Excitatory-inhibitory Networks Research Articles

Phase-locking patterns underlying effective communication in exact firing rate models of neural networks.

Macroscopic oscillations in the brain have been observed to be involved in many cognitive tasks but their role is not completely understood. One of the suggested functions of the oscillations is to dynamically modulate communication between neural circuits. The Communication Through Coherence (CTC) theory proposes that oscillations reflect rhythmic changes in excitability of the neuronal populations. Thus, populations need to be properly phase-locked so that input volleys arrive at the peaks of excitability of the receiving population to communicate effectively. Here, we present a modeling study to explore synchronization between neuronal circuits connected with unidirectional projections. We consider an Excitatory-Inhibitory (E-I) network of quadratic integrate-and-fire neurons modeling a Pyramidal-Interneuronal Network Gamma (PING) rhythm. The network receives an external periodic input from either one or two sources, simulating the inputs from other oscillating neural groups. We use recently developed mean-field models which provide an exact description of the macroscopic activity of the spiking network. This low-dimensional mean field model allows us to use tools from bifurcation theory to identify the phase-locked states between the input and the target population as a function of the amplitude, frequency and coherence of the inputs. We identify the conditions for optimal phase-locking and effective communication. We find that inputs with high coherence can entrain the network for a wider range of frequencies. Besides, faster oscillatory inputs than the intrinsic network gamma cycle show more effective communication than inputs with similar frequency. Our analysis further shows that the entrainment of the network by inputs with higher frequency is more robust to distractors, thus giving them an advantage to entrain the network and communicate effectively. Finally, we show that pulsatile inputs can switch between attended inputs in selective attention.

Early life GABAA blockade alters the synaptic plasticity and cognitive functions in male and female rats

Gamma-aminobutyric acid (GABA), the major inhibitory neurotransmitter in adults, has a critical contribution to balanced excitatory-inhibitory networks in the brain. Alteration in depolarizing action of GABA during early life is connected to a wide variety of neurodevelopmental disorders. Additionally, the effects of postnatal GABA blockade on neuronal synaptic plasticity are not known and therefore, we set out to determine whether postnatal exposure to bicuculline, a competitive antagonist of GABAA receptors, affects electrophysiologic changes in hippocampal CA1 neurons later on. To this end, male and female Wistar rats received vehicle or bicuculline (300 μg/kg) on postnatal days (PNDs) 7, 9 and 11, and then underwent different behavioral and electrophysiological examinations in adulthood. Postnatal exposure to bicuculline did not affect basic synaptic transmission but led to a pronounced decrease in paired-pulse facilitation (PPF) in CA1 pyramidal neurons. Bicuculline treatment also attenuated the long-term potentiation (LTP) and long-term depression (LTD) of CA1 neurons accompanied by decreased theta-burst responses in male and female adult rats. These electrophysiology findings together with the reduced brain-derived neurotrophic factor (BDNF) levels in the hippocampus and prefrontal cortex reliably explain the disturbance in spatial reference and working memories of bicuculline-treated animals. This study suggests that postnatal GABAA blockade deteriorates short- and long-term synaptic plasticity of hippocampal CA1 neurons and related encoding of spatial memory in adulthood.

Sparse balance: Excitatory-inhibitory networks with small bias currents and broadly distributed synaptic weights.

Cortical circuits generate excitatory currents that must be cancelled by strong inhibition to assure stability. The resulting excitatory-inhibitory (E-I) balance can generate spontaneous irregular activity but, in standard balanced E-I models, this requires that an extremely strong feedforward bias current be included along with the recurrent excitation and inhibition. The absence of experimental evidence for such large bias currents inspired us to examine an alternative regime that exhibits asynchronous activity without requiring unrealistically large feedforward input. In these networks, irregular spontaneous activity is supported by a continually changing sparse set of neurons. To support this activity, synaptic strengths must be drawn from high-variance distributions. Unlike standard balanced networks, these sparse balance networks exhibit robust nonlinear responses to uniform inputs and non-Gaussian input statistics. Interestingly, the speed, not the size, of synaptic fluctuations dictates the degree of sparsity in the model. In addition to simulations, we provide a mean-field analysis to illustrate the properties of these networks.

Spiking Recurrent Neural Networks Represent Task-Relevant Neural Sequences in Rule-Dependent Computation.

