Dynamic influences on coincidence detection in neocortical pyramidal neurons

Increased Signal Delays and Unaltered Synaptic Input Pattern Recognition in Layer III Neocortical Pyramidal Neurons of the rTg4510 Mouse Model of Tauopathy: A Computer Simulation Study With Passive Membrane

Abnormal tau proteins are involved in pathology of many neurodegenerative disorders. Transgenic rTg4510 mice express high levels of human tau protein with P301L mutation linked to chromosome 17 that has been associated with frontotemporal dementia with parkinsonism. By 9 months of age, these mice recapitulate key features of human tauopathies, including presence of hyperphosphorylated tau and neurofibrillary tangles (NFTs) in brain tissue, atrophy and loss of neurons and synapses, and hyperexcitability of neurons, as well as cognitive deficiencies. We investigated effects of such human mutant tau protein on neuronal membrane, subthreshold dendritic signaling, and synaptic input pattern recognition/discrimination in layer III frontal transgenic (TG) pyramidal neurons of 9-month-old rTg4510 mice and compared these characteristics to those of wild-type (WT) pyramidal neurons from age-matched control mice. Passive segmental cable models of WT and TG neurons were set up in the NEURON simulator by using three-dimensionally reconstructed morphology and electrophysiological data of these cells. Our computer simulations predict leakage resistance and capacitance of neuronal membrane to be unaffected by the mutant tau protein. Computer models of TG neurons showed only modest alterations in distance dependence of somatopetal voltage and current transfers along dendrites and in rise times and half-widths of somatic Excitatory Postsynaptic Potential (EPSPs) relative to WT control. In contrast, a consistent and statistically significant slowdown was detected in the speed of simulated subthreshold dendritic signal propagation in all regions of the dendritic surface of mutant neurons. Predictors of synaptic input pattern recognition/discrimination remained unaltered in model TG neurons. This suggests that tau pathology is primarily associated with failures/loss in synaptic connections rather than with altered intraneuronal synaptic integration in neurons of affected networks.

Extracellular GABA waves regulate coincidence detection in excitatory circuits

KEY POINTS

Rapid changes in neuronal network activity trigger widespread waves of extracellular GABA in hippocampal neuropil. Elevations of extracellular GABA narrow the coincidence detection window for excitatory inputs to CA1 pyramidal cells. GABA transporters control the effect of extracellular GABA on coincidence detection. Small changes in the kinetics of dendritic excitatory currents amplify when reaching the soma.

ABSTRACT

Coincidence detection of excitatory inputs by principal neurons underpins the rules of signal integration and Hebbian plasticity in the brain. In the hippocampal circuitry, detection fidelity is thought to depend on the GABAergic synaptic input through a feedforward inhibitory circuit also involving the hyperpolarisation-activated Ih current. However, afferent connections often bypass feedforward circuitry, suggesting that a different GABAergic mechanism might control coincidence detection in such cases. To test whether fluctuations in the extracellular GABA concentration [GABA] could play a regulatory role here, we use a GABA 'sniffer' patch in acute hippocampal slices of the rat and document strong dependence of [GABA] on network activity. We find that blocking GABAergic signalling strongly widens the coincidence detection window of direct excitatory inputs to pyramidal cells whereas increasing [GABA] through GABA uptake blockade shortens it. The underlying mechanism involves membrane-shunting tonic GABAA receptor current; it does not have to rely on Ih but depends strongly on the neuronal GABA transporter GAT-1. We use dendrite-soma dual patch-clamp recordings to show that the strong effect of membrane shunting on coincidence detection relies on nonlinear amplification of changes in the decay of dendritic synaptic currents when they reach the soma. Our results suggest that, by dynamically regulating extracellular GABA, brain network activity can optimise signal integration rules in local excitatory circuits.

