The response of a classical Hodgkin-Huxley neuron to an inhibitory input pulse

Persistent Interruption in Parvalbumin-Positive Inhibitory Interneurons: Biophysical and Mathematical Mechanisms

Persistent activity in excitatory pyramidal cells (PYRs) is a putative mechanism for maintaining memory traces during working memory. We have recently demonstrated persistent interruption of firing in fast-spiking parvalbumin-expressing interneurons (PV-INs), a phenomenon that could serve as a substrate for persistent activity in PYRs through disinhibition lasting hundreds of milliseconds. Here, we find that hippocampal CA1 PV-INs exhibit type 2 excitability, like striatal and neocortical PV-INs. Modeling and mathematical analysis showed that the slowly inactivating potassium current KV1 contributes to type 2 excitability, enables the multiple firing regimes observed experimentally in PV-INs, and provides a mechanism for robust persistent interruption of firing. Using a fast/slow separation of times scales approach with the KV1 inactivation variable as a bifurcation parameter shows that the initial inhibitory stimulus stops repetitive firing by moving the membrane potential trajectory onto a coexisting stable fixed point corresponding to a nonspiking quiescent state. As KV1 inactivation decays, the trajectory follows the branch of stable fixed points until it crosses a subcritical Hopf bifurcation (HB) and then spirals out into repetitive firing. In a model describing entorhinal cortical PV-INs without KV1, interruption of firing could be achieved by taking advantage of the bistability inherent in type 2 excitability based on a subcritical HB, but the interruption was not robust to noise. Persistent interruption of firing is therefore broadly applicable to PV-INs in different brain regions but is only made robust to noise in the presence of a slow variable, KV1 inactivation.

Persistent Interruption in Parvalbumin Positive Inhibitory Interneurons: Biophysical and Mathematical Mechanisms

Persistent activity in principal cells is a putative mechanism for maintaining memory traces during working memory. We recently demonstrated persistent interruption of firing in fast-spiking parvalbumin-expressing interneurons (PV-INs), a phenomenon which could serve as a substrate for persistent activity in principal cells through disinhibition lasting hundreds of milliseconds. Here, we find that hippocampal CA1 PV-INs exhibit type 2 excitability, like striatal and neocortical PV-INs. Modelling and mathematical analysis showed that the slowly inactivating potassium current Kv1 contributes to type 2 excitability, enables the multiple firing regimes observed experimentally in PV-INs, and provides a mechanism for robust persistent interruption of firing. Using a fast/slow separation of times scales approach with the Kv1 inactivation variable as a bifurcation parameter shows that the initial inhibitory stimulus stops repetitive firing by moving the membrane potential trajectory onto a co-existing stable fixed point corresponding to a non-spiking quiescent state. As Kv1 inactivation decays, the trajectory follows the branch of stable fixed points until it crosses a subcritical Hopf bifurcation then spirals out into repetitive firing. In a model describing entorhinal cortical PV-INs without Kv1, interruption of firing could be achieved by taking advantage of the bistability inherent in type 2 excitability based on a subcritical Hopf bifurcation, but the interruption was not robust to noise. Persistent interruption of firing is therefore broadly applicable to PV-INs in different brain regions but is only made robust to noise in the presence of a slow variable.

Flow-driven control of pulse width in excitable media

Models of pulse formation in nerve conduction have provided manifold insight not only into neuronal dynamics but also the nonlinear dynamics of pulse formation in general. Recent observation of neuronal electrochemical pulses also driving mechanical deformation of the tubular neuronal wall, and thereby generating ensuing cytoplasmic flow, now question the impact of flow on the electrochemical dynamics of pulse formation. Here, we theoretically investigate the classical Fitzhugh-Nagumo model, now accounting for advective coupling between the pulse propagator typically describing membrane potential and triggering mechanical deformations, and thus governing flow magnitude, and the pulse controller, a chemical species advected with the ensuing fluid flow. Employing analytical calculations and numerical simulations, we find that advective coupling allows for a linear control of pulse width while leaving pulse velocity unchanged. We therefore uncover an independent control of pulse width by fluid flow coupling.

