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

SpikeEvent

## Receives¶

SpikeEvent, CurrentEvent, DataLoggingRequest