Kv3 K+ currents contribute to spike-timing in dorsal cochlear nucleus principal cells

Exposure to loud sound increases burst-firing of dorsal cochlear nucleus (DCN) fusiform cells in the auditory brainstem, which has been suggested to be an electrophysiological correlate of tinnitus. The altered activity of DCN fusiform cells may be due to down-regulation of high voltage-activated (Kv3-like) K⁺ currents. Whole cell current-clamp recordings were obtained from DCN fusiform cells in brain slices from P15-P18 CBA mice. We first studied whether acoustic over-exposure (performed at P15) or pharmacological inhibition of K⁺ currents with tetraethylamonium (TEA) affect fusiform cell action potential characteristics, firing frequency and spike-timing relative to evoking current stimuli. We then tested whether AUT1, a modulator of Kv3 K⁺ currents reverses the effects of sound exposure or TEA. Both loud sound exposure and TEA decreased the amplitude of action potential after-hyperpolarization, reduced the maximum firing frequency, and disrupted spike-timing. These treatments also increased post-synaptic voltage fluctuations at baseline. AUT1 applied in the presence of TEA or following acoustic over-exposure, did not affect the firing frequency, but enhanced action potential after-hyperpolarization, prevented the increased voltage fluctuations and restored spike-timing. Furthermore AUT1 prevented the occurrence of bursts. Our study shows that the effect on spike-timing is significantly correlated with the amplitude of the action potential after-hyperpolarization and the voltage fluctuations at baseline. In conclusion, modulation of putative Kv3 K⁺ currents may restore regular spike-timing of DCN fusiform cell firing following noise exposure, and could provide a means to restore deficits in temporal encoding observed during noise-induced tinnitus.

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Whole cell recordings were performed in dorsal cochlear nucleus fusiform cells.

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Spike-timing is dependent on the action potential after-hyperpolarization.

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Spike-timing is dependent on synaptic baseline voltage fluctuations.

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Inhibition of K⁺ currents using TEA or acoustic over-exposure disrupt spike-timing.

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AUT1, a Kv3.1/3.2 K⁺ current modulator, counteracts the disruptive effects on spike-timing.

The past, present, and future of real-time control in cellular electrophysiology

For over 60 years, real-time control has been an important technique in the study of excitable cells. Two such control-based technologies are reviewed here. First, voltage-clamp methods revolutionized the study of excitable cells. In this family of techniques, membrane potential is controlled, allowing one to parameterize a powerful class of models that describe the voltage-current relationship of cell membranes simply, flexibly, and accurately. Second, dynamic-clamp methods allow the addition of new, "virtual" membrane mechanisms to living cells. Dynamic clamp allows researchers unprecedented ways of testing computationally based hypotheses in biological preparations. The review ends with predictions of how control-based technologies will be improved and adapted for new uses in the near future.

Comparison of intensity-dependent inhibition of spinal wide-dynamic range neurons by dorsal column and peripheral nerve stimulation in a rat model of neuropathic pain

BACKGROUND

Spinal cord stimulation (SCS) and peripheral nerve stimulation (PNS) are thought to reduce pain by activating a sufficient number of large myelinated (Aβ) fibres, which in turn initiate spinal segmental mechanisms of analgesia. However, the volume of neuronal activity and how this activity is associated with different treatment targets is unclear under neuropathic pain conditions.

METHODS

We sought to delineate the intensity-dependent mechanisms of SCS and PNS analgesia by in vivo extracellular recordings from spinal wide-dynamic range neurons in nerve-injured rats. To mimic therapeutic SCS and PNS, we used bipolar needle electrodes and platinum hook electrodes to stimulate the dorsal column and the tibial nerve, respectively. Compound action potentials were recorded to calibrate the amplitude of conditioning stimulation required to activate A-fibres and thus titrate the volume of activation.

RESULTS

Dorsal column stimulation (50 Hz, five intensities) inhibited the windup (a short form of neuronal sensitization) and the C-component response of wide-dynamic range neurons to graded intracutaneous electrical stimuli in an intensity-dependent manner. Tibial nerve stimulation (50 Hz, three intensities) also suppressed the windup in an intensity-dependent fashion but did not affect the acute C-component response.

CONCLUSIONS

SCS and PNS may offer similar inhibition of short-term neuronal sensitization. However, only SCS attenuates spinal transmission of acute noxious inputs under neuropathic pain conditions. Our findings begin to differentiate peripheral from spinal-targeted neuromodulation therapies and may help to select the best stimulation target and optimum therapeutic intensity for pain treatment.

