gif_psc_exp_multisynapse – Current-based generalized integrate-and-fire neuron model with multiple synaptic time constants¶
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_neurons_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¶
- 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