Synchronization of electrically coupled pairs of inhibitory interneurons in neocortex

Patterns of synchronization in 2D networks of inhibitory neurons

Neural firing in many inhibitory networks displays synchronous assembly or clustered firing, in which subsets of neurons fire synchronously, and these subsets may vary with different inputs to, or states of, the network. Most prior analytical and computational modeling of such networks has focused on 1D networks or 2D networks with symmetry (often circular symmetry). Here, we consider a 2D discrete network model on a general torus, where neurons are coupled to two or more nearest neighbors in three directions (horizontal, vertical, and diagonal), and allow different coupling strengths in all directions. Using phase model analysis, we establish conditions for the stability of different patterns of clustered firing behavior in the network. We then apply our results to study how variation of network connectivity and the presence of heterogeneous coupling strengths influence which patterns are stable. We confirm and supplement our results with numerical simulations of biophysical inhibitory neural network models. Our work shows that 2D networks may exhibit clustered firing behavior that cannot be predicted as a simple generalization of a 1D network, and that heterogeneity of coupling can be an important factor in determining which patterns are stable.

On the Diverse Functions of Electrical Synapses

Electrical synapses are the neurophysiological product of gap junctional pores between neurons that allow bidirectional flow of current between neurons. They are expressed throughout the mammalian nervous system, including cortex, hippocampus, thalamus, retina, cerebellum, and inferior olive. Classically, the function of electrical synapses has been associated with synchrony, logically following that continuous conductance provided by gap junctions facilitates the reduction of voltage differences between coupled neurons. Indeed, electrical synapses promote synchrony at many anatomical and frequency ranges across the brain. However, a growing body of literature shows there is greater complexity to the computational function of electrical synapses. The paired membranes that embed electrical synapses act as low-pass filters, and as such, electrical synapses can preferentially transfer spike after hyperpolarizations, effectively providing spike-dependent inhibition. Other functions include driving asynchronous firing, improving signal to noise ratio, aiding in discrimination of dissimilar inputs, or dampening signals by shunting current. The diverse ways by which electrical synapses contribute to neuronal integration merits furthers study. Here we review how functions of electrical synapses vary across circuits and brain regions and depend critically on the context of the neurons and brain circuits involved. Computational modeling of electrical synapses embedded in multi-cellular models and experiments utilizing optical control and measurement of cellular activity will be essential in determining the specific roles performed by electrical synapses in varying contexts.

Linking α-synuclein-induced synaptopathy and neural network dysfunction in early Parkinson's disease

The prodromal phase of Parkinson's disease is characterized by aggregation of the misfolded pathogenic protein α-synuclein in select neural centres, co-occurring with non-motor symptoms including sensory and cognitive loss, and emotional disturbances. It is unclear whether neuronal loss is significant during the prodrome. Underlying these symptoms are synaptic impairments and aberrant neural network activity. However, the relationships between synaptic defects and network-level perturbations are not established. In experimental models, pathological α-synuclein not only impacts neurotransmission at the synaptic level, but also leads to changes in brain network-level oscillatory dynamics-both of which likely contribute to non-motor deficits observed in Parkinson's disease. Here we draw upon research from both human subjects and experimental models to propose a 'synapse to network prodrome cascade' wherein before overt cell death, pathological α-synuclein induces synaptic loss and contributes to aberrant network activity, which then gives rise to prodromal symptomology. As the disease progresses, abnormal patterns of neural activity ultimately lead to neuronal loss and clinical progression of disease. Finally, we outline goals and research needed to unravel the basis of functional impairments in Parkinson's disease and other α-synucleinopathies.

Spatially localized cluster solutions in inhibitory neural networks

Neurons in the inhibitory network of the striatum display cell assembly firing patterns which recent results suggest may consist of spatially compact neural clusters. Previous computational modeling of striatal neural networks has indicated that non-monotonic, distance-dependent coupling may promote spatially localized cluster firing. Here, we identify conditions for the existence and stability of cluster firing solutions in which clusters consist of spatially adjacent neurons in inhibitory neural networks. We consider simple non-monotonic, distance-dependent connectivity schemes in weakly coupled 1-D networks where cells make stronger connections with their kth nearest neighbors on each side and weaker connections with closer neighbors. Using the phase model reduction of the network system, we prove the existence of cluster solutions where neurons that are spatially close together are also synchronized in the same cluster, and find stability conditions for these solutions. Our analysis predicts the long-term behavior for networks of neurons, and we confirm our results by numerical simulations of biophysical neuron network models. Our results demonstrate that an inhibitory network with non-monotonic, distance-dependent connectivity can exhibit cluster solutions where adjacent cells fire together.

Efficient Communication in Distributed Simulations of Spiking Neuronal Networks With Gap Junctions

Investigating the dynamics and function of large-scale spiking neuronal networks with realistic numbers of synapses is made possible today by state-of-the-art simulation code that scales to the largest contemporary supercomputers. However, simulations that involve electrical interactions, also called gap junctions, besides chemical synapses scale only poorly due to a communication scheme that collects global data on each compute node. In comparison to chemical synapses, gap junctions are far less abundant. To improve scalability we exploit this sparsity by integrating an existing framework for continuous interactions with a recently proposed directed communication scheme for spikes. Using a reference implementation in the NEST simulator we demonstrate excellent scalability of the integrated framework, accelerating large-scale simulations with gap junctions by more than an order of magnitude. This allows, for the first time, the efficient exploration of the interactions of chemical and electrical coupling in large-scale neuronal networks models with natural synapse density distributed across thousands of compute nodes.

Exact firing rate model reveals the differential effects of chemical versus electrical synapses in spiking networks

Chemical and electrical synapses shape the dynamics of neuronal networks. Numerous theoretical studies have investigated how each of these types of synapses contributes to the generation of neuronal oscillations, but their combined effect is less understood. This limitation is further magnified by the impossibility of traditional neuronal mean-field models-also known as firing rate models or firing rate equations-to account for electrical synapses. Here, we introduce a firing rate model that exactly describes the mean-field dynamics of heterogeneous populations of quadratic integrate-and-fire (QIF) neurons with both chemical and electrical synapses. The mathematical analysis of the firing rate model reveals a well-established bifurcation scenario for networks with chemical synapses, characterized by a codimension-2 cusp point and persistent states for strong recurrent excitatory coupling. The inclusion of electrical coupling generally implies neuronal synchrony by virtue of a supercritical Hopf bifurcation. This transforms the cusp scenario into a bifurcation scenario characterized by three codimension-2 points (cusp, Takens-Bogdanov, and saddle-node separatrix loop), which greatly reduces the possibility for persistent states. This is generic for heterogeneous QIF networks with both chemical and electrical couplings. Our results agree with several numerical studies on the dynamics of large networks of heterogeneous spiking neurons with electrical and chemical couplings.

Understanding the Molecular and Cell Biological Mechanisms of Electrical Synapse Formation

In this review article, we will describe the recent advances made towards understanding the molecular and cell biological mechanisms of electrical synapse formation. New evidence indicates that electrical synapses, which are gap junctions between neurons, can have complex molecular compositions including protein asymmetries across joined cells, diverse morphological arrangements, and overlooked similarities with other junctions, all of which indicate new potential roles in neurodevelopmental disease. Aquatic organisms, and in particular the vertebrate zebrafish, have proven to be excellent models for elucidating the molecular mechanisms of electrical synapse formation. Zebrafish will serve as our main exemplar throughout this review and will be compared with other model organisms. We highlight the known cell biological processes that build neuronal gap junctions and compare these with the assemblies of adherens junctions, tight junctions, non-neuronal gap junctions, and chemical synapses to explore the unknown frontiers remaining in our understanding of the critical and ubiquitous electrical synapse.

