Phase resetting curves and oscillatory stability in interneurons of rat somatosensory cortex

Synchronous oscillations in neural activity are found over wide areas of the cortex. Specific populations of interneurons are believed to play a significant role in generating these synchronized oscillations through mutual synaptic and gap-junctional interactions. Little is known, though, about the mechanism of how oscillations are maintained stably by particular types of interneurons and by their local networks. To obtain more insight into this, we measured membrane-potential responses to small current-pulse perturbations during regular firing, to construct phase resetting curves (PRCs) for three types of interneurons: nonpyramidal regular-spiking (NPRS), low-threshold spiking (LTS), and fast-spiking (FS) cells. Within each cell type, both monophasic and biphasic PRCs were observed, but the proportions and sensitivities to perturbation amplitude were clearly correlated to cell type. We then analyzed the experimentally measured PRCs to predict oscillation stability, or firing reliability, of cells for a complex stochastic input, as occurs in vivo. To do this, we used a method from random dynamical system theory to estimate Lyapunov exponents of the simplified phase model on the circle. The results indicated that LTS and NPRS cells have greater oscillatory stability (are more reliably entrained) in small noisy inputs than FS cells, which is consistent with their distinct types of threshold dynamics.     

Regulation of rhythm genesis by volume-limited,astroglia-like signals in neural networks

Rhythmic activity of the brain often depends on synchronized spiking of interneuronal networks interacting with principal neurons. The quest for physiological mechanisms regulating network synchronization has therefore been firmly focused on synaptic circuits. However, it has recently emerged that synaptic efficacy could be influenced by astrocytes that release signalling molecules into their macroscopic vicinity. To understand how this volume-limited synaptic regulation can affect oscillations in neural populations, here we explore an established artificial neural network mimicking hippocampal basket cells receiving inputs from pyramidal cells. We find that network oscillation frequencies and average cell firing rates are resilient to changes in excitatory input even when such changes occur in a significant proportion of participating interneurons, be they randomly distributed or clustered in space. The astroglia-like, volume-limited regulation of excitatory synaptic input appears to better preserve network synchronization (compared with a similar action evenly spread across the network) while leading to a structural segmentation of the network into cell subgroups with distinct firing patterns. These observations provide us with some previously unknown insights into the basic principles of neural network control by astroglia.     

Spontaneous Local Gamma Oscillation Selectively Enhances Neural Network Responsiveness

Synchronized oscillation is very commonly observed in many neuronal systems and might play an important role in the response properties of the system. We have studied how the spontaneous oscillatory activity affects the responsiveness of a neuronal network, using a neural network model of the visual cortex built from Hodgkin-Huxley type excitatory (E-) and inhibitory (I-) neurons. When the isotropic local E-I and I-E synaptic connections were sufficiently strong, the network commonly generated gamma frequency oscillatory firing patterns in response to random feed-forward (FF) input spikes. This spontaneous oscillatory network activity injects a periodic local current that could amplify a weak synaptic input and enhance the network's responsiveness. When E-E connections were added, we found that the strength of oscillation can be modulated by varying the FF input strength without any changes in single neuron properties or interneuron connectivity. The response modulation is proportional to the oscillation strength, which leads to self-regulation such that the cortical network selectively amplifies various FF inputs according to its strength, without requiring any adaptation mechanism. We show that this selective cortical amplification is controlled by E-E cell interactions. We also found that this response amplification is spatially localized, which suggests that the responsiveness modulation may also be spatially selective. This suggests a generalized mechanism by which neural oscillatory activity can enhance the selectivity of a neural network to FF inputs.     

Perisomatic inhibition and cortical circuit dysfunction in schizophrenia

Deficits of cognitive control in schizophrenia are associated with altered gamma oscillations in the prefrontal cortex. Paralbumin basket interneurons, which innervate the perisomatic region of pyramidal neurons, appear to play a key role in generating cortical gamma oscillations. In the prefrontal cortex of subjects with schizophrenia, alterations are present in both pre- and post-synaptic markers of the strength of GABA inputs from parvalbumin basket neurons to pyramidal neurons. These alterations may contribute to the neural substrate for impaired gamma oscillations in schizophrenia.     