The role of coincidence-detector neurons in the reliability and precision of subthreshold signal detection in noise

Subthreshold signal detection is an important task for animal survival in complex environments, where noise increases both the external signal response and the spontaneous spiking of neurons. The mechanism by which neurons process the coding of signals is not well understood. Here, we propose that coincidence detection, one of the ways to describe the functionality of a single neural cell, can improve the reliability and the precision of signal detection through detection of presynaptic input synchrony. Using a simplified neuronal network model composed of dozens of integrate-and-fire neurons and a single coincidence-detector neuron, we show how the network reads out the subthreshold noisy signals reliably and precisely. We find suitable pairing parameters, the threshold and the detection time window of the coincidence-detector neuron, that optimize the precision and reliability of the neuron. Furthermore, it is observed that the refractory period induces an oscillation in the spontaneous firing, but the neuron can inhibit this activity and improve the reliability and precision further. In the case of intermediate intrinsic states of the input neuron, the network responds to the input more efficiently. These results present the critical link between spiking synchrony and noisy signal transfer, which is utilized in coincidence detection, resulting in enhancement of temporally sensitive coding scheme.

Tonotopic tuning in a sound localization circuit

Nucleus laminaris (NL) neurons encode interaural time difference (ITD), the cue used to localize low-frequency sounds. A physiologically based model of NL input suggests that ITD information is contained in narrow frequency bands around harmonics of the sound frequency. This suggested a theory, which predicts that, for each tone frequency, there is an optimal time course for synaptic inputs to NL that will elicit the largest modulation of NL firing rate as a function of ITD. The theory also suggested that neurons in different tonotopic regions of NL require specialized tuning to take advantage of the input gradient. Tonotopic tuning in NL was investigated in brain slices by separating the nucleus into three regions based on its anatomical tonotopic map. Patch-clamp recordings in each region were used to measure both the synaptic and the intrinsic electrical properties. The data revealed a tonotopic gradient of synaptic time course that closely matched the theoretical predictions. We also found postsynaptic band-pass filtering. Analysis of the combined synaptic and postsynaptic filters revealed a frequency-dependent gradient of gain for the transformation of tone amplitude to NL firing rate modulation. Models constructed from the experimental data for each tonotopic region demonstrate that the tonotopic tuning measured in NL can improve ITD encoding across sound frequencies.

Adaptation of firing rate and spike-timing precision in the avian cochlear nucleus

Adaptation is commonly defined as a decrease in response to a constant stimulus. In the auditory system such adaptation is seen at multiple levels. However, the first-order central neurons of the interaural time difference detection circuit encode information in the timing of spikes rather than the overall firing rate. We investigated adaptation during in vitro whole-cell recordings from chick nucleus magnocellularis neurons. Injection of noisy, depolarizing current caused an increase in firing rate and a decrease in spike time precision that developed over approximately 20 s. This adaptation depends on sustained depolarization, is independent of firing, and is eliminated by alpha-dendrotoxin (0.1 microM), implicating slow inactivation of low-threshold voltage-activated K+ channels as its mechanism. This process may alter both firing rate and spike-timing precision of phase-locked inputs to coincidence detector neurons in nucleus laminaris and thereby adjust the precision of sound localization.

Regulation of information passing by synaptic transmission: a short review

The largest part of information passed among neurons in the brain occurs by the means of chemical synapses connecting the axons of presynaptic neurons to the dendritic tree of the postsynaptic ones. In the present paper, the most relevant open problems related to the mechanisms of control of the information passing among neurons by synaptic transmission will be shortly reviewed. The "cross talking" between synapses, their mutual interactions and the control of the information flow between different areas of the dendritic tree will be also considered. The threshold mechanism based on the "reversal potential" will be considered for its role in the control of information transfer among neurons and also for its contribution to the information flow among different areas of the dendritic tree and to the computational ability of the single neuron. The concept of "competition for plasticity" will be proposed as a mechanism of competition based on the synaptic activation time.

Gamma oscillations and stimulus selection

More coherent excitatory stimuli are known to have a competitive advantage over less coherent ones. We show here that this advantage is amplified greatly when the target includes inhibitory interneurons acting via GABA(A)-receptor-mediated synapses and the coherent input oscillates at gamma frequency. We hypothesize that therein lies, at least in part, the functional significance of the experimentally observed link between attentional biasing of stimulus competition and gamma frequency rhythmicity.

