Synchronization and sensitivity enhancement of the Hodgkin-Huxley neurons due to inhibitory inputs

Recent experimental results imply that inhibitory postsynaptic potentials can play a functional role in realizing synchronization of neuronal firing in the brain. In order to examine the relation between inhibition and synchronous firing of neurons theoretically, we analyze possible effects of synchronization and sensitivity enhancement caused by inhibitory inputs to neurons with a biologically realistic model of the Hodgkin-Huxley equations. The result shows that, after an inhibitory spike, the firing probability of a single postsynaptic neuron exposed to random excitatory background activity oscillates with time. The oscillation of the firing probability can be related to synchronous firing of neurons receiving an inhibitory spike simultaneously. Further, we show that when an inhibitory spike input precedes an excitatory spike input, the presence of such preceding inhibition raises the firing probability peak of the neuron after the excitatory input. The result indicates that an inhibitory spike input can enhance the sensitivity of the postsynaptic neuron to the following excitatory spike input. Two neural network models based on these effects on postsynaptic neurons caused by inhibitory inputs are proposed to demonstrate possible mechanisms of detecting particular spatiotemporal spike patterns. Received: 15 April 1999 /Accepted in revised form: 25 November 1999     

Impact of correlated inputs to neurons: modeling observations from in vivo intracellular recordings

In vivo recordings in rat somatosensory cortex suggest that excitatory and inhibitory inputs are often correlated during spontaneous and sensory-evoked activity. Using a computational approach, we study how the interplay of input correlations and timing observed in experiments controls the spiking probability of single neurons. Several correlation-based mechanisms are identified, which can effectively switch a neuron on and off. In addition, we investigate the transfer of input correlation to output correlation in pairs of neurons, at the spike train and the membrane potential levels, by considering spike-driving and non-spike-driving inputs separately. In particular, we propose a plausible explanation for the in vivo finding that membrane potentials in neighboring neurons are correlated, but the spike-triggered averages of membrane potentials preceding a spike are not: Neighboring neurons possibly receive an ongoing bombardment of correlated subthreshold background inputs, and occasionally uncorrelated spike-driving inputs.     

Inhibitory Contribution to Suprathreshold Corticostriatal Responses: An Experimental and Modeling Study

Neostriatal neurons may undergo events of spontaneous synchronization as those observed in recurrent networks of excitatory neurons, even when cortical afferents are transected. It is necessary to explain these events because the neostriatum is a recurrent network of inhibitory neurons. Synchronization of neuronal activity may be caused by plateau-like depolarizations. Plateau-like orthodromic depolarizations that resemble up-states in medium spiny neostriatal neurons (MSNs) may be induced by a single corticostriatal suprathreshold stimulus. Slow synaptic depolarizations may last hundreds of milliseconds, decay slower than the monosynaptic glutamatergic synaptic potentials that induce them, and sustain repetitive firing. Because inhibitory inputs impinging onto MSNs have a reversal potential above the resting membrane potential but below the threshold for firing, they conform a type of “shunting inhibition”. This work asks if shunting GABAergic inputs onto MSNs arrive asynchronously enough as to help in sustaining the plateau-like corticostriatal response after a single cortical stimulus. This may help to begin explaining autonomous processing in the striatal micro-circuitry in the presence of a tonic excitatory drive and independently of spatio-temporally organized inputs. It is shown here that besides synaptic currents from AMPA/KA- and NMDA-receptors, as well as L-type intrinsic Ca²⁺- currents, inhibitory synapses help in maintaining the slow depolarization, although they accomplish the role of depressing firing at the beginning of the response. We then used a NEURON model of spiny cells to show that inhibitory synapses arriving asynchronously on the dendrites can help to simulate a plateau potential similar to that observed experimentally. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Divisive Gain Modulation with Dynamic Stimuli in Integrate-and-Fire Neurons

The modulation of the sensitivity, or gain, of neural responses to input is an important component of neural computation. It has been shown that divisive gain modulation of neural responses can result from a stochastic shunting from balanced (mixed excitation and inhibition) background activity. This gain control scheme was developed and explored with static inputs, where the membrane and spike train statistics were stationary in time. However, input statistics, such as the firing rates of pre-synaptic neurons, are often dynamic, varying on timescales comparable to typical membrane time constants. Using a population density approach for integrate-and-fire neurons with dynamic and temporally rich inputs, we find that the same fluctuation-induced divisive gain modulation is operative for dynamic inputs driving nonequilibrium responses. Moreover, the degree of divisive scaling of the dynamic response is quantitatively the same as the steady-state responses—thus, gain modulation via balanced conductance fluctuations generalizes in a straight-forward way to a dynamic setting.     