The response of cortical neurons to in vivo-like input current: theory and experiment: II. Time-varying and spatially distributed inputs

The response of a population of neurons to time-varying synaptic inputs can show a rich phenomenology, hardly predictable from the dynamical properties of the membrane’s inherent time constants. For example, a network of neurons in a state of spontaneous activity can respond significantly more rapidly than each single neuron taken individually. Under the assumption that the statistics of the synaptic input is the same for a population of similarly behaving neurons (mean field approximation), it is possible to greatly simplify the study of neural circuits, both in the case in which the statistics of the input are stationary (reviewed in La Camera et al. in Biol Cybern, 2008) and in the case in which they are time varying and unevenly distributed over the dendritic tree. Here, we review theoretical and experimental results on the single-neuron properties that are relevant for the dynamical collective behavior of a population of neurons. We focus on the response of integrate-and-fire neurons and real cortical neurons to long-lasting, noisy, in vivo-like stationary inputs and show how the theory can predict the observed rhythmic activity of cultures of neurons. We then show how cortical neurons adapt on multiple time scales in response to input with stationary statistics in vitro. Next, we review how it is possible to study the general response properties of a neural circuit to time-varying inputs by estimating the response of single neurons to noisy sinusoidal currents. Finally, we address the dendrite–soma interactions in cortical neurons leading to gain modulation and spike bursts, and show how these effects can be captured by a two-compartment integrate-and-fire neuron. Most of the experimental results reviewed in this article have been successfully reproduced by simple integrate-and-fire model neurons.     

Classification and function of GABAergic interneurons of the mammalian cerebral cortex

GABAergic interneurons make up about 20% of neurons in the cortex and are a heterogeneous group of cells. In recent years it has become clear that different populations of interneurons not only provide the balance of excitation and inhibition in neural networks but are also critically important for generation of rhythmic activity, successful processing of sensory information, implementation of synaptic plasticity and a number of other functions. We examine current approaches to classification of interneurons and review the properties and the functional role of basket cells, chandelier cells, neurogliaform interneurons, Martinotti cells, and some other classes of interneurons based on morphological, immunohistochemical, electrophysiological and optogenetic studies. Besides, we consider the opportunities of the selective impact on target population of interneurons and review the data on the role of different types of interneurons in the pathogenesis of epilepsy and schizophrenia.     

Synaptic State Matching: A Dynamical Architecture for Predictive Internal Representation and Feature Detection

Here we explore the possibility that a core function of sensory cortex is the generation of an internal simulation of sensory environment in real-time. A logical elaboration of this idea leads to a dynamical neural architecture that oscillates between two fundamental network states, one driven by external input, and the other by recurrent synaptic drive in the absence of sensory input. Synaptic strength is modified by a proposed synaptic state matching (SSM) process that ensures equivalence of spike statistics between the two network states. Remarkably, SSM, operating locally at individual synapses, generates accurate and stable network-level predictive internal representations, enabling pattern completion and unsupervised feature detection from noisy sensory input. SSM is a biologically plausible substrate for learning and memory because it brings together sequence learning, feature detection, synaptic homeostasis, and network oscillations under a single unifying computational framework.     

K+ channels at the axon initial segment dampen near-threshold excitability of neocortical fast-spiking GABAergic interneurons

Fast-spiking cells (FS cells) are a prominent subtype of neocortical GABAergic interneurons with important functional roles. Multiple FS cell properties are coordinated for rapid response. Here, we describe an FS cell feature that serves to gate the powerful inhibition produced by FS cell activity. We show that FS cells in layer 2/3 barrel cortex possess a dampening mechanism mediated by Kv1.1-containing potassium channels localized to the axon initial segment. These channels powerfully regulate action potential threshold and allow FS cells to respond preferentially to large inputs that are fast enough to "outrun" Kv1 activation. In addition, Kv1.1 channel blockade converts the delay-type discharge pattern of FS cells to one of continuous fast spiking without influencing the high-frequency firing that defines FS cells. Thus, Kv1 channels provide a key counterbalance to the established rapid-response characteristics of FS cells, regulating excitability through a unique combination of electrophysiological properties and discrete subcellular localization.     

