Warning

This is A PREVIEW for NEST 3.0 and NOT an OFFICIAL RELEASE! Some functionality may not be available and information may be incomplete!

gif_cond_exp_multisynapse – Conductance-based generalized integrate-and-fire neuron with multiple synaptic time constants

Description

gif_cond_exp_multisynapse is the generalized integrate-and-fire neuron according to Mensi et al. (2012) 1 and Pozzorini et al. (2015) 2, with postsynaptic conductances in the form of truncated exponentials.

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:

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

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:

\[\tau_{\eta_i}*d{\eta_i}/dt = -\eta_i\]

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:

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

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:

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

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:

\[q_{\eta,giftoolbox} = q_{\eta,NEST} * (1 - \exp( -\tau_{ref} / \tau_\eta ))\]

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 synaptic conductance is exponential.

Parameters

The following parameters can be set in the status dictionary.

Membrane Parameters

C_m

pF

Capacity of the membrane

t_ref

ms

Duration of refractory period

V_reset

mV

Reset value for V_m after a spike

E_L

mV

Leak reversal potential

g_L

nS

Leak conductance

I_e

pA

Constant external 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

real

Stochastic intensity at firing threshold V_T i n 1/s.

V_T_star

mV

Base threshold

Synaptic parameters

tau_syn

list of ms

Time constants of the synaptic conductance (same size as E_rev)

E_rev

list of mV

Reversal potentials (same size as tau_syn)

Integration parameters

gsl_error_tol

real

This parameter controls the admissible error of the GSL integrator. Reduce it if NEST complains about numerical instabilities

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