Adjacent Interspike Intervals Research Articles

Effects of Neuropeptide Y on Neuron Spike Activity in the Rat Suprachiasmatic Nucleus in Vitro

Experiments on sagittal hippocampus slices from male Wistar rats addressed the effects of 10 nM neuropeptide Y on the level of electrical activity in neurons in the suprachiasmatic nucleus and parameters of spike-based information encoding. Application of neuropeptide Y led to a decrease in the action potential generation frequency in 35 of the 81 neurons recorded; eight cells showed increases in this parameter, and the remaining 38 neurons showed no change in the level of spike activity. The decrease in the spike generation frequency in suprachiasmatic nucleus neurons was accompanied by increases in the entropy of the distribution of interspike intervals and the mutual information between adjacent interspike intervals, which is evidence for increases in the degree of irregularity in these intervals and the patterning of spike information in response to neuropeptide Y. These results demonstrate the ability of neuropeptide Y to modulate the activity level and affect the spike code in the relatively numerous population of neurons in the circadian oscillator of the suprachiasmatic nucleus.

Non-renewal spiking and neural dynamics - a simple theory of interspike-interval correlations in adapting neurons

There is accumulating evidence that the spiking of many neurons is not a renewal process but is characterized by correlations between interspike intervals (ISIs) [1]. These correlations are crucial for understanding signal processing in single neurons, however, their origin and structure is still poorly understood theoretically. Here, we present a simple theory of correlations in neural oscillators with spike-triggered adaptation currents, which are a major source of non-renewal spiking. These currents mediate spike-frequency adaptation and are commonly believed to result in negative correlations between adjacent ISIs. For such adapting neurons, we show that the serial correlation coefficient (SCC) is fundamentally related to the neuron's phase response curve (PRC). The relation predicts possible correlation patterns that characterize how correlations depend on the lag between ISIs. Different patterns arise from the specific interplay between nonlinear neural dynamics and adaptation dynamics. In particular, the correlation structure can be determined by a single parameter that includes the shape of the PRC as well as the strength and time scale of the adaptation current (Fig.1). For a positive PRC (type I), the SCC is always negative at lag 1. At higher lags, we find either a monotonically decaying (Fig.1A) or oscillating (Fig.1C) behavior of the SCC depending on the strength of adaptation. Similar correlation structures have been observed in different experimental studies (see e.g. [2]). Despite the distinct patterns, the total correlation as expressed by the sum of the SCC over all lags displays a universal value close to -0.5 at high firing rates and strong adaptation. As an example of a type I neuron, we discuss one-dimensional integrate-and-fire (IF) neurons with adaptation (like e.g. the adaptive exponential IF model [3]) operating in the supra-threshold regime. For these models, the different behaviors of the SCC can be explained by qualitatively different structures of the phase plane spanned by the voltage and the adaptation variables. Our theory also predicts that adapting neurons with a partly negative PRC (type II phase resetting) can additionally exhibit non-negative ISI correlations, which is indeed found in a two-dimensional IF model with adaptation (Fig.1D,E). Thus, adapting neurons can show a richer repertoire of correlation patterns than previously thought. Figure 1 Possible patterns of ISI correlations of an adapting neuron (bottom). The correlation pattern is determined by the area under the weighted PRCs (top). Shown are data for a two-dimensional noisy resonate-and-fire model with adaptation (simulations: circles, ...

The maintained discharge of rat retinal ganglion cells

Action potentials were recorded from rat retinal ganglion cell fibers in the presence of a uniform field, and the maintained discharge pattern was characterized. Spike trains recorded under ketaminexylazine. The majority of cells had multimodal interval distributions, with the first peak in the range of 25.00.97). Both ON and OFF cells show serial correlations between adjacent interspike intervals, while ON cells also showed second-order correlations. Cells with multimodal interval distribution showed a strong peak at high frequencies in the power spectra in the range of 28.9-41.4 Hz. Oscillations were present under both anesthetic conditions and persisted in the dark at a slightly lower frequency, implying that the oscillations are generated independent of any light stimulus but can be modulated by light level. The oscillation frequency varied slightly between cells of the same type and in the same eye, suggesting that multiple oscillatory generating mechanisms exist within the retina. Cells with high-frequency oscillations were described well by an integrate-and-fire model with the input consisting of Gaussian noise plus a sinusoid where the phase was jittered randomly to account for the bandwidth present in the oscillations.

