scholarly journals Population dynamics of the modified theta model: macroscopic phase reduction and bifurcation analysis link microscopic neuronal interactions to macroscopic gamma oscillation

2014 ◽  
Vol 11 (95) ◽  
pp. 20140058 ◽  
Author(s):  
Kiyoshi Kotani ◽  
Ikuhiro Yamaguchi ◽  
Lui Yoshida ◽  
Yasuhiko Jimbo ◽  
G. Bard Ermentrout
Keyword(s):  
Bifurcation Analysis ◽  
Field Potential ◽  
Reversal Potential ◽  
Planck Equation ◽  
Gamma Oscillations ◽  
Gamma Oscillation ◽  
Synaptic Coupling ◽  
Time Constants ◽  
Shunting Inhibition ◽  
Synaptic Interactions

Gamma oscillations of the local field potential are organized by collective dynamics of numerous neurons and have many functional roles in cognition and/or attention. To mathematically and physiologically analyse relationships between individual inhibitory neurons and macroscopic oscillations, we derive a modification of the theta model, which possesses voltage-dependent dynamics with appropriate synaptic interactions. Bifurcation analysis of the corresponding Fokker–Planck equation (FPE) enables us to consider how synaptic interactions organize collective oscillations. We also develop the adjoint method (infinitesimal phase resetting curve) for simultaneous equations consisting of ordinary differential equations representing synaptic dynamics and a partial differential equation for determining the probability distribution of the membrane potential. This method provides a macroscopic phase response function (PRF), which gives insights into how it is modulated by external perturbation or internal changes of parameters. We investigate the effects of synaptic time constants and shunting inhibition on these gamma oscillations. The sensitivity of rising and decaying time constants is analysed in the oscillatory parameter regions; we find that these sensitivities are not largely dependent on rate of synaptic coupling but, rather, on current and noise intensity. Analyses of shunting inhibition reveal that it can affect both promotion and elimination of gamma oscillations. When the macroscopic oscillation is far from the bifurcation, shunting promotes the gamma oscillations and the PRF becomes flatter as the reversal potential of the synapse increases, indicating the insensitivity of gamma oscillations to perturbations. By contrast, when the macroscopic oscillation is near the bifurcation, shunting eliminates gamma oscillations and a stable firing state appears. More interestingly, under appropriate balance of parameters, two branches of bifurcation are found in our analysis of the FPE. In this case, shunting inhibition can effect both promotion and elimination of the gamma oscillation depending only on the reversal potential.

Aluminum Suppresses Effect of Nicotine on Gamma Oscillations (20-40 Hz) in Mouse Hippocampal Slices

2018 ◽  
Vol 17 (6) ◽  
pp. 404-411 ◽  
Author(s):  
Syeda Mehpara Farhat ◽  
Touqeer Ahmed
Keyword(s):  
Nicotinic Acetylcholine Receptors ◽  
Cholinergic System ◽  
Acetylcholine Receptors ◽  
Peak Power ◽  
Hippocampal Slices ◽  
Field Potential ◽  
Gamma Oscillations ◽  
Gamma Oscillation ◽  
Facilitatory Effect

Background: Aluminum (Al) causes neurodegeneration and its toxic effects on cholinergic system in the brain is well documented. However, it is unknown whether and how Al changes oscillation patterns, driven by the cholinergic system, in the hippocampus. Objective: We studied acute effects of Al on nicotinic acetylcholine receptors (nAChRs)-mediated modulation of persistent gamma oscillations in the hippocampus. Method: The field potential recording was done in CA3 area of acute hippocampal slices. Results: Carbachol-induced gamma oscillation peak power increased (1.32±0.09mV2/Hz, P<0.01) in control conditions (without Al) by application of 10µM nicotine as compared to baseline value normalized to 1. This nicotine-induced facilitation of gamma oscillation peak power was found to depend on non-α7 nAChRs. In slices with Al pre-incubation for three to four hours, gamma oscillation peak power was reduced (5.4±1.8mV2/Hz, P<0.05) and facilitatory effect of nicotine on gamma oscillation peak power was blocked as compared to the control (18.06±2.1mV2/Hz) or one hour Al pre-incubated slices (11.3±2.5mV2/Hz). Intriguingly wash-out, after three to four hours of Al incubation, failed to restore baseline oscillation power and its facilitation by nicotine as no difference was observed in gamma oscillation peak power between Al wash-out slices (3.4±1.1mV2/Hz) and slices without washout (3.6±0.9mV2/Hz). Conclusion: This study shows that at cellular level, exposure of hippocampal tissue to Al compromised nAChR-mediated facilitation of cholinergic hippocampal gamma oscillations. Longer in vitro Al exposure caused permanent changes in hippocampal oscillogenic circuitry and changed its sensitivity to nAChR-modulation. This study will help to understand the possible mechanism of cognitive decline induced by Al.

