gif_psc_exp_multisynapse – Current-based generalized integrate-and-fire neuron (GIF) model with multiple synaptic time constants (from the Gerstner lab)¶
Description¶
gif_psc_exp_multisynapse
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:
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:
and in case of spike emission, its value increased by a constant (which can be positive or negative):
Neuron produces spikes stochastically according to a point process with the firing intensity:
where \(V_T(t)\) is a time-dependent firing threshold:
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:
and in case of spike emission, its value increased by a constant (which can be positive or negative):
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:
The same formula applies for \(q_{\gamma}\).
On the postsynaptic side, there can be arbitrarily many synaptic time constants
(gif_psc_exp
has exactly two: tau_syn_ex
and tau_syn_in
). This can be reached
by specifying separate receptor ports, each for a different time constant. The
port number has to match the respective receptor_type
in the connectors.
The shape of postsynaptic current is exponential.
Note
If tau_m
is very close to a synaptic time constant, the model
will numerically behave as if tau_m
is equal to the synaptic
time constant, 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 |
||
Delta_V |
mV |
Noise level of escape rate |
tau_m |
ms |
Membrane time constant |
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 |
list of ms |
Time constants of the synaptic currents |
References¶
Sends¶
SpikeEvent
Receives¶
SpikeEvent, CurrentEvent, DataLoggingRequest