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Statistics of subthreshold neuronal voltage fluctuations due to conductance-based synaptic shot noise
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10.1063/1.2203409
/content/aip/journal/chaos/16/2/10.1063/1.2203409
http://aip.metastore.ingenta.com/content/aip/journal/chaos/16/2/10.1063/1.2203409
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Figures

Image of FIG. 1.
FIG. 1.

Comparison of the shot-noise and diffusion-approximation voltage dynamics. (a)–(c) A case demonstrating the boundary error of the diffusion approximation: a neuron receiving both excitatory and strong inhibitory drive bringing it close to the inhibitory potential , with a leak potential also set at . (a) Shot-noise simulation of the dynamics. Between pulses the neuronal voltage relaxes to . (b) Diffusion simulation using Eq. (11) . Note that the voltage erroneously crosses the inhibitory reversal potential, which is not possible under the correct dynamics. (c) The steady-state shot-noise and diffusion-level voltage distributions. The diffusion approximation [simulation, Eq. (11) ; exact solution, Eq. (13) ] gives a significant weight to the forbidden region below . (d)–(f) A case demonstrating the skew error of the diffusion approximation: a neuron receiving excitatory drive only with a leak potential . (d) Shot-noise simulation and (e) diffusion-level simulation. The average voltage is in both cases (dotted lines). (f) The shot-noise distribution is positively skewed (peak left of the average, tail to the right) whereas its diffusion approximation predicts a negative skew with the peak to the right of the average voltage. The parameters used for the drive were as follows: (a)–(c) {0.5, 0.01, 10, 0.05}, (d)–(f) {0.25, 0.04, 0, 0} with the rates given in kHz.

Image of FIG. 2.
FIG. 2.

Comparison of the voltage moments calculated for the shot-noise and diffusion-level dynamics. Three cases are considered for which is held constant (marked on panels) while is varied over its full range {0, 1} in the absence of inhibition. In the upper panels, for all cases (a)–(c), it is seen that the diffusion-level mean, Eq. (10) , and variance, Eq. (15) (here plotted in the form of the standard deviation), agree with the corresponding shot-noise moments derived from Eq. (19) . The diffusion-level skew, Eq. (16) , however, can be seen to be incorrect in comparison with the shot-noise form, Eq. (21) , even in its expected range of validity for small large. (a) Lower panel: the true skew is positive, whereas the diffusion approximation predicts a negative value. (c) Lower panel: both the shot-noise and diffusion-approximation skew are negative, but with different magnitudes. (b) Lower panel: the intermediate case. In all examples and .

Image of FIG. 3.
FIG. 3.

Comparison of shot-noise, diffusion-level, and Gaussian-approximation voltage densities for neurons receiving synapses with a distribution of amplitudes. The upper panels show example voltage trajectories for each case, where from (a) to (c), the dynamics becomes more diffusive and less shot-like. (a) Large-amplitude shot noise; , giving mean pulse amplitudes of from the leak potential . The Gaussian approximation gives a slightly better account of the full distribution, which is positively skewed, than the diffusion approximation does, which itself is negatively skewed. (b) Moderate-amplitude shot noise; , giving mean pulse amplitudes of from the leak potential . Again the full distribution shows a significant positive skew. As can be seen in the inset, the diffusion approximation, and to a lesser extent, the Gaussian approximation underestimate the probability density for . Despite being at the tail of this distribution, this difference could potentially cause a significant error for estimations of the firing rate of neurons in the presence of a threshold for the generation of outgoing action potentials, which is typically set in the range . (c) Low-amplitude shot noise; , giving mean pulse amplitudes of from the reversal leak . In this high-rate case corresponding to the diffusion limit, both the diffusion approximation and the full shot-noise distribution approach the Gaussian approximation. For all cases, the shot-noise distribution was calculated using the numerical scheme given in Eq. (37) with the leak potential set at and with .

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/content/aip/journal/chaos/16/2/10.1063/1.2203409
2006-06-30
2014-04-24
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Statistics of subthreshold neuronal voltage fluctuations due to conductance-based synaptic shot noise
http://aip.metastore.ingenta.com/content/aip/journal/chaos/16/2/10.1063/1.2203409
10.1063/1.2203409
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