scholarly journals The Generation and Modulation of Distinct Gamma Oscillations with Local, Horizontal, and Feedback Connections in the Primary Visual Cortex: A Model Study on Large-Scale Networks

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Chuanliang Han ◽  
Tian Wang ◽  
Yujie Wu ◽  
Yang Li ◽  
Yi Yang ◽  
...  
Keyword(s):  
Visual Cortex ◽  
Primary Visual Cortex ◽  
Information Integration ◽  
Large Scale ◽  
Spatial Scales ◽  
Field Potential ◽  
Gamma Oscillations ◽  
Gamma Oscillation ◽  
Response Property ◽  
The Brain

Gamma oscillation (GAMMA) in the local field potential (LFP) is a synchronized activity commonly found in many brain regions, and it has been thought as a functional signature of network connectivity in the brain, which plays important roles in information processing. Studies have shown that the response property of GAMMA is related to neural interaction through local recurrent connections (RC), feed-forward (FF), and feedback (FB) connections. However, the relationship between GAMMA and long-range horizontal connections (HC) in the brain remains unclear. Here, we aimed to understand this question in a large-scale network model for the primary visual cortex (V1). We created a computational model composed of multiple excitatory and inhibitory units with biologically plausible connectivity patterns for RC, FF, FB, and HC in V1; then, we quantitated GAMMA in network models at different strength levels of HC and other connection types. Surprisingly, we found that HC and FB, the two types of large-scale connections, play very different roles in generating and modulating GAMMA. While both FB and HC modulate a fast gamma oscillation (around 50-60 Hz) generated by FF and RC, HC generates a new GAMMA oscillating around 30 Hz, whose power and peak frequency can also be modulated by FB. Furthermore, response properties of the two GAMMAs in a network with both HC and FB are different in a way that is highly consistent with a recent experimental finding for distinct GAMMAs in macaque V1. The results suggest that distinct GAMMAs are signatures for neural connections in different spatial scales and they might be related to different functions for information integration. Our study, for the first time, pinpoints the underlying circuits for distinct GAMMAs in a mechanistic model for macaque V1, which might provide a new framework to study multiple gamma oscillations in other cortical regions.

scholarly journals Distinct effects of heterogeneity and noise on gamma oscillation in a model of neuronal network with different reversal potential

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Tianyi Zheng ◽  
Kiyoshi Kotani ◽  
Yasuhiko Jimbo
Keyword(s):  
Neuronal Network ◽  
Temporal Dynamics ◽  
Finite Size ◽  
Reversal Potential ◽  
Planck Equation ◽  
Attentional Selection ◽  
Gamma Oscillation ◽  
Stochastic Fluctuation ◽  
Brain Functions ◽  
Gabaergic Synapses

AbstractGamma oscillation is crucial in brain functions such as attentional selection, and is inextricably linked to both heterogeneity and noise (or so-called stochastic fluctuation) in neuronal networks. However, under coexistence of these factors, it has not been clarified how the synaptic reversal potential modulates the entraining of gamma oscillation. Here we show distinct effects of heterogeneity and noise in a population of modified theta neurons randomly coupled via GABAergic synapses. By introducing the Fokker-Planck equation and circular cumulants, we derive a set of two-cumulant macroscopic equations. In bifurcation analyses, we find a stabilizing effect of heterogeneity and a nontrivial effect of noise that results in promoting, diminishing, and shifting the oscillatory region, and is largely dependent on the reversal potential of GABAergic synapses. These findings are verified by numerical simulations of a finite-size neuronal network. Our results reveal that slight changes in reversal potential and magnitude of stochastic fluctuations can lead to immediate control of gamma oscillation, which would results in complex spatio-temporal dynamics for attentional selection and recognition.

