Complexity of spatiotemporal activity of a neural network model which depends on the degree of synchronization

Exact mean-field models for spiking neural networks with adaptation

Networks of spiking neurons with adaption have been shown to be able to reproduce a wide range of neural activities, including the emergent population bursting and spike synchrony that underpin brain disorders and normal function. Exact mean-field models derived from spiking neural networks are extremely valuable, as such models can be used to determine how individual neurons and the network they reside within interact to produce macroscopic network behaviours. In the paper, we derive and analyze a set of exact mean-field equations for the neural network with spike frequency adaptation. Specifically, our model is a network of Izhikevich neurons, where each neuron is modeled by a two dimensional system consisting of a quadratic integrate and fire equation plus an equation which implements spike frequency adaptation. Previous work deriving a mean-field model for this type of network, relied on the assumption of sufficiently slow dynamics of the adaptation variable. However, this approximation did not succeed in establishing an exact correspondence between the macroscopic description and the realistic neural network, especially when the adaptation time constant was not large. The challenge lies in how to achieve a closed set of mean-field equations with the inclusion of the mean-field dynamics of the adaptation variable. We address this problem by using a Lorentzian ansatz combined with the moment closure approach to arrive at a mean-field system in the thermodynamic limit. The resulting macroscopic description is capable of qualitatively and quantitatively describing the collective dynamics of the neural network, including transition between states where the individual neurons exhibit asynchronous tonic firing and synchronous bursting. We extend the approach to a network of two populations of neurons and discuss the accuracy and efficacy of our mean-field approximations by examining all assumptions that are imposed during the derivation. Numerical bifurcation analysis of our mean-field models reveals bifurcations not previously observed in the models, including a novel mechanism for emergence of bursting in the network. We anticipate our results will provide a tractable and reliable tool to investigate the underlying mechanism of brain function and dysfunction from the perspective of computational neuroscience.

The change of picrotoxin-induced epileptiform discharges to the beta oscillation by carbachol in rat hippocampal slices

The study aimed to determine whether and how the activation of the acetylcholine receptor affects epileptiform discharges in the CA3 region in a rat hippocampus. Picrotoxin (100 μM), a GABA_A receptor antagonist, was applied to a hippocampal slice to induce epileptiform discharges. The effects of the cholinergic agonist, carbachol, on the discharges were examined at the several concentrations (1–30 μM). Carbachol had different impacts on epileptiform discharges at the different concentrations. Relatively low concentrations of carbachol (<10 μM) increased the frequency but decreased the amplitude of the discharges. At 10 μM, carbachol induced the discharges, including bursts of theta frequency oscillations. At 30 μM, carbachol could induce bursts of beta frequency oscillations instead of epileptiform discharges. The amplitudes of the oscillations were smaller than those of the discharges. Carbachol suppressed the evoked population EPSPs (pEPSPs) in a dose-dependent manner. These effects were blocked by the muscarinic cholinergic receptor antagonist atropine sulfate. The high level of muscarinic receptor activation can replace epileptiform discharges with theta or beta oscillation. These results suggest that the dose-dependent alternation of the acetylcholine receptor activation may provide the three different stages the epileptiform discharges, the bursts of theta oscillation, and the bursts of the beta oscillation.

Pronounced differences in signal processing and synaptic plasticity between piriform-hippocampal network stages: a prominent role for adenosine

KEY POINTS

Extended trains of theta rhythm afferent activity lead to a biphasic response facilitation in field CA1 but not in the lateral perforant path input to the dentate gyrus. Processes that reverse long-term potentiation in field CA1 are not operative in the lateral perforant path: multiple lines of evidence indicate that this reflects differences in adenosine signalling. Adenosine A1 receptors modulate baseline synaptic transmission in the lateral olfactory tract but not the associational afferents of the piriform cortex. Levels of ecto-5'-nucleotidase (CD73), an enzyme that converts extracellular ATP into adenosine, are markedly different between regions and correlate with adenosine signalling and the efficacy of theta pulse stimulation in reversing long-term potentiation. Variations in transmitter mobilization, CD73 levels, and afferent divergence result in multivariate differences in signal processing through nodes in the cortico-hippocampal network.