A biophysical model of striatal microcircuits suggests gamma and beta oscillations interleaved at delta/theta frequencies mediate periodicity in motor control

Striatal oscillatory activity is associated with movement, reward, and decision-making, and observed in several interacting frequency bands. Local field potential recordings in rodent striatum show dopamine- and reward-dependent transitions between two states: a "spontaneous" state involving β (∼15-30 Hz) and low γ (∼40-60 Hz), and a state involving θ (∼4-8 Hz) and high γ (∼60-100 Hz) in response to dopaminergic agonism and reward. The mechanisms underlying these rhythmic dynamics, their interactions, and their functional consequences are not well understood. In this paper, we propose a biophysical model of striatal microcircuits that comprehensively describes the generation and interaction of these rhythms, as well as their modulation by dopamine. Building on previous modeling and experimental work suggesting that striatal projection neurons (SPNs) are capable of generating β oscillations, we show that networks of striatal fast-spiking interneurons (FSIs) are capable of generating δ/θ (ie, 2 to 6 Hz) and γ rhythms. Under simulated low dopaminergic tone our model FSI network produces low γ band oscillations, while under high dopaminergic tone the FSI network produces high γ band activity nested within a δ/θ oscillation. SPN networks produce β rhythms in both conditions, but under high dopaminergic tone, this β oscillation is interrupted by δ/θ-periodic bursts of γ-frequency FSI inhibition. Thus, in the high dopamine state, packets of FSI γ and SPN β alternate at a δ/θ timescale. In addition to a mechanistic explanation for previously observed rhythmic interactions and transitions, our model suggests a hypothesis as to how the relationship between dopamine and rhythmicity impacts motor function. We hypothesize that high dopamine-induced periodic FSI γ-rhythmic inhibition enables switching between β-rhythmic SPN cell assemblies representing the currently active motor program, and thus that dopamine facilitates movement in part by allowing for rapid, periodic shifts in motor program execution.

Connexins-Based Hemichannels/Channels and Their Relationship with Inflammation, Seizures and Epilepsy

Connexins (Cxs) are a family of 21 protein isoforms, eleven of which are expressed in the central nervous system, and they are found in neurons and glia. Cxs form hemichannels (connexons) and channels (gap junctions/electric synapses) that permit functional and metabolic coupling between neurons and astrocytes. Altered Cx expression and function is involved in inflammation and neurological diseases. Cxs-based hemichannels and channels have a relevance to seizures and epilepsy in two ways: First, this pathological condition increases the opening probability of hemichannels in glial cells to enable gliotransmitter release, sustaining the inflammatory process and exacerbating seizure generation and epileptogenesis, and second, the opening of channels favors excitability and synchronization through coupled neurons. These biological events highlight the global pathological mechanism of epilepsy, and the therapeutic potential of Cxs-based hemichannels and channels. Therefore, this review describes the role of Cxs in neuroinflammation and epilepsy and examines how the blocking of channels and hemichannels may be therapeutic targets of anti-convulsive and anti-epileptic treatments.

Synchronization of Electrically Coupled Resonate-and-Fire Neurons

Electrical coupling between neurons is broadly present across brain areas and is typically assumed to synchronize network activity. However, intrinsic properties of the coupled cells can complicate this simple picture. Many cell types with electrical coupling show a diversity of post-spike subthreshold fluctuations, often linked to subthreshold resonance, which are transmitted through electrical synapses in addition to action potentials. Using the theory of weakly coupled oscillators, we explore the effect of both subthreshold and spike-mediated coupling on synchrony in small networks of electrically coupled resonate-and-fire neurons, a hybrid neuron model with damped subthreshold oscillations and a range of post-spike voltage dynamics. We calculate the phase response curve using an extension of the adjoint method that accounts for the discontinuous post-spike reset rule. We find that both spikes and subthreshold fluctuations can jointly promote synchronization. The subthreshold contribution is strongest when the voltage exhibits a significant post-spike elevation in voltage, or plateau potential. Additionally, we show that the geometry of trajectories approaching the spiking threshold causes a "reset-induced shear" effect that can oppose synchrony in the presence of network asymmetry, despite having no effect on the phase-locking of symmetrically coupled pairs.

Frequency-dependent entrainment of striatal fast-spiking interneurons

Striatal fast-spiking interneurons (FSIs) fire in variable-length runs of action potentials at 20-200 spikes/s separated by pauses. In vivo, or with fluctuating applied current, both runs and pauses become briefer and more variable. During runs, spikes are entrained specifically to gamma-frequency components of the input fluctuations. We stimulated parvalbumin-expressing striatal FSIs in mouse brain slices with broadband noise currents added to direct current steps and measured spike entrainment across all frequencies. As the constant current level was increased, FSIs produced longer runs and showed sharper frequency tuning, with best entrainment at the stimulus frequency matching their intrarun firing rate. We separated the contributions of previous spikes from that of the fluctuating stimulus, revealing a strong contribution of previous action potentials to gamma-frequency entrainment. In contrast, after subtraction of the effect inherited from the previous spike, the remaining stimulus contribution to spike generation was less sharply tuned, showing a larger contribution of lower frequencies. The frequency specificity of entrainment within a run was reproduced with a phase resetting model based on experimentally measured phase resetting curves of the same FSIs. In the model, broadly tuned phase entrainment for the first spike in a run evolved into sharply tuned gamma entrainment over the next few spikes. The data and modeling results indicate that for FSIs firing in brief runs and pauses firing within runs is entrained by gamma-frequency components of the input, whereas the onset timing of runs may be sensitive to a wider range of stimulus frequency components.NEW & NOTEWORTHY Specific types of neurons entrain their spikes to particular oscillation frequencies in their synaptic input. This entrainment is commonly understood in terms of the subthreshold voltage response, but how this translates to spiking is not clear. We show that in striatal fast-spiking interneurons, entrainment to gamma-frequency input depends on rhythmic spike runs and is explained by the phase resetting curve, whereas run initiation can be triggered by a broad range of input frequencies.

ELFENN: A Generalized Platform for Modeling Ephaptic Coupling in Spiking Neuron Models

The transmembrane ionic currents that underlie changes in a cell's membrane potential give rise to electric fields in the extracellular space. In the context of brain activity, these electric fields form the basis for extracellularly recorded signals, such as multiunit activity, local field potentials and electroencephalograms. Understanding the underlying neuronal dynamics and localizing current sources using these signals is often challenging, and therefore effective computational modeling approaches are critical. Typically, the electric fields from neural activity are modeled in a post-hoc form, i.e., a traditional neuronal model is used to first generate the membrane currents, which in turn are then used to calculate the electric fields. When the conductivity of the extracellular space is high, the electric fields are weak, and therefore treating membrane currents and electric fields separately is justified. However, in brain regions of lower conductivity, extracellular fields can feed back and significantly influence the underlying transmembrane currents and dynamics of nearby neurons—this is often referred to as ephaptic coupling. The closed-loop nature of ephaptic coupling cannot be modeled using the post-hoc approaches implemented by existing software tools; instead, electric fields and neuronal dynamics must be solved simultaneously. To this end, we have developed a generalized modeling toolbox for studying ephaptic coupling in compartmental neuron models: E_LFENN (E_Lectric Field Effects in Neural Networks). In open loop conditions, we validate the separate components of E_LFENN for modeling membrane dynamics and associated field potentials against standard approaches (NEURON and LFPy). Unlike standard approaches however, E_LFENN enables the closed-loop condition to be modeled as well, in that the field potentials can feed back and influence membrane dynamics. As an example closed-loop case, we use E_LFENN to study phase-locking of action potentials generated by a population of axons running parallel in a bundle. Being able to efficiently explore ephaptic coupling from a computational perspective using tools, such as E_LFENN will allow us to better understand the physical basis of electric fields in the brain, as well as the conditions in which these fields may influence neuronal dynamics in general.