Variability and coding efficiency of noisy neural spike encoders

Encoding synaptic inputs as a train of action potentials is a fundamental function of nerve cells. Although spike trains recorded in vivo have been shown to be highly variable, it is unclear whether variability in spike timing represents faithful encoding of temporally varying synaptic inputs or noise inherent in the spike encoding mechanism. It has been reported that spike timing variability is more pronounced for constant, unvarying inputs than for inputs with rich temporal structure. This could have significant implications for the nature of neural coding, particularly if precise timing of spikes and temporal synchrony between neurons is used to represent information in the nervous system. To study the potential functional role of spike timing variability, we estimate the fraction of spike timing variability which conveys information about the input for two types of noisy spike encoders--an integrate and fire model with randomly chosen thresholds and a model of a patch of neuronal membrane containing stochastic Na(+) and K(+) channels obeying Hodgkin-Huxley kinetics. The quality of signal encoding is assessed by reconstructing the input stimuli from the output spike trains using optimal linear mean square estimation. A comparison of the estimation performance of noisy neuronal models of spike generation enables us to assess the impact of neuronal noise on the efficacy of neural coding. The results for both models suggest that spike timing variability reduces the ability of spike trains to encode rapid time-varying stimuli. Moreover, contrary to expectations based on earlier studies, we find that the noisy spike encoding models encode slowly varying stimuli more effectively than rapidly varying ones.     

Membrane properties and the balance between excitation and inhibition control gamma-frequency oscillations arising from feedback inhibition

Computational studies as well as in vivo and in vitro results have shown that many cortical neurons fire in a highly irregular manner and at low average firing rates. These patterns seem to persist even when highly rhythmic signals are recorded by local field potential electrodes or other methods that quantify the summed behavior of a local population. Models of the 30-80 Hz gamma rhythm in which network oscillations arise through 'stochastic synchrony' capture the variability observed in the spike output of single cells while preserving network-level organization. We extend upon these results by constructing model networks constrained by experimental measurements and using them to probe the effect of biophysical parameters on network-level activity. We find in simulations that gamma-frequency oscillations are enabled by a high level of incoherent synaptic conductance input, similar to the barrage of noisy synaptic input that cortical neurons have been shown to receive in vivo. This incoherent synaptic input increases the emergent network frequency by shortening the time scale of the membrane in excitatory neurons and by reducing the temporal separation between excitation and inhibition due to decreased spike latency in inhibitory neurons. These mechanisms are demonstrated in simulations and in vitro current-clamp and dynamic-clamp experiments. Simulation results further indicate that the membrane potential noise amplitude has a large impact on network frequency and that the balance between excitatory and inhibitory currents controls network stability and sensitivity to external inputs.     

Membrane Capacitive Memory Alters Spiking in Neurons Described by the Fractional-Order Hodgkin-Huxley Model

Excitable cells and cell membranes are often modeled by the simple yet elegant parallel resistor-capacitor circuit. However, studies have shown that the passive properties of membranes may be more appropriately modeled with a non-ideal capacitor, in which the current-voltage relationship is given by a fractional-order derivative. Fractional-order membrane potential dynamics introduce capacitive memory effects, i.e., dynamics are influenced by a weighted sum of the membrane potential prior history. However, it is not clear to what extent fractional-order dynamics may alter the properties of active excitable cells. In this study, we investigate the spiking properties of the neuronal membrane patch, nerve axon, and neural networks described by the fractional-order Hodgkin-Huxley neuron model. We find that in the membrane patch model, as fractional-order decreases, i.e., a greater influence of membrane potential memory, peak sodium and potassium currents are altered, and spike frequency and amplitude are generally reduced. In the nerve axon, the velocity of spike propagation increases as fractional-order decreases, while in a neural network, electrical activity is more likely to cease for smaller fractional-order. Importantly, we demonstrate that the modulation of the peak ionic currents that occurs for reduced fractional-order alone fails to reproduce many of the key alterations in spiking properties, suggesting that membrane capacitive memory and fractional-order membrane potential dynamics are important and necessary to reproduce neuronal electrical activity.     

