Magnus JE Richardson

Mark J Wall

Paul M Harrison

BMC Neuroscience

PubMed

Springer - Publisher Connector

POSTER PRESENTATION Open Access
Slow sodium-channel inactivation underlies
spike threshold variability
Paul M Harrison1,2,3*, Mark J Wall2, Magnus JE Richardson3
From Twenty Second Annual Computational Neuroscience Meeting: CNS*2013
Paris, France. 13-18 July 2013
Action potentials are triggered once a neuron has
received sufficient synaptic input to be depolarised
above threshold; however, this threshold is dynamic and
strongly correlated to the recent voltage history and
time since the last spike. Previous experimental mea-
surements from cortical layer-5 pyramidal neurons have
shown that after an action potential the threshold can
jump up to 10 mV and subsequently decays exponen-
tially back to its baseline value over a period of tens of
milliseconds [1,2]. Our recent experimental data indicate
that this behaviour is a common feature of neocortical
excitatory cells in different cortical layers.
One mechanism that modulates the spike threshold is
the degree and duration of sodium-channel inactivation.
In the standard Hodgkin-Huxley formulation of the
action potential only fast inactivation is present, with a
return to the baseline state within a few milliseconds
post-spike. However, a slow component of sodium inac-
tivation is also known to be present in neocortical cells
[3] with a time constant - of the order of tens of millise-
conds - that is similar to the experimentally measured
threshold decay.
To model the influence this mechanism has on spike
threshold we added a slow sodium inactivation variable
to the sodium current of an existing conductance-based
model [4]. We found that the augmented model now
exhibited a decaying threshold that was not present in
the original model, with similar properties to that
observed experimentally. An analysis of the spike-trig-
gered slow-inactivation variable dynamics demonstrated
that it could be accurately described by two parameters:
the post-spike level of inactivation and the time constant
of its decay back to an activated state. These gating
variable parameters could in turn be directly related to
the corresponding magnitude of the post-spike increase
of the threshold and the time constant of its decay to
baseline.
We next added this mechanism to the Exponential
Integrate-and-Fire model [5] to better quantitatively
understand the role of slow inactivation in modifying
spike behaviour under conditions of stochastic synaptic
drive at both the neuronal and network levels. Though
in general this is a two variable system comprising of
voltage and the post-spike threshold dynamics, we show
that if the membrane and threshold-relaxation time con-
stants are the same the system can be reduced to an
effective one-dimensional model amenable to standard
Fokker-Planck methods [6]. Finally, a perturbative
approach is introduced that allows for the calculation of
experimentally relevant quantities like the first-passage-
time density and spike-train spectra for the general case
where the two time constants differ.
Acknowledgements
We gratefully acknowledge funding for a studentship from the Engineering
and Physical Sciences Research Council through the MOAC Doctoral Training
Centre at the University of Warwick.
Author details
1MOAC DTC, University of Warwick, Coventry, CV4 7AL, UK. 2School of Life
Sciences, University of Warwick, Coventry, CV4 7AL, UK. 3Warwick Systems
Biology Centre, University of Warwick, Coventry, CV4 7AL, UK.
Published: 8 July 2013
References
1. Badel L, Lefort S, Brette R, Petersen CCH, Gerstner W, Richardson MJE:
Dynamic I-V Curves Are Reliable Predictors of Naturalistic Pyramidal-
Neuron Voltage Traces. Neurophysiol 2008, 99:656-666.
2. Badel L, Lefort S, Berger TK, Petersen CCH, Gerstner W, Richardson MJE:
Extracting Non-Linear Integrate-and-Fire Models from Experimental Data
Using Dynamic I-V Curves. Biol Cybern 2008, 99:361-370.
3. Fleidervish IA, Friedman A, Gutnick MJ: Slow Inactivation of Na+ Current
and Slow Cumulative Spike Adaptation in Mouse and Guinea-Pig
Neocortical Neurones in Slices. J Physiol 1996, , 493: 83-97.
* Correspondence: paul.harrison@warwick.ac.uk
1MOAC DTC, University of Warwick, Coventry, CV4 7AL, UK
Full list of author information is available at the end of the article
Harrison et al. BMC Neuroscience 2013, 14(Suppl 1):P322
http://www.biomedcentral.com/1471-2202/14/S1/P322
© 2013 Harrison et al; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons
Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in
any medium, provided the original work is properly cited.
4. Wang X, Buzsáki G: Gamma Oscillation by Synaptic Inhibition in a
Hippocampal Interneuronal Network Model. J Neurosci 1996,
16(20):6402-6413.
5. Fourcaud-Trocmé N, Hansel D, van Vreeswijk C, Brunel N: How Spike
Generation Mechanisms Determine the Neuronal Response to
Fluctuating Inputs. J Neurosci 23(37):11628-11640.
6. Richardson MJE: Firing-rate response of linear and nonlinear integrate-
and-fire neurons to modulated current-based and conductance-based
synaptic drive. Phys Rev E 2007, 76:021919.
doi:10.1186/1471-2202-14-S1-P322
Cite this article as: Harrison et al.: Slow sodium-channel inactivation
underlies spike threshold variability. BMC Neuroscience 2013 14(Suppl 1):
P322.
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Slow sodium-channel inactivation underlies spike threshold variability

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Slow sodium-channel inactivation underlies spike threshold variability

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