Onset of negative interspike interval correlations in adapting neurons

Urdapilleta, Eugenio

doi:10.1103/physreve.84.041904

Cited by 22 publications

(53 citation statements)

References 43 publications

(117 reference statements)

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“…Overall, we find five basic patterns corresponding to the cases −α −1 < ϑ < 0, ϑ = 0, 0 < ϑ < 1, ϑ = 1 and 1 < ϑ < α −1 . These basic patterns cover all interval correlations discussed in previous theoretical studies (Schwalger and Lindner, 2010; Urdapilleta, 2011). Our geometric formula generalizes the theory for the perfect IF model with adaptation (Schwalger et al, 2010) to more realistic, nonlinear multi-dimensional IF models with adaptation.…”

Section: Resultssupporting

confidence: 75%

“…In the stationary state, these adaptation mechanisms are typically associated with short-range correlations with a negative SCC at lag k = 1 and a reduced Fano factor as demonstrated by several numerical (Geisler and Goldberg, 1966; Wang, 1998; Liu and Wang, 2001; Benda et al, 2010) and analytical studies (Schwalger et al, 2010; Schwalger and Lindner, 2010; Farkhooi et al, 2011; Urdapilleta, 2011). The correlation structure of adapting neurons can show qualitatively different patterns, ranging from monotonically decaying correlations to damped oscillations when plotted as a function of the lag (Ratnam and Nelson, 2000).…”

Section: Introductionmentioning

confidence: 99%

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Patterns of interval correlations in neural oscillators with adaptation

Schwalger

Lindner

2013

Front. Comput. Neurosci.

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Neural firing is often subject to negative feedback by adaptation currents. These currents can induce strong correlations among the time intervals between spikes. Here we study analytically the interval correlations of a broad class of noisy neural oscillators with spike-triggered adaptation of arbitrary strength and time scale. Our weak-noise theory provides a general relation between the correlations and the phase-response curve (PRC) of the oscillator, proves anti-correlations between neighboring intervals for adapting neurons with type I PRC and identifies a single order parameter that determines the qualitative pattern of correlations. Monotonically decaying or oscillating correlation structures can be related to qualitatively different voltage traces after spiking, which can be explained by the phase plane geometry. At high firing rates, the long-term variability of the spike train associated with the cumulative interval correlations becomes small, independent of model details. Our results are verified by comparison with stochastic simulations of the exponential, leaky, and generalized integrate-and-fire models with adaptation.

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Section: Resultssupporting

confidence: 75%

Section: Introductionmentioning

confidence: 99%

Patterns of interval correlations in neural oscillators with adaptation

Schwalger

Lindner

2013

Front. Comput. Neurosci.

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“…Its computation has uncovered enhanced information transmission in single neurons via the effect of noise shaping [2] and increased detectability of weak signals [3]. In particular, it is now possible to compute, in some cases even analytically, the SCC for single-neuron models in the presence of spike-frequency adaptation [4], colored noise [5] and time-dependent deterministic or stochastic firing thresholds [6]. Recently, it was also shown that, at short observation times, negative ISI correlations can enhance the resolution of a nonlinear dynamical sensor whose design was inspired by a simple non-renewal neuron model [7].…”

Section: Introductionmentioning

confidence: 99%

Interspike interval correlations in networks of inhibitory integrate-and-fire neurons

Braun

Longtin

2019

Phys. Rev. E

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We study temporal correlations of interspike intervals (ISIs), quantified by the network-averaged serial correlation coefficient (SCC), in networks of both current-and conductance-based purely inhibitory integrate-and-fire neurons. Numerical simulations reveal transitions to negative SCCs at intermediate values of bias current drive and network size. As bias drive and network size are increased past these values, the SCC returns to zero. The SCC is maximally negative at an intermediate value of the network oscillation strength. The dependence of the SCC on two canonical schemes for synaptic connectivity is studied, and it is shown that the results occur robustly in both schemes. For conductance-based synapses, the SCC becomes negative at the onset of both a fast and slow coherent network oscillation. Finally, we devise a noise-reduced diffusion approximation for current-based networks that accounts for the observed temporal correlation transitions.

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“…We consider the white-noise-driven PIF model with a spike-triggered adaptation current [27,38,39]. In this model, the dynamics of the membrane potential V and the adaptation current a are given bẏ…”

Section: Model and Quantities Of Interestmentioning

confidence: 99%

Analytical approach to an integrate-and-fire model with spike-triggered adaptation

Schwalger

Lindner

2015

Phys. Rev. E

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The calculation of the steady-state probability density for multidimensional stochastic systems that do not obey detailed balance is a difficult problem. Here we present the analytical derivation of the stationary joint and various marginal probability densities for a stochastic neuron model with adaptation current. Our approach assumes weak noise but is valid for arbitrary adaptation strength and time scale. The theory predicts several effects of adaptation on the statistics of the membrane potential of a tonically firing neuron: (i) a membrane potential distribution with a convex shape, (ii) a strongly increased probability of hyperpolarized membrane potentials induced by strong and fast adaptation, and (iii) a maximized variability associated with the adaptation current at a finite adaptation time scale.

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Onset of negative interspike interval correlations in adapting neurons

Cited by 22 publications

References 43 publications

Patterns of interval correlations in neural oscillators with adaptation

Patterns of interval correlations in neural oscillators with adaptation

Interspike interval correlations in networks of inhibitory integrate-and-fire neurons

Analytical approach to an integrate-and-fire model with spike-triggered adaptation

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