Development of gerbil medial superior olive: integration of temporally delayed excitation and inhibition at physiological temperature

The sensitivity of medial superior olive (MSO) neurons to tens of microsecond differences in interaural temporal delay (ITD) derives in part from their membrane electrical characteristics, kinetics and timing of excitatory and inhibitory inputs, and dendrite structure. However, maturation of these physiological and structural characteristics are little studied, especially in relationship to the onset of auditory experience. We showed, using brain slices at physiological temperature, that MSO neurons exhibited sensitivity to simulated temporally delayed (TD) EPSCs (simEPSC), injected through the recording electrode, by the initial phase of hearing onset at P10, and TD sensitivity was reduced by block of low threshold potassium channels. The spike generation mechanism matured between P10 and P16 to support TD sensitivity to adult-like excitatory stimuli (1-4 ms duration) by P14. IPSP duration was shorter at physiological temperature than reported for lower temperatures, was longer than EPSP duration at young ages, but approached the duration of EPSPs by P16, when hearing thresholds neared maturity. Dendrite branching became less complex over a more restricted time frame between P10 and P12. Because many physiological and structural properties approximated mature values between P14 and P16, we studied temporal integration of simEPSCs and IPSPs at P15. Only a narrow range of relative onset times (< 1 ms) yielded responses showing sensitivity to TD. We propose that shaping of excitatory circuitry to mediate TD sensitivity can begin before airborne sound is detectable, and that inhibitory inputs having suboptimal neural delays may then be pruned by cellular mechanisms activated by sensitivity to ITD.

Coincidence-enhanced stochastic resonance: experimental evidence challenges the psychophysical theory behind stochastic resonance

Stochastic resonance (SR) is the counterintuitive phenomenon in which noise enhances detection of sub-threshold stimuli. The SR psychophysical threshold theory establishes that the required amplitude to exceed the sensory threshold barrier can be reached by adding noise to a sub-threshold stimulus. The aim of this study was to test the SR theory by comparing detection results from two different randomly-presented stimulus conditions. In the first condition, optimal noise was present during the whole attention interval; in the second, the optimal noise was restricted to the same time interval as the stimulus. SR threshold theory predicts no difference between the two conditions because noise helps the sub-threshold stimulus to reach threshold in both cases. The psychophysical experimental method used a 300 ms rectangular force pulse as a stimulus within an attention interval of 1.5 s, applied to the index finger of six human subjects in the two distinct conditions. For all subjects we show that in the condition in which the noise was present only when synchronized with the stimulus, detection was better (p<0.05) than in the condition in which the noise was delivered throughout the attention interval. These results provide the first direct evidence that SR threshold theory is incomplete and that a new phenomenon has been identified, which we call Coincidence-Enhanced Stochastic Resonance (CESR). We propose that CESR might occur because subject uncertainty is reduced when noise points at the same temporal window as the stimulus.

Action potential timing precision in dorsal cochlear nucleus pyramidal cells

Many studies of the dorsal cochlear nucleus (DCN) have focused on the representation of acoustic stimuli in terms of average firing rate. However, recent studies have emphasized the role of spike timing in information encoding. We sought to ascertain whether DCN pyramidal cells might employ similar strategies and to what extent intrinsic excitability regulates spike timing. Gaussian distributed low-pass noise current was injected into pyramidal cells in a brain slice preparation. The shuffled autocorrelation-based analysis was used to compute a correlation index of spike times across trials. The noise causes the cells to fire with temporal precision (SD congruent with 1-2 ms) and high reproducibility. Increasing the coefficient of variation of the noise improved the reproducibility of the spike trains, whereas increasing the firing rate of the neuron decreased the neurons' ability to respond with predictable patterns of spikes. Simulated inhibitory postsynaptic potentials superimposed on the noise stimulus enhanced spike timing for >300 ms, although the enhancement was greatest during the first 100 ms. We also found that populations of pyramidal neurons respond to the same noise stimuli with correlated spike trains, suggesting that ensembles of neurons in the DCN receiving shared input can fire with similar timing. These results support the hypothesis that spike timing can be an important aspect of information coding in the DCN.

