Spontaneous Local Gamma Oscillation Selectively Enhances Neural Network Responsiveness

Synchronized oscillation is very commonly observed in many neuronal systems and might play an important role in the response properties of the system. We have studied how the spontaneous oscillatory activity affects the responsiveness of a neuronal network, using a neural network model of the visual cortex built from Hodgkin-Huxley type excitatory (E-) and inhibitory (I-) neurons. When the isotropic local E-I and I-E synaptic connections were sufficiently strong, the network commonly generated gamma frequency oscillatory firing patterns in response to random feed-forward (FF) input spikes. This spontaneous oscillatory network activity injects a periodic local current that could amplify a weak synaptic input and enhance the network's responsiveness. When E-E connections were added, we found that the strength of oscillation can be modulated by varying the FF input strength without any changes in single neuron properties or interneuron connectivity. The response modulation is proportional to the oscillation strength, which leads to self-regulation such that the cortical network selectively amplifies various FF inputs according to its strength, without requiring any adaptation mechanism. We show that this selective cortical amplification is controlled by E-E cell interactions. We also found that this response amplification is spatially localized, which suggests that the responsiveness modulation may also be spatially selective. This suggests a generalized mechanism by which neural oscillatory activity can enhance the selectivity of a neural network to FF inputs.     

Coexistence of lateral and co-tuned inhibitory configurations in cortical networks

The responses of neurons in sensory cortex depend on the summation of excitatory and inhibitory synaptic inputs. How the excitatory and inhibitory inputs scale with stimulus depends on the network architecture, which ranges from the lateral inhibitory configuration where excitatory inputs are more narrowly tuned than inhibitory inputs, to the co-tuned configuration where both are tuned equally. The underlying circuitry that gives rise to lateral inhibition and co-tuning is yet unclear. Using large-scale network simulations with experimentally determined connectivity patterns and simulations with rate models, we show that the spatial extent of the input determined the configuration: there was a smooth transition from lateral inhibition with narrow input to co-tuning with broad input. The transition from lateral inhibition to co-tuning was accompanied by shifts in overall gain (reduced), output firing pattern (from tonic to phasic) and rate-level functions (from non-monotonic to monotonically increasing). The results suggest that a single cortical network architecture could account for the extended range of experimentally observed response types between the extremes of lateral inhibitory versus co-tuned configurations.     

Neuronal firing rates account for distractor effects on mnemonic accuracy in a visuo-spatial working memory task

Persistent neural activity constitutes one neuronal correlate of working memory, the ability to hold and manipulate information across time, a prerequisite for cognition. Yet, the underlying neuronal mechanisms are still elusive. Here, we design a visuo- spatial delayed-response task to identify the relationship between the cue-distractor spatial distance and mnemonic accuracy. Using a shared experimental and computational test protocol, we probe human subjects in computer experiments, and subsequently we evaluate different neural mechanisms underlying persistent activity using an in silico prefrontal network model. Five modes of action of the network were tested: weak or strong synaptic interactions, wide synaptic arborization, cellular bistability and reduced synaptic NMDA component. The five neural mechanisms and the human behavioral data, all exhibited a significant deterioration of the mnemonic accuracy with decreased spatial distance between the distractor and the cue. A subsequent computational analysis revealed that the firing rate and not the neural mechanism per se, accounted for the positive correlation between mnemonic accuracy and spatial distance. Moreover, the computational modeling predicts an inverse correlation between accuracy and distractibility. In conclusion, any pharmacological modulation, pathological condition or memory training paradigm targeting the underlying neural circuitry and altering the net population firing rate during the delay is predicted to determine the amount of influence of a visual distraction.     

