A network model of the modulation of gamma oscillations by NMDA receptors in cerebral cortex

This preprint (2021) used computational models of cortical networks generating gamma oscillations (frequency of brainwaves) while integrating the actions of NMDA-receptor drugs like ketamine to better understand the mechanism by which these drugs produce gamma oscillations as seen in disorders like schizophrenia. It was found that ketamine (like substances) induce an increased excitability state and increase the response to external inputs which may help to explain phenomena like hallucinations.

Abstract

“Psychotic drugs such as ketamine induce symptoms close to schizophrenia, and stimulate the production of gamma oscillations, as also seen in patients, but the underlying mechanisms are still unclear. Here, we have used computational models of cortical networks generating gamma oscillations, and have integrated the action of drugs such as ketamine to partially block n-methyl-d-aspartate (NMDA) receptors. The model can reproduce the modulation of gamma oscillations by NMDA-receptor antagonists, assuming that antagonists affect NMDA receptors predominantly on inhibitory interneurons. We next used the model to compare the responsiveness of the network to external stimuli, and found that when NMDA channels are blocked an increase of Gamma power is observed altogether with an increase of network responsiveness. However, this responsiveness increase applies not only to gamma states but also to asynchronous states with no apparent gamma. We conclude that NMDA antagonists induce increased excitability state, which may or may not produce gamma oscillations, but the response to external inputs is exacerbated, which may explain phenomena such as altered perception or hallucinations.”

Authors: Eduarda Susin & Alain Destexhe

Summary

I. I NTRODUCTION

Schizophrenia is a mental disorder characterized by three classes of symptoms: positive symptoms, negative symptoms, and cognitive deficits. Gamma oscillations are commonly reported to present increased power and/or phase synchronization in early-course schizophrenia patients.

NMDA receptor antagonists induce a psychotic state in animal and human models of Schizophrenia, and increase Gamma power amplitude. This increase in Gamma power amplitude affects the network response, and provides an interpretation for the observed correlation.

Computational model reproduces experimental features

Several preparations with sub-anesthetics doses of NMDAR antagonists have reported to produce neural excitation. This behavior is intriguing and may be explained by NMDAR antagonists acting preferentially on inhibitory neurons.

In sub-anesthetics doses, NMDAR antagonists increase the Gamma-band activity in the brain, which is observed in human, monkey and rat brains, during cognitive tasks or free movement. The network model developed in the present work is able to reproduce both of these features.

We measured the network dynamics and its capacity to respond to external stimulus at different levels of NMDA synaptic strength. The stimulus consisted of a variation in time of the external Poissonian drive, in a Gaussian manner.

Network responsiveness increased with the increased level of NMDAR block, while network excitability decreased. This is because NMDA receptors block depolarizes RS cells, while FS neurons are overall hyperpolarized.

Gamma states vs. AI states

Gamma oscillations are believed to be involved in information processing, and have been associated with different high-level cognitive functions, such as memory, perception, attention, focused arousal and prediction. In contrast, Asynchronous-and-Irregular (AI) states are usually associated to conscious states, being observed during awake and aroused states.

In the present study, we compare the responsiveness of RS neurons in AI and Gamma states at different levels of NMDAR block. The results show that the responsiveness in AI states is always superior to the one in Gamma.

III. D ISCUSSION

In this work, we used computational models to investigate how psychotic drugs such as ketamine affect cerebral cortex. We found that NMDA receptors antagonists modulate gamma oscillations and increase responsiveness to external inputs.

The model predicts that NMDA receptor antagonism affects predominantly NMDAR receptors on interneurons, and that this feature is supported by a number of observations. The model could reproduce the increase of Gamma power induced by NMDA receptor antagonists.

The network has a marked increased responsiveness under the boosted Gamma condition, which could be tested experimentally with NMDA antagonists.

The antagonism of NMDA receptors produces an overall depolarization of RS cells, and a corresponding decrease in responsiveness of FS cells. This results in an increase of responsiveness of RS cells.

Possible implications to understand brain pathologies

Our model can explain the symptoms associated to ketamine and other NMDA receptor antagonists, such as hallucinations. It also seems to be consistent with the role for FS neurons in schizophrenia, which are reduced in post-mortem analysis of schizophrenic patient brains.

The model could reproduce all the experimental observations only assuming a larger decrease of the NMDA synaptic strengths in FS cells than in RS cells. This result supports the idea that PV-positive Fast Spiking inhibitory neurons play a key role in schizophrenia.

Neuronal Model

The subthreshold adaptation current increases by an amount b every time the neuron i emits a spike at times tj and decays exponentially with time scale w .

During simulations, the membrane potential is numerically integrated until a spike is generated. After the refractory period, the equations start being integrated again.

Synaptic Models

The post-synaptic current received by each neuron is composed by three components: two excitatory, referent to AMPA and NMDA synaptic channels, and one inhibitory, referent to GABAA channels.

The synaptic conductances of AMPA and GABAA channels increase discontinuously and subsequently decay exponentially with a decay time constant.

AMPA and GABAA synapses have a decay time constant of 1.5 ms and 7.5 ms, respectively, while NMDA synapses have a rise time constant of 2 ms.

NMDA and AMPA synapses were chosen according to parameter search, while GABAA and NMDA synapses were chosen according to previous works. All synapses were delayed by time of 1.5 ms.

Network Structure

The network developed in this work is composed of 5000 neurons, and each neuron receives 500 excitatory synapses and 100 inhibitory synapses.

