The dynamical response properties of neocortical neurons to temporally modulated noisy inputs in vitro.
ABSTRACT: Cortical neurons are often classified by current-frequency relationship. Such a static description is inadequate to interpret neuronal responses to time-varying stimuli. Theoretical studies suggested that single-cell dynamical response properties are necessary to interpret ensemble responses to fast input transients. Further, it was shown that input-noise linearizes and boosts the response bandwidth, and that the interplay between the barrage of noisy synaptic currents and the spike-initiation mechanisms determine the dynamical properties of the firing rate. To test these model predictions, we estimated the linear response properties of layer 5 pyramidal cells by injecting a superposition of a small-amplitude sinusoidal wave and a background noise. We characterized the evoked firing probability across many stimulation trials and a range of oscillation frequencies (1-1000 Hz), quantifying response amplitude and phase-shift while changing noise statistics. We found that neurons track unexpectedly fast transients, as their response amplitude has no attenuation up to 200 Hz. This cut-off frequency is higher than the limits set by passive membrane properties (approximately 50 Hz) and average firing rate (approximately 20 Hz) and is not affected by the rate of change of the input. Finally, above 200 Hz, the response amplitude decays as a power-law with an exponent that is independent of voltage fluctuations induced by the background noise.
Project description:At low stimulation rates, electrically stimulated auditory nerve fibers typically fire regularly, in lock-step to the applied stimulus. At high stimulation rates, however, these same fibers fire irregularly. Firing irregularity has been attributed to the random opening and closing of voltage-gated sodium channels at the spike generation site. We demonstrate, however, that the nonlinear dynamics of neural excitation and refractoriness embodied in the FitzHugh-Nagumo (FN) model produce realistic firing irregularity at high stimulus rates, even in the complete absence of ongoing physiological noise. Indeed, we show that ongoing noise can actually regularize the response at low discharge rates. The degree of stimulus-dependent irregularity is determined not so much by the level of ongoing physiological noise as by the dynamical instability. Our work suggests that the dynamical instability, quantified by the Lyapunov exponent, controls neural sensitivity to input signals and to physiological noise, as well the amount of mutual desynchronization between similarly stimulated fibers. This instability, quantified by the value of the Lyapunov exponent, may play a critical role in determining modulation sensitivity and dynamic range in cochlear implants.
Project description:The effects of noise on neuronal dynamical systems are of much current interest. Here, we investigate noise-induced changes in the rhythmic firing activity of single Hodgkin-Huxley neurons. With additive input current, there is, in the absence of noise, a critical mean value mu=mu(c) above which sustained periodic firing occurs. With initial conditions as resting values, for a range of values of the mean micro near the critical value, we have found that the firing rate is greatly reduced by noise, even of quite small amplitudes. Furthermore, the firing rate may undergo a pronounced minimum as the noise increases. This behavior has the opposite character to stochastic resonance and coherence resonance. We found that these phenomena occurred even when the initial conditions were chosen randomly or when the noise was switched on at a random time, indicating the robustness of the results. We also examined the effects of conductance-based noise on Hodgkin-Huxley neurons and obtained similar results, leading to the conclusion that the phenomena occur across a wide range of neuronal dynamical systems. Further, these phenomena will occur in diverse applications where a stable limit cycle coexists with a stable focus.
Project description:Fundamental properties of phasic firing neurons are usually characterized in a noise-free condition. In the absence of noise, phasic neurons exhibit Class 3 excitability, which is a lack of repetitive firing to steady current injections. For time-varying inputs, phasic neurons are band-pass filters or slope detectors, because they do not respond to inputs containing exclusively low frequencies or shallow slopes. However, we show that in noisy conditions, response properties of phasic neuron models are distinctly altered. Noise enables a phasic model to encode low-frequency inputs that are outside of the response range of the associated deterministic model. Interestingly, this seemingly stochastic-resonance (SR) like effect differs significantly from the classical SR behavior of spiking systems in both the signal-to-noise ratio and the temporal response pattern. Instead of being most sensitive to the peak of a subthreshold signal, as is typical in a classical SR system, phasic models are most sensitive to the signal's rising and falling phases where the slopes are steep. This finding is consistent with the fact that there is not an absolute input threshold in terms of amplitude; rather, a response threshold is more properly defined as a stimulus slope/frequency. We call the encoding of low-frequency signals with noise by phasic models a slope-based SR, because noise can lower or diminish the slope threshold for ramp stimuli. We demonstrate here similar behaviors in three mechanistic models with Class 3 excitability in the presence of slow-varying noise and we suggest that the slope-based SR is a fundamental behavior associated with general phasic properties rather than with a particular biological mechanism.