Relating Alpha Power and Phase to Population Firing and Hemodynamic Activity Using a Thalamo-cortical Neural Mass Model

Oscillations are ubiquitous phenomena in the animal and human brain. Among them, the alpha rhythm in human EEG is one of the most prominent examples. However, its precise mechanisms of generation are still poorly understood. It was mainly this lack of knowledge that motivated a number of simultaneous electroencephalography (EEG) – functional magnetic resonance imaging (fMRI) studies. This approach revealed how oscillatory neuronal signatures such as the alpha rhythm are paralleled by changes of the blood oxygenation level dependent (BOLD) signal. Several such studies revealed a negative correlation between the alpha rhythm and the hemodynamic BOLD signal in visual cortex and a positive correlation in the thalamus. In this study we explore the potential generative mechanisms that lead to those observations. We use a bursting capable Stefanescu-Jirsa 3D (SJ3D) neural-mass model that reproduces a wide repertoire of prominent features of local neuronal-population dynamics. We construct a thalamo-cortical network of coupled SJ3D nodes considering excitatory and inhibitory directed connections. The model suggests that an inverse correlation between cortical multi-unit activity, i.e. the firing of neuronal populations, and narrow band local field potential oscillations in the alpha band underlies the empirically observed negative correlation between alpha-rhythm power and fMRI signal in visual cortex. Furthermore the model suggests that the interplay between tonic and bursting mode in thalamus and cortex is critical for this relation. This demonstrates how biophysically meaningful modelling can generate precise and testable hypotheses about the underpinnings of large-scale neuroimaging signals.     

Neural adaptation facilitates oscillatory responses to static inputs in a recurrent network of ON and OFF cells

We investigate the role of adaptation in a neural field model, composed of ON and OFF cells, with delayed all-to-all recurrent connections. As external spatially profiled inputs drive the network, ON cells receive inputs directly, while OFF cells receive an inverted image of the original signals. Via global and delayed inhibitory connections, these signals can cause the system to enter states of sustained oscillatory activity. We perform a bifurcation analysis of our model to elucidate how neural adaptation influences the ability of the network to exhibit oscillatory activity. We show that slow adaptation encourages input-induced rhythmic states by decreasing the Andronov–Hopf bifurcation threshold. We further determine how the feedback and adaptation together shape the resonant properties of the ON and OFF cell network and how this affects the response to time-periodic input. By introducing an additional frequency in the system, adaptation alters the resonance frequency by shifting the peaks where the response is maximal. We support these results with numerical experiments of the neural field model. Although developed in the context of the circuitry of the electric sense, these results are applicable to any network of spontaneously firing cells with global inhibitory feedback to themselves, in which a fraction of these cells receive external input directly, while the remaining ones receive an inverted version of this input via feedforward di-synaptic inhibition. Thus the results are relevant beyond the many sensory systems where ON and OFF cells are usually identified, and provide the backbone for understanding dynamical network effects of lateral connections and various forms of ON/OFF responses.     

Asynchronous Rate Chaos in Spiking Neuronal Circuits

The brain exhibits temporally complex patterns of activity with features similar to those of chaotic systems. Theoretical studies over the last twenty years have described various computational advantages for such regimes in neuronal systems. Nevertheless, it still remains unclear whether chaos requires specific cellular properties or network architectures, or whether it is a generic property of neuronal circuits. We investigate the dynamics of networks of excitatory-inhibitory (EI) spiking neurons with random sparse connectivity operating in the regime of balance of excitation and inhibition. Combining Dynamical Mean-Field Theory with numerical simulations, we show that chaotic, asynchronous firing rate fluctuations emerge generically for sufficiently strong synapses. Two different mechanisms can lead to these chaotic fluctuations. One mechanism relies on slow I-I inhibition which gives rise to slow subthreshold voltage and rate fluctuations. The decorrelation time of these fluctuations is proportional to the time constant of the inhibition. The second mechanism relies on the recurrent E-I-E feedback loop. It requires slow excitation but the inhibition can be fast. In the corresponding dynamical regime all neurons exhibit rate fluctuations on the time scale of the excitation. Another feature of this regime is that the population-averaged firing rate is substantially smaller in the excitatory population than in the inhibitory population. This is not necessarily the case in the I-I mechanism. Finally, we discuss the neurophysiological and computational significance of our results.     