M-channels modulate the intrinsic excitability and synaptic responses of layer 2/3 pyramidal neurons in auditory cortex

Neurons in the auditory cortex are believed to utilize temporal patterns of neural activity to accurately process auditory information but the intrinsic neuronal mechanism underlying the control of auditory neural activity is not known. The slowly activating, persistent K⁺ channel, also called M-channel that belongs to the Kv7 family, is already known to be important in regulating subthreshold neural excitability and synaptic summation in neocortical and hippocampal pyramidal neurons. However, its functional role in the primary auditory cortex (A1) has never been characterized. In this study, we investigated the roles of M-channels on neuronal excitability, short-term plasticity, and synaptic summation of A1 layer 2/3 regular spiking pyramidal neurons with whole-cell current-clamp recordings in vitro. We found that blocking M-channels with a selective M-channel blocker, XE991, significantly increased neural excitability of A1 layer 2/3 pyramidal neurons. Furthermore, M-channels controled synaptic responses of intralaminar-evoked excitatory postsynaptic potentials (EPSPs); XE991 significantly increased EPSP amplitude, decreased the rate of short-term depression, and increased the synaptic summation. These results suggest that M-channels are involved in controlling spike output patterns and synaptic responses of A1 layer 2/3 pyramidal neurons, which would have important implications in auditory information processing.     

GABAergic contributions to gating, timing, and phase precession of hippocampal neuronal activity during theta oscillations

Successful spatial exploration requires gating, storage, and retrieval of spatial memories in the correct order. The hippocampus is known to play an important role in the temporal organization of spatial information. Temporally ordered spatial memories are encoded and retrieved by the firing rate and phase of hippocampal pyramidal cells and inhibitory interneurons with respect to ongoing network theta oscillations paced by intra- and extrahippocampal areas. Much is known about the anatomical, physiological, and molecular characteristics as well as the connectivity and synaptic properties of various cell types in the hippocampal microcircuits, but how these detailed properties of individual neurons give rise to temporal organization of spatial memories remains unclear. We present a model of the hippocampal CA1 microcircuit based on observed biophysical properties of pyramidal cells and six types of inhibitory interneurons: axo-axonic, basket, bistratistified, neurogliaform, ivy, and oriens lacunosum-moleculare cells. The model simulates a virtual rat running on a linear track. Excitatory transient inputs come from the entorhinal cortex (EC) and the CA3 Schaffer collaterals and impinge on both the pyramidal cells and inhibitory interneurons, whereas inhibitory inputs from the medial septum impinge only on the inhibitory interneurons. Dopamine operates as a gate-keeper modulating the spatial memory flow to the PC distal dendrites in a frequency-dependent manner. A mechanism for spike-timing-dependent plasticity in distal and proximal PC dendrites consisting of three calcium detectors, which responds to the instantaneous calcium level and its time course in the dendrite, is used to model the plasticity effects. The model simulates the timing of firing of different hippocampal cell types relative to theta oscillations, and proposes functional roles for the different classes of the hippocampal and septal inhibitory interneurons in the correct ordering of spatial memories as well as in the generation and maintenance of theta phase precession of pyramidal cells (place cells) in CA1. The model leads to a number of experimentally testable predictions that may lead to a better understanding of the biophysical computations in the hippocampus and medial septum.     

Synaptic Plasticity Controls Sensory Responses through Frequency-Dependent Gamma Oscillation Resonance

Synchronized gamma frequency oscillations in neural networks are thought to be important to sensory information processing, and their effects have been intensively studied. Here we describe a mechanism by which the nervous system can readily control gamma oscillation effects, depending selectively on visual stimuli. Using a model neural network simulation, we found that sensory response in the primary visual cortex is significantly modulated by the resonance between “spontaneous” and “stimulus-driven” oscillations. This gamma resonance can be precisely controlled by the synaptic plasticity of thalamocortical connections, and cortical response is regulated differentially according to the resonance condition. The mechanism produces a selective synchronization between the afferent and downstream neural population. Our simulation results explain experimental observations such as stimulus-dependent synchronization between the thalamus and the cortex at different oscillation frequencies. The model generally shows how sensory information can be selectively routed depending on its frequency components.     