Intrinsic mechanisms of spike frequency adaption lead to negative serial correlations of inter-spike intervals

Event Abstract Back to Event Intrinsic mechanisms of spike frequency adaption lead to negative serial correlations of inter-spike intervals Farzad Farkhooi1, 2*, Martin P. Nawrot1, 2, Hermann Cuntz3 and Eilif Muller4 1 Freie Universitat Berlin , Germany 2 BCCN Berlin, Germany 3 University College London, United Kingdom 4 Ecole Polytechnique Federale de Lausanne , Switzerland It has been reported that many neurons in various different systems illustrate a pattern of negative serial dependence between adjacent inter-spike intervals, when measured under stationary firing rates (for review see [3]). We studied a biophysical model of spike frequency adaptation with M-type currents, which are caused by slow, voltage-dependent, high-threshold potassium channels ([2] and [4]). This model in the presence of white noise current injection exhibited serial negative correlation between inter-spike interval sequences. We analysed the dependency of serial correlation on the input statistics, this result shows in the physiological spiking frequency range, the inter-spike serial correlation is a persistence phenomena. We investigate the generality of this effect with two different phenomenological Integrate-and-Fire neuron models with spike frequency adaptation proposed in [5] and [1]. Both models captured the negative serial correlation between subsequent intervals. We describe the relationship of the input statistics with the observed serial dependency between the inter-spike intervals. We compare both models with respect to produced inter-spike serial correlation and their input coefficient of variation. Furthermore, we showed the strength of the observed correlation is rate dependent for both models. We argue that the feature of negatively correlated intervals is likely to be a neuron intrinsic property caused by cellular mechanisms that underlie spike frequency adaptation and the particular input statistics affects the modulation of the negative serial dependency between two following spiking intervals.

Spike coding from the perspective of a neurone

In this paper, we compare existing methods for quantifying the coding capacity of a spike train, and review recent developments in the application of information theory to neural coding. We present novel methods for characterising single-unit activity based on the perspective of a downstream neurone and propose a simple yet universally applicable framework to characterise the order of complexity of neural coding by single units. We establish four orders of complexity in the capacity for neural coding. First-order coding, quantified by firing rates, is conveyed by frequencies and is thus entirely described by first moment processes. Second-order coding, represented by the variability of interspike intervals, is quantified by the log interval entropy. Third-order coding is the result of spike motifs that associate adjacent inter-spike intervals beyond chance levels; it is described by the joint interval histogram, and is measured by the mutual information between adjacent log intervals. Finally, nonstationarities in activity represent coding of the fourth-order that arise from the effects of a known or unknown stimulus.

Altered temporal pattern of evoked afferent activity in a rat model of vincristine-induced painful peripheral neuropathy

It is known that the level of activity in nociceptive primary afferent nerve fibers increases in neuropathic conditions that produce pain, but changes in the temporal patterning of action potentials have not been analyzed in any detail. Because the patterning of action potentials in sensory nerve fibers might play a role in the development of pathological pain states, we studied patterning of mechanical stimulus-evoked action potential trains in nociceptive primary afferents in a rat model of vincristine-induced painful peripheral neuropathy. Systemic administration of vincristine (100 μg/kg) caused approximately half the C-fiber nociceptors to become markedly hyperresponsive to mechanical stimulation. Instantaneous frequency plots showed that vincristine induced an irregular pattern of action-potential firing in hyperresponsive C-fibers, characterized by interspersed occurrences of high- and low-frequency firing. This pattern was associated with an increase in the percentage of interspike intervals 100–199 ms in duration compared with that in C-fibers from control rats and vincristine-treated C-fibers that did not become hyperresponsive. Variability in the temporal pattern of action potential firing was quantified by determining the coefficient of variability (CV2) for adjacent interspike intervals. This analysis revealed that vincristine altered the pattern of action-potential timing, so that combinations of higher firing frequency and higher variability occurred that were not observed in control fibers. The abnormal temporal structure of nociceptor responses induced by vincristine in some C-fiber nociceptors could contribute to the pathogenesis of chemotherapy-induced neuropathic pain, perhaps by inducing activity-dependent post-synaptic effects in sensory pathways.