Prefrontal cortical neurons play essential roles in performing rule-dependent tasks and working memory-based decision making. Motivated by PFG recordings of task-performing mice, we developed an excitatory-inhibitory spiking recurrent neural network (SRNN) to perform a rule-dependent two-alternative forced choice (2AFC) task. We imposed several important biological constraints onto the SRNN, and adapted spike frequency adaptation (SFA) and SuperSpike gradient methods to train the SRNN efficiently. The trained SRNN produced emergent rule-specific tunings in single-unit representations, showing rule-dependent population dynamics that resembled experimentally observed data. Under varying test conditions, we manipulated the SRNN parameters or configuration in computer simulations, and we investigated the impacts of rule-coding error, delay duration, recurrent weight connectivity and sparsity, and excitation/inhibition (E/I) balance on both task performance and neural representations. Overall, our modeling study provides a computational framework to understand neuronal representations at a fine timescale during working memory and cognitive control, and provides new experimentally testable hypotheses in future experiments.

Synchronization Through Uncorrelated Noise in Excitatory-Inhibitory Networks.

Gamma rhythms play a major role in many different processes in the brain, such as attention, working memory, and sensory processing. While typically considered detrimental, counterintuitively noise can sometimes have beneficial effects on communication and information transfer. Recently, Meng and Riecke showed that synchronization of interacting networks of inhibitory neurons in the gamma band (i.e., gamma generated through an ING mechanism) increases while synchronization within these networks decreases when neurons are subject to uncorrelated noise. However, experimental and modeling studies point towardz an important role of the pyramidal-interneuronal network gamma (PING) mechanism in the cortex. Therefore, we investigated the effect of uncorrelated noise on the communication between excitatory-inhibitory networks producing gamma oscillations via a PING mechanism. Our results suggest that, at least in a certain range of noise strengths and natural frequency differences between the regions, synaptic noise can have a supporting role in facilitating inter-regional communication, similar to the ING case for a slightly larger parameter range. Furthermore, the noise-induced synchronization between networks is generated via a different mechanism than when synchronization is mediated by strong synaptic coupling. Noise-induced synchronization is achieved by lowering synchronization within networks which allows the respective other network to impose its own gamma rhythm resulting in synchronization between networks.

A mechanism for inter-areal coherence through communication based on connectivity and oscillatory power

SummaryInter-areal coherence between field potentials is a widespread phenomenon in cortex. Coherence has been hypothesized to reflect phase-synchronization between oscillators and flexibly gate communication according to behavioral and cognitive demands. We reveal an alternative mechanism where coherence is not the cause but the consequence of communication and naturally emerges because spiking activity in a sending area causes post-synaptic potentials both in the same and in other areas. Consequently, coherence depends in a lawful manner on power and phase-locking in the sender and connectivity. Changes in oscillatory power explained prominent changes in fronto-parietal and LGN-V1 coherence across behavioral conditions. Optogenetic experiments and excitatory-inhibitory network simulations identified afferent synaptic inputs rather than spiking entrainment as the principal determinant of coherence. These findings suggest that unique spectral profiles of different brain areas automatically give rise to large-scale coherence patterns that follow anatomical connectivity and continuously reconfigure as a function of behavior and cognition.

Mechanisms of Flexible Information Sharing through Noisy Oscillations.