Firing rate models for gamma oscillations

Gamma oscillations are readily observed in a variety of brain regions during both waking and sleeping states. Computational models of gamma oscillations typically involve simulations of large networks of synaptically coupled spiking units. These networks can exhibit strongly synchronized gamma behavior, whereby neurons fire in near synchrony on every cycle, or weakly modulated gamma behavior, corresponding to stochastic, sparse firing of the individual units on each cycle of the population gamma rhythm. These spiking models offer valuable biophysical descriptions of gamma oscillations; however, because they involve many individual neuronal units they are limited in their ability to communicate general network-level dynamics. Here we demonstrate that few-variable firing rate models with established synaptic timescales can account for both strongly synchronized and weakly modulated gamma oscillations. These models go beyond the classical formulations of rate models by including at least two dynamic variables per population: firing rate and synaptic activation. The models' flexibility to capture the broad range of gamma behavior depends directly on the timescales that represent recruitment of the excitatory and inhibitory firing rates. In particular, we find that weakly modulated gamma oscillations occur robustly when the recruitment timescale of inhibition is faster than that of excitation. We present our findings by using an extended Wilson-Cowan model and a rate model derived from a network of quadratic integrate-and-fire neurons. These biophysical rate models capture the range of weakly modulated and coherent gamma oscillations observed in spiking network models, while additionally allowing for greater tractability and systems analysis. NEW & NOTEWORTHY Here we develop simple and tractable models of gamma oscillations, a dynamic feature observed throughout much of the brain with significant correlates to behavior and cognitive performance in a variety of experimental contexts. Our models depend on only a few dynamic variables per population, but despite this they qualitatively capture features observed in previous biophysical models of gamma oscillations that involve many individual spiking units.

Inhibition increases response variability and reduces stimulus discrimination in random networks of cortical neurons

Much of what is known about the contribution of inhibition to stimulus discrimination is due to extensively studied sensory systems, which are highly structured neural circuits. The effect of inhibition on stimulus representation in less structured networks is not as clear. Here we exercise a biosynthetic approach in order to study the impacts of inhibition on stimulus representation in non-specialized network anatomy. Combining pharmacological manipulation, multisite electrical stimulation and recording from ex-vivo randomly rewired networks of cortical neurons, we quantified the effects of inhibition on response variability and stimulus discrimination at the population and single unit levels. We find that blocking inhibition quenches variability of responses evoked by repeated stimuli and enhances discrimination between stimuli that invade the network from different spatial loci. Enhanced stimulus discrimination is reserved for representation schemes that are based on temporal relation between spikes emitted in groups of neurons. Our data indicate that - under intact inhibition - the response to a given stimulus is a noisy version of the response evoked in the absence of inhibition. Spatial analysis suggests that the dispersion effect of inhibition is due to disruption of an otherwise coherent, wave-like propagation of activity.

Neuronal Dynamics Underlying Communication Signals in a Weakly Electric Fish: Implications for Connectivity in a Pacemaker Network

Neuronal networks can produce stable oscillations and synchrony that are under tight control yet flexible enough to rapidly switch between dynamical states. The pacemaker nucleus in the weakly electric fish comprises a network of electrically coupled neurons that fire synchronously at high frequency. This activity sets the timing for an oscillating electric organ discharge with the lowest cycle-to-cycle variability of all known biological oscillators. Despite this high temporal precision, pacemaker activity is behaviorally modulated on millisecond time-scales for the generation of electrocommunication signals. The network mechanisms that allow for this combination of stability and flexibility are not well understood. In this study, we use an in vitro pacemaker preparation from Apteronotus leptorhynchus to characterize the neural responses elicited by the synaptic inputs underlying electrocommunication. These responses involve a variable increase in firing frequency and a prominent desynchronization of neurons that recovers within 5 oscillation cycles. Using a previously developed computational model of the pacemaker network, we show that the frequency changes and rapid resynchronization observed experimentally are most easily explained when model neurons are interconnected more densely and with higher coupling strengths than suggested by published data. We suggest that the pacemaker network achieves both stability and flexibility by balancing coupling strength with interconnectivity and that variation in these network features may provide a substrate for species-specific evolution of electrocommunication signals.

Inhibitory Interneurons Regulate Temporal Precision and Correlations in Cortical Circuits

GABAergic interneurons, which are highly diverse, have long been thought to contribute to the timing of neural activity as well as to the generation and shaping of brain rhythms. GABAergic activity is crucial not only for entrainment of oscillatory activity across a neural population, but also for precise regulation of the timing of action potentials and the suppression of slow-timescale correlations. The diversity of inhibition provides the potential for flexible regulation of patterned activity, but also poses a challenge to identifying the elements of excitatory-inhibitory interactions underlying network engagement. This review highlights the key roles of inhibitory interneurons in spike correlations and brain rhythms, describes several scales on which GABAergic inhibition regulates timing in neural networks, and identifies potential consequences of inhibitory dysfunction.

Analyzing the competition of gamma rhythms with delayed pulse-coupled oscillators in phase representation

Networks of neurons can generate oscillatory activity as result of various types of coupling that lead to synchronization. A prominent type of oscillatory activity is gamma (30-80 Hz) rhythms, which may play an important role in neuronal information processing. Two mechanisms have mainly been proposed for their generation: (1) interneuron network gamma (ING) and (2) pyramidal-interneuron network gamma (PING). In vitro and in vivo experiments have shown that both mechanisms can exist in the same cortical circuits. This raises the questions: How do ING and PING interact when both can in principle occur? Are the network dynamics a superposition, or do ING and PING interact in a nonlinear way and if so, how? In this article, we first generalize the phase representation for nonlinear one-dimensional pulse coupled oscillators as introduced by Mirollo and Strogatz to type II oscillators whose phase response curve (PRC) has zero crossings. We then give a full theoretical analysis for the regular gamma-like oscillations of simple networks consisting of two neural oscillators, an "E neuron" mimicking a synchronized group of pyramidal cells, and an "I neuron" representing such a group of interneurons. Motivated by experimental findings, we choose the E neuron to have a type I PRC [leaky integrate-and-fire (LIF) neuron], while the I neuron has either a type I or type II PRC (LIF or "sine" neuron). The phase representation allows us to define in a simple manner scenarios of interaction between the two neurons, which are independent of the types and the details of the neuron models. The presence of delay in the couplings leads to an increased number of scenarios relevant for gamma-like oscillatory patterns. We analytically derive the set of such scenarios and describe their occurrence in terms of parameter values such as synaptic connectivity and drive to the E and I neurons. The networks can be tuned to oscillate in an ING or PING mode. We focus particularly on the transition region where both rhythms compete to govern the network dynamics and compare with oscillations in reduced networks, which can only generate either ING or PING. Our analytically derived oscillation frequency diagrams indicate that except for small coexistence regions, the networks generate ING if the oscillation frequency of the reduced ING network exceeds that of the reduced PING network, and vice versa. For networks with the LIF I neuron, the network oscillation frequency slightly exceeds the frequencies of corresponding reduced networks, while it lies between them for networks with the sine I neuron. In networks oscillating in ING (PING) mode, the oscillation frequency responds faster to changes in the drive to the I (E) neuron than to changes in the drive to the E (I) neuron. This finding suggests a method to analyze which mechanism governs an observed network oscillation. Notably, also when the network operates in ING mode, the E neuron can spike before the I neuron such that relative spike times of the pyramidal cells and the interneurons alone are not conclusive for distinguishing ING and PING.