Expression of Kv1.3 potassium channels regulates density of cortical interneurons

The Kv1.3 protein is a member of the large family of voltage‐dependent K⁺ subunits (Kv channels), which assemble to form tetrameric membrane‐spanning channels that provide a selective pore for the conductance of K⁺ across the cell membrane. Kv1.3 differs from most other Kv channels in that deletion of Kv1.3 gene produces very striking changes in development and structure of the olfactory bulb, where Kv1.3 is expressed at high levels, resulting in a lower threshold for detection of odors, an increased number of synaptic glomeruli and alterations in the levels of a variety of neuronal signaling molecules. Because Kv1.3 is also expressed in the cerebral cortex, we have now examined the effects of deletion of the Kv1.3 gene on the expression of interneuron populations of the cerebral cortex. Using unbiased stereology we found an increase in the number of parvalbumin (PV) cells in whole cerebral cortex of Kv1.3^?/? mice relative to that in wild‐type mice, and a decrease in the number of calbindin (CB), calretinin (CR), neuropeptide Y (NPY), vasoactive intestinal peptide (VIP), and somatostatin (SOM) interneurons. These changes are accompanied by a decrease in the cortical volume such that the cell density of PV interneurons is significantly increased and that of SOM neurons is decreased in Kv1.3^?/? animals. Our studies suggest that, as in the olfactory bulb, Kv1.3 plays a unique role in neuronal differentiation and/or survival of interneuron populations and that expression of Kv1.3 is required for normal cortical function. © 2013 Wiley Periodicals, Inc. Develop Neurobiol 73:841–855, 2013     

Role of local nonspiking interneurons in the generation of rhythmic motor activity in the stick insect

Local nonspiking interneurons in the thoracic ganglia of insects are important premotor elements in posture control and locomotion. It was investigated whether these interneurons are involved in the central neuronal circuits generating the oscillatory motor output of the leg muscle system during rhythmic motor activity. Intracellular recordings from premotor nonspiking interneurons were made in the isolated and completely deafferented mesothoracic ganglion of the stick insect in preparations exhibiting rhythmic motor activity induced by the muscarinic agonist pilocarpine. All interneurons investigated provided synaptic drive to one or more motoneuron pools supplying the three proximal leg joints, that is, the thoraco-coxal joint, the coxa-trochanteral joint and the femur-tibia joint. During rhythmicity in 83% (n=67) of the recorded interneurons, three different kinds of synaptic oscillations in membrane potential were observed: (1) Oscillations were closely correlated with the activity of motoneuron pools affected; (2) membrane potential oscillations reflected only certain aspects of motoneuronal rhythmicity; and (3) membrane potential oscillations were correlated mainly with the occurrence of spontaneous recurrent patterns (SRP) of activity in the motoneuron pools. In individual interneurons membrane potential oscillations were associated with phase-dependent changes in the neuron's membrane conductance. Artificial changes in the interneurons' membrane potential strongly influenced motor activity. Injecting current pulses into individual interneurons caused a reset of rhythmicity in motoneurons. Furthermore, current injection into interneurons influenced shape and probability of occurrence for SRPs. Among others, identified nonspiking interneurons that are involved in posture control of leg joints were found to exhibit the above properties. From these results, the following conclusions on the role of nonspiking interneurons in the generation of rhythmic motor activity, and thus potentially also during locomotion, emerge: (1) During rhythmic motor activity most nonspiking interneurons receive strong synaptic drive from central rhythm-generating networks; and (2) individual nonspiking interneurons some of which underlie sensory-motor pathways in posture control, are elements of central neuronal networks that generate alternating activity in antagonistic leg motoneuron pools. © 1995 John Wiley & Sons, Inc.     

The response of cortical neurons to in vivo-like input current: theory and experiment

The study of several aspects of the collective dynamics of interacting neurons can be highly simplified if one assumes that the statistics of the synaptic input is the same for a large population of similarly behaving neurons (mean field approach). In particular, under such an assumption, it is possible to determine and study all the equilibrium points of the network dynamics when the neuronal response to noisy, in vivo-like, synaptic currents is known. The response function can be computed analytically for simple integrate-and-fire neuron models and it can be measured directly in experiments in vitro. Here we review theoretical and experimental results about the neural response to noisy inputs with stationary statistics. These response functions are important to characterize the collective neural dynamics that are proposed to be the neural substrate of working memory, decision making and other cognitive functions. Applications to the case of time-varying inputs are reviewed in a companion paper (Giugliano et al. in Biol Cybern, 2008). We conclude that modified integrate-and-fire neuron models are good enough to reproduce faithfully many of the relevant dynamical aspects of the neuronal response measured in experiments on real neurons in vitro.     