External Input

The network was stimulated with 5000 independent and identically distributed excitatory Poissonian spike trains with a spiking frequency ext . The external drive mimicked cortical input, like if the network was embedded in a much bigger one.

To test network responsiveness, an additional external input was included in the simulations. This input consisted of 5000 independent and identically distributed excitatory Poissonian spike trains, connected to the network with a 10% probability.

Population activity: LFP model

We simulated a Local Field Potential (LFP) generated by a network, using a recent method developed by [98]. This method assumes a spatial neuronal displacement, so we randomly displaced part of the network (50 neurons) in 2-D grid.

Responsiveness

A network’s responsiveness to an stimulus is measured by the difference between the spikes generated by the network due to the stimulus and the spikes generated in the absence of the stimulus.

ACKNOWLEDGMENTS

This research was supported by the CNRS, the European Community and the Fondation pour la Recherche Medicale.

Longitudinal studies of cognition in first episode psychosis have shown that cortical inhibitory neurons are involved. Researchers found that n-methyl-d-aspartate receptor antagonists could lead to excitation instead of inhibition in the brain, and that gamma-band power alterations in schizophrenia revealed e/i-balance abnormalities across illness-stages.

K. M. Spencer, D. F. Salisbury, M. E. Shenton, and R. W. McCarley found that gamma band auditory steady-state responses were impaired in first episode psychosis, and that left auditory cortex gamma synchronization and auditory hallucination symptoms were associated with schizophrenia. Ketamine, a noncompetitive nmda antagonist, induces wake-related aberrant oscillations in the rat neocortex and is associated with clinical symptoms. These oscillations may be related to the effects of ketamine on cognition, perception, and neuroendocrine systems. The role of nr2a and nr2b subunits in n-methyl-d-aspartate receptor antagonist-induced aberrant cortical gamma oscillations is discussed.

Ketamine induces converged synchronous gamma oscillations in the cortico-basal ganglia network of nonhuman primates and may be a novel step in the pathway from nmda receptor blockade to dopaminergic and cognitive disruptions associated with the prefrontal cortex. Ketamine activates psychosis and alters limbic blood flow in schizophrenia. The prefrontal cortex is activated in healthy volunteers and phencyclidine induces tonic activation of medial prefrontal cortex neurons in freely moving rats. M. E. Jackson, H. Homayoun, B. Moghaddam, D. C. Rotaru, D. A. Lewis, G. B. Ermentrout, and G. Gonzalez-Burgos studied NMDA receptors in the prefrontal cortex. Nmda receptor hypofunction produces opposite effects on prefrontal cortex interneurons and pyramidal neurons, and may explain the rapid antidepressant efficacy of ketamine.

Several studies have shown that long-term exposure to nmdar antagonist suppresses inhibitory synaptic transmission in prefrontal cortex, and that ketamine increases human motor cortex excitability to transcranial magnetic stimulation. W. Singer and C. M. Gray suggested that visual feature integration and the temporal correlation hypothesis were related, and that neuronal synchrony was a versatile code for the definition of relations.

M. F. Carr, M. P. Karlsson, and L. M. Frank found that slow gamma synchrony underlies hippocampal memory replay, and E. Rodriguez found that long-distance synchronization of human brain activity correlates with conscious perception. Attention modulates oscillatory neuronal synchronization in awake monkey area v4 by modifying high-frequency, long-range coupling between prefrontal and visual cortex during attention. A study in 2013 found that the load dependence of and oscillations predicts individual capacity of visual attention, and a study in 2006 found that gamma-band synchronization in visual cortex predicts speed of change detection.

W. R. Softky, C. Koch, and R. J. Douglas investigated the variability of cortical cell discharge in vitro and in vivo, and found that the variability was inconsistent with temporal integration of random epsps. J. A. Henrie, R. Shapley, P. Tiesinga and T. J. Sejnowski studied LFP power spectra in v1 cortex, and D. S. Ling and L. S. Benardo studied activity-dependent depression of monosynaptic fast ipscs in hippocampus. A review of the literature shows that gabaergic neurons in the neocortex receive and differently integrate callosal input, and that nmda receptor hypofunction leads to generalized and persistent aberrant oscillations independent of hyperlocomotion and the state of consciousness.

Gene expression for glutamic acid decarboxylase is reduced without loss of neurons in the prefrontal cortex of schizophrenics. A subset of prefrontal cortical -aminobutyric acid neurons has decreased glutamic acid decarboxylase67 messenger rna expression in subjects with schizophrenia, and Nmda receptor ablation on parvalbumin-positive interneurons impairs hippocampal synchrony, spatial representations, and working memory. [82] Belforte, V. Zsiros, E. R. Sklar, Z. Jiang, G. Yu, Y. Li, Quinlan, E. M., and Nakazawa, K., “Postnatal nmda receptor ablation in corticolimbic interneurons confers schizophrenia-like phenotypes,” Nature neuroscience, vol. 13, no. 1, 2010. K. Nakao and K. Nakazawa found abnormal lfp activity in the auditory cortex of a schizophrenia mouse model. Gamma neurons and the mechanisms of network oscillations: implications for understanding cortical dysfunction in schizophrenia. Adaptive exponential integrate-and-fire model is an effective description of neuronal activity. Single-shot channel activation accounts for duration of inhibitory postsynaptic potentials. Several studies have been done to determine the kinetic properties of nmda receptor-mediated synaptic currents in rat hippocampal pyramidal cells versus interneurones, and to determine the functional properties of ampa and nmda receptors expressed in identified types of basal ganglia neurons.