Are the input parameters of white noise driven integrate and fire neurons uniquely determined by rate and CV?

Vilela, Rafael D.; Lindner, Benjamin

doi:10.1016/j.jtbi.2008.11.004

Cited by 49 publications

(35 citation statements)

References 52 publications

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“…Rather than expressing as a function of the input parameters and , we use an equivalent parameterization in terms of the output, expressing as a function of and the coefficient of variation (CV) of the spiking models. The space has a one-to-one mapping with the space [14], and working in this space allows us to plot results for all three neuron models on comparable axes. In Figure 2B–D, we show the imaginary and real parts of along the curves in the space of values depicted by the different colored traces in Figure 2A (these are curves of fixed for the exponential integrate-and-fire model, in particular = 1, 2 and 4 mV).…”

Section: Resultsmentioning

confidence: 99%

A Complex-Valued Firing-Rate Model That Approximates the Dynamics of Spiking Networks

2013

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Firing-rate models provide an attractive approach for studying large neural networks because they can be simulated rapidly and are amenable to mathematical analysis. Traditional firing-rate models assume a simple form in which the dynamics are governed by a single time constant. These models fail to replicate certain dynamic features of populations of spiking neurons, especially those involving synchronization. We present a complex-valued firing-rate model derived from an eigenfunction expansion of the Fokker-Planck equation and apply it to the linear, quadratic and exponential integrate-and-fire models. Despite being almost as simple as a traditional firing-rate description, this model can reproduce firing-rate dynamics due to partial synchronization of the action potentials in a spiking model, and it successfully predicts the transition to spike synchronization in networks of coupled excitatory and inhibitory neurons.

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Section: Resultsmentioning

confidence: 99%

A Complex-Valued Firing-Rate Model That Approximates the Dynamics of Spiking Networks

2013

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“…The solution adopted by a wide range of systems consists of exploiting stochastic resonance, i.e., the addition of an optimized amount of noise that induces a moderate, highly irregular, spontaneous background activity. Stimulus-evoked modulations of this spontaneous activity then provide threshold-free detection [1], [2], [3]. Stochastic resonance theory explains that noise is essential for linearization and actually helps rather than hinders detection [4].…”

Section: Introductionmentioning

confidence: 99%

Spike-Interval Triggered Averaging Reveals a Quasi-Periodic Spiking Alternative for Stochastic Resonance in Catfish Electroreceptors

et al. 2012

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Catfish detect and identify invisible prey by sensing their ultra-weak electric fields with electroreceptors. Any neuron that deals with small-amplitude input has to overcome sensitivity limitations arising from inherent threshold non-linearities in spike-generation mechanisms. Many sensory cells solve this issue with stochastic resonance, in which a moderate amount of intrinsic noise causes irregular spontaneous spiking activity with a probability that is modulated by the input signal. Here we show that catfish electroreceptors have adopted a fundamentally different strategy. Using a reverse correlation technique in which we take spike interval durations into account, we show that the electroreceptors generate a supra-threshold bias current that results in quasi-periodically produced spikes. In this regime stimuli modulate the interval between successive spikes rather than the instantaneous probability for a spike. This alternative for stochastic resonance combines threshold-free sensitivity for weak stimuli with similar sensitivity for excitations and inhibitions based on single interspike intervals.

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“…The parameter c is constrained to 0 Յ c Յ 1 and represents the relative strength of the signal. We use nondimensional units for the membrane potential v and choose v T ϭ 1 for the threshold and v R ϭ 0 for the reset point (Vilela and Lindner 2009a). A stochastic Euler procedure was used to integrate Eq.…”

Section: Methodsmentioning

confidence: 99%

A frequency-resolved mutual information rate and its application to neural systems

Bernardi

Lindner

2015

Journal of Neurophysiology

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Bernardi D, Lindner B. A frequency-resolved mutual information rate and its application to neural systems. J Neurophysiol 113: 1342-1357, 2015. First published December 4, 2014 doi:10.1152/jn.00354.2014.-The encoding and processing of time-dependent signals into sequences of action potentials of sensory neurons is still a challenging theoretical problem. Although, with some effort, it is possible to quantify the flow of information in the model-free framework of Shannon's information theory, this yields just a single number, the mutual information rate. This rate does not indicate which aspects of the stimulus are encoded. Several studies have identified mechanisms at the cellular and network level leading to low-or high-pass filtering of information, i.e., the selective coding of slow or fast stimulus components. However, these findings rely on an approximation, specifically, on the qualitative behavior of the coherence function, an approximate frequency-resolved measure of information flow, whose quality is generally unknown. Here, we develop an assumption-free method to measure a frequency-resolved information rate about a time-dependent Gaussian stimulus. We demonstrate its application for three paradigmatic descriptions of neural firing: an inhomogeneous Poisson process that carries a signal in its instantaneous firing rate; an integrator neuron (stochastic integrate-and-fire model) driven by a time-dependent stimulus; and the synchronous spikes fired by two commonly driven integrator neurons. In agreement with previous coherence-based estimates, we find that Poisson and integrate-and-fire neurons are broadband and low-pass filters of information, respectively. The band-pass information filtering observed in the coherence of synchronous spikes is confirmed by our frequency-resolved information measure in some but not all parameter configurations. Our results also explicitly show how the response-response coherence can fail as an upper bound on the information rate. information transmission; information filter; neural variability; stochastic spike trains SENSORY SYSTEMS SEND INFORMATION about external stimuli to the brain in the form of spike trains (Rieke et al. 1996;Borst and Theunissen 1999). Identifying what features of signals are selected by a neuron or neural population is important for understanding the functional physiology of any neural circuit. A basic classification scheme arises in the frequency domain: how much information does a neuron encode about fast or slow components of a stimulus? Put differently, does a neuron select information about high-or low-frequency bands of a timedependent signal? Such a form of information filtering has been studied in the vestibular (Sadeghi et al. 2007; Massot et al.

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Are the input parameters of white noise driven integrate and fire neurons uniquely determined by rate and CV?

Cited by 49 publications

References 52 publications

A Complex-Valued Firing-Rate Model That Approximates the Dynamics of Spiking Networks

A Complex-Valued Firing-Rate Model That Approximates the Dynamics of Spiking Networks

Spike-Interval Triggered Averaging Reveals a Quasi-Periodic Spiking Alternative for Stochastic Resonance in Catfish Electroreceptors

A frequency-resolved mutual information rate and its application to neural systems

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