Populations Of Inhibitory Neurons Research Articles

"Distinct inhibitory neurons differently shape neuronal codes for sound intensity in the auditory cortex".

Cortical circuits contain multiple types of inhibitory neurons which shape how information is processed within neuronal networks. Here, we asked whether somatostatin-expressing (SST) and vasoactive intestinal peptide-expressing (VIP) inhibitory neurons have distinct effects on population neuronal responses to noise bursts of varying intensities. We optogenetically stimulated SST or VIP neurons while simultaneously measuring the calcium responses of populations of hundreds of neurons in the auditory cortex of male and female awake, head-fixed mice to sounds. Upon SST neuronal activation, noise bursts representations became more discrete for different intensity levels, relying on cell identity rather than strength. By contrast, upon VIP neuronal activation, noise bursts of different intensity level activated overlapping neuronal populations, albeit at different response strengths. At the single-cell level, SST and VIP neuronal activation differentially activated the response-level curves of monotonic and nonmonotonic neurons. SST neuronal activation effects were consistent with a shift of the neuronal population responses toward a more localist code with different cells responding to sounds of different intensity. By contrast, VIP neuronal activation shifted responses towards a more distributed code, in which sounds of different intensity level are encoded in the relative response of similar populations of cells. These results delineate how distinct inhibitory neurons in the auditory cortex dynamically control cortical population codes. Different inhibitory neuronal populations may be recruited under different behavioral demands, depending on whether categorical or invariant representations are advantageous for the task.

Approximating Nonlinear Functions With Latent Boundaries in Low-Rank Excitatory-Inhibitory Spiking Networks.

Deep feedforward and recurrent neural networks have become successful functional models of the brain, but they neglect obvious biological details such as spikes and Dale's law. Here we argue that these details are crucial in order to understand how real neural circuits operate. Towards this aim, we put forth a new framework for spike-based computation in low-rank excitatory-inhibitory spiking networks. By considering populations with rank-1 connectivity, we cast each neuron's spiking threshold as a boundary in a low-dimensional input-output space. We then show how the combined thresholds of a population of inhibitory neurons form a stable boundary in this space, and those of a population of excitatory neurons form an unstable boundary. Combining the two boundaries results in a rank-2 excitatory-inhibitory (EI) network with inhibition-stabilized dynamics at the intersection of the two boundaries. The computation of the resulting networks can be understood as the difference of two convex functions and is thereby capable of approximating arbitrary non-linear input-output mappings. We demonstrate several properties of these networks, including noise suppression and amplification, irregular activity and synaptic balance, as well as how they relate to rate network dynamics in the limit that the boundary becomes soft. Finally, while our work focuses on small networks (5-50 neurons), we discuss potential avenues for scaling up to much larger networks. Overall, our work proposes a new perspective on spiking networks that may serve as a starting point for a mechanistic understanding of biological spike-based computation.

Two inhibitory neuronal classes govern acquisition and recall of spinal sensorimotor adaptation.

Spinal circuits are central to movement adaptation, yet the mechanisms within the spinal cord responsible for acquiring and retaining behavior upon experience remain unclear. Using a simple conditioning paradigm, we found that dorsal inhibitory neurons are indispensable for adapting protective limb-withdrawal behavior by regulating the transmission of a specific set of somatosensory information to enhance the saliency of conditioning cues associated with limb position. By contrast, maintaining previously acquired motor adaptation required the ventral inhibitory Renshaw cells. Manipulating Renshaw cells does not affect the adaptation itself but flexibly alters the expression of adaptive behavior. These findings identify a circuit basis involving two distinct populations of spinal inhibitory neurons, which enables lasting sensorimotor adaptation independently from the brain.

Development and characterization of a Gucy2d-cre mouse to selectively manipulate a subset of inhibitory spinal dorsal horn interneurons.