Learning of Precise Spike Times with Homeostatic Membrane Potential Dependent Synaptic Plasticity

Precise spatio-temporal patterns of neuronal action potentials underly e.g. sensory representations and control of muscle activities. However, it is not known how the synaptic efficacies in the neuronal networks of the brain adapt such that they can reliably generate spikes at specific points in time. Existing activity-dependent plasticity rules like Spike-Timing-Dependent Plasticity are agnostic to the goal of learning spike times. On the other hand, the existing formal and supervised learning algorithms perform a temporally precise comparison of projected activity with the target, but there is no known biologically plausible implementation of this comparison. Here, we propose a simple and local unsupervised synaptic plasticity mechanism that is derived from the requirement of a balanced membrane potential. Since the relevant signal for synaptic change is the postsynaptic voltage rather than spike times, we call the plasticity rule Membrane Potential Dependent Plasticity (MPDP). Combining our plasticity mechanism with spike after-hyperpolarization causes a sensitivity of synaptic change to pre- and postsynaptic spike times which can reproduce Hebbian spike timing dependent plasticity for inhibitory synapses as was found in experiments. In addition, the sensitivity of MPDP to the time course of the voltage when generating a spike allows MPDP to distinguish between weak (spurious) and strong (teacher) spikes, which therefore provides a neuronal basis for the comparison of actual and target activity. For spatio-temporal input spike patterns our conceptually simple plasticity rule achieves a surprisingly high storage capacity for spike associations. The sensitivity of the MPDP to the subthreshold membrane potential during training allows robust memory retrieval after learning even in the presence of activity corrupted by noise. We propose that MPDP represents a biophysically plausible mechanism to learn temporal target activity patterns.     

Membrane potential synchrony in primary visual cortex during sensory stimulation

When the primary visual cortex (V1) is activated by sensory stimulation, what is the temporal correlation between the synaptic inputs to nearby neurons? This question underlies the origin of correlated activity, the mechanism of how visually evoked activity emerges and propagates in cortical circuits, and the relationship between spontaneous and evoked activity. Here, we have recorded membrane potential from pairs of V1 neurons in anesthetized cats and found that visual stimulation suppressed low-frequency membrane potential synchrony (0-10 Hz), and often increased synchrony at high frequencies (20-80 Hz). The increase in high-frequency synchrony occurred for neurons with similar orientation preferences and for neurons with different orientation preferences and occurred for a wide range of stimulus orientations. Thus, while only a subset of neurons spike in response to visual stimulation, a far larger proportion of the circuit is correlated with spiking activity through subthreshold, high-frequency synchronous activity that crosses functional domains.     

A Threshold Equation for Action Potential Initiation

In central neurons, the threshold for spike initiation can depend on the stimulus and varies between cells and between recording sites in a given cell, but it is unclear what mechanisms underlie this variability. Properties of ionic channels are likely to play a role in threshold modulation. We examined in models the influence of Na channel activation, inactivation, slow voltage-gated channels and synaptic conductances on spike threshold. We propose a threshold equation which quantifies the contribution of all these mechanisms. It provides an instantaneous time-varying value of the threshold, which applies to neurons with fluctuating inputs. We deduce a differential equation for the threshold, similar to the equations of gating variables in the Hodgkin-Huxley formalism, which describes how the spike threshold varies with the membrane potential, depending on channel properties. We find that spike threshold depends logarithmically on Na channel density, and that Na channel inactivation and K channels can dynamically modulate it in an adaptive way: the threshold increases with membrane potential and after every action potential. Our equation was validated with simulations of a previously published multicompartemental model of spike initiation. Finally, we observed that threshold variability in models depends crucially on the shape of the Na activation function near spike initiation (about −55 mV), while its parameters are adjusted near half-activation voltage (about −30 mV), which might explain why many models exhibit little threshold variability, contrary to experimental observations. We conclude that ionic channels can account for large variations in spike threshold.     