ABSTRACT

The present study evaluated learning-related synaptic operations across the serial stages of the olfactory cortex-hippocampus network. Theta frequency stimulation produced very different time-varying responses in the Schaffer-commissural projections than in the lateral perforant path (LPP), an effect associated with distinctions in transmitter mobilization. Long-term potentiation (LTP) had a higher threshold in LPP field potential studies but not in voltage clamped neurons; coupled with input/output relationships, these results suggest that LTP threshold differences reflect the degree of input divergence. Theta pulse stimulation erased LTP in CA1 but not in the dentate gyrus (DG), although adenosine eliminated potentiation in both areas, suggesting that theta increases extracellular adenosine to a greater degree in CA1. Moreover, adenosine A1 receptor antagonism had larger effects on theta responses in CA1 than in the DG, and concentrations of ecto-5'-nucleotidase (CD73) were much higher in CA1. Input/output curves for two connections in the piriform cortex were similar to those for the LPP, whereas adenosine modulation again correlated with levels of CD73. In sum, multiple relays in a network extending from the piriform cortex through the hippocampus can be differentiated along three dimensions (input divergence, transmitter mobilization, adenosine modulation) that potently influence throughput and plasticity. A model that incorporates the regional differences, supplemented with data for three additional links, suggests that network output goes through three transitions during the processing of theta input. It is proposed that individuated relays allow the circuit to deal with different types of behavioural problems.

A neural network model of reliably optimized spike transmission

We studied the detailed structure of a neuronal network model in which the spontaneous spike activity is correctly optimized to match the experimental data and discuss the reliability of the optimized spike transmission. Two stochastic properties of the spontaneous activity were calculated: the spike-count rate and synchrony size. The synchrony size, expected to be an important factor for optimization of spike transmission in the network, represents a percentage of observed coactive neurons within a time bin, whose probability approximately follows a power-law. We systematically investigated how these stochastic properties could matched to those calculated from the experimental data in terms of the log-normally distributed synaptic weights between excitatory and inhibitory neurons and synaptic background activity induced by the input current noise in the network model. To ensure reliably optimized spike transmission, the synchrony size as well as spike-count rate were simultaneously optimized. This required changeably balanced log-normal distributions of synaptic weights between excitatory and inhibitory neurons and appropriately amplified synaptic background activity. Our results suggested that the inhibitory neurons with a hub-like structure driven by intensive feedback from excitatory neurons were a key factor in the simultaneous optimization of the spike-count rate and synchrony size, regardless of different spiking types between excitatory and inhibitory neurons.

Restoring the encoding properties of a stochastic neuron model by an exogenous noise

Here we evaluate the possibility of improving the encoding properties of an impaired neuronal system by superimposing an exogenous noise to an external electric stimulation signal. The approach is based on the use of mathematical neuron models consisting of stochastic HH-like circuit, where the impairment of the endogenous presynaptic inputs is described as a subthreshold injected current and the exogenous stimulation signal is a sinusoidal voltage perturbation across the membrane. Our results indicate that a correlated Gaussian noise, added to the sinusoidal signal can significantly increase the encoding properties of the impaired system, through the Stochastic Resonance (SR) phenomenon. These results suggest that an exogenous noise, suitably tailored, could improve the efficacy of those stimulation techniques used in neuronal systems, where the presynaptic sensory neurons are impaired and have to be artificially bypassed.