Simple SummaryTo properly interact with our environment, the brain must be able to identify external stimuli, process them, and make the right decisions all in a short time. This may involve several brain regions interacting together by sharing information birectionally via rhythmic activity. Such flexibility requires the functional connectivity between the areas to be dynamic, and a key question is the relevant parameter and operating regimes that make this possible in spite of fixed structural connectivity. Working towards this goal, we consider two coupled brain regions, each of which exhibits a noisy rhythm, a commonly observed type of neural activity. Such rhythms can be induced by the stochasticity in the neural circuitry, or be autonomously generated through nonlinearities and not necessitating noise. For these two types of rhythms, we computed the amount of information shared between the brain areas and the preferred direction(s) of sharing. We found that without the coupling delay, the flexibility needed by the brain to perform cognitive tasks requires the rhythms to be autogenerated rather than noise-induced. This is the case even with asymmetry or heterogeneity. This suggests that the importance of the dynamical regime has to be taken into account when modeling interacting neural rhythms from an information theoretical point of view.Brain areas must be able to interact and share information in a time-varying, dynamic manner on a fast timescale. Such flexibility in information sharing has been linked to the synchronization of rhythm phases between areas. One definition of flexibility is the number of local maxima in the delayed mutual information curve between two connected areas. However, the precise relationship between phase synchronization and information sharing is not clear, nor is the flexibility in the face of the fixed structural connectivity and noise. Here, we consider two coupled oscillatory excitatory-inhibitory networks connected through zero-delay excitatory connections, each of which mimics a rhythmic brain area. We numerically compute phase-locking and delayed mutual information between the phases of excitatory local field potential (LFPs) of the two networks, which measures the shared information and its direction. The flexibility in information sharing is shown to depend on the dynamical origin of oscillations, and its properties in different regimes are found to persist in the presence of asymmetry in the connectivity as well as system heterogeneity. For coupled noise-induced rhythms (quasi-cycles), phase synchronization is robust even in the presence of asymmetry and heterogeneity. However, they do not show flexibility, in contrast to noise-perturbed rhythms (noisy limit cycles), which are shown here to exhibit two local information maxima, i.e., flexibility. For quasi-cycles, phase difference and information measures for the envelope-phase dynamics obtained from previous analytical work using the Stochastic Averaging Method (SAM) are found to be in good qualitative agreement with those obtained from the original dynamics. The relation between phase synchronization and communication patterns is not trivial, particularly in the noisy limit cycle regime. There, complex patterns of information sharing can be observed for a single value of the phase difference. The mechanisms reported here can be extended to I-I networks since their phase synchronizations are similar. Our results set the stage for investigating information sharing between several connected noisy rhythms in neural and other complex biological networks.

Theta-gamma coupling emerges from spatially heterogeneous cholinergic neuromodulation.

Theta and gamma rhythms and their cross-frequency coupling play critical roles in perception, attention, learning, and memory. Available data suggest that forebrain acetylcholine (ACh) signaling promotes theta-gamma coupling, although the mechanism has not been identified. Recent evidence suggests that cholinergic signaling is both temporally and spatially constrained, in contrast to the traditional notion of slow, spatially homogeneous, and diffuse neuromodulation. Here, we find that spatially constrained cholinergic stimulation can generate theta-modulated gamma rhythms. Using biophysically-based excitatory-inhibitory (E-I) neural network models, we simulate the effects of ACh on neural excitability by varying the conductance of a muscarinic receptor-regulated K+ current. In E-I networks with local excitatory connectivity and global inhibitory connectivity, we demonstrate that theta-gamma-coupled firing patterns emerge in ACh modulated network regions. Stable gamma-modulated firing arises within regions with high ACh signaling, while theta or mixed theta-gamma activity occurs at the peripheries of these regions. High gamma activity also alternates between different high-ACh regions, at theta frequency. Our results are the first to indicate a causal role for spatially heterogenous ACh signaling in the emergence of localized theta-gamma rhythmicity. Our findings also provide novel insights into mechanisms by which ACh signaling supports the brain region-specific attentional processing of sensory information.

A Hypothesis for Theta Rhythm Frequency Control in CA1 Microcircuits.

Computational models of neural circuits with varying levels of biophysical detail have been generated in pursuit of an underlying mechanism explaining the ubiquitous hippocampal theta rhythm. However, within the theta rhythm are at least two types with distinct frequencies associated with different behavioral states, an aspect that must be considered in pursuit of these mechanistic explanations. Here, using our previously developed excitatory-inhibitory network models that generate theta rhythms, we investigate the robustness of theta generation to intrinsic neuronal variability by building a database of heterogeneous excitatory cells and implementing them in our microcircuit model. We specifically investigate the impact of three key “building block” features of the excitatory cell model that underlie our model design: these cells' rheobase, their capacity for post-inhibitory rebound, and their spike-frequency adaptation. We show that theta rhythms at various frequencies can arise dependent upon the combination of these building block features, and we find that the speed of these oscillations are dependent upon the excitatory cells' response to inhibitory drive, as encapsulated by their phase response curves. Taken together, these findings support a hypothesis for theta frequency control that includes two aspects: (i) an internal mechanism that stems from the building block features of excitatory cell dynamics; (ii) an external mechanism that we describe as “inhibition-based tuning” of excitatory cell firing. We propose that these mechanisms control theta rhythm frequencies and underlie their robustness.

