive field of the orofacial area (36 neurons showed no receptive field) and they were classified as non-nociceptive (low-threshold mechanoreceptive; 6/27, 22%) and nociceptive neurons. Nociceptive neurons were further divided into wide-dynamic range neurons (3/27, 11%) and nociceptive-specific neurons (18/27, 67%). In the majority of these neurons, a proportion of the excitatory postsynaptic potentials (EPSPs) reached the threshold, and then generated random discharges of action potentials. Noxious mechanical stimuli applied to the receptive field elicited a discharge of action potentials on the barrage of EPSPs. In the case of noxious chemical stimulation applied as mustard oil to the orofacial area, the membrane potential shifted depolarization and the rate of spontaneous discharges gradually increased as did the noxious pinch-evoked discharge rates, which were usually associated with potentiated EPSP amplitudes.The present study provides evidence that SI neurons in deep layers III-V respond to the temporal summation of EPSPs due to noxious mechanical and chemical stimulation applied to the orofacial area and that these neurons may contribute to the processing of nociceptive information, including hyperalgesia.Many studies have reported that multiple cortical areas, including the primary somatosensory (SI) cortex, are involved in nociception [1-3]. The processing of the SI cortex has been analysed by non-invasive imaging techniques such as magnetoencephalography, positron emission tomography and functional magnetic resonance imaging, and the human SI cortex responds to noxious stimuli [4]. Extracellular unit recording techniques have demonstrated that monkey and cat SI neurons in the deeper lamina encode the intensity of noxious mechanical, thermal, chemical stimulation [5-9], and that rat SI cortical n
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