A nonlinear coupling between the firing threshold and the membrane potential enhances coding of rapid signals
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1
EPFL, Brain Mind Institute, Switzerland
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2
EPFL, Brain Mind Institute, Switzerland
In the field of computational neuroscience it is of crucial importance to dispose of simplified spiking models that carefully capture the spiking activity of real neurons. Generalized Integrate-and-Fire (GIF) models have recently been shown to predict the occurrence of individual spikes of both inhibitory and excitatory neurons with millisecond precision. However, while the f-I curves of inhibitory fast-spiking neurons are in good agreement with the ones predicted by GIF models, the same is not true for excitatory pyramidal neurons. In particular, standard GIF models do not capture saturation at relatively low rates. Moreover, in contrast to what has been observed in pyramidal neurons, the firing threshold of standard GIF models does not depend on the speed at which the membrane potential approaches this threshold.
To solve this problem, we propose a new model in which a stochastic GIF model equipped with both a spike-triggered current and a spike-triggered movement of the firing threshold is extended with a subthreshold adaptation mechanism consisting of a nonlinear coupling between the firing threshold and the membrane potential. This additional mechanism can be interpreted as a phenomenological model of sodium channel inactivation. Importantly, all the model parameters, including the timescale and the functional shape of the nonlinear coupling, are not assumed a priori but are extracted from in vitro recordings using a convex optimization procedure.
Our results demonstrate that, in pyramidal neurons, the firing threshold and the subthreshold membrane potential are indeed nonlinearly coupled. Consistent with the dynamics of sodium channel inactivation, we found that this mechanism operates on a relatively short timescale (5 ms) and makes the firing threshold dependent on the speed at which the threshold is approached. The precise shape of the nonlinear coupling extracted from the experimental data accounts for both the saturation at low rates and the noise sensitivity observed in pyramidal neurons. Moreover, accounting for sodium channel inactivation significantly improved the ability to predict individual spikes with millisecond precision.
Our results suggest that the firing threshold dynamics enhances sensitivity to rapid fluctuations of the input and makes pyramidal neurons respond as differentiate-and-fire rather than integrate-and-fire.
Keywords:
spiking neuron models,
Single Neuron Dynamics,
Neural coding,
Single Neuron Adaptation,
spike-frequency adaptation
Conference:
Neuroinformatics 2013, Stockholm, Sweden, 27 Aug - 29 Aug, 2013.
Presentation Type:
Poster
Topic:
Computational neuroscience
Citation:
Pozzorini
C,
Mensi
S,
Hagens
O and
Gerstner
W
(2013). A nonlinear coupling between the firing threshold and the membrane potential enhances coding of rapid signals.
Front. Neuroinform.
Conference Abstract:
Neuroinformatics 2013.
doi: 10.3389/conf.fninf.2013.09.00119
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Received:
29 Apr 2013;
Published Online:
11 Jul 2013.
*
Correspondence:
Mr. Christian Pozzorini, EPFL, Brain Mind Institute, Lausanne, Vaud, CH-1015, Switzerland, christian.pozzorini@epfl.ch