Training Spiking Neural Networks in the Strong Coupling Regime.

Recurrent neural networks trained to perform complex tasks can provide insight into the dynamic mechanism that underlies computations performed by cortical circuits. However, due to a large number of unconstrained synaptic connections, the recurrent connectivity that emerges from network training may not be biologically plausible. Therefore, it remains unknown if and how biological neural circuits implement dynamic mechanisms proposed by the models. To narrow this gap, we developed a training scheme that, in addition to achieving learning goals, respects the structural and dynamic properties of a standard cortical circuit model: strongly coupled excitatory-inhibitory spiking neural networks. By preserving the strong mean excitatory and inhibitory coupling of initial networks, we found that most of trained synapses obeyed Dale's law without additional constraints, exhibited large trial-to-trial spiking variability, and operated in inhibition-stabilized regime. We derived analytical estimates on how training and network parameters constrained the changes in mean synaptic strength during training. Our results demonstrate that training recurrent neural networks subject to strong coupling constraints can result in connectivity structure and dynamic regime relevant to cortical circuits.

Cell-type-specific imaging of neurotransmission reveals a disrupted excitatory-inhibitory cortical network in isoflurane anaesthesia.

BackgroundDespite the fundamental clinical significance of general anaesthesia, the cortical mechanism underlying anaesthetic-induced loss of consciousness (aLOC) remains elusive.MethodsHere, we measured the dynamics of two major cortical neurotransmitters, gamma-aminobutyric acid (GABA) and glutamate, through in vivo two-photon imaging and genetically encoded neurotransmitter sensors in a cell type-specific manner in the primary visual (V1) cortex.FindingsWe found a general decrease in cortical GABA transmission during aLOC. However, the glutamate transmission varies among different cortical cell types, where in it is almost preserved on pyramidal cells and is significantly reduced on inhibitory interneurons. Cortical interneurons expressing vasoactive intestinal peptide (VIP) and parvalbumin (PV) specialize in disinhibitory and inhibitory effects, respectively. During aLOC, VIP neuronal activity was delayed, and PV neuronal activity was dramatically inhibited and highly synchronized.InterpretationThese data reveal that aLOC resembles a cortical state with a disrupted excitatory-inhibitory network and suggest that a functional inhibitory network is indispensable in the maintenance of consciousness.FundingThis work was supported by the grants of the National Natural Science Foundation of China (grant nos. 81620108012 and 82030038 to H.D. and grant nos. 31922029, 61890951, and 61890950 to J.H.).

NMDA receptors promote hippocampal sharp-wave ripples and the associated coactivity of CA1 pyramidal cells.

Hippocampal sharp-wave ripples (SWRs) support the reactivation of memory representations, relaying information to neocortex during "offline" and sleep-dependent memory consolidation. While blockade of NMDA receptors (NMDAR) is known to affect both learning and subsequent consolidation, the specific contributions of NMDAR activation to SWR-associated activity remain unclear. Here, we combine biophysical modeling with in vivo local field potential (LFP) and unit recording to quantify changes in SWR dynamics following inactivation of NMDAR. In a biophysical model of CA3-CA1 SWR activity, we find that NMDAR removal leads to reduced SWR density, but spares SWR properties such as duration, cell recruitment and ripple frequency. These predictions are confirmed by experiments in which NMDAR-mediated transmission in rats was inhibited using three different NMDAR antagonists, while recording dorsal CA1 LFP. In the model, loss of NMDAR-mediated conductances also induced a reduction in the proportion of cell pairs that co-activate significantly above chance across multiple events. Again, this prediction is corroborated by dorsal CA1 single-unit recordings, where the NMDAR blocker ketamine disrupted correlated spiking during SWR. Our results are consistent with a framework in which NMDA receptors both promote activation of SWR events and organize SWR-associated spiking content. This suggests that, while SWR are short-lived events emerging in fast excitatory-inhibitory networks, slower network components including NMDAR-mediated currents contribute to ripple density and promote consistency in the spiking content across ripples, underpinning mechanisms for fine-tuning of memory consolidation processes.

Presynaptic inhibition rapidly stabilises recurrent excitation in the face of plasticity.

