Excitatory-inhibitory Networks Research Articles

Effects of spike-time-dependent plasticity on stochastic resonance in excitatory-inhibitory neuronal networks

Effects of spike-time-dependent plasticity on stochastic resonance in excitatory-inhibitory neuronal networks

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.

Statistically inferred neuronal connections in subsampled neural networks strongly correlate with spike train covariances.

Statistically inferred neuronal connections from observed spike train data are often skewed from ground truth by factors such as model mismatch, unobserved neurons, and limited data. Spike train covariances, sometimes referred to as "functional connections," are often used as a proxy for the connections between pairs of neurons, but reflect statistical relationships between neurons, not anatomical connections. Moreover, covariances are not causal: spiking activity is correlated in both the past and the future, whereas neurons respond only to synaptic inputs in the past. Connections inferred by maximum likelihood inference, however, can be constrained to be causal. However, we show in this work that the inferred connections in spontaneously active networks modeled by stochastic leaky integrate-and-fire networks strongly correlate with the covariances between neurons, and may reflect noncausal relationships, when many neurons are unobserved or when neurons are weakly coupled. This phenomenon occurs across different network structures, including random networks and balanced excitatory-inhibitory networks. We use a combination of simulations and a mean-field analysis with fluctuation corrections to elucidate the relationships between spike train covariances, inferred synaptic filters, and ground-truth connections in partially observed networks.

Chaos shapes transient synchrony activities and switchings in the excitatory-inhibitory networks

Chaos shapes transient synchrony activities and switchings in the excitatory-inhibitory networks

Chimera-like state in the bistable excitatory-inhibitory cortical neuronal network

In recent years, the coexistence of different states in the neural system has attracted widespread interest. Researchers have found a coexisting state of spiking and resting in homogeneous networks, which is known as the chimera-like state. The real cortical network is a much more complex and heterogeneous network. Therefore, the excitatory-inhibitory cortical neuronal network is constructed based on Hodgkin-Huxley neuronal model in this paper, and the chimera-like state is further investigated in the heterogeneous network. It is found that the chimera-like state is related to the balance between excitatory and inhibitory synaptic currents. The excitatory coupling current can counteract the initial condition effect and promote synchronized firing of neurons in the network. The inhibitory coupling current desynchronizes the network and thus induces synaptic noise, resulting in an inverse bell-shaped dependence of the change in the number of spiking neurons. We analyzed the underlying mechanisms of synaptic noise in the phase plane diagram and found it has asymmetry for the neuronal state transition. In addition, neurons with low degrees have a higher probability of undergoing state transitions. Finally, we verified that the chimera-like state is robust to network topology and initial conditions. The results provide a new insight into neuronal interactions in heterogeneous networks and might help to reveal the mechanisms of coexistence of different states in the cortical network.

Excitation-Inhibition Balance, Neural Criticality, and Activities in Neuronal Circuits.

Neural activities in local circuits exhibit complex and multilevel dynamic features. Individual neurons spike irregularly, which is believed to originate from receiving balanced amounts of excitatory and inhibitory inputs, known as the excitation-inhibition balance. The spatial-temporal cascades of clustered neuronal spikes occur in variable sizes and durations, manifested as neural avalanches with scale-free features. These may be explained by the neural criticality hypothesis, which posits that neural systems operate around the transition between distinct dynamic states. Here, we summarize the experimental evidence for and the underlying theory of excitation-inhibition balance and neural criticality. Furthermore, we review recent studies of excitatory-inhibitory networks with synaptic kinetics as a simple solution to reconcile these two apparently distinct theories in a single circuit model. This provides a more unified understanding of multilevel neural activities in local circuits, from spontaneous to stimulus-response dynamics.

Acetylcholine facilitates localized synaptic potentiation and location specific feature binding.

