Sequential interval histogram analysis of non-stationary neuronal spike trains

Sanderson, Arthur C.; Kobler, Ben

doi:10.1007/bf00320131

Cited by 45 publications

(13 citation statements)

References 25 publications

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“…Here, ISI i+1 was scatter-plotted against ISI i for each i N À 2. To characterize the local density of the return maps, we calculated joint-interval probability density distributions by convolving the points in the return maps with a two-variable Gaussian kernel (half-width: 0.75 ms, resolution: 0.1 ms) (Sanderson and Kobler, 1976;Szücs et al, 2003). The probability density distributions are plotted in grayscale.…”

Section: Discussionmentioning

confidence: 99%

Consistent dynamics suggests tight regulation of biophysical parameters in a small network of bursting neurons

Szűcs¹,

Selverston²

2006

J. Neurobiol.

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The neuronal firing patterns in the pyloric network of crustaceans are remarkably consistent among animals. Although this characteristic of the pyloric network is well-known, the biophysical mechanisms underlying the regulation of the systems output are receiving renewed attention. Computer simulations of the pyloric network recently demonstrated that consistent motor output can be achieved from neurons with disparate biophysical parameters among animals. Here we address this hypothesis by pharmacologically manipulating the pyloric network and analyzing the emerging voltage oscillations and firing patterns. Our results show that the pyloric network of the lobster stomatogastric ganglion maintains consistent and regular firing patterns even when entire populations of specific voltage-gated channels and synaptic receptors are blocked. The variations of temporal parameters used to characterize the burst patterns of the neurons as well as their intraburst spike dynamics do not display statistically significant increase after blocking the transient K-currents (with 4-aminopyridine), the glutamatergic inhibitory synapses (with picrotoxin), or the cholinergic synapses (with atropine) in pyloric networks from different animals. These data suggest that in this very compact circuit, the biophysical parameters are cell-specific and tightly regulated.

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Section: Discussionmentioning

confidence: 99%

Consistent dynamics suggests tight regulation of biophysical parameters in a small network of bursting neurons

Szűcs¹,

Selverston²

2006

J. Neurobiol.

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“…Within the context of spike train analysis, several different approaches have been formulated to address the sampling problem, that is, the estimation of a probability function from a finite sample size, and different correction factors have been proposed (Optican et al, 1991;Panzeri & Treves, 1996;Sanderson & Kobler, 1976;Wolpert & Wolf, 1995). Here, the sampling problem is addressed by employing a best-fit analytic distribution to approximate the limit of an infinitely long data set.…”

Section: Estimating the Interval Entropy (H I )mentioning

confidence: 99%

Estimating the Temporal Interval Entropy of Neuronal Discharge

Reeke

Coop²

2004

Neural Computation

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To better understand the role of timing in the function of the nervous system, we have developed a methodology that allows the entropy of neuronal discharge activity to be estimated from a spike train record when it may be assumed that successive interspike intervals are temporally uncorrelated. The so-called interval entropy obtained by this methodology is based on an implicit enumeration of all possible spike trains that are statistically indistinguishable from a given spike train. The interval entropy is calculated from an analytic distribution whose parameters are obtained by maximum likelihood estimation from the interval probability distribution associated with a given spike train. We show that this approach reveals features of neuronal discharge not seen with two alternative methods of entropy estimation. The methodology allows for validation of the obtained data models by calculation of confidence intervals for the parameters of the analytic distribution and the testing of the significance of the fit between the observed and analytic interval distributions by means of Kolmogorov-Smirnov and Anderson-Darling statistics. The method is demonstrated by analysis of two different data sets: simulated spike trains evoked by either Poissonian or near-synchronous pulsed activation of a model cerebellar Purkinje neuron and spike trains obtained by extracellular recording from spontaneously discharging cultured rat hippocampal neurons.

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“…Commonly used methods are characterized by several inherent limitations. For example, while the (peristimulus) rate histogram method which averages responses over many trials is still widely used (e.g., Dickman and Correia, 1989;Hullar et al, 2005;Hullar and Minor, 1999), its utility is limited by the implicit assumption that variations in firing rate pattern over the duration of a bin do not encode information, and it is prone to 'localization error' near bin edges (Bayly, 1968;French and Holden, 1971;Paulin, 1992;Richmond et al, 1990;Sanderson and Kobler, 1976). Likewise, the reciprocal interspike interval method, which is frequently used to obtain a measure of "instantaneous" firing (e.g., Dickman and Correia, 1989;Shaikh et al, 2004), is characterized by nonlinear behaviour and sensitivity to noise at high frequencies (Richmond et al, 1990).…”

Section: Introductionmentioning

confidence: 99%