Hebbian plasticity, a mechanism believed to be the substrate of learning and memory, detects and further enhances correlated neural activity. Because this constitutes an unstable positive feedback loop, it requires additional homeostatic control. Computational work suggests that in recurrent networks, the homeostatic mechanisms observed in experiments are too slow to compensate instabilities arising from Hebbian plasticity and need to be complemented by rapid compensatory processes. We suggest presynaptic inhibition as a candidate that rapidly provides stability by compensating recurrent excitation induced by Hebbian changes. Presynaptic inhibition is mediated by presynaptic GABA receptors that effectively and reversibly attenuate transmitter release. Activation of these receptors can be triggered by excess network activity, hence providing a stabilising negative feedback loop that weakens recurrent interactions on sub-second timescales. We study the stabilising effect of presynaptic inhibition in recurrent networks, in which presynaptic inhibition is implemented as a multiplicative reduction of recurrent synaptic weights in response to increasing inhibitory activity. We show that networks with presynaptic inhibition display a gradual increase of firing rates with growing excitatory weights, in contrast to traditional excitatory-inhibitory networks. This alleviates the positive feedback loop between Hebbian plasticity and network activity and thereby allows homeostasis to act on timescales similar to those observed in experiments. Our results generalise to spiking networks with a biophysically more detailed implementation of the presynaptic inhibition mechanism. In conclusion, presynaptic inhibition provides a powerful compensatory mechanism that rapidly reduces effective recurrent interactions and thereby stabilises Hebbian learning.

Phasic cholinergic signaling promotes emergence of local gamma rhythms in excitatory-inhibitory networks.

Recent experimental results have shown that the detection of cues in behavioral attention tasks relies on transient increases of acetylcholine (ACh) release in frontal cortex and cholinergically driven oscillatory activity in the gamma frequency band (Howe et al. Journal of Neuroscience, 2017, 37, 3215). The cue-induced gamma rhythmic activity requires stimulation of M1 muscarinic receptors. Using biophysical computational modeling, we show that a network of excitatory (E) and inhibitory (I) neurons that initially displays asynchronous firing can generate transient gamma oscillatory activity in response to simulated brief pulses of ACh. ACh effects are simulated as transient modulation of the conductance of an M-type K+ current which is blocked by activation of muscarinic receptors and has significant effects on neuronal excitability. The ACh-induced effects on the M current conductance, gKs , change network dynamics to promote the emergence of network gamma rhythmicity through a Pyramidal-Interneuronal Network Gamma mechanism. Depending on connectivity strengths between and among E and I cells, gamma activity decays with the simulated gKs transient modulation or is sustained in the network after the gKs transient has completely dissipated. We investigated the sensitivity of the emergent gamma activity to synaptic strengths, external noise and simulated levels of gKs modulation. To address recent experimental findings that cholinergic signaling is likely spatially focused and dynamic, we show that localized gKs modulation can induce transient changes of cellular excitability in local subnetworks, subsequently causing population-specific gamma oscillations. These results highlight dynamical mechanisms underlying localization of ACh-driven responses and suggest that spatially localized, cholinergically induced gamma may contribute to selectivity in the processing of competing external stimuli, as occurs in attentional tasks.

Neural Dynamics and Gamma Oscillation on a Hybrid Excitatory-Inhibitory Complex Network (Student Abstract)

This paper investigates the neural dynamics and gamma oscillation on a complex network with excitatory and inhibitory neurons (E-I network), as such network is ubiquitous in the brain. The system consists of a small-world network of neurons, which are emulated by Izhikevich model. Moreover, mixed Regular Spiking (RS) and Chattering (CH) neurons are considered to imitate excitatory neurons, and Fast Spiking (FS) neurons are used to mimic inhibitory neurons. Besides, the relationship between synchronization and gamma rhythm is explored by adjusting the critical parameters of our model. Experiments visually demonstrate that the gamma oscillations are generated by synchronous behaviors of our neural network. We also discover that the Chattering(CH) excitatory neurons can make the system easier to synchronize.