Bistability at the onset of neuronal oscillations

The Hodgkin-Huxley (HH) model and squid axon (bathed in reduced Ca²⁺) fire repetitively for steady current injection. Moreover, for a current-range just suprathreshold, repetitive firing coexists with a stable steady state. Neuronal excitability, as such, shows bistability and hysteresis providing the opportunity for the system to perform as switchable between firing and non-firing states with transient input and providing the backbone as a dynamical mechanism for bursting oscillations. Some conditions for bistability can be derived by intricate analysis (bifurcation theory) and characterized by simulation, but conditions for emergence and robustness of such bistability do not typically follow from intuition. Here, we demonstrate with a semi-quantitative two-variable, V-w, reduction of the HH model features that promote/reduce bistability. Visualization of flow and trajectories in the V-w phase plane provides an intuitive grasp for bistability. The geometry of action potential recovery involves a late phase during which the dynamic negative feedback of [Formula: see text] inactivation and [Formula: see text] activation over/undershoot, respectively, their resting values, thereby leading to hyperexcitabilty and an intrinsically generated opportunity to by-pass the spiral-like stable rest state and initiate the next spike upstroke. We illustrate control of bistability and dependence of the degree of hysteresis on recovery timescales and gating properties. Our dynamical dissection reveals the strongly attracting depolarized phase of the spike, enabling approximations like the resetting feature of adapting integrate-and-fire models. We extend our insights and show that the Morris-Lecar model can also exhibit robust bistability.

Paradoxical phase response of gamma rhythms facilitates their entrainment in heterogeneous networks

The synchronization of different γ-rhythms arising in different brain areas has been implicated in various cognitive functions. Here, we focus on the effect of the ubiquitous neuronal heterogeneity on the synchronization of ING (interneuronal network gamma) and PING (pyramidal-interneuronal network gamma) rhythms. The synchronization properties of rhythms depends on the response of their collective phase to external input. We therefore determine the macroscopic phase-response curve for finite-amplitude perturbations (fmPRC) of ING- and PING-rhythms in all-to-all coupled networks comprised of linear (IF) or quadratic (QIF) integrate-and-fire neurons. For the QIF networks we complement the direct simulations with the adjoint method to determine the infinitesimal macroscopic PRC (imPRC) within the exact mean-field theory. We show that the intrinsic neuronal heterogeneity can qualitatively modify the fmPRC and the imPRC. Both PRCs can be biphasic and change sign (type II), even though the phase-response curve for the individual neurons is strictly non-negative (type I). Thus, for ING rhythms, say, external inhibition to the inhibitory cells can, in fact, advance the collective oscillation of the network, even though the same inhibition would lead to a delay when applied to uncoupled neurons. This paradoxical advance arises when the external inhibition modifies the internal dynamics of the network by reducing the number of spikes of inhibitory neurons; the advance resulting from this disinhibition outweighs the immediate delay caused by the external inhibition. These results explain how intrinsic heterogeneity allows ING- and PING-rhythms to become synchronized with a periodic forcing or another rhythm for a wider range in the mismatch of their frequencies. Our results identify a potential function of neuronal heterogeneity in the synchronization of coupled γ-rhythms, which may play a role in neural information transfer via communication through coherence.

The interaction of a large number of oscillating units can lead to the emergence of a collective, macroscopic oscillation in which many units oscillate in near-unison or near-synchrony. This has been exploited technologically, e.g., to combine many coherently interacting, individual lasers to form a single powerful laser. Collective oscillations are also important in biology. For instance, the circadian rhythm of animals is controlled by the near-synchronous dynamics of a large number of individually oscillating cells. In animals and humans brain rhythms reflect the coherent dynamics of a large number of neurons and are surmised to play an important role in the communication between different brain areas. To be functionally relevant, these rhythms have to respond to external inputs and have to be able to synchronize with each other. We show that the ubiquitous heterogeneity in the properties of the individual neurons in a network can contribute to that ability. It can allow the external inputs to modify the internal network dynamics such that the network can follow these inputs over a wider range of frequencies. Paradoxically, while an external perturbation may delay individual neurons, their ensuing within-network interaction can overcompensate this delay, leading to an overall advance of the rhythm.

