For the paper:

Platkiewicz J, Brette R (2011) Impact of fast sodium channel
inactivation on spike threshold dynamics and synaptic
integration. PLoS Comput Biol 7:e1001129-78


Neurons spike when their membrane potential exceeds a threshold
value. In central neurons, the spike threshold is not constant but
depends on the stimulation. Thus, input-output properties of neurons
depend both on the effect of presynaptic spikes on the membrane
potential and on the dynamics of the spike threshold. Among the
possible mechanisms that may modulate the threshold, one strong
candidate is Na channel inactivation, because it specifically impacts
spike initiation without affecting the membrane potential. We
collected voltage-clamp data from the literature and we found, based
on a theoretical criterion, that the properties of Na inactivation
could indeed cause substantial threshold variability by itself. By
analyzing simple neuron models with fast Na inactivation (one channel
subtype), we found that the spike threshold is correlated with the
mean membrane potential and negatively correlated with the preceding
depolarization slope, consistent with experiments. We then analyzed
the impact of threshold dynamics on synaptic integration. The
difference between the postsynaptic potential (PSP) and the dynamic
threshold in response to a presynaptic spike defines an effective
PSP. When the neuron is sufficiently depolarized, this effective PSP
is briefer than the PSP. This mechanism regulates the temporal window
of synaptic integration in an adaptive way. Finally, we discuss the
role of other potential mechanisms. Distal spike initiation, channel
noise and Na activation dynamics cannot account for the observed
negative slope-threshold relationship, while adaptive conductances
(e.g. K+) and Na inactivation can. We conclude that Na inactivation is
a metabolically efficient mechanism to control the temporal resolution
of synaptic integration.

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