Dopamine D1 receptor activation regulates sodium channel-dependent EPSP amplification in rat prefrontal cortex pyramidal neurons

Dopamine (DA) effects on prefrontal cortex (PFC) neurons are essential for the cognitive functions mediated by this cortical area. However, the cellular mechanisms of DA neuromodulation in neocortex are not well understood. We characterized the effects of D1-type DA receptor (D1R) activation on the amplification (increase in duration and area) of excitatory postsynaptic potentials (EPSPs) at depolarized potentials, in layer 5 pyramidal neurons from rat PFC. Simulated EPSPs (sEPSPs) were elicited by current injection, to determine the effects of D1R activation independent of modulation of transmitter release or glutamate receptor currents. Application of the D1R agonist SKF81297 attenuated sEPSP amplification at depolarized potentials in a concentration-dependent manner. The SKF81297 effects were inhibited by the D1R antagonist SCH23390. The voltage-gated Na+ channel blocker tetrodotoxin (TTX) abolished the effects of SKF81297 on sEPSP amplification, suggesting that Na+ currents are necessary for the D1R effect. Furthermore, blockade of 4-AP- and TEA-sensitive K+ channels in the presence of TTX significantly increased EPSP amplification, arguing against the possibility that SKF81297 up-regulates currents that attenuate sEPSP amplification. SKF81297 application attenuated the subthreshold response to injection of depolarizing current ramps, in a manner consistent with a decrease in the persistent Na+ current. In addition, D1R activation decreased the effectiveness of temporal EPSP summation during 20 Hz sEPSP trains, selectively at depolarized membrane potentials. Therefore, the effects of D1R activation on Na+ channel-dependent EPSP amplification may regulate the impact of coincidence detection versus temporal integration mechanisms in PFC pyramidal neurons.

Spike timing and reliability in cortical pyramidal neurons: effects of EPSC kinetics, input synchronization and background noise on spike timing

In vivo studies have shown that neurons in the neocortex can generate action potentials at high temporal precision. The mechanisms controlling timing and reliability of action potential generation in neocortical neurons, however, are still poorly understood. Here we investigated the temporal precision and reliability of spike firing in cortical layer V pyramidal cells at near-threshold membrane potentials. Timing and reliability of spike responses were a function of EPSC kinetics, temporal jitter of population excitatory inputs, and of background synaptic noise. We used somatic current injection to mimic population synaptic input events and measured spike probability and spike time precision (STP), the latter defined as the time window (Δt) holding 80% of response spikes. EPSC rise and decay times were varied over the known physiological spectrum. At spike threshold level, EPSC decay time had a stronger influence on STP than rise time. Generally, STP was highest (≤2.45 ms) in response to synchronous compounds of EPSCs with fast rise and decay kinetics. Compounds with slow EPSC kinetics (decay time constants>6 ms) triggered spikes at lower temporal precision (≥6.58 ms). We found an overall linear relationship between STP and spike delay. The difference in STP between fast and slow compound EPSCs could be reduced by incrementing the amplitude of slow compound EPSCs. The introduction of a temporal jitter to compound EPSCs had a comparatively small effect on STP, with a tenfold increase in jitter resulting in only a five fold decrease in STP. In the presence of simulated synaptic background activity, precisely timed spikes could still be induced by fast EPSCs, but not by slow EPSCs.

Correlated neural activity as the driving force for functional changes in auditory cortex

The functional role of neural synchrony is reflected in cortical tonotopic map reorganization and in the emergence of pathological phenomena such as tinnitus. First of all experimenter-centered and subject-centered views of neural activity will be contrasted; this argues against the use of stimulus-correction procedures and favors the use of a correction procedure based on neural activity without reference to stimulus timing. Within a cortical column neurons fired synchronously with on average about 6% of their spikes in a 1 ms bin and occasionally showing 30% or more of such coincident spikes. For electrode separations exceeding 200 microm the average peak correlation strength only occasionally reached 3%. The experimental evidence for coincidence of neural activity, neural correlation and neural synchrony shows that horizontal fibers activity can induce strong neural correlations. Cortico-cortical connections for a large part connect cell groups with characteristic frequencies differing by more than one octave. Such neurons have generally non-overlapping receptive fields but still can have sizeable peak cross-correlations. Correlated neural activity and heterotopic neural interconnections are presented as the substrates for cortical reorganization; increased neural synchrony and tonotopic map reorganization go hand in hand. This links cortical reorganization with hypersynchrony that can be considered as an important driving force underlying tinnitus.