Recent transcriptomic studies identified Gucy2d (encoding guanylate cyclase D) as a highly enriched gene within inhibitory dynorphin interneurons in the mouse spinal dorsal horn. To facilitate investigations into the role of the Gucy2d+ population in somatosensation, Gucy2d-cre transgenic mice were created to permit chemogenetic or optogenetic manipulation of this subset of spinal neurons. Gucy2d-cre mice created via CRISPR/Cas9 genomic knock-in were bred to mice expressing a cre-dependent reporter (either tdTomato or Sun1.GFP fusion protein), and the resulting offspring were characterized. Surprisingly, a much wider population of spinal neurons was labeled by cre-dependent reporter expression than previous mRNA-based studies would suggest. Although the cre-dependent reporter expression faithfully labeled ~75% of cells expressing Gucy2d mRNA in the adult dorsal horn, it also labeled a substantial number of additional inhibitory neurons in which no Gucy2d or Pdyn mRNA was detected. Moreover, cre-dependent reporter was also expressed in various regions of the brain, including the spinal trigeminal nucleus, cerebellum, thalamus, somatosensory cortex, and anterior cingulate cortex. Injection of AAV-CAG-FLEX-tdTomato viral vector into adult Gucy2d-cre mice produced a similar pattern of cre-dependent reporter expression in the spinal cord and brain, which excludes the possibility that the unexpected reporter-labeling of cells in the deep dorsal horn and brain was due to transient Gucy2d expression during early stages of development. Collectively, these results suggest that Gucy2d is expressed in a wider population of cells than previously thought, albeit at levels low enough to avoid detection with commonly used mRNA-based assays. Therefore, it is unlikely that these Gucy2d-cre mice will permit selective manipulation of inhibitory signaling mediated by spinal dynorphin interneurons, but this novel cre driver line may nevertheless be useful to target a broader population of inhibitory spinal dorsal horn neurons.

Biophysical modulation and robustness of itinerant complexity in neuronal networks.

Transient synchronization of bursting activity in neuronal networks, which occurs in patterns of metastable itinerant phase relationships between neurons, is a notable feature of network dynamics observed in vivo. However, the mechanisms that contribute to this dynamical complexity in neuronal circuits are not well understood. Local circuits in cortical regions consist of populations of neurons with diverse intrinsic oscillatory features. In this study, we numerically show that the phenomenon of transient synchronization, also referred to as metastability, can emerge in an inhibitory neuronal population when the neurons' intrinsic fast-spiking dynamics are appropriately modulated by slower inputs from an excitatory neuronal population. Using a compact model of a mesoscopic-scale network consisting of excitatory pyramidal and inhibitory fast-spiking neurons, our work demonstrates a relationship between the frequency of pyramidal population oscillations and the features of emergent metastability in the inhibitory population. In addition, we introduce a method to characterize collective transitions in metastable networks. Finally, we discuss potential applications of this study in mechanistically understanding cortical network dynamics.

Emergent dynamics in fractional-order Wilson–Cowan neural network systems

The firing dynamics of excitable systems are critical to understand organized responses in cortical networks. In this paper, we examine a fractional-order Wilson–Cowan (W–C) neural network model composed of excitatory and inhibitory neuron populations, utilizing Caputo’s fractional-order derivative formalism to explore the influence of fractional-order dynamics on firing behavior. The significance of extending to the fractional-order domain lies in the model’s theoretical framework, which inherently retains memory and hereditary characteristics. We investigate memory-dependent response functions and average neuronal characteristics, enabling us to formulate a fractional-order model that incorporates past dynamics into the neuronal populations’ features. This generalized model is capable of producing alternations between spiking and bursting phenomena, including mixed-mode oscillations (MMOs). Using stability and bifurcation analyses, we delineate the parameter space within which variations in firing patterns emerge. One notable impact of the model’s memory property is the potential stabilization of neuronal activity. We demonstrate that our numerical findings are in alignment with the analytical predictions and that the memory trace depends on the fractional-order dynamics.

Compressive sensing of functional connectivity maps from patterned optogenetic stimulation of neuronal ensembles

Mapping functional connectivity between neurons is an essential step toward probing the neural computations mediating behavior. Accurately determining synaptic connectivity maps in populations of neurons is challenging in terms of yield, accuracy, and experimental time. Here, we developed a compressive sensing approach to reconstruct synaptic connectivity maps based on random two-photon cell-targeted optogenetic stimulation and membrane voltage readout of many putative postsynaptic neurons. Using a biophysical network model of interconnected populations of excitatory and inhibitory neurons, we characterized mapping recall and precision as a function of network observability, sparsity, number of neurons stimulated, off-target stimulation, synaptic reliability, propagation latency, and network topology. We found that mapping can be achieved with far fewer measurements than the standard pairwise sequential approach, with network sparsity and synaptic reliability serving as primary determinants of the performance. Our results suggest a rapid and efficient method to reconstruct functional connectivity of sparsely connected neuronal networks.

