Spike generation estimated from stationary spike trains in a variety of neurons in vivo (original) (raw)
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Journal of Neuroscience Methods, 2008
Cortical neurons are subject to sustained and irregular synaptic activity which causes important fluctuations of the membrane potential (V m ). We review here different methods to characterize this activity and its impact on spike generation. The simplified, fluctuating point-conductance model of synaptic activity provides the starting point of a variety of methods for the analysis of intracellular V m recordings. In this model, the synaptic excitatory and inhibitory conductances are described by Gaussian-distributed stochastic variables, or "colored conductance noise". The matching of experimentally recorded V m distributions to an invertible theoretical expression derived from the model allows the extraction of parameters characterizing the synaptic conductance distributions. This analysis can be complemented by the matching of experimental V m power spectral densities (PSDs) to a theoretical template, even though the unexpected scaling properties of experimental PSDs limit the precision of this latter approach. Building on this stochastic characterization of synaptic activity, we also propose methods to qualitatively and quantitatively evaluate spike-triggered averages of synaptic time-courses preceding spikes. This analysis points to an essential role for synaptic conductance variance in determining spike times. The presented methods are evaluated using controlled conductance injection in cortical neurons in vitro with the dynamic-clamp technique. We review their applications to the analysis of in vivo intracellular recordings in cat association cortex, which suggest a predominant role for inhibition in determining both sub-and supra-threshold dynamics of cortical neurons embedded in active networks.
Biological Cybernetics, 2011
A wide diversity of models have been proposed to account for the spiking response of central neurons, from the integrate-and-fire (IF) model and its quadratic and exponential variants, to multiple-variable models such as the Izhikevich (IZ) model and the well-known Hodgkin-Huxley (HH) type models. Such models can capture different aspects of the spiking response of neurons, but there is few objective comparison of their performance. In this article, we provide such a comparison in the context of well-defined stimulation protocols, including, for each cell, DC stimulation, and a series of excitatory conductance injections, arising in the presence of synaptic background activity. We use the dynamic-clamp technique to characterize the response of regular-spiking neurons from guinea-pig visual cortex by computing families of post-stimulus time histograms (PSTH), for different stimulus intensities, and for two different background activities (low-and high-conductance states). The data obtained are then used to fit different classes of models such as the IF, IZ, or HH types, which are constrained by the whole data set. This analysis shows that HH models are generally more accurate to fit the series of experimental PSTH, but their performance is almost equaled by much simpler models, such as the exponential or pulse-based IF models. Similar conclusions were also reached by performing partial fitting of the data, and examining the ability of different models to predict responses that were not used for the fitting. Although such results must be qualified by using more sophisticated stimulation protocols, they suggest that nonlinear IF models can capture surprisingly well the response of cortical regularspiking neurons and appear as useful candidates for network simulations with conductance-based synaptic interactions.
The European Physical Journal Special Topics, 2021
Neurons in the nervous system are submitted to distinct sources of noise, such as ionic-channel and synaptic noise, which introduces variability in their responses to repeated presentations of identical stimuli. This motivates the use of stochastic models to describe neuronal behavior. In this work, we characterize an intrinsically stochastic neuron model based on a voltage-dependent spike probability function. We determine the effect of the intrinsic noise in single neurons by measuring the spike time reliability and study the stochastic resonance phenomenon. The model was able to show increased reliability for non-zero intrinsic noise values, according to what is known from the literature, and the addition of intrinsic stochasticity in it enhanced the region in which stochastic-resonance is present. We proceeded to the study at the network level where we investigated the behavior of a random network composed of stochastic neurons. In this case, the addition of an extra dimension, represented by the intrinsic noise, revealed dynamic states of the system that could not be found otherwise. Finally, we propose a method to estimate the spike probability curve from in vitro electrophysiological data.
Characterizing neuronal activity by describing the membrane potential as a stochastic process
Journal of Physiology-Paris, 2009
Cortical neurons behave similarly to stochastic processes, as a consequence of their irregularity and dense connectivity. Their firing pattern is close to a Poisson process, and their membrane potential ðV m Þ is analogous to colored noise. One way to characterize this activity is to identify V m to a multidimensional stochastic process. We review here this approach and how it can be used to extract important statistical signatures of neuronal activity. The ''VmD method" consists of fitting the V m distribution obtained intracellularly to analytic expressions derived from stochastic processes, and thereby deduce synaptic conductance parameters. However, this method requires at least two levels of V m , which prevents applications to single-trial measurements. We also discuss methods that can be applied to single V m traces, such as power spectral analysis and the ''STA method" to calculate spike-triggered average conductances based on a maximum likelihood procedure. A recently proposed method, the ''VmT method", is based on the fusion of these two concepts. This method is analogous to the VmD method and estimates the mean excitatory and inhibitory conductances and their variances. However, it does so by using a maximumlikelihood estimation, and can thus be applied to single V m traces. All methods were tested using controlled conductance injection in dynamic-clamp experiments.