Membrane Potential Fluctuations Determine the Precision of Spike Timing and Synchronous Activity: A Model Study

It is much debated on what time scale information is encoded by neuronal spike activity. With a phenomenological model that transforms time-dependent membrane potential fluctuations into spike trains, we investigate constraints for the timing of spikes and for synchronous activity of neurons with common input. The model of spike generation has a variable threshold that depends on the time elapsed since the previous action potential and on the preceding membrane potential changes. To ensure that the model operates in a biologically meaningful range, the model was adjusted to fit the responses of a fly visual interneuron to motion stimuli. The dependence of spike timing on the membrane potential dynamics was analyzed. Fast membrane potential fluctuations are needed to trigger spikes with a high temporal precision. Slow fluctuations lead to spike activity with a rate about proportional to the membrane potential. Thus, for a given level of stochastic input, the frequency range of membrane potential fluctuations induced by a stimulus determines whether a neuron can use a rate code or a temporal code. The relationship between the steepness of membrane potential fluctuations and the timing of spikes has also implications for synchronous activity in neurons with common input. Fast membrane potential changes must be shared by the neurons to produce synchronous activity.     

神经元放电阈值的可变性及其意义

神经元能够将不同时空模式的突触输入转化为时序精确的动作电位输出，这种灵活、可靠的信息编码方式是神经集群在动态环境或特定任务下产生所需活动模式的重要基础。动作电位的产生遵循全或无规律，只有当细胞膜电压达到放电阈值时，神经元才产生动作电位。放电阈值在细胞内和细胞间具有高度可变性，具体动态依赖于刺激输入和放电历史。特别是，放电阈值对动作电位起始前的膜电压变化十分敏感，这种状态依赖性产生的生物物理根源包括Na⁺失活和K⁺激活。在绝大多数神经元中，动作电位的触发位置是轴突起始端，这个位置处的阈值可变性是决定神经元对时空输入转化规律的关键因素。但是，电生理实验中动作电位的记录位置却通常是胞体或近端树突，此处的阈值可变性高于轴突起始端，而其产生的重要根源是轴突动作电位的反向传播。基于胞体测量的相关研究显示，放电阈值动态能够增强神经元的时间编码、特征选择、增益调控和同时侦测能力。本文首先介绍放电阈值的概念及量化方法，然后详细梳理近年来国内外关于放电阈值可变性及产生根源的研究进展，在此基础上归纳总结放电阈值可变性对神经元编码的重要性，最后对未来放电阈值的研究方向进行展望。     

Calcium dependence of electrical and mechanical activity in rat ileum examined by the sucrose-gap technique

1. Single sucrose gap recordings showed that spontaneous action potentials of rat ileal smooth muscle consisted of slow waves and superimposed spikes which generated rhythmic contractions. As external potassium was raised, the resting potential progressively depolarized.2. Calcium-free salines inhibited spontaneous mechanical activity and inhibited the plateau phase of the action potential, but spontaneous spike depolarizations persisted.3. Verapamil, nifedipine and diltiazem all inhibited spontaneous mechanical activity and the plateau phase of the action potential, while in addition diltiazem augmented spike amplitude.4. Mn ions also inhibited mechanical activity and the action potential plateau, without affecting spike activity while the calcium ionophore A23187 enhanced both mechanical and electrical activity with a pronounced effect on spike amplitude.5. These results are consistent with the view that the plateau phase of the ileal smooth muscle action potential is dependent upon an influx of extracellular calcium possibly through voltage dependent slow calcium channels.     

Correlation of Transmitter Release with Membrane Properties of the Presynaptic Fiber of the Squid Giant Synapse

Depolarization of the presynaptic terminal by current produced a postsynaptic potential (PSP) which increased with increasing presynaptic polarization and then reached a plateau. Iontophoretic injection of tetraethylammonium ions (TEA) into the presynaptic axon near the terminal produced a prolonged presynaptic spike. The resulting PSP is increased in size and its time course closely followed that of the presynaptic spike. The presynaptic fiber no longer exhibited rectification and strong depolarizations revealed that the PSP reached a maximum with about 110 mv depolarization. Further depolarization produced a decrease in PSP amplitude and finally transmission was blocked. However, a PSP then always appeared on withdrawal of the depolarizing current. Under the conditions of these experiments, the PSP could be considered a direct measure of transmitter release. Bathing the TEA-injected synapse with concentrations of tetrodotoxin (TTX) sufficient to block spike activity in both pre- and postsynaptic axons did not greatly modify postsynaptic electrogenesis. However, doubling TTX concentration reversibly blocked PSP. Thus the permeability changes to Na and K accompanying the spike do not appear necessary for transmitter release. Some other processes related to the level of presynaptic polarization must be involved to explain the data. The inhibition of transmitter release by strong depolarizations appears to be related to Ca action. A membrane Ca current may also be necessary for normal transmitter release.     