A MODEL OF HIPPOCAMPAL MEMORY BASED ON AN ADAPTIVE LEARNING RULE OF SYNAPSES

We constructed a neural network of the hippocampus and proposed an adaptive learning rule of synapses to simulate the storing and retrieving processes of memory in the hippocampus by a mechanism of resonance. The hippocampus network consists of CA1, CA3 and DG, in particular, CA1 is a storage of memory, which receives inputs from both EC through perforant path (PP) and CA3 through Schaffer collaterals (SC). The stimulated results showed that the memory trace was unable to be encoded in CA1 when only a single subthreshold signal from EC or CA3 was inputted, of which the main reason might be lack of the resonance of the two signals. We calculated signal-to-noise ratio (SNR) of the network, and found it reached a peak value at appropriate SC connection strength, indicating that a typical stochastic resonance phenomenon appeared in PP signal detection. The inputs from EC and CA3 were able to enhance the memory representation in CA1, although still incomplete. We used a learning rule to modify synaptic weights by which the network could learn an external pattern. The hippocampus network tended to be stable after sufficient evolution. Some CA1 neurons show synchronized firings which are used to represent memory and are clearer than observed memory traces before learning. The model and results provide a good guidance to our understanding of the mechanism of the hippocampus memory.

Emergence of sequence sensitivity in a hippocampal CA3–CA1 model

Recent studies have shown that place cells in the hippocampal CA1 region fire in a sequence sensitive manner. In this study we tested if hippocampal CA3 and CA1 regions can give rise to the sequence sensitivity. We used a two-layer CA3-CA1 hippocampal model that consisted of Hodgkin-Huxley style neuron models. Sequential input signals that mimicked signals projected from the entorhinal cortex gradually modified the synaptic conductances between CA3 pyramidal cells through spike-timing-dependent plasticity (STDP) and produced propagations of neuronal activity in the radial direction from stimulated pyramidal cells. This sequence dependent spatio-temporal activity was picked up by specific CA1 pyramidal cells through modification of Schaffer collateral synapses with STDP. After learning, these CA1 pyramidal cells responded with the highest probability to the learned sequence, while responding with a lower probability to different sequences. These results demonstrate that sequence sensitivity of CA1 place cells would emerge through computation in the CA3 and CA1 regions.

fMRI MODELS OF DENDRITIC AND ASTROCYTIC NETWORKS

In order to elucidate the relationships between hierarchical structures within the neocortical neuropil and the information carried by an ensemble of neurons encompassing a single voxel, it is essential to predict through volume conductor modeling LFPs representing average extracellular potentials, which are expressed in terms of interstitial potentials of individual cells in networks of gap-junctionally connected astrocytes and synaptically connected neurons. These relationships have been provided and can then be used to investigate how the underlying neuronal population activity can be inferred from the measurement of the BOLD signal through electrovascular coupling mechanisms across the blood-brain barrier. The importance of both synaptic and extrasynaptic transmission as the basis of electrophysiological indices triggering vascular responses between dendritic and astrocytic networks, and sequential configurations of firing patterns in composite neural networks is emphasized. The purpose of this review is to show how fMRI data may be used to draw conclusions about the information transmitted by individual neurons in populations generating the BOLD signal.

Regulation of spontaneous rhythmic activity and organization of pacemakers as memory traces by spike-timing-dependent synaptic plasticity in a hippocampal model

It is widely believed that memory traces can be stored through synaptic conductance modification of dense excitatory recurrent connections (ERCs) in the hippocampal CA3 region, namely associative memory. ERCs, on the other hand, are crucial to maintain spontaneous rhythmic activity in CA3. Since it is experimentally suggested that synaptic conductances of ERCs are modified through spike-timing-dependent synaptic plasticity (STDP), rhythmic activity might modify ERCs with the presence of STDP because rhythmic activity involves discharges of pyramidal cells. Memory patterns that are stored using ERCs might thus be modified or even destroyed. Rhythmic activity itself might also be modified. In this study, we assumed that the synaptic modification in the hippocampal CA3 was subject to STDP, and examined the coexistence of memory traces and rhythmic activity. The activity of the network was dominated by radially propagating burst activities (radial activities) that initiated at local regions and acted as pacemakers. The frequency of the rhythmic activity converged into one specific frequency with time, depending on the shape of the STDP functions. This indicates that rhythmic activity could be regulated by STDP. By applying theta burst stimulation locally to the network, we found that the stimulation whose frequency was higher than that of the spontaneous rhythmic activity could organize a new radial activity at the stimulus site. Newly organized radial activities were preserved for seconds after the termination of the stimulation. These results imply that CA3 with STDP has an ability to self-regulate rhythmic activity and that memory traces can coexist with the rhythmic activity by means of radial activity.