Dynamic clamp analyses of cardiac, endocrine, and neural function

The dynamic clamp introduces artificial conductances into cells to simulate electrical coupling, votage-dependent, leak, and synaptic conductances. This review describes how the dynamic clamp has been used to address various questions in the cardiac, endocrine, and nervous systems.

Diversity of gain modulation by noise in neocortical neurons: regulation by the slow afterhyperpolarization conductance

Neuronal firing is known to depend on the variance of synaptic input as well as the mean input current. Several studies suggest that input variance, or "noise," has a divisive effect, reducing the slope or gain of the firing frequency-current (f-I) relationship. We measured the effects of current noise on f-I relationships in pyramidal neurons and fast-spiking (FS) interneurons in slices of rat sensorimotor cortex. In most pyramidal neurons, noise had a multiplicative effect on the steady-state f-I relationship, increasing gain. In contrast, noise reduced gain in FS interneurons. Gain enhancement in pyramidal neurons increased with stimulus duration and was correlated with the amplitude of the slow afterhyperpolarization (sAHP), a major mechanism of spike-frequency adaptation. The 5-HT2 receptor agonist alpha-methyl-5-HT reduced the sAHP and eliminated gain increases, whereas augmenting the sAHP conductance by spike-triggered dynamic-current clamp enhanced the gain increase. These results indicate that the effects of noise differ fundamentally between classes of neocortical neurons, depending on specific biophysical properties including the sAHP conductance. Thus, noise from background synaptic input may enhance network excitability by increasing gain in pyramidal neurons with large sAHPs and reducing gain in inhibitory FS interneurons.

Statistics of subthreshold neuronal voltage fluctuations due to conductance-based synaptic shot noise

Neurons in the central nervous system, and in the cortex in particular, are subject to a barrage of pulses from their presynaptic populations. These synaptic pulses are mediated by conductance changes and therefore lead to increases or decreases of the neuronal membrane potential with amplitudes that are dependent on the voltage: synaptic noise is multiplicative. The statistics of the membrane potential are of experimental interest because the measurement of a single subthreshold voltage can be used to probe the activity occurring across the presynaptic population. Though the interpulse interval is not always significantly smaller than the characteristic decay time of the pulses, and so the fluctuations have the nature of shot noise, the majority of results available in the literature have been calculated in the diffusion limit, which is valid for high-rate pulses. Here the effects that multiplicative conductance noise and shot noise have on the voltage fluctuations are examined. It is shown that both these aspects of synaptic drive sculpt high-order features of the subthreshold voltage distribution, such as the skew. It is further shown that the diffusion approximation can only capture the effects arising from the multiplicative conductance noise, predicting a negative voltage skew for excitatory drive. Exact results for the full dynamics are derived from a master-equation approach, predicting positively skewed distributions with long tails in voltage ranges typical for action potential generation. It is argued that, although the skew is a high-order feature of subthreshold voltage distributions, the increased probability of reaching firing threshold suggests a potential role for shot noise in shaping the neuronal transfer function.

Short-term synaptic depression causes a non-monotonic response to correlated stimuli

Unreliability is a ubiquitous feature of synaptic transmission in the brain. The information conveyed in the discharges of an ensemble of cells (e.g., in the spike count or in the timing of synchronous events) may not be faithfully transmitted to the postsynaptic cell because a large fraction of the spikes fail to elicit a synaptic response. In addition, short-term depression increases the failure rate with the presynaptic activity. We use a simple neuron model with stochastic depressing synapses to understand the transformations undergone by the spatiotemporal patterns of incoming spikes as these are first converted into synaptic current and afterward into the cell response. We analyze the mean and SD of the current produced by different stimuli with spatiotemporal correlations. We find that the mean, which carries information only about the spike count, rapidly saturates as the input rate increases. In contrast, the current deviation carries information about the correlations. If the afferent action potentials are uncorrelated, it saturates monotonically, whereas if they are correlated it increases, reaches a maximum, and then decreases to the value produced by the uncorrelated stimulus. This means that, at high input rates, depression erases from the synaptic current any trace of the spatiotemporal structure of the input. The non-monotonic behavior of the deviation can be inherited by the response rate provided that the mean current saturates below the current threshold setting the cell in the fluctuation-driven regimen. Afferent correlations therefore enable the modulation of the response beyond the saturation of the mean current.