Inhibitory stabilized network behaviour in a balanced neural mass model of a cortical column

Strong inhibitory recurrent connections can reduce the tendency for a neural network to become unstable. This is known as inhibitory stabilization; networks that are unstable in the absence of strong inhibitory feedback because of their unstable excitatory recurrent connections are known as Inhibition Stabilized Networks (ISNs). One of the characteristics of ISNs is their “paradoxical response”, where perturbing the inhibitory neurons with additional excitatory input results in a decrease in their activity after a temporal delay instead of increasing their activity. Here, we develop a model of populations of neurons across different layers of cortex. Within each layer, there is one population of inhibitory neurons and one population of excitatory neurons. The connectivity weights across different populations in the model are derived from a synaptic physiology database provided by the Allen Institute. The model shows a gradient of excitation–inhibition balance across different layers in the cortex, where superficial layers are more inhibitory dominated compared to deeper layers. To investigate the presence of ISNs across different layers, we measured the membrane potentials of neural populations in the model after perturbing inhibitory populations. The results show that layer 2/3 in the model does not operate in the ISN regime but layers 4 and 5 do operate in the ISN regime. These results accord with neurophysiological findings that explored the presence of ISNs across different layers in the cortex. The results show that there may be a systematic macroscopic gradient of inhibitory stabilization across different layers in the cortex that depends on the level of excitation–inhibition balance, and that the strength of the paradoxical response increases as the model moves closer to bifurcation points.

Sleep waves in a large-scale corticothalamic model constrained by activities intrinsic to neocortical networks and single thalamic neurons.

Many biophysical and non-biophysical models have been able to reproduce the corticothalamic activities underlying different EEG sleep rhythms but none of them included the known ability of neocortical networks and single thalamic neurons to generate some of these waves intrinsically. We built a large-scale corticothalamic model with a high fidelity in anatomical connectivity consisting of a single cortical column and first- and higher-order thalamic nuclei. The model is constrained by different neocortical excitatory and inhibitory neuronal populations eliciting slow (<1 Hz) oscillations and by thalamic neurons generating sleep waves when isolated from the neocortex. Our model faithfully reproduces all EEG sleep waves and the transition from a desynchronized EEG to spindles, slow (<1 Hz) oscillations, and delta waves by progressively increasing neuronal membrane hyperpolarization as it occurs in the intact brain. Moreover, our model shows that slow (<1 Hz) waves most often start in a small assembly of thalamocortical neurons though they can also originate in cortical layer 5. Moreover, the input of thalamocortical neurons increases the frequency of EEG slow (<1 Hz) waves compared to those generated by isolated cortical networks. Our simulations challenge current mechanistic understanding of the temporal dynamics of sleep wave generation and suggest testable predictions.

Multi-band oscillations emerge from a simple spiking network.

In the brain, coherent neuronal activities often appear simultaneously in multiple frequency bands, e.g., as combinations of alpha (8-12 Hz), beta (12.5-30 Hz), and gamma (30-120 Hz) oscillations, among others. These rhythms are believed to underlie information processing and cognitive functions and have been subjected to intense experimental and theoretical scrutiny. Computational modeling has provided a framework for the emergence of network-level oscillatory behavior from the interaction of spiking neurons. However, due to the strong nonlinear interactions between highly recurrent spiking populations, the interplay between cortical rhythms in multiple frequency bands has rarely been theoretically investigated. Many studies invoke multiple physiological timescales (e.g., various ion channels or multiple types of inhibitory neurons) or oscillatory inputs to produce rhythms in multi-bands. Here, we demonstrate the emergence of multi-band oscillations in a simple network consisting of one excitatory and one inhibitory neuronal population driven by constant input. First, we construct a data-driven, Poincaré section theory for robust numerical observations of single-frequency oscillations bifurcating into multiple bands. Then, we develop model reductions of the stochastic, nonlinear, high-dimensional neuronal network to capture the appearance of multi-band dynamics and the underlying bifurcations theoretically. Furthermore, when viewed within the reduced state space, our analysis reveals conserved geometrical features of the bifurcations on low-dimensional dynamical manifolds. These results suggest a simple geometric mechanism behind the emergence of multi-band oscillations without appealing to oscillatory inputs or multiple synaptic or neuronal timescales. Thus, our work points to unexplored regimes of stochastic competition between excitation and inhibition behind the generation of dynamic, patterned neuronal activities.