Perisomatic feedback inhibition underlies cholinergically induced fast network oscillations in the rat hippocampus in vitro

Gamma frequency network oscillations are assumed to be important in cognitive processes, including hippocampal memory operations, but the precise functions of these oscillations remain unknown. Here, we examine the cellular and network mechanisms underlying carbachol-induced fast network oscillations in the hippocampus in vitro, which closely resemble hippocampal gamma oscillations in the behaving rat. Using a combination of planar multielectrode array recordings, imaging with voltage-sensitive dyes, and recordings from single hippocampal neurons within the CA3 gamma generator, active current sinks and sources were localized to the stratum pyramidale. These proximal currents were driven by phase-locked rhythmic inhibitory inputs to pyramidal cells from identified perisomatic-targeting interneurons. AMPA receptor-mediated recurrent excitation was necessary for the synchronization of interneuronal discharge, which strongly supports a synaptic feedback model for the generation of hippocampal gamma oscillations.     

Dopamine D4 receptor activation increases hippocampal gamma oscillations by enhancing synchronization of fast-spiking interneurons

Background

Gamma oscillations are electric activity patterns of the mammalian brain hypothesized to serve attention, sensory perception, working memory and memory encoding. They are disrupted or altered in schizophrenic patients with associated cognitive deficits, which persist in spite of treatment with antipsychotics. Because cognitive symptoms are a core feature of schizophrenia it is relevant to explore signaling pathways that potentially regulate gamma oscillations. Dopamine has been reported to decrease gamma oscillation power via D1-like receptors. Based on the expression pattern of D4 receptors (D4R) in hippocampus, and pharmacological effects of D4R ligands in animals, we hypothesize that they are in a position to regulate gamma oscillations as well.

Methodology/Principal Findings

To address this hypothesis we use rat hippocampal slices and kainate-induced gamma oscillations. Local field potential recordings as well as intracellular recordings of pyramidal cells, fast-spiking and non-fast-spiking interneurons were carried out. We show that D4R activation with the selective ligand PD168077 increases gamma oscillation power, which can be blocked by the D4R-specific antagonist L745,870 as well as by the antipsychotic drug Clozapine. Pyramidal cells did not exhibit changes in excitatory or inhibitory synaptic current amplitudes, but inhibitory currents became more coherent with the oscillations after application of PD168077. Fast-spiking, but not non-fast spiking, interneurons, increase their action potential phase-coupling and coherence with regard to ongoing gamma oscillations in response to D4R activation. Among several possible mechanisms we found that the NMDA receptor antagonist AP5 also blocks the D4R mediated increase in gamma oscillation power.

Conclusions/Significance

We conclude that D4R activation affects fast-spiking interneuron synchronization and thereby increases gamma power by an NMDA receptor-dependent mechanism. This suggests that converging deficits on fast-spiking interneurons may lead to decreased network function and thus aberrant gamma oscillations and cognitive decline in schizophrenia.     

The dynamical stability of reverberatory neural circuits

The concept of reverberation proposed by Lorente de Nó and Hebb is key to understanding strongly recurrent cortical networks. In particular, synaptic reverberation is now viewed as a likely mechanism for the active maintenance of working memory in the prefrontal cortex. Theoretically, this has spurred a debate as to how such a potentially explosive mechanism can provide stable working-memory function given the synaptic and cellular mechanisms at play in the cerebral cortex. We present here new evidence for the participation of NMDA receptors in the stabilization of persistent delay activity in a biophysical network model of conductance-based neurons. We show that the stability of working-memory function, and the required NMDA/AMPA ratio at recurrent excitatory synapses, depend on physiological properties of neurons and synaptic interactions, such as the time constants of excitation and inhibition, mutual inhibition between interneurons, differential NMDA receptor participation at excitatory projections to pyramidal neurons and interneurons, or the presence of slow intrinsic ion currents in pyramidal neurons. We review other mechanisms proposed to enhance the dynamical stability of synaptically generated attractor states of a reverberatory circuit. This recent work represents a necessary and significant step towards testing attractor network models by cortical electrophysiology.     