Modelling Feedback Excitation,Pacemaker Properties and Sensory Switching of Electrically Coupled Brainstem Neurons Controlling Rhythmic Activity

What cellular and network properties allow reliable neuronal rhythm generation or firing that can be started and stopped by brief synaptic inputs? We investigate rhythmic activity in an electrically-coupled population of brainstem neurons driving swimming locomotion in young frog tadpoles, and how activity is switched on and off by brief sensory stimulation. We build a computational model of 30 electrically-coupled conditional pacemaker neurons on one side of the tadpole hindbrain and spinal cord. Based on experimental estimates for neuron properties, population sizes, synapse strengths and connections, we show that: long-lasting, mutual, glutamatergic excitation between the neurons allows the network to sustain rhythmic pacemaker firing at swimming frequencies following brief synaptic excitation; activity persists but rhythm breaks down without electrical coupling; NMDA voltage-dependency doubles the range of synaptic feedback strengths generating sustained rhythm. The network can be switched on and off at short latency by brief synaptic excitation and inhibition. We demonstrate that a population of generic Hodgkin-Huxley type neurons coupled by glutamatergic excitatory feedback can generate sustained asynchronous firing switched on and off synaptically. We conclude that networks of neurons with NMDAR mediated feedback excitation can generate self-sustained activity following brief synaptic excitation. The frequency of activity is limited by the kinetics of the neuron membrane channels and can be stopped by brief inhibitory input. Network activity can be rhythmic at lower frequencies if the neurons are electrically coupled. Our key finding is that excitatory synaptic feedback within a population of neurons can produce switchable, stable, sustained firing without synaptic inhibition.     

Reciprocal inhibition and slow calcium decay in perigeniculate interneurons explain changes of spontaneous firing of thalamic cells caused by cortical inactivation

The role of cortical feedback in the thalamocortical processing loop has been extensively investigated over the last decades. With an exception of several cases, these searches focused on the cortical feedback exerted onto thalamo-cortical relay (TC) cells of the dorsal lateral geniculate nucleus (LGN). In a previous, physiological study, we showed in the cat visual system that cessation of cortical input, despite decrease of spontaneous activity of TC cells, increased spontaneous firing of their recurrent inhibitory interneurons located in the perigeniculate nucleus (PGN). To identify mechanisms underlying such functional changes we conducted a modeling study in NEURON on several networks of point neurons with varied model parameters, such as membrane properties, synaptic weights and axonal delays. We considered six network topologies of the retino-geniculo-cortical system. All models were robust against changes of axonal delays except for the delay between the LGN feed-forward interneuron and the TC cell. The best representation of physiological results was obtained with models containing reciprocally connected PGN cells driven by the cortex and with relatively slow decay of intracellular calcium. This strongly indicates that the thalamic reticular nucleus plays an essential role in the cortical influence over thalamo-cortical relay cells while the thalamic feed-forward interneurons are not essential in this process. Further, we suggest that the dependence of the activity of PGN cells on the rate of calcium removal can be one of the key factors determining individual cell response to elimination of cortical input.     

A Simulation Study to Examine the Effect of Common Motoneuron Inputs on Correlated Patterns of Motor Unit Discharge

The influence of common oscillatory inputs to the motoneuron pool on correlated patterns of motor unit discharge was examined using model simulations. Motor unit synchronization, in-phase fluctuations in mean firing rates known as ‘common drive’, and the coefficient of variation of the muscle force were examined as the frequency and amplitude of common oscillatory inputs to the motoneuron pool were varied. The amount of synchronization, the peak correlation between mean firing rates and the coefficient of variation of the force varied with both the frequency and amplitude of the common input signal. Values for ‘common drive’ and the force coefficient of variation were highest for oscillatory inputs at frequencies less than 5 Hz, while synchronization reached a maximum when the frequency of the common input was close to the average motor unit firing rate. The frequency of the common input signal for which the highest levels of synchronization were observed increased as motoneuron firing rates increased in response to higher target force levels. The simulation results suggest that common low-frequency oscillations in motor unit firing rates and short-term synchronization result from oscillatory activity in different bands of the frequency spectrum of shared motoneuron inputs. The results also indicate that the amount of synchronization between motor unit discharges depends not only on the amplitude of the shared input signal, but also on its frequency in relation to the present firing rates of the individual motor units.     