Global nonlinear approach for mapping parameters of neural mass models.

Neural mass models (NMMs) are important for helping us interpret observations of brain dynamics. They provide a means to understand data in terms of mechanisms such as synaptic interactions between excitatory and inhibitory neuronal populations. To interpret data using NMMs we need to quantitatively compare the output of NMMs with data, and thereby find parameter values for which the model can produce the observed dynamics. Mapping dynamics to NMM parameter values in this way has the potential to improve our understanding of the brain in health and disease. Though abstract, NMMs still comprise of many parameters that are difficult to constrain a priori. This makes it challenging to explore the dynamics of NMMs and elucidate regions of parameter space in which their dynamics best approximate data. Existing approaches to overcome this challenge use a combination of linearising models, constraining the values they can take and exploring restricted subspaces by fixing the values of many parameters a priori. As such, we have little knowledge of the extent to which different regions of parameter space of NMMs can yield dynamics that approximate data, how nonlinearities in models can affect parameter mapping or how best to quantify similarities between model output and data. These issues need to be addressed in order to fully understand the potential and limitations of NMMs, and to aid the development of new models of brain dynamics in the future. To begin to overcome these issues, we present a global nonlinear approach to recovering parameters of NMMs from data. We use global optimisation to explore all parameters of nonlinear NMMs simultaneously, in a minimally constrained way. We do this using multi-objective optimisation (multi-objective evolutionary algorithm, MOEA) so that multiple data features can be quantified. In particular, we use the weighted horizontal visibility graph (wHVG), which is a flexible framework for quantifying different aspects of time series, by converting them into networks. We study EEG alpha activity recorded during the eyes closed resting state from 20 healthy individuals and demonstrate that the MOEA performs favourably compared to single objective approaches. The addition of the wHVG objective allows us to better constrain the model output, which leads to the recovered parameter values being restricted to smaller regions of parameter space, thus improving the practical identifiability of the model. We then use the MOEA to study differences in the alpha rhythm observed in EEG recorded from 20 people with epilepsy. We find that a small number of parameters can explain this difference and that, counterintuitively, the mean excitatory synaptic gain parameter is reduced in people with epilepsy compared to control. In addition, we propose that the MOEA could be used to mine for the presence of pathological rhythms, and demonstrate the application of this to epileptiform spike-wave discharges.

Inhibitory circuits in fear memory and fear-related disorders.

Fear learning and memory rely on dynamic interactions between the excitatory and inhibitory neuronal populations that make up the prefrontal cortical, amygdala, and hippocampal circuits. Whereas inhibition of excitatory principal cells (PCs) by GABAergic neurons restrains their excitation, inhibition of GABAergic neurons promotes the excitation of PCs through a process called disinhibition. Specifically, GABAergic interneurons that express parvalbumin (PV+) and somatostatin (SOM+) provide inhibition to different subcellular domains of PCs, whereas those that express the vasoactive intestinal polypeptide (VIP+) facilitate disinhibition of PCs by inhibiting PV+ and SOM+ interneurons. Importantly, although the main connectivity motifs and the underlying network functions of PV+, SOM+, and VIP+ interneurons are replicated across cortical and limbic areas, these inhibitory populations play region-specific roles in fear learning and memory. Here, we provide an overview of the fear processing in the amygdala, hippocampus, and prefrontal cortex based on the evidence obtained in human and animal studies. Moreover, focusing on recent findings obtained using genetically defined imaging and intervention strategies, we discuss the population-specific functions of PV+, SOM+, and VIP+ interneurons in fear circuits. Last, we review current insights that integrate the region-specific inhibitory and disinhibitory network patterns into fear memory acquisition and fear-related disorders.