Injection of Fully-Defined Signal Mixtures: A Novel High-Throughput Tool to Study Neuronal Encoding and Computations

Understanding of how neurons transform fluctuations of membrane potential, reflecting input activity, into spike responses, which communicate the ultimate results of single-neuron computation, is one of the central challenges for cellular and computational neuroscience. To study this transformation under controlled conditions, previous work has used a signal immersed in noise paradigm where neurons are injected with a current consisting of fluctuating noise that mimics on-going synaptic activity and a systematic signal whose transmission is studied. One limitation of this established paradigm is that it is designed to examine the encoding of only one signal under a specific, repeated condition. As a result, characterizing how encoding depends on neuronal properties, signal parameters, and the interaction of multiple inputs is cumbersome. Here we introduce a novel fully-defined signal mixture paradigm, which allows us to overcome these problems. In this paradigm, current for injection is synthetized as a sum of artificial postsynaptic currents (PSCs) resulting from the activity of a large population of model presynaptic neurons. PSCs from any presynaptic neuron(s) can be now considered as “signal”, while the sum of all other inputs is considered as “noise”. This allows us to study the encoding of a large number of different signals in a single experiment, thus dramatically increasing the throughput of data acquisition. Using this novel paradigm, we characterize the detection of excitatory and inhibitory PSCs from neuronal spike responses over a wide range of amplitudes and firing-rates. We show, that for moderately-sized neuronal populations the detectability of individual inputs is higher for excitatory than for inhibitory inputs during the 2–5 ms following PSC onset, but becomes comparable after 7–8 ms. This transient imbalance of sensitivity in favor of excitation may enhance propagation of balanced signals through neuronal networks. Finally, we discuss several open questions that this novel high-throughput paradigm may address.     

Lateral dendritic shunt inhibition can regularize mitral cell spike patterning

Mitral cells, the principal output neurons of the olfactory bulb, receive direct synaptic activation from primary sensory neurons. Shunting inhibitory inputs delivered by granule cell interneurons onto mitral cell lateral dendrites, while poorly positioned to prevent spike initiation, are believed to influence spike timing and underlie coordinated field potential oscillations. We investigated this phenomenon in a reduced compartmental mitral cell model suitable for incorporation into network simulations. Lateral dendritic shunt conductances delayed spiking to a degree dependent on both their electrotonic distance and phase of onset. Moreover, when the afferent activation of mitral cells was loosely coordinated in time, recurrent inhibition significantly narrowed the distribution of mitral cell spike times, illustrating a tendency towards coordinated synchronous activity. However, if mitral cell activity was initially disorganized, recurrent inhibition actually increased the variance in spike timing. This result suggests an essential role for early mechanisms of temporal coordination in olfaction, such as sniffing and the initial synchronization of mitral cell intrinsic oscillations by periglomerular cell-mediated inhibition.     

Role of voltage-dependent modulation of store Ca2+ release in synchronization of Ca2+ oscillations

Slow waves are rhythmic depolarizations that underlie mechanical activity of many smooth muscles. Slow waves result through rhythmic Ca(2+) release from intracellular Ca(2+) stores through inositol 1,4,5-trisphosphate (IP(3)) sensitive receptors and Ca(2+)-induced Ca(2+) release. Ca(2+) oscillations are transformed into membrane depolarizations by generation of a Ca(2+)-activated inward current. Importantly, the store Ca(2+) oscillations that underlie slow waves are entrained across many cells over large distances. It has been shown that IP(3) receptor-mediated Ca(2+) release is enhanced by membrane depolarization. Previous studies have implicated diffusion of Ca(2+) or the second messenger IP(3) across gap junctions in synchronization of Ca(2+) oscillations. In this study, a novel mechanism of Ca(2+) store entrainment through depolarization-induced IP(3) receptor-mediated Ca(2+) release is investigated. This mechanism is significantly different from chemical coupling-based mechanisms, as membrane potential has a coupling effect over distances several orders of magnitude greater than either diffusion of Ca(2+) or IP(3) through gap junctions. It is shown that electrical coupling acting through voltage-dependent modulation of store Ca(2+) release is able to synchronize oscillations of cells even when cells are widely separated and have different intrinsic frequencies of oscillation.     

