iaf_psc_alpha – Leaky integrate-and-fire neuron model with alpha-function shaped PSCs ===================================================================================== Description +++++++++++ iaf_psc_alpha is an implementation of a leaky integrate-and-fire model with alpha-function shaped postsynaptic currents (PSCs). Thus, postsynaptic currents have a finite rise time. The threshold crossing is followed by an absolute refractory period (t_ref) during which the membrane potential is clamped to the resting potential. The linear subthreshold dynamics are integrated by the Exact Integration scheme [1]_. The neuron dynamics are solved on the time grid given by the computational step size. Incoming as well as emitted spikes are forced into that grid. An additional state variable and the corresponding differential equation represent a piecewise constant external current. For conversion between postsynaptic potentials (PSPs) and PSCs, please refer to the ``postsynaptic_potential_to_current`` function in the ``helpers.py`` script of the Cortical Microcircuit model of [2]_. .. 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. Parameters ++++++++++ The following parameters can be set in the status dictionary. ============ ======= ======================================================== V_m_rel mV Membrane potential in mV (relative to resting potential) I_syn_ex pA Excitatory synaptic current I_syn_in pA Inhibitory synaptic current tau_m ms Membrane time constant C_m pF Capacity of the membrane E_L mV Resting membrane potential I_e pA Constant input current Theta_rel mV Spike threshold in mV (relative to resting potential) V_reset_rel mV Reset membrane potential after a spike tau_syn_ex ms Exponential decay time constant of excitatory synaptic current kernel tau_syn_in ms Exponential decay time constant of inhibitory synaptic current kernel t_ref ms Duration of refractory period (V_m = V_reset) den_delay ms Dendritic delay ============ ======= ======================================================== References ++++++++++ .. [1] Rotter S, Diesmann M (1999). Exact simulation of time-invariant linear systems with applications to neuronal modeling. Biologial Cybernetics 81:381-402. DOI: https://doi.org/10.1007/s004220050570 .. [2] Potjans TC. and Diesmann M. 2014. The cell-type specific cortical microcircuit: relating structure and activity in a full-scale spiking network model. Cerebral Cortex. 24(3):785–806. DOI: https://doi.org/10.1093/cercor/bhs358. See also ++++++++ :doc:`Neuron `, :doc:`Integrate-And-Fire `, :doc:`Current-Based `