Spike propagation during the refractory period in the stochastic Hodgkin-Huxley model

The effects of noise on a spike train propagating on a nerve fiber during the relative refractory period are studied by using a stochastic version of the Hodgkin-Huxley model. Fluctuations in spike speeds due to the noise cause negative correlation between adjacent interspike intervals, while the dispersion relation due to the refractory causes positive correlation. A kinematic description of spike propagation yields expressions for changes in the autocorrelation and power spectrum of the interspike intervals during propagation. The power spectrum of the interspike intervals of an initially regular spike train first grows in proportion to 1 - cos(?) and then becomes a white noise spectrum. Computer simulation shows that the form of the power spectrum is considerably changed on a small nerve fiber.

Enhanced specificity of information in axons with negatively correlated adjacent interspike intervals.

A model is formulated for the conversion of a motoneuron's spike train to tension in a muscle. This model demonstrates that a spike train whose adjacent interspike intervals are negatively correlated results in a steady-state tension which fluctuates less about its mean value than if the interspike intervals are randomly arranged. The ability of a spike train to develop more distinguishable levels of tension by negative correlation between adjacent interspike intervals is more significant for interspike interval distributions with greater dispersion. The number of distinguishable tension levels increases by about 33 percent when a typical set of neuromuscular parameters are used. These results may be generalized to the smoothing of postsynaptic potentials and the regulation of blood pressure.

Stochastic properties of spontaneous impulse activity in central single neurons.

Stochastic dependence of the consecutive interspike intervals of the spontaneous discharges of the central single neurons has been studied in cats. Out of 35 neurons examined with the stationarity test, 16 passed it: 3 from the ventrobasal complex where the modality was hair (VB), 6 from the lateral geniculate nucleus (LGN), 4 from the mesencephalic reticular formation (MRF), and 3 from the red nucleus (RN). The interspike interval histogram in the VB and the LGN nuerons resembled the exponential and the bimodal distribution, while that in the MRF and the RN neurons did the gamma distribution. The quantitative measures of correlation between interspike intervals were furnished by the serial correlation coefficient, the variance function and the joint interval histogram. They showed that there were no correlation in most of the VB and the LGN neurons, while there existed correlation in most of the MRF and the RN nuerons. Approximately similar results were obtained by the X2 test for Markov process. A new quantitative measure which reflects Markov properties of the consecutive impulse sequences has been developed. It estimates the statistical dependency, d(τ), on the basis of Shannon's entropy. It has been confirmed theoretically that this measure is applicable in practice. The value of d(τ) of adjacent interspike intervals obtained from the VB and the LGN neurons was approximately equal to that of the shuffled ones, while that from the MRF and the RN neurons was larger than that of the shuffled ones. This is to be regarded as the evidence of the fact that the spontaneous impulse activity of the VB and the LGN neurons has no Markov property, while that of the MRF and the RN neurons has at least first order Markov property. The differentiation in two groups of the neurons is suggested to correlate with other functional characteristics of these neuron populations. However, the number of neurons sampled would have to be increased several-fold before the statistical differences in patterns of discharge could be made the basis for widely applicable generalizations about function.

Use of the principles of computer statistical analysis for investigating the background impulse activity of neurons

A program for complex statistical analysis of the background impulse activity of neurons on a computer is proposed. The program includes: determination of the portion of the recording having a stable statistical structure; calculation of histograms of the probability density function of the interspike intervals (ISI) and statistical indexes related with them; correlation-spectral analysis of the ISI sequence; correlation-spectral analysis of the instants of appearance of impulses (from the frequency graph and graph of the function of recovery of impulse activity); and determination of the type and degree of relation of the lengths of adjacent ISI's and entropy analysis of this connection. A method is described for determining the portion of burst and group activity of the investigated neuron in the recording. The effectiveness of using the proposed program was checked by analyzing the background activity of pyramidal cells of the cat cortex. An analysis of neurons equal in frequency of background activity and rate of conduction of impulses in axons showed that the differences in the internal statistical structure of their impulses are very substantial.

Statistical dependency between intervals in neuronal impulse sequences

The statistical dependency between adjacent interspike intervals of spontaneous discharges of thalamic reticular neurons has been studied in cats. Two “entropies” are defined, H 0 in terms of the probabilities of occurrence of intervals of various length and H 1 in terms of the probabilities of occurrence of successive pairs of intervals of various length. Thus the internal dependency, D, is given by the following formula: D = (H 0-H 1 H 0 . The empirical results are well represented by the formula D = ( τ a ) −b , where τ is the unit of time and a and b are constants. The values, a and b, vary from cell to cell and a is interpreted as the dead time or the absolute refractory period of the neuron.