Theta-gamma phase amplitude coupling in a hippocampal CA1 microcircuit.

Phase amplitude coupling (PAC) between slow and fast oscillations is found throughout the brain and plays important functional roles. Its neural origin remains unclear. Experimental findings are often puzzling and sometimes contradictory. Most computational models rely on pairs of pacemaker neurons or neural populations tuned at different frequencies to produce PAC. Here, using a data-driven model of a hippocampal microcircuit, we demonstrate that PAC can naturally emerge from a single feedback mechanism involving an inhibitory and excitatory neuron population, which interplay to generate theta frequency periodic bursts of higher frequency gamma. The model suggests the conditions under which a CA1 microcircuit can operate to elicit theta-gamma PAC, and highlights the modulatory role of OLM and PVBC cells, recurrent connectivity, and short term synaptic plasticity. Surprisingly, the results suggest the experimentally testable prediction that the generation of the slow population oscillation requires the fast one and cannot occur without it.

Visual Cortical Plasticity: Molecular Mechanisms as Revealed by Induction Paradigms in Rodents

Assessing the molecular mechanism of synaptic plasticity in the cortex is vital for identifying potential targets in conditions marked by defective plasticity. In plasticity research, the visual cortex represents a target model for intense investigation, partly due to the availability of different in vivo plasticity-induction protocols. Here, we review two major protocols: ocular-dominance (OD) and cross-modal (CM) plasticity in rodents, highlighting the molecular signaling pathways involved. Each plasticity paradigm has also revealed the contribution of different populations of inhibitory and excitatory neurons at different time points. Since defective synaptic plasticity is common to various neurodevelopmental disorders, the potentially disrupted molecular and circuit alterations are discussed. Finally, new plasticity paradigms are presented, based on recent evidence. Stimulus-selective response potentiation (SRP) is one of the paradigms addressed. These options may provide answers to unsolved neurodevelopmental questions and offer tools to repair plasticity defects.

Mechanisms and functions of respiration-driven gamma oscillations in the primary olfactory cortex.

Gamma oscillations are believed to underlie cognitive processes by shaping the formation of transient neuronal partnerships on a millisecond scale. These oscillations are coupled to the phase of breathing cycles in several brain areas, possibly reflecting local computations driven by sensory inputs sampled at each breath. Here, we investigated the mechanisms and functions of gamma oscillations in the piriform (olfactory) cortex of awake mice to understand their dependence on breathing and how they relate to local spiking activity. Mechanistically, we find that respiration drives gamma oscillations in the piriform cortex, which correlate with local feedback inhibition and result from recurrent connections between local excitatory and inhibitory neuronal populations. Moreover, respiration-driven gamma oscillations are triggered by the activation of mitral/tufted cells in the olfactory bulb and are abolished during ketamine/xylazine anesthesia. Functionally, we demonstrate that they locally segregate neuronal assemblies through a winner-take-all computation leading to sparse odor coding during each breathing cycle. Our results shed new light on the mechanisms of gamma oscillations, bridging computation, cognition, and physiology.

Coupled stochastic systems of Skorokhod type: Well‐posedness of a mathematical model and its applications

Population dynamics with complex biological interactions, accounting for uncertainty quantification, are critical for many application areas. However, due to the complexity of biological systems, the mathematical formulation of the corresponding problems faces the challenge that the corresponding stochastic processes should, in most cases, be considered in bounded domains. We propose a model based on a coupled system of reflecting Skorokhod‐type stochastic differential equations with jump‐like exit from a boundary. The setting describes the population dynamics of active and passive populations. As main working techniques, we use compactness methods and Skorokhod's representation of solutions to SDEs posed in bounded domains to prove the well‐posedness of the system. This functional setting is a new point of view in the field of modeling and simulation of population dynamics. We provide the details of the model, as well as representative numerical examples, and discuss the applications of a Wilson–Cowan‐type system, modeling the dynamics of two interacting populations of excitatory and inhibitory neurons. Furthermore, the presence of random input current, reflecting factors together with Poisson jumps, increases firing activity in neuronal systems.