Forebrain acetylcholine (ACh) signaling has been shown to drive attention and learning. Recent experimental evidence of spatially and temporally constrained cholinergic signaling has sparked interest to investigate how it facilitates stimulus-induced learning. We use biophysical excitatory-inhibitory (E-I) multi-module neural network models to show that external stimuli and ACh signaling can mediate spatially constrained synaptic potentiation patterns. The effects of ACh on neural excitability are simulated by varying the conductance of a muscarinic receptor-regulated hyperpolarizing slow K+ current (m-current). Each network module consists of an E-I network with local excitatory connectivity and global inhibitory connectivity. The modules are interconnected with plastic excitatory synaptic connections, that change via a spike-timing-dependent plasticity (STDP) rule. Our results indicate that spatially constrained ACh release influences the information flow represented by network dynamics resulting in selective reorganization of inter-module interactions. Moreover the information flow depends on the level of synchrony in the network. For highly synchronous networks, the more excitable module leads firing in the less excitable one resulting in strengthening of the outgoing connections from the former and weakening of its incoming synapses. For networks with more noisy firing patterns, activity in high ACh regions is prone to induce feedback firing of synchronous volleys and thus strengthening of the incoming synapses to the more excitable region and weakening of outgoing synapses. Overall, these results suggest that spatially and directionally specific plasticity patterns, as are presumed necessary for feature binding, can be mediated by spatially constrained ACh release.

Relating local connectivity and global dynamics in recurrent excitatory-inhibitory networks.

How the connectivity of cortical networks determines the neural dynamics and the resulting computations is one of the key questions in neuroscience. Previous works have pursued two complementary approaches to quantify the structure in connectivity. One approach starts from the perspective of biological experiments where only the local statistics of connectivity motifs between small groups of neurons are accessible. Another approach is based instead on the perspective of artificial neural networks where the global connectivity matrix is known, and in particular its low-rank structure can be used to determine the resulting low-dimensional dynamics. A direct relationship between these two approaches is however currently missing, and in particular it remains to be clarified how local connectivity statistics and the global low-rank connectivity structure are inter-related and shape the low-dimensional activity. To bridge this gap, here we develop a method for mapping local connectivity statistics onto an approximate global low-rank structure. Our method rests on approximating the global connectivity matrix using dominant eigenvectors, which we compute using perturbation theory for random matrices. We demonstrate that multi-population networks defined from local connectivity statistics for which the central limit theorem holds can be approximated by low-rank connectivity with Gaussian-mixture statistics. We specifically apply this method to excitatory-inhibitory networks with reciprocal motifs, and show that it yields reliable predictions for both the low-dimensional dynamics, and statistics of population activity. Importantly, it analytically accounts for the activity heterogeneity of individual neurons in specific realizations of local connectivity. Altogether, our approach allows us to disentangle the effects of mean connectivity and reciprocal motifs on the global recurrent feedback, and provides an intuitive picture of how local connectivity shapes global network dynamics.

Bifurcations of a Neural Network Model with Symmetry

We analyze a family of clustered excitatory-inhibitory neural networks and the underlying bifurcation structures that arise because of permutation symmetries in the network as the global coupling strength $g$ is varied. We primarily consider two network topologies: an all-to-all connected network which excludes self-connections, and a network in which the excitatory cells are broken into clusters of equal size. Although in both cases the bifurcation structure is determined by symmetries in the system, the behavior of the two systems is qualitatively different. In the all-to-all connected network, the system undergoes Hopf bifurcations leading to periodic orbit solutions; notably, for large $g$, there is a single, stable periodic orbit solution and no stable fixed points. By contrast, in the clustered network, there are no Hopf bifurcations, and there is a family of stable fixed points for large $g$.

