Role of Synaptic Filtering on the Firing Response of Simple Model Neurons

Moreno-Bote, Rubén; Parga, Néstor

doi:10.1103/physrevlett.92.028102

Cited by 85 publications

(121 citation statements)

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“…(17), becomes then an exponential with the same time constant as that of the synaptic filter, τ s (see e.g. (Brunel and Sergi, 1998;Moreno-Bote and Parga, 2004)). At the same time, the exponential term in the correlation function results after filtering in two additional exponentials, with time constants τ c and τ s , respectively.…”

Section: Discussionmentioning

confidence: 99%

“…Particular cases of this interesting problem (e.g. when the two timescales are disparate) could be addressed analytically by using the techniques developed to study simultaneous fast and slow synaptic filtering (Moreno-Bote and Parga, 2004). …”

Section: Discussionmentioning

confidence: 99%

“…Since y is slow compared to the voltage dynamics (τ c > τ m ), the firing rate of a LIF neuron receiving correlated noise can be calculated by multiplying the firing rate of the LIF neuron receiving a frozen current proportional to y (plus mean µ and white noise with amplitude σ w ; this corresponds to the function into the square brackets, divided by τ m (Ricciardi, 1977) 5 ) and the probability density of having the value y, which in this case is a normal distribution because y obeys an Ornstein-Uhlenbeck process, eq (33). This expression, obtained here to describe the effect of exponentially correlated inputs, has also been used to describe the effects of synaptic filtering with both fast and slow linear synapses on the output firing rate of a LIF neuron (Moreno-Bote and Parga, 2004).…”

Section: Long τ C Limit Using the Second Representationmentioning

confidence: 99%

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Theory of Input Spike Auto- and Cross-Correlations and Their Effect on the Response of Spiking Neurons

2008

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Spike correlations between neurons are ubiquitous in the cortex, but their role is at present not understood. Here we describe the firing response of a leaky integrate-and-fire neuron (LIF) when it receives a temporarily correlated input generated by presynaptic correlated neuronal populations. Input correlations are characterized in terms of the firing rates, Fano factors, correlation coefficients and correlation timescale of the neurons driving the target neuron. We show that the sum of the presynaptic spike trains cannot be well described by a Poisson process. In fact, the total input current has a non trivial two-point correlation function described by two main parameters: the correlation timescale (how precise the input correlations are in time), and the correlation magnitude (how strong they are). Therefore, the total current generated by the input spike trains is not well described by a white noise Gaussian process. Instead, we model the total current as a colored Gaussian process with the same mean and two-point correlation function, leading to the formulation of the problem in terms of a Fokker-Planck equation. Solutions of the output firing rate are found in the limit of short and long correlation time scales. The solutions described here expand and improve our previous 1 results ( by presenting new analytical expressions for the output firing rate for general IF neurons, extending the validity of the results for arbitrarily large correlation magnitude, and by describing the differential effect of correlations on the mean driven or noise dominated firing regimes. Also the details of this novel formalism are given here for the first time. We employ numerical simulations to confirm the analytical solutions and to study the firing response to sudden changes in the input correlations. We expect this formalism to be useful for the study of correlations in neuronal networks and their role in neural processing and information transmission.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Long τ C Limit Using the Second Representationmentioning

confidence: 99%

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Theory of Input Spike Auto- and Cross-Correlations and Their Effect on the Response of Spiking Neurons

2008

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“…This application goes beyond the stationary framework in which the mean field approach is derived, and provides us with an approximated solution of a complex Fokker-Plank equation in a two-or higher dimensional space (Brunel and Sergi 1998;Brunel and Hakim 1999;Moreno et al 2002;Nykamp and Tranchina 2001;Fourcaud and Brunel 2002;Moreno-Bote and Parga 2004;Gigante et al 2007a,b). We present a case study where the use of the stationary response function provides a good approximation to the full approach (Renart et al 2003).…”