How stimulation frequency and intensity impact on the long-lasting effects of coordinated reset stimulation

Several brain diseases are characterized by abnormally strong neuronal synchrony. Coordinated Reset (CR) stimulation was computationally designed to specifically counteract abnormal neuronal synchronization processes by desynchronization. In the presence of spike-timing-dependent plasticity (STDP) this may lead to a decrease of synaptic excitatory weights and ultimately to an anti-kindling, i.e. unlearning of abnormal synaptic connectivity and abnormal neuronal synchrony. The long-lasting desynchronizing impact of CR stimulation has been verified in pre-clinical and clinical proof of concept studies. However, as yet it is unclear how to optimally choose the CR stimulation frequency, i.e. the repetition rate at which the CR stimuli are delivered. This work presents the first computational study on the dependence of the acute and long-term outcome on the CR stimulation frequency in neuronal networks with STDP. For this purpose, CR stimulation was applied with Rapidly Varying Sequences (RVS) as well as with Slowly Varying Sequences (SVS) in a wide range of stimulation frequencies and intensities. Our findings demonstrate that acute desynchronization, achieved during stimulation, does not necessarily lead to long-term desynchronization after cessation of stimulation. By comparing the long-term effects of the two different CR protocols, the RVS CR stimulation turned out to be more robust against variations of the stimulation frequency. However, SVS CR stimulation can obtain stronger anti-kindling effects. We revealed specific parameter ranges that are favorable for long-term desynchronization. For instance, RVS CR stimulation at weak intensities and with stimulation frequencies in the range of the neuronal firing rates turned out to be effective and robust, in particular, if no closed loop adaptation of stimulation parameters is (technically) available. From a clinical standpoint, this may be relevant in the context of both invasive as well as non-invasive CR stimulation.

Dichotomous Dynamics in E-I Networks with Strongly and Weakly Intra-connected Inhibitory Neurons

The interconnectivity between excitatory and inhibitory neural networks informs mechanisms by which rhythmic bursts of excitatory activity can be produced in the brain. One such mechanism, Pyramidal Interneuron Network Gamma (PING), relies primarily upon reciprocal connectivity between the excitatory and inhibitory networks, while also including intra-connectivity of inhibitory cells. The causal relationship between excitatory activity and the subsequent burst of inhibitory activity is of paramount importance to the mechanism and has been well studied. However, the role of the intra-connectivity of the inhibitory network, while important for PING, has not been studied in detail, as most analyses of PING simply assume that inhibitory intra-connectivity is strong enough to suppress subsequent firing following the initial inhibitory burst. In this paper we investigate the role that the strength of inhibitory intra-connectivity plays in determining the dynamics of PING-style networks. We show that networks with weak inhibitory intra-connectivity exhibit variations in burst dynamics of both the excitatory and inhibitory cells that are not obtained with strong inhibitory intra-connectivity. Networks with weak inhibitory intra-connectivity exhibit excitatory rhythmic bursts with weak excitatory-to-inhibitory synapses for which classical PING networks would show no rhythmic activity. Additionally, variations in dynamics of these networks as the excitatory-to-inhibitory synaptic weight increases illustrates the important role that consistent pattern formation in the inhibitory cells serves in maintaining organized and periodic excitatory bursts. Finally, motivated by these results and the known diversity of interneurons, we show that a PING-style network with two inhibitory subnetworks, one strongly intra-connected and one weakly intra-connected, exhibits organized and periodic excitatory activity over a larger parameter regime than networks with a homogeneous inhibitory population. Taken together, these results serve to better articulate the role of inhibitory intra-connectivity in generating PING-like rhythms, while also revealing how heterogeneity amongst inhibitory synapses might make such rhythms more robust to a variety of network parameters.