scholarly journals Impaired spike-gamma coupling of area CA3 fast-spiking interneurons as the earliest functional impairment in the AppNL-G-F mouse model of Alzheimer’s disease

2021 ◽  
Author(s):  
Luis Enrique Arroyo-García ◽  
Arturo G. Isla ◽  
Yuniesky Andrade-Talavera ◽  
Hugo Balleza-Tapia ◽  
Raúl Loera-Valencia ◽  
...  
Keyword(s):  
Alzheimer’S Disease ◽  
Alzheimer's Disease ◽  
Cognitive Impairment ◽  
Mouse Model ◽  
Functional Impairment ◽  
Amyloid Β ◽  
Gamma Oscillations ◽  
Gamma Oscillation ◽  
Gamma Rhythm ◽  
Fast Spiking

AbstractIn Alzheimer’s disease (AD) the accumulation of amyloid-β (Aβ) correlates with degradation of cognition-relevant gamma oscillations. The gamma rhythm relies on proper neuronal spike-gamma coupling, specifically of fast-spiking interneurons (FSN). Here we tested the hypothesis that decrease in gamma power and FSN synchrony precede amyloid plaque deposition and cognitive impairment in AppNL-G-F knock-in mice (AppNL-G-F). The aim of the study was to evaluate the amyloidogenic pathology progression in the novel AppNL-G-F mouse model using in vitro electrophysiological network analysis. Using patch clamp of FSNs and pyramidal cells (PCs) with simultaneous gamma oscillation recordings, we compared the activity of the hippocampal network of wild-type mice (WT) and the AppNL-G-F mice at four disease stages (1, 2, 4, and 6 months of age). We found a severe degradation of gamma oscillation power that is independent of, and precedes Aβ plaque formation, and the cognitive impairment reported previously in this animal model. The degradation correlates with increased Aβ1-42 concentration in the brain. Analysis on the cellular level showed an impaired spike-gamma coupling of FSN from 2 months of age that correlates with the degradation of gamma oscillations. From 6 months of age PC firing becomes desynchronized also, correlating with reports in the literature of robust Aβ plaque pathology and cognitive impairment in the AppNL-G-F mice. This study provides evidence that impaired FSN spike-gamma coupling is one of the earliest functional impairment caused by the amyloidogenic pathology progression likely is the main cause for the degradation of gamma oscillations and consequent cognitive impairment. Our data suggests that therapeutic approaches should be aimed at restoring normal FSN spike-gamma coupling and not just removal of Aβ.

scholarly journals Superimposed gratings induce diverse response patterns of gamma oscillations in primary visual cortex

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Bin Wang ◽  
Chuanliang Han ◽  
Tian Wang ◽  
Weifeng Dai ◽  
Yang Li ◽  
...  
Keyword(s):  
Visual Cortex ◽  
Primary Visual Cortex ◽  
Field Potential ◽  
Gamma Oscillations ◽  
Neural Mechanisms ◽  
Model Parameters ◽  
Response Patterns ◽  
Region Difference ◽  
High Gamma ◽  
Spiking Activity

