thesis

218 Détection de coïncidences dans les neurones bruités
a
σ (mV)
b
σ (mV)
p=10
Theory S
w (mV)
Theory Sp
σ (mV)
c
Sp
pw (mV) pw (mV)
Simulation S
w (mV)
Figure 8.8 – Influence of background noise on coincidence sensitivity in a neuron
model. a. Coincidence sensitivity (color-coded) as a function of the standard deviation σ of
the membrane potential and the PSP size w, according to our theory (probabilistic model of
Figure 8.5) and measured in numerical simulations. The threshold was 10 mV above the mean
membrane potential and the time constant of background fluctuations was τN = 15 ms. b.
Coincidence sensitivity Sp for p coincident vs. non-coincident spikes, as a function of σ and the
total depolarization pw, for p = 10. c. Coincidence sensitivity Sp for σ = 4 mV as a function of
pw, when both p and w are varied (grey area). The dashed line shows the theoretical prediction
for many small PSPs S∞.
distribution is flat (all voltages are equally likely) and two coincident spikes have
the same effect as two non-coincident spikes. These theoretical predictions accurately
matched numerical results obtained in neuron models with simulated input
currents (Figure 8.8a, right).
It could be argued that 5 mV is unreasonably large for a PSP. However, the
same analysis applies when considering p small PSPs instead of 2 large PSPs
(Figure 8.8b, p = 10 and w is varied between 0 and 1 mV) : 10 coincident PSPs of
1 mV produce on average 0.5 more output spikes than if they were not coincident.
In fact, when the number of input spikes p is large, the coincidence sensitivity Sp
is mainly determined by the total depolarization pw, because small isolated PSPs