Bidirectional modulation of neuronal responses by depolarizing GABAergic inputs

The reversal potential of GABAA receptor channels is known to be less negative than the resting membrane potential under some cases. Recent electrophysiological experiments revealed that a GABAergic unitary conductance with such a depolarized reversal potential could not only prevent but also facilitate action potential generation depending on the timing of its application relative to the excitatory unitary conductance. Using a two-dimensional point neuron model, we simulate the experiments regarding the integration of unitary conductances, and execute bifurcation analysis. Then we extend our analysis to the case in which the neuron receives two kinds of periodic input trains-an excitatory one and a GABAergic one. We show that the periodic depolarizing GABAergic input train can modulate the output time-averaged firing rate bidirectionally, namely as an increase or a decrease, in a devil's-staircase-like manner depending on the phase difference with the excitatory input train. Bifurcation analysis reveals the existence of a wide variety of phase-locked solutions underlying such a graded response of the neuron. We examine how the input time-width and the value of the GABAA reversal potential affect the response. Moreover, considering a neuronal population, we show that depolarizing GABAergic inputs bidirectionally modulate the amplitude of the oscillatory population activity.

Stimulus Competition by Inhibitory Interference

When two stimuli are present in the receptive field of a V4 neuron, the firing rate response is between the weakest and strongest response elicited by each of the stimuli when presented alone (Reynolds, Chelazzi, & Desimone, 1999). When attention is directed toward the stimulus eliciting the strongest response (the preferred stimulus), the response to the pair is increased, whereas the response decreases when attention is directed to the other stimulus (the poor stimulus). When attention is directed to either of the two stimuli presented alone, the firing rate remains the same or increases slightly, but the coherence between the neuron's spike train and the local field potential can increase (Fries, Reynolds, Rorie, & Desimone, 2001). These experimental results were reproduced in a model of a V4 neuron under the assumption that attention modulates the activity of local interneuron networks. The V4 model neuron received stimulus-specific excitation from V2 and synchronous inhibitory inputs from two local interneuron networks in V4. Each interneuron network was driven by stimulus-specific excitatory inputs from V2 and was modulated by the activity of the frontal eye fields. Stimulus competition was present because of a delay in arrival time of synchronous volleys from each interneuron network. For small delays, the firing rate was close to the rate elicited by the preferred stimulus alone, whereas for larger delays, it approached the firing rate of the poor stimulus. When either stimulus was presented alone, the neuron's response was not altered by the change in delay, but could change due to modulation of the degree of synchrony of the corresponding interneuron network. The model suggests that top-down attention biases the competition between V2 columns for control of V4 neurons primarily by changing the relative timing of inhibition, whereas changes in the degree of synchrony of interneuron networks modulate the response to a single stimulus. The new mechanism proposed here for attentional modulation of firing rate, gain modulation by inhibitory interference, is likely to have more general applicability to cortical information processing.

Maturation of glycinergic inhibition in the gerbil medial superior olive after hearing onset

The neurones of the medial superior olive (MSO) are the most temporally sensitive neurones in the brain. They respond to the arrival time difference of sound at the two ears with a microsecond resolution; these interaural time differences are used to localize low-frequency sounds. In addition to the excitatory inputs from each ear, the MSO neurones also receive binaural glycinergic projections, which have a critical role in sound localization processing. Recently, it was shown that the glycinergic input to the MSO undergoes an experience-dependent structural reorganization after hearing onset. To explore the maturation of inhibition during the development of sound localization on a cellular level, glycinergic currents and potentials were measured in gerbil MSO principal cells from postnatal (P) day P12-P25 by whole-cell patch-clamp recordings. The synaptic glycinergic currents accelerated to rapid decay kinetics (approximately 2 ms) and rise times (approximately 0.4 ms) after hearing onset, reaching maturity around P17. Since the kinetics of miniature glycinergic currents did not change with age, it is likely that a higher degree of transmitter release synchrony is the underlying mechanism influencing the acceleration of the kinetics. During the same period, the synaptic glycinergic potentials accelerated four-fold, largely as a result of a prominent decrease in input resistance. In accordance with a reorganization of the glycinergic inputs, the evoked peak conductances decreased more than two-fold, together with a three-fold reduction in the frequency of miniature events after hearing onset. These age-dependent changes were absent in animals that had been reared in omni-directional noise, indicating that an experience-dependent pruning of synaptic inputs is important for the maturation of functional inhibition in the MSO. Taken together, these striking developmental adjustments of the glycinergic inhibition in the MSO most probably reflect an adaptation to improve the encoding of auditory cues with great temporal precision and fidelity during the maturation of sound localization behaviour.