Regional Homogeneity: A Multimodal, Multiscale Neuroimaging Marker of the Human Connectome

Much effort has been made to understand the organizational principles of human brain function using functional magnetic resonance imaging (fMRI) methods, among which resting-state fMRI (rfMRI) is an increasingly recognized technique for measuring the intrinsic dynamics of the human brain. Functional connectivity (FC) with rfMRI is the most widely used method to describe remote or long-distance relationships in studies of cerebral cortex parcellation, interindividual variability, and brain disorders. In contrast, local or short-distance functional interactions, especially at a scale of millimeters, have rarely been investigated or systematically reviewed like remote FC, although some local FC algorithms have been developed and applied to the discovery of brain-based changes under neuropsychiatric conditions. To fill this gap between remote and local FC studies, this review will (1) briefly survey the history of studies on organizational principles of human brain function; (2) propose local functional homogeneity as a network centrality to characterize multimodal local features of the brain connectome; (3) render a neurobiological perspective on local functional homogeneity by linking its temporal, spatial, and individual variability to information processing, anatomical morphology, and brain development; and (4) discuss its role in performing connectome-wide association studies and identify relevant challenges, and recommend its use in future brain connectomics studies.

Cooperation and competition of gamma oscillation mechanisms

Oscillations of neuronal activity in different frequency ranges are thought to reflect important aspects of cortical network dynamics. Here we investigate how various mechanisms that contribute to oscillations in neuronal networks may interact. We focus on networks with inhibitory, excitatory, and electrical synapses, where the subnetwork of inhibitory interneurons alone can generate interneuron gamma (ING) oscillations and the interactions between interneurons and pyramidal cells allow for pyramidal-interneuron gamma (PING) oscillations. What type of oscillation will such a network generate? We find that ING and PING oscillations compete: The mechanism generating the higher oscillation frequency "wins"; it determines the frequency of the network oscillation and suppresses the other mechanism. For type I interneurons, the network oscillation frequency is equal to or slightly above the higher of the ING and PING frequencies in corresponding reduced networks that can generate only either of them; if the interneurons belong to the type II class, it is in between. In contrast to ING and PING, oscillations mediated by gap junctions and oscillations mediated by inhibitory synapses may cooperate or compete, depending on the type (I or II) of interneurons and the strengths of the electrical and chemical synapses. We support our computer simulations by a theoretical model that allows a full theoretical analysis of the main results. Our study suggests experimental approaches to deciding to what extent oscillatory activity in networks of interacting excitatory and inhibitory neurons is dominated by ING or PING oscillations and of which class the participating interneurons are.

Synchronization of Biological Clock Neurons by Light and Peripheral Feedback Systems Promotes Circadian Rhythms and Health

In mammals, the suprachiasmatic nucleus (SCN) functions as a circadian clock that drives 24-h rhythms in both physiology and behavior. The SCN is a multicellular oscillator in which individual neurons function as cell-autonomous oscillators. The production of a coherent output rhythm is dependent upon mutual synchronization among single cells and requires both synaptic communication and gap junctions. Changes in phase-synchronization between individual cells have consequences on the amplitude of the SCN’s electrical activity rhythm, and these changes play a major role in the ability to adapt to seasonal changes. Both aging and sleep deprivation negatively affect the circadian amplitude of the SCN, whereas behavioral activity (i.e., exercise) has a positive effect on amplitude. Given that the amplitude of the SCN’s electrical activity rhythm is essential for achieving robust rhythmicity in physiology and behavior, the mechanisms that underlie neuronal synchronization warrant further study. A growing body of evidence suggests that the functional integrity of the SCN contributes to health, well-being, cognitive performance, and alertness; in contrast, deterioration of the 24-h rhythm is a risk factor for neurodegenerative disease, cancer, depression, and sleep disorders.

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.

Neurons in the brain engage in collective oscillations at different frequencies. Gamma and high-gamma oscillations (30–100 Hz and higher) have been associated with cognitive functions, and are altered in psychiatric disorders such as schizophrenia and autism. Our understanding of how high-frequency oscillations are orchestrated in the brain is still limited, but it is necessary for the development of effective clinical approaches to the treatment of these disorders. Some neuron types exhibit dynamical properties that can favour synchronization. The theory of weakly coupled oscillators showed how the phase response of individual neurons can predict the patterns of phase relationships that are observed at the network level. However, neurons in vivo do not behave like regular oscillators, but fire irregularly in a regime dominated by fluctuations. Hence, which intrinsic dynamical properties matter for synchronization, and in which regime, is still an open question. Here, we show how single-cell damped subthreshold oscillations enhance synchrony in interneuronal networks by introducing a depolarizing component, mediated by post-inhibitory rebound, that is correlated among neurons due to common inhibitory input.