Electrical coupling between hippocampal neurons: contrasting roles of principal cell gap junctions and interneuron gap junctions

There is considerable experimental evidence, anatomical and physiological, that gap junctions exist in the hippocampus. Electrical coupling through these gap junctions may be divided into three types: between principal neurons, between interneurons and at mixed chemical (glutamatergic)/electrical synapses. An approach, combining in vitro experimental with modeling techniques, sheds some light on the functional consequences of electrical coupling, for network oscillations and for seizures. Additionally, in vivo experiments, using mouse connexin knockouts, suggest that the presence of electrical coupling is important for optimal performance on selected behavioral tasks; however, the interpretation of such data, in cellular terms, has so far proven difficult. Given that invertebrate central pattern generators so often depend on both chemical and electrical synapses, our hypothesis is that hippocampus-mediated and -influenced behaviors will act likewise. Experiments, likely hard ones, will be required to test this intuition.

Firing rate equations require a spike synchrony mechanism to correctly describe fast oscillations in inhibitory networks

Recurrently coupled networks of inhibitory neurons robustly generate oscillations in the gamma band. Nonetheless, the corresponding Wilson-Cowan type firing rate equation for such an inhibitory population does not generate such oscillations without an explicit time delay. We show that this discrepancy is due to a voltage-dependent spike-synchronization mechanism inherent in networks of spiking neurons which is not captured by standard firing rate equations. Here we investigate an exact low-dimensional description for a network of heterogeneous canonical Class 1 inhibitory neurons which includes the sub-threshold dynamics crucial for generating synchronous states. In the limit of slow synaptic kinetics the spike-synchrony mechanism is suppressed and the standard Wilson-Cowan equations are formally recovered as long as external inputs are also slow. However, even in this limit synchronous spiking can be elicited by inputs which fluctuate on a time-scale of the membrane time-constant of the neurons. Our meanfield equations therefore represent an extension of the standard Wilson-Cowan equations in which spike synchrony is also correctly described.

Population models describing the average activity of large neuronal ensembles are a powerful mathematical tool to investigate the principles underlying cooperative function of large neuronal systems. However, these models do not properly describe the phenomenon of spike synchrony in networks of neurons. In particular, they fail to capture the onset of synchronous oscillations in networks of inhibitory neurons. We show that this limitation is due to a voltage-dependent synchronization mechanism which is naturally present in spiking neuron models but not captured by traditional firing rate equations. Here we investigate a novel set of macroscopic equations which incorporate both firing rate and membrane potential dynamics, and that correctly generate fast inhibition-based synchronous oscillations. In the limit of slow-synaptic processing oscillations are suppressed, and the model reduces to an equation formally equivalent to the Wilson-Cowan model.

Pyramidal Cell-Interneuron Circuit Architecture and Dynamics in Hippocampal Networks

Excitatory control of inhibitory neurons is poorly understood due to the difficulty of studying synaptic connectivity in vivo. We inferred such connectivity through analysis of spike timing and validated this inference using juxtacellular and optogenetic control of presynaptic spikes in behaving mice. We observed that neighboring CA1 neurons had stronger connections and that superficial pyramidal cells projected more to deep interneurons. Connection probability and strength were skewed, with a minority of highly connected hubs. Divergent presynaptic connections led to synchrony between interneurons. Synchrony of convergent presynaptic inputs boosted postsynaptic drive. Presynaptic firing frequency was read out by postsynaptic neurons through short-term depression and facilitation, with individual pyramidal cells and interneurons displaying a diversity of spike transmission filters. Additionally, spike transmission was strongly modulated by prior spike timing of the postsynaptic cell. These results bridge anatomical structure with physiological function.

Anatomical and Electrophysiological Clustering of Superficial Medial Entorhinal Cortex Interneurons

Local GABAergic interneurons regulate the activity of spatially-modulated principal cells in the medial entorhinal cortex (MEC), mediating stellate-to-stellate connectivity and possibly enabling grid formation via recurrent inhibitory circuitry. Despite the important role interneurons seem to play in the MEC cortical circuit, the combination of low cell counts and functional diversity has made systematic electrophysiological studies of these neurons difficult. For these reasons, there remains a paucity of knowledge on the electrophysiological profiles of superficial MEC interneuron populations. Taking advantage of glutamic acid decarboxylase 2 (GAD2)-IRES-tdTomato and PV-tdTomato transgenic mice, we targeted GABAergic interneurons for whole-cell patch-clamp recordings and characterized their passive membrane features, basic input/output properties and action potential (AP) shape. These electrophysiologically characterized cells were then anatomically reconstructed, with emphasis on axonal projections and pial depth. K-means clustering of interneuron anatomical and electrophysiological data optimally classified a population of 106 interneurons into four distinct clusters. The first cluster is comprised of layer 2- and 3-projecting, slow-firing interneurons. The second cluster is comprised largely of PV+ fast-firing interneurons that project mainly to layers 2 and 3. The third cluster contains layer 1- and 2-projecting interneurons, and the fourth cluster is made up of layer 1-projecting horizontal interneurons. These results, among others, will provide greater understanding of the electrophysiological characteristics of MEC interneurons, help guide future in vivo studies, and may aid in uncovering the mechanism of grid field formation.

Does layer 4 in the barrel cortex function as a balanced circuit when responding to whisker movements?

Neurons in one barrel in layer 4 (L4) in the mouse vibrissa somatosensory cortex are innervated mostly by neurons from the VPM nucleus and by other neurons within the same barrel. During quiet wakefulness or whisking in air, thalamic inputs vary slowly in time, and excitatory neurons rarely fire. A barrel in L4 contains a modest amount of neurons; the synaptic conductances are not very strong and connections are not sparse. Are the dynamical properties of the L4 circuit similar to those expected from fluctuation-dominated, balanced networks observed for large, strongly coupled and sparse cortical circuits? To resolve this question, we analyze a network of 150 inhibitory parvalbumin-expressing fast-spiking inhibitory interneurons innervated by the VPM thalamus with random connectivity, without or with 1600 low-firing excitatory neurons. Above threshold, the population-average firing rate of inhibitory cortical neurons increases linearly with the thalamic firing rate. The coefficient of variation CV is somewhat less than 1. Moderate levels of synchrony are induced by converging VPM inputs and by inhibitory interaction among neurons. The strengths of excitatory and inhibitory currents during whisking are about three times larger than threshold. We identify values of numbers of presynaptic neurons, synaptic delays between inhibitory neurons, and electrical coupling within the experimentally plausible ranges for which spike synchrony levels are low. Heterogeneity in in-degrees increases the width of the firing rate distribution to the experimentally observed value. We conclude that an L4 circuit in the low-synchrony regime exhibits qualitative dynamical properties similar to those of balanced networks.

Transitions between classes of neuronal excitability and bifurcations induced by autapse

Neuronal excitabilities behave as the basic and important dynamics related to the transitions between firing and resting states, and are characterized by distinct bifurcation types and spiking frequency responses. Switches between class I and II excitabilities induced by modulations outside the neuron (for example, modulation to M-type potassium current) have been one of the most concerning issues in both electrophysiology and nonlinear dynamics. In the present paper, we identified switches between 2 classes of excitability and firing frequency responses when an autapse, which widely exists in real nervous systems and plays important roles via self-feedback, is introduced into the Morris-Lecar (ML) model neuron. The transition from class I to class II excitability and from class II to class I spiking frequency responses were respectively induced by the inhibitory and excitatory autapse, which are characterized by changes of bifurcations, frequency responses, steady-state current-potential curves, and nullclines. Furthermore, we identified codimension-1 and -2 bifurcations and the characteristics of the current-potential curve that determine the transitions. Our results presented a comprehensive relationship between 2 classes of neuronal excitability/spiking characterized by different types of bifurcations, along with a novel possible function of autapse or self-feedback control on modulating neuronal excitability.