Excitatory-inhibitory recurrent dynamics produce robust visual grids and stable attractors

Spatially modulated grid cells have been recently found in the rat secondary visual cortex (V2) during active navigation. However, the computational mechanism and functional significance of V2 grid cells remain unknown. To address the knowledge gap, we train a biologically inspired excitatory-inhibitory recurrent neural network to perform a two-dimensional spatial navigation task with multisensory input. We find grid-like responses in both excitatory and inhibitory RNN units, which are robust with respect to spatial cues, dimensionality of visual input, and activation function. Population responses reveal a low-dimensional, torus-like manifold and attractor. We find a link between functional grid clusters with similar receptive fields and structured excitatory-to-excitatory connections. Additionally, multistable torus-like attractors emerged with increasing sparsity in inter- and intra-subnetwork connectivity. Finally, irregular grid patterns are found in recurrent neural network (RNN) units during a visual sequence recognition task. Together, our results suggest common computational mechanisms of V2 grid cells for spatial and non-spatial tasks.

Influence of temperature and noise on the propagation of subthreshold signal in feedforward neural network

Temperature is an important environmental factor that all creatures depend on. Suitable temperature is essential for maintaining the normal physiological functions of nervous system. Subthreshold signal is generated by weak activities in the nervous system that is difficult to be detected. Based on an improved Hodgkin-Huxley (HH) neuron model considering temperature and noise, the ten-layers pure excitatory feedforward neural network and the ten-layers excitatory-inhibitory (EI) neural network are constructed to study the propagation of subthreshold excitatory postsynaptic current signal. It's found that increasing temperature can restrain the signal propagation, and raise the noises intensity threshold where the failed signal propagation can transform into succeed signal propagation. Under the large noise, the signal propagation in network of different temperatures exhibits different anti-noise capabilities. Moreover, temperature and noise can modulate the spontaneous activity of the EI neural network to transform between the synchronous regular (SR) state and the asynchronous irregular (AI) state. The EI network's spontaneous activity will completely cover subthreshold signal, and block the signal propagation under large noise. The jumping phenomenon in the value of fidelity, which measures the quality of signal propagation, appears in both pure excitatory network and EI network. This paper provides potential value for understanding the regulation of both temperature and noise in information propagation in neural network.

Heterogeneous mechanisms for synchronization of networks of resonant neurons under different E/I balance regimes.

Rhythmic synchronization of neuronal firing patterns is a widely present phenomenon in the brain-one that seems to be essential for many cognitive processes. A variety of mechanisms contribute to generation and synchronization of network oscillations, ranging from intrinsic cellular excitability to network mediated effects. However, it is unclear how these mechanisms interact together. Here, using computational modeling of excitatory-inhibitory neural networks, we show that different synchronization mechanisms dominate network dynamics at different levels of excitation and inhibition (i.e. E/I levels) as synaptic strength is systematically varied. Our results show that with low synaptic strength networks are sensitive to external oscillatory drive as a synchronizing mechanism-a hallmark of resonance. In contrast, in a strongly-connected regime, synchronization is driven by network effects via the direct interaction between excitation and inhibition, and spontaneous oscillations and cross-frequency coupling emerge. Unexpectedly, we find that while excitation dominates network synchrony at low excitatory coupling strengths, inhibition dominates at high excitatory coupling strengths. Together, our results provide novel insights into the oscillatory modulation of firing patterns in different excitation/inhibition regimes.

Synchronization and oscillation behaviors of excitatory and inhibitory populations with spike-timing-dependent plasticity.

The effect of synaptic plasticity on the synchronization mechanism of the cerebral cortex has been a hot research topic over the past two decades. There are a great deal of literatures on excitatory pyramidal neurons, but the mechanism of interaction between the inhibitory interneurons is still under exploration. In this study, we consider a complex network consisting of excitatory (E) pyramidal neurons and inhibitory (I) interneurons interacting with chemical synapses through spike-timing-dependent plasticity(STDP). To study the effects of eSTDP and iSTDP on synchronization and oscillation behaviors emerged in an excitatory-inhibitory balanced network, we analyzed three different cases, a small-world network of purely excitatory neurons with eSTDP, a small-world network of purely inhibitory neurons with iSTDP and a small-world network with excitatory-inhibitory balanced neurons. By varying the number of inhibitory interneurons, and that of connected edges in a small-world network, and the coupling strength, these networks exhibit different synchronization and oscillation behaviors. We found that the eSTDP facilitates synchronization effectively, while iSTDP has no significant impact on it. In addition, eSTDP and iSTDP restrict the balance of the excitatory-inhibitory balanced neuronal network together and play a fundamental role in maintaining network stability and synchronization. They also can be used to guide the treatment and further research of neurodegenerative diseases.