Stochastic resonance in the hippocampal CA3-CA1 model: a possible memory recall mechanism

Stochastic resonance (SR) in a hippocampal network model was investigated. The hippocampal model consists of two layers, CA3 and CA1. Pyramidal cells in CA3 are connected to pyramidal cells in CA1 through Schaffer collateral synapses. The CA3 network causes spontaneous irregular activity (broadband spectrum peaking at around 3 Hz), while the CA1 network does not. The activity of CA3 causes membrane potential fluctuations in CA1 pyramidal cells. The CA1 network also receives a subthreshold signal (2.5 or 50 Hz) through the perforant path (PP). The subthreshold PP signals can fire CA1 pyramidal cells in cooperation with the membrane potential fluctuations that work as noise. The firing of the CA1 network shows typical features of SR. When the frequency of the PP signal is in the gamma range (50 Hz), SR that takes place in the present model shows distinctive features. 50 Hz firing of CA1 pyramidal cells is modulated by the membrane potential fluctuations, resulting in bursts. Such burst firing in the CA1 network, which resembles the firing patterns observed in the real hippocampal CA1, improves performance of subthreshold signal detection in CA1. Moreover, memory embedded at Schaffer collateral synapses can be recalled by means of SR. When Schaffer collateral synapses in subregions of CA1 are augmented three-fold as a memory pattern. pyramidal cells in the subregions respond to the subthreshold PP signal due to SR, while pyramidal cells in the rest of CA1 do not fire.

Long-term change in synaptic transmission in CA3 circuits followed by spontaneous rhythmic activity in rat hippocampal slices

The relevance of long-term potentiation (LTP) at excitatory synapses in CA3 circuits to generation of spontaneous epileptiform bursts in CA3 was investigated using rat hippocampal slices. CA3 pyramidal cells were antidromically stimulated through Schaffer collaterals. Evoked field potentials were extracellularly recorded from the stratum pyramidale and the stratum radiatum in CA3. Therefore, field potentials reflecting recurrent excitatory post-synaptic potentials (EPSPs) and inhibitory post-synaptic potentials (IPSPs) were positive at the stratum pyramidale and negative at the stratum radiatum. First, we tested how the amplitude of the evoked field potentials depends on a gamma-aminobutyric acid (GABA(A)) antagonist. Both of the positive and negative field potential peaks reduced in the medium containing penicillin (2 mM) or bicuculline (20 microM). This suggests that unmasked EPSPs due to suppression of IPSPs do not result in an increase in the evoked potentials. Second, CA3 pyramidal cells were antidromically stimulated by tetanic stimulation of Schaffer collaterals in order to induce LTP at synapses in CA3 circuits. Both of the positive and negative field potentials increased, suggesting that recurrent EPSPs were enhanced by tetanic stimulation. Induction of LTP at recurrent excitatory synapses was followed by spontaneous epileptiform bursts which persisted throughout experiments (approximately 1.5 h), while LTP of afferent synaptic potential evoked by hilar test stimulation was not induced. These results suggest that LTP at the afferent synapses is not necessary to spontaneous epileptiform bursts in CA3, but LTP at excitatory synapses between CA3 pyramidal cells contribute to spontaneous epileptiform bursts.