AbstractStimulus-dependence of gamma oscillations (GAMMA, 30–90 Hz) has not been fully understood, but it is important for revealing neural mechanisms and functions of GAMMA. Here, we recorded spiking activity (MUA) and the local field potential (LFP), driven by a variety of plaids (generated by two superimposed gratings orthogonal to each other and with different contrast combinations), in the primary visual cortex of anesthetized cats. We found two distinct narrow-band GAMMAs in the LFPs and a variety of response patterns to plaids. Similar to MUA, most response patterns showed that the second grating suppressed GAMMAs driven by the first one. However, there is only a weak site-by-site correlation between cross-orientation interactions in GAMMAs and those in MUAs. We developed a normalization model that could unify the response patterns of both GAMMAs and MUAs. Interestingly, compared with MUAs, the GAMMAs demonstrated a wider range of model parameters and more diverse response patterns to plaids. Further analysis revealed that normalization parameters for high GAMMA, but not those for low GAMMA, were significantly correlated with the discrepancy of spatial frequency between stimulus and sites’ preferences. Consistent with these findings, normalization parameters and diversity of high GAMMA exhibited a clear transition trend and region difference between area 17 to 18. Our results show that GAMMAs are also regulated in the form of normalization, but that the neural mechanisms for these normalizations might differ from those of spiking activity. Normalizations in different brain signals could be due to interactions of excitation and inhibitions at multiple stages in the visual system.

Propagating Neuronal Discharges in Neocortical Slices: Computational and Experimental Study

1997 ◽  
Vol 78 (3) ◽  
pp. 1199-1211 ◽  
Author(s):  
David Golomb ◽  
Yael Amitai
Keyword(s):  
Experimental Study ◽  
Ampa Receptors ◽  
Potassium Current ◽  
Initial Conditions ◽  
Field Potential ◽  
Integration Time ◽  
Synaptic Coupling ◽  
Discharge Velocity ◽  
Slow Potassium ◽  
Typical Cell

Golomb, David and Yael Amitai. Propagating neuronal discharges in neocortical slices: computational and experimental study. J. Neurophysiol. 78: 1199–1211, 1997. We studied the propagation of paroxysmal discharges in disinhibited neocortical slices by developing and analyzing a model of excitatory regular-spiking neocortical cells with spatially decaying synaptic efficacies and by field potential recording in rat slices. Evoked discharges may propagate both in the model and in the experiment. The model discharge propagates as a traveling pulse with constant velocity and shape. The discharge shape is determined by an interplay between the synaptic driving force and the neuron's intrinsic currents, in particular the slow potassium current. In the model, N-methyl-d-aspartate (NMDA) conductance contributes much less to the discharge velocity than amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) conductance. Blocking NMDA receptors experimentally with 2-amino-5-phosphonovaleric acid (APV) has no significant effect on the discharge velocity. In both model and experiments, propagation occurs for AMPA synaptic coupling g AMPA above a certain threshold, at which the velocity is finite (non-zero). The discharge velocity grows linearly with the g AMPA for g AMPA much above the threshold. In the experiments, blocking AMPA receptors gradually by increasing concentrations of 6-cyano-7-nitroquinoxaline-2,3-dione (CNQX) in the perfusing solution results in a gradual reduction of the discharge velocity until propagation stops altogether, thus confirming the model prediction. When discharges are terminated in the model by the slow potassium current, a network with the same parameter set may display discharges with several forms, which have different velocities and numbers of spikes; initial conditions select the exhibited pattern. When the discharge is also terminated by strong synaptic depression, there is only one discharge form for a particular parameter set; the velocity grows continuously with increased synaptic conductances. No indication for more than one discharge velocity was observed experimentally. If the AMPA decay rate increases while the maximal excitatory postsynaptic conductance (EPSC) a cell receives is kept fixed, the velocity increases by ∼20% until it reaches a saturated value. Therefore the discharge velocity is determined mainly by the cells' integration time of input EPSCs. We conclude, on the basis of both the experiments and the model, that the total amount of excitatory conductance a typical cell receives in a control slice exhibiting paroxysmal discharges is only ∼5 times larger than the excitatory conductance needed for raising the potential of a resting cell above its action potential threshold.

scholarly journals Frontal eye field microstimulation induces task-dependent gamma oscillations in the lateral intraparietal area