Gap Junctions Link Regular-Spiking and Fast-Spiking Interneurons in Layer 5 Somatosensory Cortex

Gap junctions form electrical synapses that modulate neuronal activity by synchronizing action potential (AP) firing of cortical interneurons (INs). Gap junctions are thought to form predominantly within cortical INs of the same functional class and are therefore considered to act within discrete neuronal populations. Here, we challenge that view and show that the probability of electrical coupling is the same within and between regular-spiking (RS) and fast-spiking (FS) cortical INs in 16–21 days old mice. Firing properties of these two populations were distinct from other INs types including neurogliaform and low-threshold spiking (LTS) cells. We also demonstrate that pre-junctional APs can depolarize post-junctional neurons and increase the probability of firing. Our findings of frequent gap junction coupling between functionally distinct IN subtypes suggest that cortical IN networks are much more extensive and heterogeneous than previously thought. This may have implications on mechanisms ranging from cognitive functions to modulation of pathological states in epilepsy and other neurological disorders.

Synchrony and so much more: Diverse roles for electrical synapses in neural circuits

Electrical synapses are neuronal gap junctions that are ubiquitous across brain regions and species. The biophysical properties of most electrical synapses are relatively simple-transcellular channels allow nearly ohmic, bidirectional flow of ionic current. Yet these connections can play remarkably diverse roles in different neural circuit contexts. Recent findings illustrate how electrical synapses may excite or inhibit, synchronize or desynchronize, augment or diminish rhythms, phase-shift, detect coincidences, enhance signals relative to noise, adapt, and interact with nonlinear membrane and transmitter-release mechanisms. Most of these functions are likely to be widespread in central nervous systems. © 2016 Wiley Periodicals, Inc. Develop Neurobiol 77: 610-624, 2017.

Mathematical Frameworks for Oscillatory Network Dynamics in Neuroscience

The tools of weakly coupled phase oscillator theory have had a profound impact on the neuroscience community, providing insight into a variety of network behaviours ranging from central pattern generation to synchronisation, as well as predicting novel network states such as chimeras. However, there are many instances where this theory is expected to break down, say in the presence of strong coupling, or must be carefully interpreted, as in the presence of stochastic forcing. There are also surprises in the dynamical complexity of the attractors that can robustly appear-for example, heteroclinic network attractors. In this review we present a set of mathematical tools that are suitable for addressing the dynamics of oscillatory neural networks, broadening from a standard phase oscillator perspective to provide a practical framework for further successful applications of mathematics to understanding network dynamics in neuroscience.

Intrinsic Cellular Properties and Connectivity Density Determine Variable Clustering Patterns in Randomly Connected Inhibitory Neural Networks

The plethora of inhibitory interneurons in the hippocampus and cortex play a pivotal role in generating rhythmic activity by clustering and synchronizing cell firing. Results of our simulations demonstrate that both the intrinsic cellular properties of neurons and the degree of network connectivity affect the characteristics of clustered dynamics exhibited in randomly connected, heterogeneous inhibitory networks. We quantify intrinsic cellular properties by the neuron's current-frequency relation (IF curve) and Phase Response Curve (PRC), a measure of how perturbations given at various phases of a neurons firing cycle affect subsequent spike timing. We analyze network bursting properties of networks of neurons with Type I or Type II properties in both excitability and PRC profile; Type I PRCs strictly show phase advances and IF curves that exhibit frequencies arbitrarily close to zero at firing threshold while Type II PRCs display both phase advances and delays and IF curves that have a non-zero frequency at threshold. Type II neurons whose properties arise with or without an M-type adaptation current are considered. We analyze network dynamics under different levels of cellular heterogeneity and as intrinsic cellular firing frequency and the time scale of decay of synaptic inhibition are varied. Many of the dynamics exhibited by these networks diverge from the predictions of the interneuron network gamma (ING) mechanism, as well as from results in all-to-all connected networks. Our results show that randomly connected networks of Type I neurons synchronize into a single cluster of active neurons while networks of Type II neurons organize into two mutually exclusive clusters segregated by the cells' intrinsic firing frequencies. Networks of Type II neurons containing the adaptation current behave similarly to networks of either Type I or Type II neurons depending on network parameters; however, the adaptation current creates differences in the cluster dynamics compared to those in networks of Type I or Type II neurons. To understand these results, we compute neuronal PRCs calculated with a perturbation matching the profile of the synaptic current in our networks. Differences in profiles of these PRCs across the different neuron types reveal mechanisms underlying the divergent network dynamics.

Neurons as oscillators

Regularly spiking neurons can be described as oscillators. In this article we review some of the insights gained from this conceptualization and their relevance for systems neuroscience. First, we explain how a regularly spiking neuron can be viewed as an oscillator and how the phase-response curve (PRC) describes the response of the neuron's spike times to small perturbations. We then discuss the meaning of the PRC for a single neuron's spiking behavior and review the PRCs measured from a variety of neurons in a range of spiking regimes. Next, we show how the PRC can be related to a number of common measures used to quantify neuronal firing, such as the spike-triggered average and the peristimulus histogram. We further show that the response of a neuron to correlated inputs depends on the shape of the PRC. We then explain how the PRC of single neurons can be used to predict neural network behavior. Given the PRC, conduction delays, and the waveform and time course of the synaptic potentials, it is possible to predict neural population behavior such as synchronization. The PRC also allows us to quantify the robustness of the synchronization to heterogeneity and noise. We finally ask how to combine the measured PRCs and the predictions based on PRC to further the understanding of systems neuroscience. As an example, we discuss how the change of the PRC by the neuromodulator acetylcholine could lead to a destabilization of cortical network dynamics. Although all of these studies are grounded in mathematical abstractions that do not strictly hold in biology, they provide good estimates for the emergence of the brain's network activity from the properties of individual neurons. The study of neurons as oscillators can provide testable hypotheses and mechanistic explanations for systems neuroscience.

Electrical coupling regulates layer 1 interneuron microcircuit formation in the neocortex

The coexistence of electrical and chemical synapses among interneurons is essential for interneuron function in the neocortex. However, it remains largely unclear whether electrical coupling between interneurons influences chemical synapse formation and microcircuit assembly during development. Here, we show that electrical and GABAergic chemical connections robustly develop between interneurons in neocortical layer 1 over a similar time course. Electrical coupling promotes action potential generation and synchronous firing between layer 1 interneurons. Furthermore, electrically coupled interneurons exhibit strong GABA-A receptor-mediated synchronous synaptic activity. Disruption of electrical coupling leads to a loss of bidirectional, but not unidirectional, GABAergic connections. Moreover, a reduction in electrical coupling induces an increase in excitatory synaptic inputs to layer 1 interneurons. Together, these findings strongly suggest that electrical coupling between neocortical interneurons plays a critical role in regulating chemical synapse development and precise formation of circuits.

Complicating connectomes: Electrical coupling creates parallel pathways and degenerate circuit mechanisms

Electrical coupling in circuits can produce non‐intuitive circuit dynamics, as seen in both experimental work from the crustacean stomatogastric ganglion and in computational models inspired by the connectivity in this preparation. Ambiguities in interpreting the results of electrophysiological recordings can arise if sets of pre‐ or postsynaptic neurons are electrically coupled, or if the electrical coupling exhibits some specificity (e.g. rectifying, or voltage‐dependent). Even in small circuits, electrical coupling can produce parallel pathways that can allow information to travel by monosynaptic and/or polysynaptic pathways. Consequently, similar changes in circuit dynamics can arise from entirely different underlying mechanisms. When neurons are coupled both chemically and electrically, modifying the relative strengths of the two interactions provides a mechanism for flexibility in circuit outputs. This, together with neuromodulation of gap junctions and coupled neurons is important both in developing and adult circuits. © 2016 Wiley Periodicals, Inc. Develop Neurobiol 77: 597–609, 2017

Synchronized gamma-frequency inhibition in neocortex depends on excitatory-inhibitory interactions but not electrical synapses

