Firing-Rate Response of a Neuron Receiving Excitatory and Inhibitory Synaptic Shot Noise

Richardson, Magnus J. E.; Swarbrick, Rupert

doi:10.1103/physrevlett.105.178102

Cited by 97 publications

(125 citation statements)

References 19 publications

(30 reference statements)

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“…This is consistent with a "shotnoise" model of synaptic inputs with very large amplitudes. It can be shown that f-I curves of LIF neurons in the presence of such inputs also exhibit an expansive nonlinearity (Richardson and Swarbrick, 2010). Therefore, we expect our results to apply qualitatively also in this situation.…”

Section: Discussionsupporting

confidence: 60%

On the Distribution of Firing Rates in Networks of Cortical Neurons

Roxin¹,

Brunel²,

Hansel³

et al. 2011

J. Neurosci.

205

229

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The distribution of in vivo average firing rates within local cortical networks has been reported to be highly skewed and long tailed. The distribution of average single-cell inputs, conversely, is expected to be Gaussian by the central limit theorem. This raises the issue of how a skewed distribution of firing rates might result from a symmetric distribution of inputs. We argue that skewed rate distributions are a signature of the nonlinearity of the in vivo f-I curve. During in vivo conditions, ongoing synaptic activity produces significant fluctuations in the membrane potential of neurons, resulting in an expansive nonlinearity of the f-I curve for low and moderate inputs. Here, we investigate the effects of single-cell and network parameters on the shape of the f-I curve and, by extension, on the distribution of firing rates in randomly connected networks.

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Section: Discussionsupporting

confidence: 60%

On the Distribution of Firing Rates in Networks of Cortical Neurons

Roxin¹,

Brunel²,

Hansel³

et al. 2011

J. Neurosci.

205

229

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“…For white-noise-driven integrate-and-fire (IF) neurons this problem is generally tractable (e.g., [1][2][3][4]), but efforts to integrate key aspects of neuronal signaling into the IF formalism have added to its complexity. First, synaptic input consists of discrete action potentials, which results in non-Gaussian voltage distributions and affects firing statistics [5][6][7][8]. Second, synaptic communication is mediated by two separate (excitatory and inhibitory) systems with distinct kinetics.…”

mentioning

confidence: 99%

Firing statistics and correlations in spiking neurons: A level-crossing approach

Badel

2011

Phys. Rev. E

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We present a time-dependent level-crossing theory for linear dynamical systems perturbed by colored Gaussian noise. We apply these results to approximate the firing statistics of conductancebased integrate-and-fire neurons receiving excitatory and inhibitory Poissonian inputs. Analytical expressions are obtained for three key quantities characterizing the neuronal response to time-varying inputs: the mean firing rate, the linear response to sinusoidally-modulated inputs, and the pairwise spike-correlation for neurons receiving correlated inputs. The theory yields tractable results that are shown to accurately match numerical simulations, and provides useful tools for the analysis of interconnected neuronal populations.PACS numbers: 05.10. Gg,87.19.lj,87.19.ll,87.19.lm Understanding the dynamics of interconnected networks of neurons is of fundamental importance in theoretical neuroscience. An essential step in solving this problem is to determine the input-output relationship of individual neurons given an underlying biophysical model. For white-noise-driven integrate-and-fire (IF) neurons this problem is generally tractable (e.g., [1][2][3][4]), but efforts to integrate key aspects of neuronal signaling into the IF formalism have added to its complexity. First, synaptic input consists of discrete action potentials, which results in non-Gaussian voltage distributions and affects firing statistics [5][6][7][8]. Second, synaptic communication is mediated by two separate (excitatory and inhibitory) systems with distinct kinetics. The majority of theoretical studies include only one synaptic type and assume either fast (e.g., [9-11]) or slow [11,12] kinetics compared with the membrane integration time, but experimental evidence suggests that these timescales are often comparable [13]. Finally, neurons sharing presynaptic partners exhibit correlations in their synaptic input. While network models typically assume sparse connectivity for which correlations are negligible, recent reports suggest important functional roles for this type of "noise" correlation [14,15]. For IF neurons, obtaining the input-output relationship essentially involves computing moments of the first-passage-time (FPT) to threshold, but analytical solutions are rarely possible. Here, we show that for membrane-to-synaptic time constant ratios of the order of unity, level-crossing statistics provide good approximations to the FPT while retaining sufficient tractability to incorporate additional biological detail. Analytical expressions are given for the mean firing rate, pairwise spike-correlation and linear response to sinusoidally-modulated inputs, which compare favorably with numerical simulations of conductance-based IF neurons. The method thus provides a complete set of input- * Present address: Laboratory for Circuit Mechanisms of Sensory Perception, RIKEN Brain Science Institute, Wako, Saitama, Japan output properties needed for an analysis at the network level. Although the focus of the present paper is on neuroscience applications, the ...

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“…We then used exactly the same methods as before. It is possible to calculate the membrane distribution more precisely (Richardson and Gerstner, 2006;Richardson and Swarbrick, 2010), but this simple current-based method was already accurate enough in our case. Figure 12b shows that our theoretical prediction remains reasonably accurate in this complex situation, which is far from the ideal setting (synaptic conductances rather than currents, shot noise rather than diffusion).…”

Section: Effect Of Synaptic Conductancesmentioning

confidence: 93%

“…It is possible to calculate the membrane distribution more precisely with more sophisticated methods (Rudolph and Destexhe, 2003a;Richardson and Gerstner, 2006;Richardson and Swarbrick, 2010), but this simple method was sufficient in our case.…”

Section: Theorymentioning

confidence: 96%

Sensitivity of Noisy Neurons to Coincident Inputs

Rossant¹,

Leijon²,

Magnusson³

et al. 2011

J. Neurosci.

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How do neurons compute? Two main theories compete: neurons could temporally integrate noisy inputs (rate-based theories) or they could detect coincident input spikes (spike timing-based theories). Correlations at fine timescales have been observed in many areas of the nervous system, but they might have a minor impact. To address this issue, we used a probabilistic approach to quantify the impact of coincidences on neuronal response in the presence of fluctuating synaptic activity. We found that when excitation and inhibition are balanced, as in the sensory cortex in vivo, synchrony in a very small proportion of inputs results in dramatic increases in output firing rate. Our theory was experimentally validated with in vitro recordings of cortical neurons of mice. We conclude that not only are noisy neurons well equipped to detect coincidences, but they are so sensitive to fine correlations that a rate-based description of neural computation is unlikely to be accurate in general.

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Firing-Rate Response of a Neuron Receiving Excitatory and Inhibitory Synaptic Shot Noise

Cited by 97 publications

References 19 publications

On the Distribution of Firing Rates in Networks of Cortical Neurons

On the Distribution of Firing Rates in Networks of Cortical Neurons

Firing statistics and correlations in spiking neurons: A level-crossing approach

Sensitivity of Noisy Neurons to Coincident Inputs

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