2012 ◽  
Vol 108 (5) ◽  
pp. 1392-1402 ◽  
Author(s):  
Elsie Premereur ◽  
Wim Vanduffel ◽  
Pieter R. Roelfsema ◽  
Peter Janssen
Keyword(s):  
Spatial Attention ◽  
Field Potential ◽  
Gamma Oscillations ◽  
Oculomotor Control ◽  
Saccade Target ◽  
Frontal Eye Field ◽  
Alpha Power ◽  
Lateral Intraparietal Area ◽  
Electrical Microstimulation ◽  
Gamma Power

Macaque frontal eye fields (FEF) and the lateral intraparietal area (LIP) are high-level oculomotor control centers that have been implicated in the allocation of spatial attention. Electrical microstimulation of macaque FEF elicits functional magnetic resonance imaging (fMRI) activations in area LIP, but no study has yet investigated the effect of FEF microstimulation on LIP at the single-cell or local field potential (LFP) level. We recorded spiking and LFP activity in area LIP during weak, subthreshold microstimulation of the FEF in a delayed-saccade task. FEF microstimulation caused a highly time- and frequency-specific, task-dependent increase in gamma power in retinotopically corresponding sites in LIP: FEF microstimulation produced a significant increase in LIP gamma power when a saccade target appeared and remained present in the LIP receptive field (RF), whereas less specific increases in alpha power were evoked by FEF microstimulation for saccades directed away from the RF. Stimulating FEF with weak currents had no effect on LIP spike rates or on the gamma power during memory saccades or passive fixation. These results provide the first evidence for task-dependent modulations of LFPs in LIP caused by top-down stimulation of FEF. Since the allocation and disengagement of spatial attention in visual cortex have been associated with increases in gamma and alpha power, respectively, the effects of FEF microstimulation on LIP are consistent with the known effects of spatial attention.

scholarly journals Coherent and intermittent ensemble oscillations emerge from networks of irregular spiking neurons

2016 ◽  
Vol 115 (1) ◽  
pp. 457-469 ◽  
Author(s):  
Mahmood S. Hoseini ◽  
Ralf Wessel
Keyword(s):  
Single Neuron ◽  
Experimental Studies ◽  
Field Potential ◽  
Gamma Oscillations ◽  
Peak Frequency ◽  
Spiking Neurons ◽  
Network Activity ◽  
Cortical Circuits ◽  
Model Network ◽  
Low Rate

Local field potential (LFP) recordings from spatially distant cortical circuits reveal episodes of coherent gamma oscillations that are intermittent, and of variable peak frequency and duration. Concurrently, single neuron spiking remains largely irregular and of low rate. The underlying potential mechanisms of this emergent network activity have long been debated. Here we reproduce such intermittent ensemble oscillations in a model network, consisting of excitatory and inhibitory model neurons with the characteristics of regular-spiking (RS) pyramidal neurons, and fast-spiking (FS) and low-threshold spiking (LTS) interneurons. We find that fluctuations in the external inputs trigger reciprocally connected and irregularly spiking RS and FS neurons in episodes of ensemble oscillations, which are terminated by the recruitment of the LTS population with concurrent accumulation of inhibitory conductance in both RS and FS neurons. The model qualitatively reproduces experimentally observed phase drift, oscillation episode duration distributions, variation in the peak frequency, and the concurrent irregular single-neuron spiking at low rate. Furthermore, consistent with previous experimental studies using optogenetic manipulation, periodic activation of FS, but not RS, model neurons causes enhancement of gamma oscillations. In addition, increasing the coupling between two model networks from low to high reveals a transition from independent intermittent oscillations to coherent intermittent oscillations. In conclusion, the model network suggests biologically plausible mechanisms for the generation of episodes of coherent intermittent ensemble oscillations with irregular spiking neurons in cortical circuits.

scholarly journals Enhanced Temporal Stability of Cholinergic Hippocampal Gamma Oscillations Following Respiratory Alkalosis In Vitro

2001 ◽  
Vol 85 (5) ◽  
pp. 2063-2069 ◽  
Author(s):  
Kerstin Stenkamp ◽  
J. Matias Palva ◽  
Marylka Uusisaari ◽  
Sebastian Schuchmann ◽  
Dietmar Schmitz ◽  
...  
Keyword(s):  
Time Constant ◽  
Decay Time ◽  
Oscillation Frequency ◽  
Hippocampal Slices ◽  
Temporal Stability ◽  
Field Potential ◽  
Gamma Oscillations ◽  
Decay Time Constant ◽  
The Mean