Frontal cortical afferents facilitate striatal nitric oxide transmission in vivo via a NMDA receptor and neuronal NOS-dependent mechanism

Striatal nitric oxide (NO) signaling plays a critical role in modulating neural processing and motor behavior. Nitrergic interneurons receive synaptic inputs from corticostriatal neurons and are activated via ionotropic glutamate receptor stimulation. However, the afferent regulation of NO signaling is poorly characterized. The role of frontal cortical afferents in regulating NO transmission was assessed in anesthetized rats using amperometric microsensor measurements of NO efflux and local field potential recordings. Low frequency (3 Hz) electrical stimulation of the ipsilateral cortex did not consistently evoke detectable changes in striatal NO efflux. In contrast, train stimulation (30 Hz) of frontal cortical afferents facilitated NO efflux in a stimulus intensity-dependent manner. Nitric oxide efflux evoked by train stimulation was transient, reproducible over time, and attenuated by systemic administration of either the NMDA receptor antagonist MK-801 or the neuronal NO synthase inhibitors 7-nitroindazole and NG-propyl-L-arginine. The interaction between NO efflux evoked via train stimulation and local striatal neuron activity was assessed using dual microsensor and local field potential recordings carried out concurrently in the contralateral and ipsilateral striatum, respectively. Systemic administration of the non-specific NO synthase inhibitor methylene blue attenuated both evoked NO efflux and the peak oscillation frequency (within the delta band) of local field potentials recorded immediately after train stimulation. Taken together, these observations indicate that feed-forward activation of neuronal NO signaling by phasic activation of frontal cortical afferents facilitates the synchronization of glutamate driven oscillations in striatal neurons. Thus, NO signaling may act to amplify coherent corticostriatal transmission and synchronize striatal output.     

The emergence of Up and Down states in cortical networks

The cerebral cortex is continuously active in the absence of external stimuli. An example of this spontaneous activity is the voltage transition between an Up and a Down state, observed simultaneously at individual neurons. Since this phenomenon could be of critical importance for working memory and attention, its explanation could reveal some fundamental properties of cortical organization. To identify a possible scenario for the dynamics of Up–Down states, we analyze a reduced stochastic dynamical system that models an interconnected network of excitatory neurons with activity-dependent synaptic depression. The model reveals that when the total synaptic connection strength exceeds a certain threshold, the phase space of the dynamical system contains two attractors, interpreted as Up and Down states. In that case, synaptic noise causes transitions between the states. Moreover, an external stimulation producing a depolarization increases the time spent in the Up state, as observed experimentally. We therefore propose that the existence of Up–Down states is a fundamental and inherent property of a noisy neural ensemble with sufficiently strong synaptic connections.     

Interplay of Intrinsic and Synaptic Conductances in the Generation of High-Frequency Oscillations in Interneuronal Networks with Irregular Spiking

High-frequency oscillations (above 30 Hz) have been observed in sensory and higher-order brain areas, and are believed to constitute a general hallmark of functional neuronal activation. Fast inhibition in interneuronal networks has been suggested as a general mechanism for the generation of high-frequency oscillations. Certain classes of interneurons exhibit subthreshold oscillations, but the effect of this intrinsic neuronal property on the population rhythm is not completely understood. We study the influence of intrinsic damped subthreshold oscillations in the emergence of collective high-frequency oscillations, and elucidate the dynamical mechanisms that underlie this phenomenon. We simulate neuronal networks composed of either Integrate-and-Fire (IF) or Generalized Integrate-and-Fire (GIF) neurons. The IF model displays purely passive subthreshold dynamics, while the GIF model exhibits subthreshold damped oscillations. Individual neurons receive inhibitory synaptic currents mediated by spiking activity in their neighbors as well as noisy synaptic bombardment, and fire irregularly at a lower rate than population frequency. We identify three factors that affect the influence of single-neuron properties on synchronization mediated by inhibition: i) the firing rate response to the noisy background input, ii) the membrane potential distribution, and iii) the shape of Inhibitory Post-Synaptic Potentials (IPSPs). For hyperpolarizing inhibition, the GIF IPSP profile (factor iii)) exhibits post-inhibitory rebound, which induces a coherent spike-mediated depolarization across cells that greatly facilitates synchronous oscillations. This effect dominates the network dynamics, hence GIF networks display stronger oscillations than IF networks. However, the restorative current in the GIF neuron lowers firing rates and narrows the membrane potential distribution (factors i) and ii), respectively), which tend to decrease synchrony. If inhibition is shunting instead of hyperpolarizing, post-inhibitory rebound is not elicited and factors i) and ii) dominate, yielding lower synchrony in GIF networks than in IF networks.