Synaptic interactions mediating synchrony and oscillations in primate sensorimotor cortex.

The appearance of oscillatory modes of 'gamma' activity in many cortical areas of different species has generated interest in understanding their underlying mechanisms and possible functions. This paper reviews evidence from studies on primate motor cortex showing that oscillatory activity entrains many neurons during periods of exploratory manipulative behavior. These oscillatory episodes synchronize widely spread neurons in sensorimotor cortex bilaterally, including descending corticospinal neurons, as evidenced by correlated modulations in EMG activity. The resulting neural synchronization involves task-related and -unrelated neurons similarly, suggesting that it is more likely to play some global role in attention than mediating any obvious interactions involved in coordinating movements. Intracellular recordings have elucidated the strength and types of synaptic interactions between motor cortical neurons that are involved in both normal and oscillatory activity. Spike-triggered averages (STAs) of intracellular membrane potentials have revealed serial connections in the form of unitary excitatory and inhibitory post-synaptic potentials (EPSPs and IPSPs). More commonly, STAs showed large synchronous excitatory or inhibitory potentials (ASEPs and ASIPs) beginning before the trigger spike and composed of multiple unitary events. ASEPs involved synchronous activity in a larger and more widespread group of presynaptic neurons than ASIPs. During oscillatory episodes synchronized excitatory and inhibitory synaptic potentials occurred in varying proportions. EPSPs evoked by stimulating neighboring cortical sites during the depolarizing phase of spontaneous oscillations showed evidence of transient potentiation. These observations are consistent with several functional hypotheses, but fit best with a possible role in attention or arousal.     

Activated cortical states: Experiments, analyses and models

In awake animals, the cerebral cortex displays an "activated" state, with distinct characteristics compared to other states like slow-wave sleep or anesthesia. These characteristics include a sustained depolarized membrane potential (V(m)) and irregular firing activity. In the present paper, we evaluate our understanding of cortical activated states from a computational neuroscience point of view. We start by reviewing the electrophysiological characteristics of activated cortical states based on recordings and analysis performed in awake cat association cortex. These analyses show that cortical activity is characterized by an apparent Poisson-distributed stochastic dynamics, both at the single-cell and population levels, and that single cells display a high-conductance state dominated by inhibition. We next overview computational models of the "awake" cortex, and perform the same analyses as in the experiments. Many properties identified experimentally are indeed reproduced by models, such as depolarized V(m), irregular firing with apparent Poisson statistics, and the determinant role of inhibitory fluctuations on spiking. However, other features are not well reproduced, such as firing statistics and the conductance state of the membrane, suggesting that the network state displayed by models is not entirely correct. We also show how networks can approach a correct conductance state, suggesting ways by which future models will generate activity fully consistent with experimental data.     

Spike-rate adaptation and neuronal bursting in a mean-field model of brain activity

Spike-rate adaptation is investigated within a mean-field model of brain activity. Two different mechanisms of negative feedback are considered; one involving modulation of the mean firing threshold, and the other, modulation of the mean synaptic strength. Adaptation to a constant stimulus is shown to take place for both mechanisms, and limit-cycle oscillations in the firing rate corresponding to bursts of neuronal activity are investigated. These oscillations are found to result from a Hopf bifurcation when the equilibrium lies between the local maximum and local minimum of a given nullcline. Oscillations with amplitudes significantly below the maximum firing rate are found over a narrow range of possible equilibriums.     

Mean field model of acetylcholine mediated dynamics in the cerebral cortex

A recent continuum model of the large scale electrical activity of the cerebral cortex is generalized to include cholinergic modulation. In this model, dynamic modulation of synaptic strength acts over the time scales of nicotinic and muscarinic receptor action. The cortical model is analyzed to determine the effect of acetylcholine (ACh) on its steady states, linear stability, spectrum, and temporal responses to changes in subcortical input. ACh increases the firing rate in steady states of the system. Changing ACh concentration does not introduce oscillatory behavior into the system, but increases the overall spectral power. Model responses to pulses in subcortical input are affected by the tonic level of ACh concentration, with higher levels of ACh increasing the magnitude firing rate response of excitatory cortical neurons to pulses of subcortical input. Numerical simulations are used to explore the temporal dynamics of the model in response to changes in ACh concentration. Evidence is seen of a transition from a state in which intracortical inputs are emphasized to a state where thalamic afferents have enhanced influence. Perturbations in ACh concentration cause changes in the firing rate of cortical neurons, with rapid responses due to fast acting facilitatory effects of nicotinic receptors on subcortical afferents, and slower responses due to muscarinic suppression of intracortical connections. Together, these numerical simulations demonstrate that the actions of ACh could be a significant factor modulating early components of evoked response potentials.     