Synaptic inhibition plays a crucial role in the precise timing of spiking activity in the cerebral cortex. Synchronized, rhythmic inhibitory activity in the gamma (30-80 Hz) range is thought to be especially important for the active, information-processing neocortex, but the circuit mechanisms that give rise to synchronized inhibition are uncertain. In particular, the relative contributions of reciprocal inhibitory connections, excitatory-inhibitory interactions, and electrical synapses to precise spike synchrony among inhibitory interneurons are not well understood. Here we describe experiments on mouse barrel cortex in vitro as it spontaneously generates slow (<1 Hz) oscillations (Up and Down states). During Up states, inhibitory postsynaptic currents (IPSCs) are generated at gamma frequencies and are more synchronized than excitatory postsynaptic currents (EPSCs) among neighboring pyramidal cells. Furthermore, spikes in homotypic pairs of interneurons are more synchronized than in pairs of pyramidal cells. Comparing connexin36 knockout and wild-type animals, we found that electrical synapses make a minimal contribution to synchronized inhibition during Up states. Estimations of the delays between EPSCs and IPSCs in single pyramidal cells showed that excitation often preceded inhibition by a few milliseconds. Finally, tonic optogenetic activation of different interneuron subtypes in the absence of excitation led to only weak synchrony of IPSCs in pairs of pyramidal neurons. Our results suggest that phasic excitatory inputs are indispensable for synchronized spiking in inhibitory interneurons during Up states and that electrical synapses play a minimal role.

Membrane potential resonance frequency directly influences network frequency through electrical coupling

Oscillatory networks often include neurons with membrane potential resonance, exhibiting a peak in the voltage amplitude as a function of current input at a nonzero (resonance) frequency (f_res). Although f_res has been correlated to the network frequency (f_net) in a variety of systems, a causal relationship between the two has not been established. We examine the hypothesis that combinations of biophysical parameters that shift f_res, without changing other attributes of the impedance profile, also shift f_net in the same direction. We test this hypothesis, computationally and experimentally, in an electrically coupled network consisting of intrinsic oscillator (O) and resonator (R) neurons. We use a two-cell model of such a network to show that increasing f_res of R directly increases f_net and that this effect becomes more prominent if the amplitude of resonance is increased. Notably, the effect of f_res on f_net is independent of the parameters that define the oscillator or the combination of parameters in R that produce the shift in f_res, as long as this combination produces the same impedance vs. frequency relationship. We use the dynamic clamp technique to experimentally verify the model predictions by connecting a model resonator to the pacemaker pyloric dilator neurons of the crab Cancer borealis pyloric network using electrical synapses and show that the pyloric network frequency can be shifted by changing f_res in the resonator. Our results provide compelling evidence that f_res and resonance amplitude strongly influence f_net, and therefore, modulators may target these attributes to modify rhythmic activity.

Electrical synapses and the development of inhibitory circuits in the thalamus

KEY POINTS

The thalamus is a structure critical for information processing and transfer to the cortex. Thalamic reticular neurons are inhibitory cells interconnected by electrical synapses, most of which require the gap junction protein connexin36 (Cx36). We investigated whether electrical synapses play a role in the maturation of thalamic networks by studying neurons in mice with and without Cx36. When Cx36 was deleted, inhibitory synapses were more numerous, although both divergent inhibitory connectivity and dendritic complexity were reduced. Surprisingly, we observed non-Cx36-dependent electrical synapses with unusual biophysical properties interconnecting some reticular neurons in mice lacking Cx36. The results of the present study suggest an important role for Cx36-dependent electrical synapses in the development of thalamic circuits.

ABSTRACT

Neurons within the mature thalamic reticular nucleus (TRN) powerfully inhibit ventrobasal (VB) thalamic relay neurons via GABAergic synapses. TRN neurons are also coupled to one another by electrical synapses that depend strongly on the gap junction protein connexin36 (Cx36). Electrical synapses in the TRN precede the postnatal development of TRN-to-VB inhibition. We investigated how the deletion of Cx36 affects the maturation of TRN and VB neurons, electrical coupling and GABAergic synapses by studying wild-type (WT) and Cx36 knockout (KO) mice. The incidence and strength of electrical coupling in TRN was sharply reduced, but not abolished, in KO mice. Surprisingly, electrical synapses between Cx36-KO neurons had faster voltage-dependent decay kinetics and conductance asymmetry (rectification) than did electrical synapses between WT neurons. The properties of TRN-mediated inhibition in VB also depended on the Cx36 genotype. Deletion of Cx36 increased the frequency and shifted the amplitude distributions of miniature IPSCs, whereas the paired-pulse ratio of evoked IPSCs was unaffected, suggesting that the absence of Cx36 led to an increase in GABAergic synaptic contacts. VB neurons from Cx36-KO mice also tended to have simpler dendritic trees and fewer divergent inputs from the TRN compared to WT cells. The findings obtained in the present study suggest that proper development of thalamic inhibitory circuitry, neuronal morphology, TRN cell function and electrical coupling requires Cx36. In the absence of Cx36, some TRN neurons express asymmetric electrical coupling mediated by other unidentified connexin subtypes.

Resonant Interneurons Can Increase Robustness of Gamma Oscillations

Gamma oscillations are believed to play a critical role in in information processing, encoding, and retrieval. Inhibitory interneuronal network gamma (ING) oscillations may arise from a coupled oscillator mechanism in which individual neurons oscillate or from a population oscillator in which individual neurons fire sparsely and stochastically. All ING mechanisms, including the one proposed herein, rely on alternating waves of inhibition and windows of opportunity for spiking. The coupled oscillator model implemented with Wang-Buzsáki model neurons is not sufficiently robust to heterogeneity in excitatory drive, and therefore intrinsic frequency, to account for in vitro models of ING. Similarly, in a tightly synchronized regime, the stochastic population oscillator model is often characterized by sparse firing, whereas interneurons both in vivo and in vitro do not fire sparsely during gamma, but rather on average every other cycle. We substituted so-called resonator neural models, which exhibit class 2 excitability and postinhibitory rebound (PIR), for the integrators that are typically used. This results in much greater robustness to heterogeneity that actually increases as the average participation in spikes per cycle approximates physiological levels. Moreover, dynamic clamp experiments that show autapse-induced firing in entorhinal cortical interneurons support the idea that PIR can serve as a network gamma mechanism. Furthermore, parvalbumin-positive (PV(+)) cells were much more likely to display both PIR and autapse-induced firing than GAD2(+) cells, supporting the view that PV(+) fast-firing basket cells are more likely to exhibit class 2 excitability than other types of inhibitory interneurons.

SIGNIFICANCE STATEMENT

Gamma oscillations are believed to play a critical role in information processing, encoding, and retrieval. Networks of inhibitory interneurons are thought to be essential for these oscillations. We show that one class of interneurons with an abrupt onset of firing at a threshold frequency may allow more robust synchronization in the presence of noise and heterogeneity. The mechanism for this robustness depends on the intrinsic resonance at this threshold frequency. Moreover, we show experimentally the feasibility of the proposed mechanism and suggest a way to distinguish between this mechanism and another proposed mechanism: that of a stochastic population oscillator independent of the dynamics of individual neurons.

Modulation of synchronous sympathetic firing behaviors by endogenous GABA(A) and glycine receptor-mediated activities in the neonatal rat spinal cord in vitro

Delivering effective commands in the nervous systems require a temporal integration of neural activities such as synchronous firing. Although sympathetic nerve discharges are characterized by synchronous firing, its temporal structures and how it is modulated are largely unknown. This study used a collagenase-dissociated splanchnic sympathetic nerve-thoracic spinal cord preparation of neonatal rats in vitro as an experimental model. Several single-fiber activities were recorded simultaneously and verified by rigorous computational algorithms. Among 3763 fiber pairs that had spontaneous fiber activities, 382 fiber pairs had firing positively correlated. Their temporal relationship was quantitatively evaluated by cross-correlogram. On average, correlated firing in a fiber pair occurred in scales of ∼40ms lasting for ∼11ms. The relative frequency distribution curves of correlogram parametrical values pertinent to the temporal features were best described by trimodal Gaussians, suggesting a correlated firing originated from three or less sources. Applications of bicuculline or gabazine (noncompetitive or competitive GABA(A) receptor antagonist) and/or strychnine (noncompetitive glycine receptor antagonist) increased, decreased, or did not change individual fiber activities. Antagonist-induced enhancement and attenuation of correlated firing were demonstrated by a respective increase and decrease of the peak probability of the cross-correlograms. Heterogeneity in antagonistic responses suggests that the inhibitory neurotransmission mediated by GABA(A) and glycine receptors is not essential for but can serve as a neural substrate to modulate synchronous firing behaviors. Plausible neural mechanisms were proposed to explain the temporal structures of correlated firing between sympathetic fibers.

