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GIF model extensions
The content of this web page is associated with the publication:
Enhanced sensitivity to rapid input fluctuations by nonlinear threshold dynamics in neocortical pyramidal neurons
S. Mensi, O. Hagens, W. Gerstner and C. Pozzorini
PLOS Computational Biology 2016
In this paper, the GIF model introduced in our previous publication (Pozzorini et al. PLOS Comp. Biol. 2015) is extended by:
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Transforming the spike-triggered current in to a spike-triggered conductance;
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Coupling (nonlinearly and dynamically) the firing threshold to the subthreshold membrane potential.
The nonlinear coupling between membrane potential and firing threshold can be expressed either as a linear combination of rectangular basis functions (allowing for a non-parametric fit) or as a smooth linear rectifier accounting for fast Na-channel inactivation.
These models are now available in the GIFFittingToolbox, which was originally introduced in Pozzorini et al. 2015.
Detailed instructions on how to fit a GIF model to data can be found here. Before using the extended models, make sure you understand how to fit the GIF model to data.
The GIFFittingToolbox now includes several variants of the Generalized Integrate-and-Fire model:
Generalized Integrate-and-Fire model introduced in Pozzorini et al. 2015. Spikes are generated stochastically according to the escape rate model; the sub-threshold dynamics of the membrane potential is described by a leaky integrator extended with a spike-triggered conductance; the firing threshold dynamics is given by a baseline and includes spike-triggered movements.
GIF model extended with a dynamic, nonlinear coupling between membrane potential and firing threshold. The nonlinearity linking the firing threshold to the membrane potential is defined as a linear combination of rectangular basis function. This model, and its fitting procedure, allows to extract from data the shape of the nonlinear coupling without a priori assumptions. This model differs form the iGIF_NP model introduced in Mensi et al. PLOS Comp. Biol. 2016 only because spike-dependent adaptation is current-based and not conductance based.
To create a new model of this type, use the following code:
from iGIF_NP() import *
myiGIF_NP = iGIF_NP(0.1)
where the parameter 0.1 specify (in ms) the time step used for numerical integration.
In order to fit the iGIF_NP model to a set of experimental data previously loaded in an object Experiment use the following code:
myiGIF_NP.fit(experiment, theta_inf_nbbins=8, theta_tau_all=np.array([2.0, 6.0, 10.0]), DT_beforeSpike=5.0)
where experiment is an instance of the class Experiment containing the experimental data to be fitted; theta_if_nbbins specifies the number of rectangular functions used to define the nonlinear function coupling the firing threshold to the membrane potential; theta_tau_all is a numpy array specifying the time scales (in ms) of the threshold-voltage coupling that will be systematically explored during the fit; DT_beforeSpike defines the amount of data (in ms) that are discarded before each spike when fitting the parameters controlling the sub threshold voltage dynamics.
GIF model extended with a dynamic, nonlinear coupling between membrane potential and firing threshold. The nonlinearity linking the firing threshold to the membrane potential is defined a smooth linear rectifier. This model differs form the iGIF_Na model introduced in Mensi et al. PLOS Comp. Biol. 2016 only because spike-dependent adaptation is current-based and not conductance based.
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