When Long-Range Zero-Lag Synchronization is Feasible in Cortical Networks

Many studies have reported long-range synchronization of neuronal activity between brain areas, in particular in the beta and gamma bands with frequencies in the range of 14–30 and 40–80 Hz, respectively. Several studies have reported synchrony with zero phase lag, which is remarkable considering the synaptic and conduction delays inherent in the connections between distant brain areas. This result has led to many speculations about the possible functional role of zero-lag synchrony, such as for neuronal communication, attention, memory, and feature binding. However, recent studies using recordings of single-unit activity and local field potentials report that neuronal synchronization may occur with non-zero phase lags. This raises the questions whether zero-lag synchrony can occur in the brain and, if so, under which conditions. We used analytical methods and computer simulations to investigate which connectivity between neuronal populations allows or prohibits zero-lag synchrony. We did so for a model where two oscillators interact via a relay oscillator. Analytical results and computer simulations were obtained for both type I Mirollo–Strogatz neurons and type II Hodgkin–Huxley neurons. We have investigated the dynamics of the model for various types of synaptic coupling and importantly considered the potential impact of Spike-Timing Dependent Plasticity (STDP) and its learning window. We confirm previous results that zero-lag synchrony can be achieved in this configuration. This is much easier to achieve with Hodgkin–Huxley neurons, which have a biphasic phase response curve, than for type I neurons. STDP facilitates zero-lag synchrony as it adjusts the synaptic strengths such that zero-lag synchrony is feasible for a much larger range of parameters than without STDP.

Minimal size of cell assemblies coordinated by gamma oscillations

In networks of excitatory and inhibitory neurons with mutual synaptic coupling, specific drive to sub-ensembles of cells often leads to gamma-frequency (25–100 Hz) oscillations. When the number of driven cells is too small, however, the synaptic interactions may not be strong or homogeneous enough to support the mechanism underlying the rhythm. Using a combination of computational simulation and mathematical analysis, we study the breakdown of gamma rhythms as the driven ensembles become too small, or the synaptic interactions become too weak and heterogeneous. Heterogeneities in drives or synaptic strengths play an important role in the breakdown of the rhythms; nonetheless, we find that the analysis of homogeneous networks yields insight into the breakdown of rhythms in heterogeneous networks. In particular, if parameter values are such that in a homogeneous network, it takes several gamma cycles to converge to synchrony, then in a similar, but realistically heterogeneous network, synchrony breaks down altogether. This leads to the surprising conclusion that in a network with realistic heterogeneity, gamma rhythms based on the interaction of excitatory and inhibitory cell populations must arise either rapidly, or not at all. For given synaptic strengths and heterogeneities, there is a (soft) lower bound on the possible number of cells in an ensemble oscillating at gamma frequency, based simply on the requirement that synaptic interactions between the two cell populations be strong enough. This observation suggests explanations for recent experimental results concerning the modulation of gamma oscillations in macaque primary visual cortex by varying spatial stimulus size or attention level, and for our own experimental results, reported here, concerning the optogenetic modulation of gamma oscillations in kainate-activated hippocampal slices. We make specific predictions about the behavior of pyramidal cells and fast-spiking interneurons in these experiments.

Gamma-frequency (25–100 Hz) oscillations in the brain often arise as a result of an interaction between excitatory and inhibitory cell populations. For this mechanism to work, the interaction must be sufficiently strong, and connectivity and external drives to participating neurons must be sufficiently homogeneous. As the interactions become weaker, either because the neuronal ensembles become smaller or because synapses weaken, the rhythms deteriorate, and eventually break down. This fact, by itself, is not surprising, but details of how the breakdown occurs are subtle. In particular, our analysis leads to the conclusion that in realistically heterogeneous networks, gamma rhythms must arise quickly, within a small number of oscillation periods, if they arise at all. Our findings suggest explanations for recent experimental findings concerning the minimal spatial extent of stimuli eliciting gamma oscillations in the primary visual cortex, the modulation of gamma oscillations in the primary visual cortex by attention, as well as our own experimental results, reported here, concerning the minimal light intensity below which optogenetic drive to pyramidal cells in a kainate-activated hippocampal slice results in disruption of an ongoing gamma oscillation. Our analysis leads to experimentally testable predictions about the behavior of the excitatory and inhibitory cells in these experiments.

