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: .. math:: 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 :math:\eta_i is a spike-triggered current (stc), and the neuron model can have arbitrary number of them. Dynamic of each :math:\eta_i is described by: .. math:: \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): .. math:: \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: .. math:: \lambda(t) = \lambda_0 \cdot \exp (V(t)-V_T(t)) / \Delta_V where :math:V_T(t) is a time-dependent firing threshold: .. math:: V_T(t) = V_{T_{star}} + \gamma_1(t) + \gamma_2(t) + \ldots + \gamma_m(t) where :math:\gamma_i is a kernel of spike-frequency adaptation (sfa), and the neuron model can have arbitrary number of them. Dynamic of each :math:\gamma_i is described by: .. math:: \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): .. math:: \gamma_i = \gamma_i + q_{\gamma_i} \text{ (in case of spike emission).} Note: In the current implementation of the model, the values of :math:\eta_i and :math:\gamma_i are affected immediately after spike emission. However, GIF toolbox _, which fits the model using experimental data, requires a different set of :math:\eta_i and :math:\gamma_i. It applies the jump of :math:\eta_i and :math:\gamma_i after the refractory period. One can easily convert between :math:q_\eta/\gamma of these two approaches: .. math:: q{_\eta}_{giftoolbox} = q_{\eta_{NEST}} \cdot (1 - \exp( -\tau_{ref} / \tau_\eta )) The same formula applies for :math: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_neurons_singularity <../model_details/IAF_neurons_singularity.ipynb>_ 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 ++++++++ :doc:Neuron , :doc:Integrate-And-Fire , :doc:Current-Based