gif_psc_exp – Current-based generalized integrate-and-fire neuron (GIF) model (from the Gerstner lab)

Description

gif_psc_exp is the generalized integrate-and-fire neuron according to Mensi et al. (2012) [1] and Pozzorini et al. (2015) [2], with exponential shaped postsynaptic currents.

This model features both an adaptation current and a dynamic threshold for spike-frequency adaptation. The membrane potential (V) is described by the differential equation:

\[C \cdot dV(t)/dt = -g_L \cdot (V(t)-E_L) - \eta_1(t) - \eta_2(t) - \ldots - \eta_n(t) + I(t)\]

where each \(\eta_i\) is a spike-triggered current (stc), and the neuron model can have arbitrary number of them. Dynamic of each \(\eta_i\) is described by:

\[\tau_\eta{_i} \cdot d{\eta_i}/dt = -\eta_i\]

and in case of spike emission, its value increased by a constant (which can be positive or negative):

\[\eta_i = \eta_i + q_{\eta_i} \text{ (in case of spike emission).}\]

Neuron produces spikes stochastically according to a point process with the firing intensity:

\[\lambda(t) = \lambda_0 \cdot \exp (V(t)-V_T(t)) / \Delta_V\]

where \(V_T(t)\) is a time-dependent firing threshold:

\[V_T(t) = V_{T_{star}} + \gamma_1(t) + \gamma_2(t) + \ldots + \gamma_m(t)\]

where \(\gamma_i\) is a kernel of spike-frequency adaptation (sfa), and the neuron model can have arbitrary number of them. Dynamic of each \(\gamma_i\) is described by:

\[\tau_{\gamma_i} \cdot d\gamma_i/dt = -\gamma_i\]

and in case of spike emission, its value increased by a constant (which can be positive or negative):

\[\gamma_i = \gamma_i + q_{\gamma_i} \text{ (in case of spike emission).}\]

Note:

In the current implementation of the model, the values of \(\eta_i\) and \(\gamma_i\) are affected immediately after spike emission. However, GIF toolbox, which fits the model using experimental data, requires a different set of \(\eta_i\) and \(\gamma_i\). It applies the jump of \(\eta_i\) and \(\gamma_i\) after the refractory period. One can easily convert between \(q_\eta/\gamma\) of these two approaches:

\[q{_\eta}_{giftoolbox} = q_{\eta_{NEST}} \cdot (1 - \exp( -\tau_{ref} / \tau_\eta ))\]

The same formula applies for \(q_{\gamma}\).

The shape of postsynaptic current is exponential.

Note

If tau_m is very close to tau_syn_ex or tau_syn_in, the model will numerically behave as if tau_m is equal to tau_syn_ex or tau_syn_in, respectively, to avoid numerical instabilities.

For implementation details see the IAF Integration Singularity notebook.

Parameters

The following parameters can be set in the status dictionary.

Membrane Parameters
C_m	pF	Capacitance of the membrane
t_ref	ms	Duration of refractory period
V_reset	mV	Membrane potential is reset to this value after a spike
E_L	mV	Resting potential
g_L	nS	Leak conductance
I_e	pA	Constant input current

Spike adaptation and firing intensity parameters
q_stc	list of nA	Values added to spike-triggered currents (stc) after each spike emission
tau_stc	list of ms	Time constants of stc variables
q_sfa	list of mV	Values added to spike-frequency adaptation (sfa) after each spike emission
tau_sfa	list of ms	Time constants of sfa variables
Delta_V	mV	Stochasticity level
lambda_0	1/s	Stochastic intensity at firing threshold V_T
V_T_star	mV	Base threshold

Synaptic parameters
tau_syn_ex	ms	Time constant of excitatory synaptic conductance
tau_syn_in	ms	Time constant of the inhibitory synaptic conductance

References

[1]

Mensi S, Naud R, Pozzorini C, Avermann M, Petersen CC, Gerstner W (2012) Parameter extraction and classification of three cortical neuron types reveals two distinct adaptation mechanisms. Journal of Neurophysiology, 107(6):1756-1775. DOI: https://doi.org/10.1152/jn.00408.2011

[2]

Pozzorini C, Mensi S, Hagens O, Naud R, Koch C, Gerstner W (2015). Automated high-throughput characterization of single neurons by means of simplified spiking models. PLoS Computational Biology, 11(6), e1004275. DOI: https://doi.org/10.1371/journal.pcbi.1004275

Sends

SpikeEvent

Receives

SpikeEvent, CurrentEvent, DataLoggingRequest

See also

Neuron, Integrate-And-Fire, Current-Based

Examples using this model

• Population of GIF neuron model with oscillatory behavior

• Population rate model of generalized integrate-and-fire neurons