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Interspike interval correlations in neuron models with adaptation and correlated noise.

ABSTRACT: The generation of neural action potentials (spikes) is random but nevertheless may result in a rich statistical structure of the spike sequence. In particular, contrary to the popular renewal assumption of theoreticians, the intervals between adjacent spikes are often correlated. Experimentally, different patterns of interspike-interval correlations have been observed and computational studies have identified spike-frequency adaptation and correlated noise as the two main mechanisms that can lead to such correlations. Analytical studies have focused on the single cases of either correlated (colored) noise or adaptation currents in combination with uncorrelated (white) noise. For low-pass filtered noise or adaptation, the serial correlation coefficient can be approximated as a single geometric sequence of the lag between the intervals, providing an explanation for some of the experimentally observed patterns. Here we address the problem of interval correlations for a widely used class of models, multidimensional integrate-and-fire neurons subject to a combination of colored and white noise sources and a spike-triggered adaptation current. Assuming weak noise, we derive a simple formula for the serial correlation coefficient, a sum of two geometric sequences, which accounts for a large class of correlation patterns. The theory is confirmed by means of numerical simulations in a number of special cases including the leaky, quadratic, and generalized integrate-and-fire models with colored noise and spike-frequency adaptation. Furthermore we study the case in which the adaptation current and the colored noise share the same time scale, corresponding to a slow stochastic population of adaptation channels; we demonstrate that our theory can account for a nonmonotonic dependence of the correlation coefficient on the channel's time scale. Another application of the theory is a neuron driven by network-noise-like fluctuations (green noise). We also discuss the range of validity of our weak-noise theory and show that by changing the relative strength of white and colored noise sources, we can change the sign of the correlation coefficient. Finally, we apply our theory to a conductance-based model which demonstrates its broad applicability.

SUBMITTER: Ramlow L

PROVIDER: S-EPMC8428727 | biostudies-literature |

REPOSITORIES: biostudies-literature

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Project description:Nervous systems need to detect stimulus changes based on their neuronal responses without using any additional information on the number, times, and types of stimulus changes. Here, two relatively simple, biologically realistic change point detection methods are compared with two common analysis methods. The four methods are applied to intra- and extracellularly recorded responses of a single cricket interneuron (AN2) to acoustic simulation. Solely based on these recorded responses, the methods should detect an unknown number of different types of sound intensity in- and decreases shortly after their occurrences. For this task, the methods rely on calculating an adjusting interspike interval (ISI). Both simple methods try to separate responses to intensity in- or decreases from activity during constant stimulation. The Pure-ISI method performs this task based on the distribution of the ISI, while the ISI-Ratio method uses the ratio of actual and previous ISI. These methods are compared to the frequently used Moving-Average method, which calculates mean and standard deviation of the instantaneous spike rate in a moving interval. Additionally, a classification method provides the upper limit of the change point detection performance that can be expected for the cricket interneuron responses. The classification learns the statistical properties of the actual and previous ISI during stimulus changes and constant stimulation from a training data set. The main results are: (1) The Moving-Average method requires a stable activity in a long interval to estimate the previous activity, which was not always given in our data set. (2) The Pure-ISI method can reliably detect stimulus intensity increases when the neuron bursts, but it fails to identify intensity decreases. (3) The ISI-Ratio method detects stimulus in- and decreases well, if the spike train is not too noisy. (4) The classification method shows good performance for the detection of stimulus in- and decreases. But due to the statistical learning, this method tends to confuse responses to constant stimulation with responses triggered by a stimulus change. Our results suggest that stimulus change detection does not require computationally costly mechanisms. Simple nervous systems like the cricket's could effectively apply ISI-Ratios to solve this fundamental task.

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Interspike interval correlations in neuron models with adaptation and correlated noise.

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