The influence of depolarization block on seizure-like activity in networks of excitatory and inhibitory neurons

The inhibitory restraint necessary to suppress aberrant activity can fail when inhibitory neurons cease to generate action potentials as they enter depolarization block. We investigate possible bifurcation structures that arise at the onset of seizure-like activity resulting from depolarization block in inhibitory neurons. Networks of conductance-based excitatory and inhibitory neurons are simulated to characterize different types of transitions to the seizure state, and a mean field model is developed to verify the generality of the observed phenomena of excitatory-inhibitory dynamics. Specifically, the inhibitory population’s activation function in the Wilson-Cowan model is modified to be non-monotonic to reflect that inhibitory neurons enter depolarization block given strong input. We find that a physiological state and a seizure state can coexist, where the seizure state is characterized by high excitatory and low inhibitory firing rate. Bifurcation analysis of the mean field model reveals that a transition to the seizure state may occur via a saddle-node bifurcation or a homoclinic bifurcation. We explain the hysteresis observed in network simulations using these two bifurcation types. We also demonstrate that extracellular potassium concentration affects the depolarization block threshold; the consequent changes in bifurcation structure enable the network to produce the tonic to clonic phase transition observed in biological epileptic networks.     

Regulation of spike timing in visual cortical circuits

A train of action potentials (a spike train) can carry information in both the average firing rate and the pattern of spikes in the train. But can such a spike-pattern code be supported by cortical circuits? Neurons in vitro produce a spike pattern in response to the injection of a fluctuating current. However, cortical neurons in vivo are modulated by local oscillatory neuronal activity and by top-down inputs. In a cortical circuit, precise spike patterns thus reflect the interaction between internally generated activity and sensory information encoded by input spike trains. We review the evidence for precise and reliable spike timing in the cortex and discuss its computational role.     

Interaction of NMDA Receptor and Pacemaking Mechanisms in the Midbrain Dopaminergic Neuron

Dopamine neurotransmission has been found to play a role in addictive behavior and is altered in psychiatric disorders. Dopaminergic (DA) neurons display two functionally distinct modes of electrophysiological activity: low- and high-frequency firing. A puzzling feature of the DA neuron is the following combination of its responses: N-methyl-D-aspartate receptor (NMDAR) activation evokes high-frequency firing, whereas other tonic excitatory stimuli (-amino-3-hydroxyl-5-methyl-4-isoxazolepropionate receptor (AMPAR) activation or applied depolarization) block firing instead. We suggest a new computational model that reproduces this combination of responses and explains recent experimental data. Namely, somatic NMDAR stimulation evokes high-frequency firing and is more effective than distal dendritic stimulation. We further reduce the model to a single compartment and analyze the mechanism of the distinct high-frequency response to NMDAR activation vs. other stimuli. Standard nullcline analysis shows that the mechanism is based on a decrease in the amplitude of calcium oscillations. The analysis confirms that the nonlinear voltage dependence provided by the magnesium block of the NMDAR determine its capacity to elevate the firing frequency. We further predict that the moderate slope of the voltage dependence plays the central role in the frequency elevation. Additionally, we suggest a repolarizing current that sustains calcium-independent firing or firing in the absence of calcium-dependent repolarizing currents. We predict that the ether–a-go-go current (ERG), which has been observed in the DA neuron, is the best fit for this critical role. We show that a calcium-dependent and a calcium-independent oscillatory mechanisms form a structure of interlocked negative feedback loops in the DA neuron. The structure connects research of DA neuron firing with circadian biology and determines common minimal models for investigation of robustness of oscillations, which is critical for normal function of both systems.     