Discontinuous Galerkin approximation for excitatory-inhibitory networks with delay and refractory periods

In this study, we consider the network of noisy leaky integrate-and-fire (NNLIF) model, which governs by a second-order nonlinear time-dependent partial differential equation (PDE). This equation uses the probability density approach to describe the behavior of neurons with refractory states and the transmission delays. A numerical approximation based on the discontinuous Galerkin (DG) method is used for the spatial discretization with the analysis of stability. The strong stability-preserving explicit Runge–Kutta (SSPERK) method is performed for the temporal discretization. Finally, some test examples and numerical simulations are given to examine the behavior of the solution. The execution of the constructed scheme is measured by the quantitative comparison with the existing finite difference technique, namely weighted essentially nonoscillatory (WENO) scheme.

A simple three layer excitatory-inhibitory neuronal network for temporal decision-making

Humans and animals do not only keep track of time intervals but they can also make decisions about durations. Temporal bisection is a psychophysical task that is widely used to assess the latter ability via categorization of durations as short or long. Many existing models of performance in temporal bisection primarily account for choice proportions and tend to overlook the associated response times. We propose a time-cell neural network that implements both interval timing and temporal categorization. The proposed model can keep track of time intervals based on lurching wave activity, it can learn the reference durations along with their association with different categorization responses, and finally, it can carry out the comparison of arbitrary intermediate durations to the reference durations. We compared the model's predictions about choice behavior and response times to the empirical data previously gathered from rats. We showed that this time-cell neural network can predict the canonical behavioral signatures of temporal bisection performance. Specifically, (a) the proposed model can account for the sigmoidal relationship between the probability of the long choices and the test durations, (b) the superposition of choice functions on a relative time scale, (c) the localization of the point of subjective equality at the geometric mean of the reference durations, and (d) the differential modulation of short and long categorization response times as a function of the test durations.

Synchronization and Rhythm Transition in a Complex Neuronal Network

Synchronization and rhythm transition in an excitatory-inhibitory balanced cortical neuronal network are investigated in this paper. A small-world neuronal network is performed to be the cortical region of cerebral cortex, which is composed of different types of Izhikevich neurons. The combination of regular spiking (RS) cells, chattering (CH) cells, or mixed RS and CH cells are imitated as excitatory neurons, whereas fast spiking (FS) cells mimic inhibitory neurons. We mainly focus on the effect of different types of neurons on synchronization and rhythm transition of the neuronal network. The simulation results illustrate that it is easier for the neuronal network with CH excitatory neurons to achieve synchronization, and it is also more susceptible to the parameters than the network with RS neurons. Together with the weight of the synaptic connection, the structure of the small-world network is also explored to identify its influence on the synchronization and the rhythm transition. Moreover, we found that the synchronization performance could be improved by increasing the degree of influence among neurons. Importantly, the synchronization states are associated with the rhythm transitions. Especially, the consistency of synchronization of the neuronal network and y band rhythm is illustrated. In addition, our results could have an important significance on further understanding brain rhythms and synchrony in neuroscience.

Stability, bifurcation and phase-locking of time-delayed excitatory-inhibitory neural networks.

We study a model for a network of synaptically coupled, excitable neurons to identify the role of coupling delays in generating different network behaviors. The network consists of two distinct populations, each of which contains one excitatory-inhibitory neuron pair. The two pairs are coupled via delayed synaptic coupling between the excitatory neurons, while each inhibitory neuron is connected only to the corresponding excitatory neuron in the same population. We show that multiple equilibria can exist depending on the strength of the excitatory coupling between the populations. We conduct linear stability analysis of the equilibria and derive necessary conditions for delay-induced Hopf bifurcation. We show that these can induce two qualitatively different phase-locked behaviors, with the type of behavior determined by the sizes of the coupling delays. Numerical bifurcation analysis and simulations supplement and confirm our analytical results. Our work shows that the resting equilibrium point is unaffected by the coupling, thus the network exhibits bistability between a rest state and an oscillatory state. This may help understand how rhythms spontaneously arise in neuronal networks.

Training dynamically balanced excitatory-inhibitory networks

The construction of biologically plausible models of neural circuits is crucial for understanding the computational properties of the nervous system. Constructing functional networks composed of separate excitatory and inhibitory neurons obeying Dale’s law presents a number of challenges. We show how a target-based approach, when combined with a fast online constrained optimization technique, is capable of building functional models of rate and spiking recurrent neural networks in which excitation and inhibition are balanced. Balanced networks can be trained to produce complicated temporal patterns and to solve input-output tasks while retaining biologically desirable features such as Dale’s law and response variability.