Section: Population Response To Arbitrary Time-varying Inputsmentioning

confidence: 99%

The response of cortical neurons to in vivo-like input current: theory and experiment: II. Time-varying and spatially distributed inputs

et al. 2008

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The response of a population of neurons to time-varying synaptic inputs can show a rich phenomenology, hardly predictable from the dynamical properties of the membrane's inherent time constants. For example, a network of neurons in a state of spontaneous activity can respond significantly more rapidly than each single neuron taken individually. Under the assumption that the statistics of the synaptic input is the same for a population of similarly behaving neurons (mean field approximation), it is possible to greatly simplify the study of neural circuits, both in the case in which the statistics of the input are stationary (reviewed in La Camera et al. in Biol Cybern, 2008) and in the case in which they are time varying and unevenly distributed over the dendritic tree. Here, we review theoretical and experimental results on the single-neuron properties that are relevant for the dynamical collective behavior of a population of neurons. We focus on the response of integrate-and-fire neurons and real cortical neurons to long-lasting, noisy, in vivo-like stationary inputs and show how the theory can predict the observed rhythmic activity of cultures of neurons. We then show how cortical neurons adapt on multiple time scales in response to input with stationary statistics in vitro. Next, we review how it is possible to study the general response properties of a neural circuit to time-varying inputs by estimating the response of single neurons to noisy sinusoidal currents. Finally, we address the dendrite-soma interactions in cortical neurons leading to gain modulation and spike bursts, and show how these effects can be captured by a two-compartment integrate-and-fire neuron. Most of the experimental results reviewed in this article have been successfully reproduced by simple integrate-and-fire model neurons.

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“…Analytical approaches using this trick have been largely limited to the case of exponentially correlated noise (for an exception, see (Bauermeister et al 2013)), that can be mimicked by an Ornstein-Uhlenbeck process (one additional degree of freedom). Using perturbation techniques (small or large correlation time or small noise intensity) approximations have been worked out for the firing rate (Brunel and Sergi 1998;Moreno-Bote and Parga 2004;Alijani and Richardson 2011), the spike train's auto-correlation (Brenner et al 2002;Moreno-Bote and Parga 2006), the ISI density (Lindner 2004;Schwalger and SchimanskyGeier 2008) and ISI correlations (Lindner 2004), and the dynamical response (Brunel et al 2001;Alijani and Presynaptic spike trains have temporal structure, e.g. due to refractoriness, bursting, or rate modulations, which is expressed by non-flat power spectra S kk (f ), k = 1, .…”

Section: Introductionmentioning

confidence: 99%

Statistical structure of neural spiking under non-Poissonian or other non-white stimulation

2015

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Nerve cells in the brain generate sequences of action potentials with a complex statistics. Theoretical attempts to understand this statistics were largely limited to the case of a temporally uncorrelated input (Poissonian shot noise) from the neurons in the surrounding network. However, the stimulation from thousands of other neurons has various sorts of temporal structure. Firstly, input spike trains are temporally correlated because their firing rates can carry complex signals and because of cell-intrinsic properties like neural refractoriness, bursting, or adaptation. Secondly, at the connections between neurons, the synapses, usagedependent changes in the synaptic weight (short-term plasticity) further shape the correlation structure of the effective input to the cell. From the theoretical side, it is poorly understood how these correlated stimuli, socalled colored noise, affect the spike train statistics. In particular, no standard method exists to solve the associated first-passage-time problem for the interspikeinterval statistics with an arbitrarily colored noise. Assuming that input fluctuations are weaker than the mean neuronal drive, we derive simple formulas for the essential interspike-interval statistics for a canon- ical model of a tonically firing neuron subjected to arbitrarily correlated input from the network. We verify our theory by numerical simulations for three paradigmatic situations that lead to input correlations: (i) ratecoded naturalistic stimuli in presynaptic spike trains; (ii) presynaptic refractoriness or bursting; (iii) synaptic short-term plasticity. In all cases, we find severe effects on interval statistics. Our results provide a framework for the interpretation of firing statistics measured in vivo in the brain.

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Role of Synaptic Filtering on the Firing Response of Simple Model Neurons

Cited by 85 publications

References 12 publications

Theory of Input Spike Auto- and Cross-Correlations and Their Effect on the Response of Spiking Neurons

Theory of Input Spike Auto- and Cross-Correlations and Their Effect on the Response of Spiking Neurons

The response of cortical neurons to in vivo-like input current: theory and experiment: II. Time-varying and spatially distributed inputs

Statistical structure of neural spiking under non-Poissonian or other non-white stimulation

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