Patterns of interval correlations in neural oscillators with adaptation

Schwalger, Tilo; Lindner, Benjamin

doi:10.3389/fncom.2013.00164

Cited by 46 publications

(95 citation statements)

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“…Integrators vs. resonators. Others (Schwalger and Lindner 2013) have shown that adapting neurons that behave like integrators (their spikes times are always advanced by a small excitation) possess negative correlations between adjacent ISIs. The spike times for neurons in our study are always advanced by a small excitation (Preyer and Butera 2005), but they exhibit slow trends that presumably obliterate the negative correlation that would otherwise be observed between adjacent ISIs.…”

Section: Discussionmentioning

confidence: 99%

Stochastic slowly adapting ionic currents may provide a decorrelation mechanism for neural oscillators by causing wander in the intrinsic period

Norman

Butera

Canavier

2016

Journal of Neurophysiology

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Norman SE, Butera RJ, Canavier CC. Stochastic slowly adapting ionic currents may provide a decorrelation mechanism for neural oscillators by causing wander in the intrinsic period. J Neurophysiol 116: 1189 -1198, 2016. First published June 8, 2016 doi:10.1152/jn.00193.2016.-Oscillatory neurons integrate their synaptic inputs in fundamentally different ways than normally quiescent neurons. We show that the oscillation period of invertebrate endogenous pacemaker neurons wanders, producing random fluctuations in the interspike intervals (ISI) on a time scale of seconds to minutes, which decorrelates pairs of neurons in hybrid circuits constructed using the dynamic clamp. The autocorrelation of the ISI sequence remained high for many ISIs, but the autocorrelation of the ⌬ISI series had on average a single nonzero value, which was negative at a lag of one interval. We reproduced these results using a simple integrate and fire (IF) model with a stochastic population of channels carrying an adaptation current with a stochastic component that was integrated with a slow time scale, suggesting that a similar population of channels underlies the observed wander in the period. Using autoregressive integrated moving average (ARIMA) models, we found that a single integrator and a single moving average with a negative coefficient could simulate both the experimental data and the IF model. Feeding white noise into an integrator with a slow time constant is sufficient to produce the autocorrelation structure of the ISI series. Moreover, the moving average clearly accounted for the autocorrelation structure of the ⌬ISI series and is biophysically implemented in the IF model using slow stochastic adaptation. The observed autocorrelation structure may be a neural signature of slow stochastic adaptation, and wander generated in this manner may be a general mechanism for limiting episodes of synchronized activity in the nervous system. variability; stochastic models; noise; oscillations; synchronization; neural synchrony; ARIMA

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Section: Discussionmentioning

confidence: 99%

Stochastic slowly adapting ionic currents may provide a decorrelation mechanism for neural oscillators by causing wander in the intrinsic period

Norman

Butera

Canavier

2016

Journal of Neurophysiology

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“…(20), and accounting for the continuity and the absorbing boundary, Eqs. (23) and (24), the latter condition becomes…”

Section: A Boundary Value Problemmentioning

confidence: 99%

“…Our own recent contributions on the perfect IF (PIF) [27] and a general multidimensional IF model [20] with adaptation focus on the calculation of the serial correlation coefficient in the weak-noise limit. Other statistics, such as the probability density, have not been addressed so far (except for the adiabatic treatment in [26]), despite the accessibility of membrane potential distributions in experiments [26,[28][29][30][31][32][33][34] and the importance of this model class.…”

Section: Introductionmentioning

confidence: 99%

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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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“…They find that there is an optimal number of release sites for driving postsynaptic spiking when synchrony is present in the presynaptic spike trains. Schwalger and Lindner (2013) investigated correlations between the interspike intervals of oscillator model neurons with adaptation. They reveal a fundamental connection between interval correlations and the phase response curve of the neuron model.…”

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confidence: 99%

Correlated neuronal activity and its relationship to coding, dynamics and network architecture

2014

Frontiers Research Topics

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Correlated and synchronous activity in populations of neurons has been observed in many brain regions and has been shown to play a crucial role in cortical coding, attention, and network dynamics (Singer and Gray, 1995;Salinas and Sejnowski, 2001). However, we still lack a detailed knowledge of the origin and function, if any, of neuronal correlations. In this Research Topic, new ideas about these long standing questions are put forward. One group of studies in this Research Topic investigates the interaction of neuronal correlations with cellular and circuit mechanisms at the level of single neurons and cell pairs. Bolhasani et al. (2013) study the interaction between direct synaptic coupling between two neurons with correlated stochastic input to the neurons. They find that excitatory synaptic coupling can alter the transfer of pairwise correlations from current input to spike output. Interestingly, there is an optimal value of synaptic coupling strength for which the sensitivity of output correlations to input correlations is maximized.Bird and Richardson (2014) study the interaction between long term plasticity, synaptic vesicle depletion at multiple release sites and presynaptic spiking correlations. They find that there is an optimal number of release sites for driving postsynaptic spiking when synchrony is present in the presynaptic spike trains. Schwalger and Lindner (2013) investigated correlations between the interspike intervals of oscillator model neurons with adaptation. They reveal a fundamental connection between interval correlations and the phase response curve of the neuron model. They also show that when firing rates are high, negative interval correlations cause long-timescale variability of a model neuron's activity to be small.A second group of studies in this Research Topic investigates neuronal correlations on the level of networks. The key questions that these studies addressing are: (1) How are pairwise and higher order correlations generated in networks and which of them are important for a given network? and (2) How should we uncover and interpret spike train correlations in a given dataset?Four studies Zhou et al. In a complementary study, Barreiro et al. (2014) have focused on the emergence of pairwise and higher order correlations in retina models. The authors find that maximum entropy pairwise models capture surprisingly well the network spiking dynamics. What is surprising about these results is that higher-order correlations in this type of models can be constrained to be far lower than the statistically possible limits and that their strength depends more on the structure of the common input than on the synaptic connectivity profile. Jahnke et al. (2013) focused on spike patterns rather than correlations and proposed a mechanism for precise spike time pattern generation and replay in neural networks that lack strong densely connected feed-forward structures. The authors put forward the hypothesis that a non-linearity in synaptic summation rules may explain the lack of observed ...

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Patterns of interval correlations in neural oscillators with adaptation

Cited by 46 publications

References 57 publications

Stochastic slowly adapting ionic currents may provide a decorrelation mechanism for neural oscillators by causing wander in the intrinsic period

Stochastic slowly adapting ionic currents may provide a decorrelation mechanism for neural oscillators by causing wander in the intrinsic period

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

Correlated neuronal activity and its relationship to coding, dynamics and network architecture

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