Project description:Previous studies have shown that neurons within the vestibular nuclei (VN) can faithfully encode the time course of sensory input through changes in firing rate in vivo. However, studies performed in vitro have shown that these same VN neurons often display nonlinear synchronization (i.e. phase locking) in their spiking activity to the local maxima of sensory input, thereby severely limiting their capacity for faithful encoding of said input through changes in firing rate. We investigated this apparent discrepancy by studying the effects of in vivo conditions on VN neuron activity in vitro using a simple, physiologically based, model of cellular dynamics. We found that membrane potential oscillations were evoked both in response to step and zap current injection for a wide range of channel conductance values. These oscillations gave rise to a resonance in the spiking activity that causes synchronization to sinusoidal current injection at frequencies below 25 Hz. We hypothesized that the apparent discrepancy between VN response dynamics measured in in vitro conditions (i.e., consistent with our modeling results) and the dynamics measured in vivo conditions could be explained by an increase in trial-to-trial variability under in vivo vs. in vitro conditions. Accordingly, we mimicked more physiologically realistic conditions in our model by introducing a noise current to match the levels of resting discharge variability seen in vivo as quantified by the coefficient of variation (CV). While low noise intensities corresponding to CV values in the range 0.04-0.24 only eliminated synchronization for low (<8 Hz) frequency stimulation but not high (>12 Hz) frequency stimulation, higher noise intensities corresponding to CV values in the range 0.5-0.7 almost completely eliminated synchronization for all frequencies. Our results thus predict that, under natural (i.e. in vivo) conditions, the vestibular system uses increased variability to promote fidelity of encoding by single neurons. This prediction can be tested experimentally in vitro.
Project description:What type of principle features intrinsic inside of the fluctuated input signals could drive neurons with the maximal excitations is one of the crucial neural coding issues. In this article, we examined both experimentally and theoretically the cortical neuronal responsivity (including firing rate and spike timing reliability) to input signals with different intrinsic correlational statistics (e.g., white-type noise, showed 1/f0 power spectrum, pink noise 1/f, and brown noises 1/f2) and different frequency ranges. Our results revealed that the response sensitivity and reliability of cortical neurons is much higher in response to 1/f noise stimuli with long-term correlations than 1/f0 with short-term correlations for a broad frequency range, and also higher than 1/f2 for all frequency ranges. In addition, we found that neuronal sensitivity diverges to opposite directions for 1/f noise comparing with 1/f0 white noise as a function of cutoff frequency of input signal. As the cutoff frequency is progressively increased from 50 to 1,000 Hz, the neuronal responsiveness increased gradually for 1/f noise, while decreased exponentially for white noise. Computational simulations of a general cortical model revealed that, neuronal sensitivity and reliability to input signal statistics was majorly dominated by fast sodium inactivation, potassium activation, and membrane time constants.
Project description:GABAA receptors distributed in somatodendritic compartments play critical roles in regulating neuronal activities, including spike timing and firing pattern; however, the properties and functions of GABAA receptors at the axon are still poorly understood. By recording from the cut end (bleb) of the main axon trunk of layer -5 pyramidal neurons in prefrontal cortical slices, we found that currents evoked by GABA iontophoresis could be blocked by picrotoxin, indicating the expression of GABAA receptors in axons. Stationary noise analysis revealed that single-channel properties of axonal GABAA receptors were similar to those of somatic receptors. Perforated patch recording with gramicidin revealed that the reversal potential of the GABA response was more negative than the resting membrane potential at the axon trunk, suggesting that GABA may hyperpolarize the axonal membrane potential. Further experiments demonstrated that the activation of axonal GABAA receptors regulated the amplitude and duration of action potentials (APs) and decreased the AP-induced Ca2+ transients at the axon. Together, our results indicate that the waveform of axonal APs and the downstream Ca2+ signals are modulated by axonal GABAA receptors.