A population of gap junction-coupled neurons drives recurrent network activity in a developing visual circuit

In many regions of the vertebrate brain, microcircuits generate local recurrent activity that aids in the processing and encoding of incoming afferent inputs. Local recurrent activity can amplify, filter, and temporally and spatially parse out incoming input. Determining how these microcircuits function is of great interest because it provides glimpses into fundamental processes underlying brain computation. Within the Xenopus tadpole optic tectum, deep layer neurons display robust recurrent activity. Although the development and plasticity of this local recurrent activity has been well described, the underlying microcircuitry is not well understood. Here, using a whole brain preparation that allows for whole cell recording from neurons of the superficial tectal layers, we identified a physiologically distinct population of excitatory neurons that are gap junctionally coupled and through this coupling gate local recurrent network activity. Our findings provide a novel role for neuronal coupling among excitatory interneurons in the temporal processing of visual stimuli.

A unified framework for spiking and gap-junction interactions in distributed neuronal network simulations

Contemporary simulators for networks of point and few-compartment model neurons come with a plethora of ready-to-use neuron and synapse models and support complex network topologies. Recent technological advancements have broadened the spectrum of application further to the efficient simulation of brain-scale networks on supercomputers. In distributed network simulations the amount of spike data that accrues per millisecond and process is typically low, such that a common optimization strategy is to communicate spikes at relatively long intervals, where the upper limit is given by the shortest synaptic transmission delay in the network. This approach is well-suited for simulations that employ only chemical synapses but it has so far impeded the incorporation of gap-junction models, which require instantaneous neuronal interactions. Here, we present a numerical algorithm based on a waveform-relaxation technique which allows for network simulations with gap junctions in a way that is compatible with the delayed communication strategy. Using a reference implementation in the NEST simulator, we demonstrate that the algorithm and the required data structures can be smoothly integrated with existing code such that they complement the infrastructure for spiking connections. To show that the unified framework for gap-junction and spiking interactions achieves high performance and delivers high accuracy in the presence of gap junctions, we present benchmarks for workstations, clusters, and supercomputers. Finally, we discuss limitations of the novel technology.

Analysis of the role of the low threshold currents IT and Ih in intrinsic delta oscillations of thalamocortical neurons

Thalamocortical neurons are involved in the generation and maintenance of brain rhythms associated with global functional states. The repetitive burst firing of TC neurons at delta frequencies (1–4 Hz) has been linked to the oscillations recorded during deep sleep and during episodes of absence seizures. To get insight into the biophysical properties that are the basis for intrinsic delta oscillations in these neurons, we performed a bifurcation analysis of a minimal conductance-based thalamocortical neuron model including only the I_T channel and the sodium and potassium leak channels. This analysis unveils the dynamics of repetitive burst firing of TC neurons, and describes how the interplay between the amplifying variable m_T and the recovering variable h_T of the calcium channel I_T is sufficient to generate low threshold oscillations in the delta band. We also explored the role of the hyperpolarization activated cationic current I_h in this reduced model and determine that, albeit not required, I_h amplifies and stabilizes the oscillation.

Synchronization of action potentials during low-magnesium-induced bursting

The relationship between mono- and polysynaptic strength and action potential synchronization was explored using a reduced external Mg(2+) model. Single and dual whole cell patch-clamp recordings were performed in hippocampal cultures in three concentrations of external Mg(2+). In decreased Mg(2+) medium, the individual cells transitioned to spontaneous bursting behavior. In lowered Mg(2+) media the larger excitatory synaptic events were observed more frequently and fewer transmission failures occurred, suggesting strengthened synaptic transmission. The event synchronization was calculated for the neural action potentials of the cell pairs, and it increased in media where Mg(2+) concentration was lowered. Analysis of surrogate data where bursting was present, but no direct or indirect connections existed between the neurons, showed minimal action potential synchronization. This suggests the synchronization of action potentials is a product of the strengthening synaptic connections within neuronal networks.

On the firing rate dependency of the phase response curve of rat Purkinje neurons in vitro

Synchronous spiking during cerebellar tasks has been observed across Purkinje cells: however, little is known about the intrinsic cellular mechanisms responsible for its initiation, cessation and stability. The Phase Response Curve (PRC), a simple input-output characterization of single cells, can provide insights into individual and collective properties of neurons and networks, by quantifying the impact of an infinitesimal depolarizing current pulse on the time of occurrence of subsequent action potentials, while a neuron is firing tonically. Recently, the PRC theory applied to cerebellar Purkinje cells revealed that these behave as phase-independent integrators at low firing rates, and switch to a phase-dependent mode at high rates. Given the implications for computation and information processing in the cerebellum and the possible role of synchrony in the communication with its post-synaptic targets, we further explored the firing rate dependency of the PRC in Purkinje cells. We isolated key factors for the experimental estimation of the PRC and developed a closed-loop approach to reliably compute the PRC across diverse firing rates in the same cell. Our results show unambiguously that the PRC of individual Purkinje cells is firing rate dependent and that it smoothly transitions from phase independent integrator to a phase dependent mode. Using computational models we show that neither channel noise nor a realistic cell morphology are responsible for the rate dependent shift in the phase response curve.

A barrel-related interneuron in layer 4 of rat somatosensory cortex with a high intrabarrel connectivity

Synaptic connections between identified fast-spiking (FS), parvalbumin (PV)-positive interneurons, and excitatory spiny neurons in layer 4 (L4) of the barrel cortex were investigated using patch-clamp recordings and simultaneous biocytin fillings. Three distinct clusters of FS L4 interneurons were identified based on their axonal morphology relative to the barrel column suggesting that these neurons do not constitute a homogeneous interneuron population. One L4 FS interneuron type had an axonal domain strictly confined to a L4 barrel and was therefore named "barrel-confined inhibitory interneuron" (BIn). BIns established reliable inhibitory synaptic connections with L4 spiny neurons at a high connectivity rate of 67%, of which 69% were reciprocal. Unitary IPSPs at these connections had a mean amplitude of 0.9 ± 0.8 mV with little amplitude variation and weak short-term synaptic depression. We found on average 3.7 ± 1.3 putative inhibitory synaptic contacts that were not restricted to perisomatic areas. In conclusion, we characterized a novel type of barrel cortex interneuron in the major thalamo-recipient layer 4 forming dense synaptic networks with L4 spiny neurons. These networks constitute an efficient and powerful inhibitory feedback system, which may serve to rapidly reset the barrel microcircuitry following sensory activation.