Bistable,Irregular Firing and Population Oscillations in a Modular Attractor Memory Network

Attractor neural networks are thought to underlie working memory functions in the cerebral cortex. Several such models have been proposed that successfully reproduce firing properties of neurons recorded from monkeys performing working memory tasks. However, the regular temporal structure of spike trains in these models is often incompatible with experimental data. Here, we show that the in vivo observations of bistable activity with irregular firing at the single cell level can be achieved in a large-scale network model with a modular structure in terms of several connected hypercolumns. Despite high irregularity of individual spike trains, the model shows population oscillations in the beta and gamma band in ground and active states, respectively. Irregular firing typically emerges in a high-conductance regime of balanced excitation and inhibition. Population oscillations can produce such a regime, but in previous models only a non-coding ground state was oscillatory. Due to the modular structure of our network, the oscillatory and irregular firing was maintained also in the active state without fine-tuning. Our model provides a novel mechanistic view of how irregular firing emerges in cortical populations as they go from beta to gamma oscillations during memory retrieval.     

Diversity of Intrinsic Frequency Encoding Patterns in Rat Cortical Neurons—Mechanisms and Possible Functions

Extracellular recordings of single neurons in primary and secondary somatosensory cortices of monkeys in vivo have shown that their firing rate can increase, decrease, or remain constant in different cells, as the external stimulus frequency increases. We observed similar intrinsic firing patterns (increasing, decreasing or constant) in rat somatosensory cortex in vitro, when stimulated with oscillatory input using conductance injection (dynamic clamp). The underlying mechanism of this observation is not obvious, and presents a challenge for mathematical modelling. We propose a simple principle for describing this phenomenon using a leaky integrate-and-fire model with sinusoidal input, an intrinsic oscillation and Poisson noise. Additional enhancement of the gain of encoding could be achieved by local network connections amongst diverse intrinsic response patterns. Our work sheds light on the possible cellular and network mechanisms underlying these opposing neuronal responses, which serve to enhance signal detection.     

Modelling of cortical and thalamic 600 Hz activity by means of oscillatory networks

The purpose of this study is to investigate information processing in the primary somatosensory system with the help of oscillatory network modelling. Specifically, we consider interactions in the oscillatory 600 Hz activity between the thalamus and the cortical Brodmann areas 3b and 1. This type of cortical activity occurs after electrical stimulation of peripheral nerves such as the median nerve. Our measurements consist of simultaneous 31-channel MEG and 32-channel EEG recordings and individual 3D MRI data. We perform source localization by means of a multi-dipole model. The dipole activation time courses are then modelled by a set of coupled oscillators, described by linear second-order ordinary delay differential equations (DDEs). In particular, a new model for the thalamic activity is included in the oscillatory network. The parameters of the DDE system are successfully fitted to the data by a nonlinear evolutionary optimization method. To activate the oscillatory network, an individual input function is used, based on measurements of the propagated stimulation signal at the biceps. A significant feedback from the cortex to the thalamus could be detected by comparing the network modelling with and without feedback connections. Our finding in humans is supported by earlier animal studies. We conclude that this type of rhythmic brain activity can be modelled by oscillatory networks in order to disentangle feed forward and feedback information transfer.     

The mechanism of rate remapping in the dentate gyrus

Rate remapping is a recently revealed neural code in which sensory information modulates the firing rate of hippocampal place cells. The mechanism underlying rate remapping is unknown. Its characteristic modulation, however, must arise from the interaction of the two major inputs to the hippocampus, the medial entorhinal cortex (MEC), in which grid cells represent the spatial position of the rat, and the lateral entorhinal cortex (LEC), in which cells represent the sensory properties of the environment. We have used computational methods to elucidate the mechanism by which this interaction produces rate remapping. We show that the convergence of LEC and MEC inputs, in conjunction with a competitive network process mediated by feedback inhibition, can account quantitatively for this phenomenon. The same principle accounts for why different place fields of the same cell vary independently as sensory information is altered. Our results show that rate remapping can be explained in terms of known mechanisms.