Establishing Communication between Neuronal Populations through Competitive Entrainment

The role of gamma frequency oscillation in neuronal interaction, and the relationship between oscillation and information transfer between neurons, has been the focus of much recent research. While the biological mechanisms responsible for gamma oscillation and the properties of resulting networks are well studied, the dynamics of changing phase coherence between oscillating neuronal populations are not well understood. To this end we develop a computational model of competitive selection between multiple stimuli, where the selection and transfer of population-encoded information arises from competition between converging stimuli to entrain a target population of neurons. Oscillation is generated by Pyramidal-Interneuronal Network Gamma through the action of recurrent synaptic connections between a locally connected network of excitatory and inhibitory neurons. Competition between stimuli is driven by differences in coherence of oscillation, while transmission of a single selected stimulus is enabled between generating and receiving neurons via Communication-through-Coherence. We explore the effect of varying synaptic parameters on the competitive transmission of stimuli over different neuron models, and identify a continuous region within the parameter space of the recurrent synaptic loop where inhibition-induced oscillation results in entrainment of target neurons. Within this optimal region we find that competition between stimuli of equal coherence results in model output that alternates between representation of the stimuli, in a manner strongly resembling well-known biological phenomena resulting from competitive stimulus selection such as binocular rivalry.

Daily and seasonal adaptation of the circadian clock requires plasticity of the SCN neuronal network

Circadian rhythms are an essential property of many living organisms, and arise from an internal pacemaker, or clock. In mammals, this clock resides in the suprachiasmatic nucleus (SCN) of the hypothalamus, and generates an intrinsic circadian rhythm that is transmitted to other parts of the CNS. We will review the evidence that basic adaptive functions of the circadian system rely on functional plasticity in the neuronal network organization, and involve a change in phase relation among oscillatory neurons. We will illustrate this for: (i) photic entrainment of the circadian clock to the light-dark cycle; and (ii) seasonal adaptation of the clock to changes in day length. Molecular studies have shown plasticity in the phase relation between the ventral and dorsal SCN during adjustment to a shifted environmental cycle. Seasonal adaptation relies predominantly on plasticity in the phase relation between the rostral and caudal SCN. Electrical activity is integrated in the SCN, and appears to reflect the sum of the differently phased molecular expression patterns. While both photic entrainment and seasonal adaptation arise from a redistribution of SCN oscillatory activity patterns, different neuronal coupling mechanisms are employed, which are reviewed in the present paper.

Gamma oscillations as a mechanism for selective information transmission

In the past decades, many studies have focussed on the relation between the input and output of neurons with the aim to understand information processing by neurons. A particular aspect of neuronal information, which has not received much attention so far, concerns the problem of information transfer when a neuron or a population of neurons receives input from two or more (populations of) neurons, in particular when these (populations of) neurons carry different types of information. The aim of the present study is to investigate the responses of neurons to multiple inputs modulated in the gamma frequency range. By a combination of theoretical approaches and computer simulations, we test the hypothesis that enhanced modulation of synchronized excitatory neuronal activity in the gamma frequency range provides an advantage over a less synchronized input for various types of neurons. The results of this study show that the spike output of various types of neurons [i.e. the leaky integrate and fire neuron, the quadratic integrate and fire neuron and the Hodgkin-Huxley (HH) neuron] and that of excitatory-inhibitory coupled pairs of neurons, like the Pyramidal Interneuronal Network Gamma (PING) model, is highly phase-locked to the larger of two gamma-modulated input signals. This implies that the neuron selectively responds to the input with the larger gamma modulation if the amplitude of the gamma modulation exceeds that of the other signals by a certain amount. In that case, the output of the neuron is entrained by one of multiple inputs and that other inputs are not represented in the output. This mechanism for selective information transmission is enhanced for short membrane time constants of the neuron.