Synaptic shot noise and conductance fluctuations affect the membrane voltage with equal significance

The subthreshold membrane voltage of a neuron in active cortical tissue is a fluctuating quantity with a distribution that reflects the firing statistics of the presynaptic population. It was recently found that conductance-based synaptic drive can lead to distributions with a significant skew. Here it is demonstrated that the underlying shot noise caused by Poissonian spike arrival also skews the membrane distribution, but in the opposite sense. Using a perturbative method, we analyze the effects of shot noise on the distribution of synaptic conductances and calculate the consequent voltage distribution. To first order in the perturbation theory, the voltage distribution is a gaussian modulated by a prefactor that captures the skew. The gaussian component is identical to distributions derived using current-based models with an effective membrane time constant. The well-known effective-time-constant approximation can therefore be identified as the leading-order solution to the full conductance-based model. The higher-order modulatory prefactor containing the skew comprises terms due to both shot noise and conductance fluctuations. The diffusion approximation misses these shot-noise effects implying that analytical approaches such as the Fokker-Planck equation or simulation with filtered white noise cannot be used to improve on the gaussian approximation. It is further demonstrated that quantities used for fitting theory to experiment, such as the voltage mean and variance, are robust against these non-Gaussian effects. The effective-time-constant approximation is therefore relevant to experiment and provides a simple analytic base on which other pertinent biological details may be added.

Dynamic spatiotemporal synaptic integration in cortical neurons: neuronal gain, revisited

Gain modulation is a ubiquitous phenomenon in cortical neurons, providing flexibility to operate under changing conditions. The prevailing view is that this modulation reflects a change in the relationship between mean input and output firing rate brought about by variation in neuronal membrane characteristics. An alternative mechanism is proposed for neuronal gain modulation that takes into account the capability of cortical neurons to process spatiotemporal synaptic correlations. Through the use of numerical simulations, it is shown that voltage-gated and leak conductances, membrane potential, noise, and input firing rate modify the sensitivity of cortical neurons to the degree of temporal correlation between their synaptic inputs. These changes are expressed in a change of the temporal window for synaptic integration and the range of input correlation over which response probability is graded. The study also demonstrates that temporal integration depends on the distance between the inputs and that this interplay of space and time is modulated by voltage-gated and leak conductances. Thus, gain modulation may reflect a change in the relationship between spatiotemporal synaptic correlations and output firing probability. It is further proposed that by acting synergistically with the network, dynamic spatiotemporal synaptic integration in cortical neurons may serve a functional role in the formation of dynamic cell assemblies.

Possible effects of depolarizing GABAA conductance on the neuronal input-output relationship: a modeling study

Recent in vitro experiments revealed that the GABAA reversal potential is about 10 mV higher than the resting potential in mature mammalian neocortical pyramidal cells; thus GABAergic inputs could have facilitatory, rather than inhibitory, effects on action potential generation under certain conditions. However, how the relationship between excitatory input conductances and the output firing rate is modulated by such depolarizing GABAergic inputs under in vivo circumstances has not yet been understood. We examine herewith the input-output relationship in a simple conductance-based model of cortical neurons with the depolarized GABAA reversal potential, and show that a tonic depolarizing GABAergic conductance up to a certain amount does not change the relationship between a tonic glutamatergic driving conductance and the output firing rate, whereas a higher GABAergic conductance prevents spike generation. When the tonic glutamatergic and GABAergic conductances are replaced by in vivo-like highly fluctuating inputs, on the other hand, the effect of depolarizing GABAergic inputs on the input-output relationship critically depends on the degree of coincidence between glutamatergic input events and GABAergic ones. Although a wide range of depolarizing GABAergic inputs hardly changes the firing rate of a neuron driven by noncoincident glutamatergic inputs, a certain range of these inputs considerably decreases the firing rate if a large number of driving glutamatergic inputs are coincident with them. These results raise the possibility that the depolarized GABAA reversal potential is not a paradoxical mystery, but is instead a sophisticated device for discriminative firing rate modulation.