Project description:We used spike-triggered current source-density analysis to examine axonal and postsynaptic currents generated in the visual cortex of awake rabbits by spontaneous spikes of individual sustained and transient dorsal lateral geniculate nucleus (LGNd) neurons. Using these data, we asked whether sustained/transient sensory responses are related to short-term synaptic dynamics at the thalamocortical synapse. Most sustained (34 of 40) and transient (24 of 25) neurons generated axonal and monosynaptic responses in layer 4 and/or 6 of the aligned cortical domain, with input from transient neurons arriving approximately 0.3 ms earlier and 100-200 microm deeper. Postsynaptic cortical responses generated by both thalamic cell classes were reduced in amplitude after a preceding impulse and slowly recovered over a period of >750 ms. We interpret this to reflect interval-dependent recovery from chronic depression at the thalamocortical synapse, caused by significant spontaneous firing of LGNd cells (approximately 8 Hz). Surprisingly, postsynaptic cortical responses generated by spontaneous spikes of sustained thalamic neurons were more depressed than those of transient neurons. This difference was seen both in layers 4 and 6. The depression saturated rapidly with multiple preceding impulses, and postsynaptic responses generated by sustained neurons during maintained visual stimulation remained sufficiently robust to allow a sustained flow of information to the cortex. Our results indicate a relationship between the sensory response properties of thalamic neurons and the short-term dynamics of their synapses, and suggest that cortical recipients of sustained and transient thalamic inputs will differ considerably in their response modulation by prior impulse activity.
Project description:Cortical fast-spiking (FS) interneurons display highly variable electrophysiological properties. Their spike responses to step currents occur almost immediately following the step onset or after a substantial delay, during which subthreshold oscillations are frequently observed. Their firing patterns include high-frequency tonic firing and rhythmic or irregular bursting (stuttering). What is the origin of this variability? In the present paper, we hypothesize that it emerges naturally if one assumes a continuous distribution of properties in a small set of active channels. To test this hypothesis, we construct a minimal, single-compartment conductance-based model of FS cells that includes transient Na(+), delayed-rectifier K(+), and slowly inactivating d-type K(+) conductances. The model is analyzed using nonlinear dynamical system theory. For small Na(+) window current, the neuron exhibits high-frequency tonic firing. At current threshold, the spike response is almost instantaneous for small d-current conductance, gd, and it is delayed for larger gd. As gd further increases, the neuron stutters. Noise substantially reduces the delay duration and induces subthreshold oscillations. In contrast, when the Na(+) window current is large, the neuron always fires tonically. Near threshold, the firing rates are low, and the delay to firing is only weakly sensitive to noise; subthreshold oscillations are not observed. We propose that the variability in the response of cortical FS neurons is a consequence of heterogeneities in their gd and in the strength of their Na(+) window current. We predict the existence of two types of firing patterns in FS neurons, differing in the sensitivity of the delay duration to noise, in the minimal firing rate of the tonic discharge, and in the existence of subthreshold oscillations. We report experimental results from intracellular recordings supporting this prediction.
Project description:The response of the auditory nerve to electrical stimulation is highly sensitive to small modulations (<0.5%). This report demonstrates that dynamical instability (i.e., a positive Lyapunov exponent) can account for this sensitivity in a modified FitzHugh-Nagumo model of spike generation, so long as the input noise is not too large. This finding suggests both that spike generator instability is necessary to account for auditory nerve sensitivity and that the amplitude of physiological noise, such as that produced by the random behavior of voltage-gated sodium channels, is small. Based on these results with direct electrical stimulation, it is hypothesized that spike generator instability may be the mechanism that reconciles high sensitivity with the cross-fiber independence observed under acoustic stimulation.
Project description:Accurately describing synaptic interactions between neurons and how interactions change over time are key challenges for systems neuroscience. Although intracellular electrophysiology is a powerful tool for studying synaptic integration and plasticity, it is limited by the small number of neurons that can be recorded simultaneously in vitro and by the technical difficulty of intracellular recording in vivo. One way around these difficulties may be to use large-scale extracellular recording of spike trains and apply statistical methods to model and infer functional connections between neurons. These techniques have the potential to reveal large-scale connectivity structure based on the spike timing alone. However, the interpretation of functional connectivity is often approximate, since only a small fraction of presynaptic inputs are typically observed. Here we use in vitro current injection in layer 2/3 pyramidal neurons to validate methods for inferring functional connectivity in a setting where input to the neuron is controlled. In experiments with partially-defined input, we inject a single simulated input with known amplitude on a background of fluctuating noise. In a fully-defined input paradigm, we then control the synaptic weights and timing of many simulated presynaptic neurons. By analyzing the firing of neurons in response to these artificial inputs, we ask 1) How does functional connectivity inferred from spikes relate to simulated synaptic input? and 2) What are the limitations of connectivity inference? We find that individual current-based synaptic inputs are detectable over a broad range of amplitudes and conditions. Detectability depends on input amplitude and output firing rate, and excitatory inputs are detected more readily than inhibitory. Moreover, as we model increasing numbers of presynaptic inputs, we are able to estimate connection strengths more accurately and detect the presence of connections more quickly. These results illustrate the possibilities and outline the limits of inferring synaptic input from spikes.