Dynamical Mechanism Analysis of Three Neuroregulatory Strategies on the Modulation of Seizures.

This paper attempts to explore and compare the regulatory mechanisms of optogenetic stimulation (OS), deep brain stimulation (DBS) and electromagnetic induction on epilepsy. Based on the Wilson-Cowan model, we first demonstrate that the external input received by excitatory and inhibitory neural populations can induce rich dynamic bifurcation behaviors such as Hopf bifurcation, and make the system exhibit epileptic and normal states. Then, both OS and DBS are shown to be effective in controlling the epileptic state to a normal low-level state, and the stimulus parameters have a broad effective range. However, electromagnetic induction cannot directly control epilepsy to this desired state, even if it can significantly reduce the oscillation frequency of neural populations. One main difference worth noting is that the high spatiotemporal specificity of OS allows it to target inhibitory neuronal populations, whereas DBS and electromagnetic induction can only stimulate excitatory as well as inhibitory neuronal populations together. Next, the propagation behavior of epilepsy is explored under a typical three-node feedback loop structure. An increase in coupling strength accelerates and exacerbates epileptic activity in other brain regions. Finally, OS and DBS applied to the epileptic focus play similar positive roles in controlling the behavior of the area of seizure propagation, while electromagnetic induction still only achieves unsatisfactory effects. It is hoped that these dynamical results can provide insights into the treatment of epilepsy as well as other neurological disorders.

Self-organized criticality in a mesoscopic model of excitatory-inhibitory neuronal populations by short-term and long-term synaptic plasticity.

Dynamics of an interconnected population of excitatory and inhibitory spiking neurons wandering around a Bogdanov-Takens (BT) bifurcation point can generate the observed scale-free avalanches at the population level and the highly variable spike patterns of individual neurons. These characteristics match experimental findings for spontaneous intrinsic activity in the brain. In this paper, we address the mechanisms causing the system to get and remain near this BT point. We propose an effective stochastic neural field model which captures the dynamics of the mean-field model. We show how the network tunes itself through local long-term synaptic plasticity by STDP and short-term synaptic depression to be close to this bifurcation point. The mesoscopic model that we derive matches the directed percolation model at the absorbing state phase transition.

Dynamic branching in a neural network model for probabilistic prediction of sequences.

An important function of the brain is to predict which stimulus is likely to occur based on the perceived cues. The present research studied the branching behavior of a computational network model of populations of excitatory and inhibitory neurons, both analytically and through simulations. Results show how synaptic efficacy, retroactive inhibition and short-term synaptic depression determine the dynamics of selection between different branches predicting sequences of stimuli of different probabilities. Further results show that changes in the probability of the different predictions depend on variations of neuronal gain. Such variations allow the network to optimize the probability of its predictions to changing probabilities of the sequences without changing synaptic efficacy.

Combining the neural mass model and Hodgkin–Huxley formalism: Neuronal dynamics modelling

Epilepsy is a neurological disorder that affects the nervous system and is characterized by recurrent seizures. Experimental data shows that increase in the extracellular potassium concentration can support the generation of seizures and that the T-type calcium channel antagonists can be effective as anti-epileptic drugs. To investigate these two phenomena in detail, we combine microscopic level modelling using Hodgkin–Huxley formalism and a macroscopic level approach using a neural mass model. The microscopic level approach describes the initiation of action potentials in individual neurons using conductance-based model. The macroscopic (neural mass model) approach is a low-dimensional phenomenological model that describes the activity of a large population of neurons. The neural mass model replicated the interactions between inhibitory and excitatory neuronal populations by using a sigmoidal function that converts neuronal postsynaptic potential into the average spiking rate of a given population. This sigmoidal function links two levels of modelling: microscopic and macroscopic. Our results are in agreement with experimental data and show that an increase in the extracellular potassium concentration or an increase in the T-type calcium conductance can cause brain network transitions from normal background to pathological seizure-like dynamics. In addition, the results show that these transitions only happen for a limited range of network parameters and that the slow-inhibitory synaptic gain has a stronger effect on network dynamics during transitions than the fast-inhibitory synaptic gain.