Millisecond timescale synchrony among hippocampal neurons

Inhibitory neurons in cortical circuits play critical roles in composing spike timing and oscillatory patterns in neuronal activity. These roles in turn require coherent activation of interneurons at different timescales. To investigate how the local circuitry provides for these activities, we applied resampled cross-correlation analyses to large-scale recordings of neuronal populations in the cornu ammonis 1 (CA1) and CA3 regions of the hippocampus of freely moving rats. Significant counts in the cross-correlation of cell pairs, relative to jittered surrogate spike-trains, allowed us to identify the effective couplings between neurons in CA1 and CA3 hippocampal regions on the timescale of milliseconds. In addition to putative excitatory and inhibitory monosynaptic connections, we uncovered prominent millisecond timescale synchrony between cell pairs, observed as peaks in the central 0 ms bin of cross-correlograms. This millisecond timescale synchrony appeared to be independent of network state, excitatory input, and γ oscillations. Moreover, it was frequently observed between cells of differing putative interneuronal type, arguing against gap junctions as the sole underlying source. Our observations corroborate recent in vitro findings suggesting that inhibition alone is sufficient to synchronize interneurons at such fast timescales. Moreover, we show that this synchronous spiking may cause stronger inhibition and rebound spiking in target neurons, pointing toward a potential function for millisecond synchrony of interneurons in shaping and affecting timing in pyramidal populations within and downstream from the circuit.

Cerebellar inhibitory input to the inferior olive decreases electrical coupling and blocks subthreshold oscillations

GABAergic projection neurons in the cerebellar nuclei (CN) innervate the inferior olive (IO) that in turn is the source of climbing fibers targeting Purkinje neurons in the cerebellar cortex. Anatomical evidence suggests that CN synapses modulate electrical coupling between IO neurons. In vivo studies indicate that they are also involved in controlling synchrony and rhythmicity of IO neurons. Here, we demonstrate using virally targeted channelrhodopsin in the cerebellar nucleo-olivary neurons that synaptic input can indeed modulate both the strength and symmetry of electrical coupling between IO neurons and alter network activity. Similar synaptic modifications of electrical coupling are likely to occur in other brain regions, where rapid modification of the spatiotemporal features of the coupled networks is needed to adequately respond to behavioral demands.

Spike firing and IPSPs in layer V pyramidal neurons during beta oscillations in rat primary motor cortex (M1) in vitro

Beta frequency oscillations (10-35 Hz) in motor regions of cerebral cortex play an important role in stabilising and suppressing unwanted movements, and become intensified during the pathological akinesia of Parkinson's Disease. We have used a cortical slice preparation of rat brain, combined with concurrent intracellular and field recordings from the primary motor cortex (M1), to explore the cellular basis of the persistent beta frequency (27-30 Hz) oscillations manifest in local field potentials (LFP) in layers II and V of M1 produced by continuous perfusion of kainic acid (100 nM) and carbachol (5 µM). Spontaneous depolarizing GABA-ergic IPSPs in layer V cells, intracellularly dialyzed with KCl and IEM1460 (to block glutamatergic EPSCs), were recorded at -80 mV. IPSPs showed a highly significant (P< 0.01) beta frequency component, which was highly significantly coherent with both the Layer II and V LFP oscillation (which were in antiphase to each other). Both IPSPs and the LFP beta oscillations were abolished by the GABAA antagonist bicuculline. Layer V cells at rest fired spontaneous action potentials at sub-beta frequencies (mean of 7.1+1.2 Hz; n = 27) which were phase-locked to the layer V LFP beta oscillation, preceding the peak of the LFP beta oscillation by some 20 ms. We propose that M1 beta oscillations, in common with other oscillations in other brain regions, can arise from synchronous hyperpolarization of pyramidal cells driven by synaptic inputs from a GABA-ergic interneuronal network (or networks) entrained by recurrent excitation derived from pyramidal cells. This mechanism plays an important role in both the physiology and pathophysiology of control of voluntary movement generation.

A blanket of inhibition: functional inferences from dense inhibitory connectivity

The function of neocortical interneurons is still unclear, and, as often happens, one may be able to draw functional insights from considering the structure. In this spirit we describe recent structural results and discuss their potential functional implications. Most GABAergic interneurons innervate nearby pyramidal neurons very densely and without any apparent specificity, as if they were extending a 'blanket of inhibition', contacting pyramidal neurons often in an overlapping fashion. While subtypes of interneurons specifically target subcellular compartments of pyramidal cells, and they also target different layers selectively, they appear to treat all neighboring pyramidal cells the same and innervate them massively. We explore the functional implications and temporal properties of dense, overlapping inhibition by four interneuron populations.

Spatial and feature-based attention in a layered cortical microcircuit model

Directing attention to the spatial location or the distinguishing feature of a visual object modulates neuronal responses in the visual cortex and the stimulus discriminability of subjects. However, the spatial and feature-based modes of attention differently influence visual processing by changing the tuning properties of neurons. Intriguingly, neurons' tuning curves are modulated similarly across different visual areas under both these modes of attention. Here, we explored the mechanism underlying the effects of these two modes of visual attention on the orientation selectivity of visual cortical neurons. To do this, we developed a layered microcircuit model. This model describes multiple orientation-specific microcircuits sharing their receptive fields and consisting of layers 2/3, 4, 5, and 6. These microcircuits represent a functional grouping of cortical neurons and mutually interact via lateral inhibition and excitatory connections between groups with similar selectivity. The individual microcircuits receive bottom-up visual stimuli and top-down attention in different layers. A crucial assumption of the model is that feature-based attention activates orientation-specific microcircuits for the relevant feature selectively, whereas spatial attention activates all microcircuits homogeneously, irrespective of their orientation selectivity. Consequently, our model simultaneously accounts for the multiplicative scaling of neuronal responses in spatial attention and the additive modulations of orientation tuning curves in feature-based attention, which have been observed widely in various visual cortical areas. Simulations of the model predict contrasting differences between excitatory and inhibitory neurons in the two modes of attentional modulations. Furthermore, the model replicates the modulation of the psychophysical discriminability of visual stimuli in the presence of external noise. Our layered model with a biologically suggested laminar structure describes the basic circuit mechanism underlying the attention-mode specific modulations of neuronal responses and visual perception.

Dynamics of action potential firing in electrically connected striatal fast-spiking interneurons

Fast-spiking interneurons (FSIs) play a central role in organizing the output of striatal neural circuits, yet functional interactions between these cells are still largely unknown. Here we investigated the interplay of action potential (AP) firing between electrically connected pairs of identified FSIs in mouse striatal slices. In addition to a loose coordination of firing activity mediated by membrane potential coupling, gap junctions (GJ) induced a frequency-dependent inhibition of spike discharge in coupled cells. At relatively low firing rates (2–20 Hz), some APs were tightly synchronized whereas others were inhibited. However, burst firing at intermediate frequencies (25–60 Hz) mostly induced spike inhibition, while at frequencies >50–60 Hz FSI pairs tended to synchronize. Spike silencing occurred even in the absence of GABAergic synapses or persisted after a complete block of GABA_A receptors. Pharmacological suppression of presynaptic spike afterhyperpolarization (AHP) caused postsynaptic spikelets to become more prone to trigger spikes at near-threshold potentials, leading to a mostly synchronous firing activity. The complex pattern of functional coordination mediated by GJ endows FSIs with peculiar dynamic properties that may be critical in controlling striatal-dependent behavior.

Effect of phase response curve skewness on synchronization of electrically coupled neuronal oscillators

We investigate why electrically coupled neuronal oscillators synchronize or fail to synchronize using the theory of weakly coupled oscillators. Stability of synchrony and antisynchrony is predicted analytically and verified using numerical bifurcation diagrams. The shape of the phase response curve (PRC), the shape of the voltage time course, and the frequency of spiking are freely varied to map out regions of parameter spaces that hold stable solutions. We find that type 1 and type 2 PRCs can hold both synchronous and antisynchronous solutions, but the shape of the PRC and the voltage determine the extent of their stability. This is achieved by introducing a five-piecewise linear model to the PRC and a three-piecewise linear model to the voltage time course, and then analyzing the resultant eigenvalue equations that determine the stability of the phase-locked solutions. A single time parameter defines the skewness of the PRC, and another single time parameter defines the spike width and frequency. Our approach gives a comprehensive picture of the relation of the PRC shape, voltage time course, and stability of the resultant synchronous and antisynchronous solutions.