The spectrum of covariance matrices of randomly connected recurrent neuronal networks with linear dynamics

A key question in theoretical neuroscience is the relation between the connectivity structure and the collective dynamics of a network of neurons. Here we study the connectivity-dynamics relation as reflected in the distribution of eigenvalues of the covariance matrix of the dynamic fluctuations of the neuronal activities, which is closely related to the network dynamics' Principal Component Analysis (PCA) and the associated effective dimensionality. We consider the spontaneous fluctuations around a steady state in a randomly connected recurrent network of stochastic neurons. An exact analytical expression for the covariance eigenvalue distribution in the large-network limit can be obtained using results from random matrices. The distribution has a finitely supported smooth bulk spectrum and exhibits an approximate power-law tail for coupling matrices near the critical edge. We generalize the results to include second-order connectivity motifs and discuss extensions to excitatory-inhibitory networks. The theoretical results are compared with those from finite-size networks and the effects of temporal and spatial sampling are studied. Preliminary application to whole-brain imaging data is presented. Using simple connectivity models, our work provides theoretical predictions for the covariance spectrum, a fundamental property of recurrent neuronal dynamics, that can be compared with experimental data.

Application of Medial Ganglionic Eminence Cell Transplantation in Diseases Associated With Interneuron Disorders.

Excitatory projection neurons and inhibitory interneurons primarily accomplish the neural activity of the cerebral cortex, and an imbalance of excitatory-inhibitory neural networks may lead to neuropsychiatric diseases. Gamma-aminobutyric acid (GABA)ergic interneurons mediate inhibition, and the embryonic medial ganglionic eminence (MGE) is a source of GABAergic interneurons. After transplantation, MGE cells migrate to different brain regions, differentiate into multiple subtypes of GABAergic interneurons, integrate into host neural circuits, enhance synaptic inhibition, and have tremendous application value in diseases associated with interneuron disorders. In the current review, we describe the fate of MGE cells derived into specific interneurons and the related diseases caused by interneuron loss or dysfunction and explore the potential of MGE cell transplantation as a cell-based therapy for a variety of interneuron disorder-related diseases, such as epilepsy, schizophrenia, autism spectrum disorder, and Alzheimer’s disease.

Complex Dynamics of Noise-Perturbed Excitatory-Inhibitory Neural Networks With Intra-Correlative and Inter-Independent Connections.

Real neural system usually contains two types of neurons, i.e., excitatory neurons and inhibitory ones. Analytical and numerical interpretation of dynamics induced by different types of interactions among the neurons of two types is beneficial to understanding those physiological functions of the brain. Here, we articulate a model of noise-perturbed random neural networks containing both excitatory and inhibitory (E&I) populations. Particularly, both intra-correlatively and inter-independently connected neurons in two populations are taken into account, which is different from the most existing E&I models only considering the independently-connected neurons. By employing the typical mean-field theory, we obtain an equivalent system of two dimensions with an input of stationary Gaussian process. Investigating the stationary autocorrelation functions along the obtained system, we analytically find the parameters’ conditions under which the synchronized behaviors between the two populations are sufficiently emergent. Taking the maximal Lyapunov exponent as an index, we also find different critical values of the coupling strength coefficients for the chaotic excitatory neurons and for the chaotic inhibitory ones. Interestingly, we reveal that the noise is able to suppress chaotic dynamics of the random neural networks having neurons in two populations, while an appropriate amount of correlation coefficient in intra-coupling strengths can enhance chaos occurrence. Finally, we also detect a previously-reported phenomenon where the parameters region corresponds to neither linearly stable nor chaotic dynamics; however, the size of the region area crucially depends on the populations’ parameters.

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.