The decrease in brain CO2 partial pressure (pCO2) that takes place both during voluntary and during pathological hyperventilation is known to induce gross alterations in cortical functions that lead to subjective sensations and altered states of consciousness. The mechanisms that mediate the effects of the decrease in pCO2 at the neuronal network level are largely unexplored. In the present work, the modulation of gamma oscillations by hypocapnia was studied in rat hippocampal slices. Field potential oscillations were induced by the cholinergic agonist carbachol under an N-methyl-D-aspartate (NMDA)-receptor blockade and were recorded in the dendritic layer of the CA3 region with parallel measurements of changes in interstitial and intraneuronal pH (pHo and pHi, respectively). Hypocapnia from 5 to 1% CO2 led to a stable monophasic increase of 0.5 and 0.2 units in pHo and pHi, respectively. The mean oscillation frequency increased slightly but significantly from 32 to 34 Hz and the mean gamma-band amplitude (20 to 80 Hz) decreased by 20%. Hypocapnia induced a dramatic enhancement of the temporal stability of the oscillations, as was indicated by a two-fold increase in the exponential decay time constant fitted to the autocorrelogram. A rise in pHi evoked by the weak base trimethylamine (TriMA) was associated with a slight increase in oscillation frequency (37 to 39 Hz) and a decrease in amplitude (30%). Temporal stability, on the other hand, was decreased by TriMA, which suggests that its enhancement in 1% CO2 was related to the rise in pHo. In 1% CO2, the decay-time constant of the evoked monosynaptic pyramidal inhibitory postsynaptic current (IPSC) was unaltered but its amplitude was enhanced. This increase in IPSC amplitude seems to significantly contribute to the enhancement of temporal stability because the enhancement was almost fully reversed by a low concentration of bicuculline. These results suggest that changes in brain pCO2 can have a strong influence on the temporal modulation of gamma rhythms.

Spike Timing of Lacunosom-Moleculare Targeting Interneurons and CA3 Pyramidal Cells During High-Frequency Network Oscillations In Vitro

2007 ◽  
Vol 98 (1) ◽  
pp. 96-104 ◽  
Author(s):  
Jay Spampanato ◽  
Istvan Mody
Keyword(s):  
High Frequency ◽  
Epileptiform Activity ◽  
Field Potential ◽  
Pyramidal Cells ◽  
Gamma Oscillations ◽  
Spike Timing ◽  
Network Activity ◽  
Network Oscillations ◽  
Ca3 Pyramidal Cells

Network activity in the 200- to 600-Hz range termed high-frequency oscillations (HFOs) has been detected in epileptic tissue from both humans and rodents and may underlie the mechanism of epileptogenesis in experimental rodent models. Slower network oscillations including theta and gamma oscillations as well as ripples are generated by the complex spike timing and interactions between interneurons and pyramidal cells of the hippocampus. We determined the activity of CA3 pyramidal cells, stratum oriens lacunosum-moleculare (O-LM) and s. radiatum lacunosum-moleculare (R-LM) interneurons during HFO in the in vitro low-Mg2+ model of epileptiform activity in GIN mice. In these animals, interneurons can be identified prior to cell-attached recordings by the expression of green-fluorescent protein (GFP). Simultaneous local field potential recordings from s. pyramidale and on-cell recordings of individual interneurons and principal cells revealed three primary firing behaviors of the active cells: 36% of O-LM interneurons and 60% of pyramidal cells fired action potentials at high frequencies during the HFO. R-LM interneurons were biphasic in that they fired at high frequency at the beginning of the HFO but stopped firing before its end. When considering only the highest frequency component of the oscillations most pyramidal cells fired on the rising phase of the oscillation. These data provide evidence for functional distinction during HFOs within otherwise homogeneous groups of O-LM interneurons and pyramidal cells.

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