Changes in response latencies of the mouse inferior colliculus neurons depending on the position and movement direction of the spectral contrast

Variability of response latency of neurons in the mouse inferior colliculus of (Mus musculus) to signals of notch noise and of noise band with regular varying of the notch/band center frequencies, have been studied. Plots of latency and spike count versus notch/band center frequency were constructed (latency functions and spike count functions). Spectral notch/noise band motion crossing boundaries of excitatory areas in the neurons frequency receptive field could produce latency function shifts (and appropriate to this spike count function shifts). Direction-dependent latency function and spike count function shifts were mostly seen for primary-like and V-shape neurons. The most interesting feature of directional sensitivity of inhibitory-dominated neurons was the selective shortening of latency and selective synchronization of the initial spikes (with appropriate to this spike count rise). The dynamic properties of inhibitory-dominated neurons can be explained on the basis of their selective sensitivity to position of spectral contrast in frequency receptive field, connected with disinhibition, and of the character of distribution of excitatory and inhibitory inputs. Manifestation of motion effects was influenced by spectral shape of noise signal and notch width.     

Dynamics of action potential initiation in the GABAergic thalamic reticular nucleus in vivo

Understanding the neural mechanisms of action potential generation is critical to establish the way neural circuits generate and coordinate activity. Accordingly, we investigated the dynamics of action potential initiation in the GABAergic thalamic reticular nucleus (TRN) using in vivo intracellular recordings in cats in order to preserve anatomically-intact axo-dendritic distributions and naturally-occurring spatiotemporal patterns of synaptic activity in this structure that regulates the thalamic relay to neocortex. We found a wide operational range of voltage thresholds for action potentials, mostly due to intrinsic voltage-gated conductances and not synaptic activity driven by network oscillations. Varying levels of synchronous synaptic inputs produced fast rates of membrane potential depolarization preceding the action potential onset that were associated with lower thresholds and increased excitability, consistent with TRN neurons performing as coincidence detectors. On the other hand the presence of action potentials preceding any given spike was associated with more depolarized thresholds. The phase-plane trajectory of the action potential showed somato-dendritic propagation, but no obvious axon initial segment component, prominent in other neuronal classes and allegedly responsible for the high onset speed. Overall, our results suggest that TRN neurons could flexibly integrate synaptic inputs to discharge action potentials over wide voltage ranges, and perform as coincidence detectors and temporal integrators, supported by a dynamic action potential threshold.     

Interval-counting neurons in the anuran auditory midbrain: factors underlying diversity of interval tuning

In anurans, the temporal patterning of sound pulses is the primary information used for differentiating between spectrally similar calls. One class of midbrain neurons, referred to as ‘interval-counting’ cells, appears to be particularly important for discriminating among calls that differ in pulse repetition rate (PRR). These cells only respond after several pulses are presented with appropriate interpulse intervals. Here we show that the range of selectivity and sharpness of interval tuning vary considerably across neurons. Whole-cell recordings revealed that neurons showing temporally summating excitatory postsynaptic potentials (EPSPs) with little or no inhibition or activity-dependent enhancement of excitation exhibited low-pass or band-pass tuning to slow PRRs. Neurons that showed inhibition and rate-dependent enhancement of excitation, however, were band-pass or high-pass to intermediate or fast PRRs. Surprisingly, across cells, interval tuning based on membrane depolarization and spike rate measures were not significantly correlated. Neurons that lacked inhibition showed the greatest disparities between these two measures of interval tuning. Cells that showed broad membrane potential-based tuning, for example, varied considerably in their spike rate-based tuning; narrow spike rate-based tuning resulted from ‘thresholding’ processes, whereby only the largest depolarizations triggered spikes. The potential constraints associated with generating interval tuning in this manner are discussed.