Intracellular recordings of cortical neurons in vivo consistently display a highly complex and irregular subthreshold synaptic activity resulting from the discharge of presynaptic neurons in the network. Here we attempted to design tools for analyzing intracellular subthreshold voltage transients with an aim to extract information about the underlying network activity. We modeled synaptic activity using both current-and conductance-based models of synaptic inputs described by random-walk (Ornstein-Uhlenbeck) processes. We show that analytic expressions for the distribution of the membrane potential (V m ) can be obtained from the passive cable equation using classic stochastic methods (Fokker-Planck equation). Current-based models yielded a symmetric (Gaussian shaped) V m -distribution, as expected from models with additive noise. This model gives a good description of subthreshold activity in low-conductance states (low-activity conditions). Conductance-based models, which correspond to multiplicative noise, yielded an asymmetric V m -distribution. These models better represent the subthreshold activity under in vivo conditions. In this case, fitting the analytic solution to intracellular recordings leads to estimates of the average synaptic conductances, and their variance, during spontaneous activity. The same method can also be used to analyze transient voltage responses to repeated stimuli. For each time bin following the stimulus, a V m -distribution is computed by cumulating different trials. Fitting the model to these V m -distributions can provide estimates of the time evolution of excitatory and inhibitory conductances, and of their variance, during the response.
Spike latency and jitter of neuronal membrane patches with stochastic Hodgkin�Huxley channels
Journal of Theoretical Biology, 2009
Ion channel stochasticity can influence the voltage dynamics of neuronal membrane, with stronger effects for smaller patches of membrane because of the correspondingly smaller number of channels. We examine this question with respect to first spike statistics in response to a periodic input of membrane patches including stochastic Hodgkin-Huxley channels, comparing these responses to spontaneous firing. Without noise, firing threshold of the model depends on frequency-a sinusoidal stimulus is subthreshold for low and high frequencies and suprathreshold for intermediate frequencies. When channel noise is added, a stimulus in the lower range of subthreshold frequencies can influence spike output, while high subthreshold frequencies remain subthreshold. Both input frequency and channel noise strength influence spike timing. Specifically, spike latency and jitter have distinct minima as a function of input frequency, showing a resonance like behavior. With either no input, or low frequency subthreshold input, or input in the low or high suprathreshold frequency range, channel noise reduces latency and jitter, with the strongest impact for the lowest input frequencies. In contrast, for an intermediate range of suprathreshold frequencies, where an optimal input gives a minimum latency, the noise effect reverses, and spike latency and jitter increase with channel noise. Thus, a resonant minimum of the spike response as a function of frequency becomes more pronounced with less noise. Spike latency and jitter also depend on the initial phase of the input, resulting in minimal latencies at an optimal phase, and depend on the membrane time constant, with a longer time constant broadening frequency tuning for minimal latency and jitter. Taken together, these results suggest how stochasticity of ion channels may influence spike timing and thus coding for neurons with functionally localized concentrations of channels, such as in ''hot spots'' of dendrites, spines or axons.
How Spike Generation Mechanisms Determine the Neuronal Response to Fluctuating Inputs
The Journal of Neuroscience, 2003
This study examines the ability of neurons to track temporally varying inputs, namely by investigating how the instantaneous firing rate of a neuron is modulated by a noisy input with a small sinusoidal component with frequency (f). Using numerical simulations of conductance-based neurons and analytical calculations of one-variable nonlinear integrate-and-fire neurons, we characterized the dependence of this modulation on f. For sufficiently high noise, the neuron acts as a low-pass filter. The modulation amplitude is approximately constant for frequencies up to a cutoff frequency, f c , after which it decays. The cutoff frequency increases almost linearly with the firing rate. For higher frequencies, the modulation amplitude decays as C/f ␣ , where the power ␣ depends on the spike initiation mechanism. For conductance-based models, ␣ ϭ 1, and the prefactor C depends solely on the average firing rate and a spike "slope factor," which determines the sharpness of the spike initiation. These results are attributable to the fact that near threshold, the sodium activation variable can be approximated by an exponential function. Using this feature, we propose a simplified one-variable model, the "exponential integrate-and-fire neuron," as an approximation of a conductance-based model. We show that this model reproduces the dynamics of a simple conductance-based model extremely well. Our study shows how an intrinsic neuronal property (the characteristics of fast sodium channels) determines the speed with which neurons can track changes in input.
Neural Computation, 1998
We propose a biophysical mechanism for the high interspike interval variability observed in cortical spike trains. The key lies in the nonlinear dynamics of cortical spike generation, which are consistent with type I membranes where saddle-node dynamics underlie excitability (Rinzel & Ermentrout, 1989). We present a canonical model for type I membranes, the θ-neuron. The θ-neuron is a phase model whose dynamics reflect salient features of type I membranes. This model generates spike trains with coefficient of variation (CV) above 0.6 when brought to firing by noisy inputs. This happens because the timing of spikes for a type I excitable cell is exquisitely sensitive to the amplitude of the suprathreshold stimulus pulses. A noisy input current, giving random amplitude “kicks” to the cell, evokes highly irregular firing across a wide range of firing rates; an intrinsically oscillating cell gives regular spike trains. We corroborate the results with simulations of the Morris-Lecar (M-L...