iaf_psc_exp – Leaky integrate-and-fire neuron model with exponential PSCs

Description

iaf_psc_exp is an implementation of a leaky integrate-and-fire model with exponential shaped postsynaptic currents (PSCs) according to equations 1, 2, 4 and 5 of [1] and equation 3 of [2]. Thus, postsynaptic currents have an infinitely short 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 and spiking is prohibited.

The linear subthreshold dynamics are integrated by the Exact Integration scheme [3]. 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 [4].

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_ex	ms	Exponential decay time constant of excitatory synaptic current kernel
tau_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]

Burkitt A N (2006). A review of the integrate-and-fire neuron model: I. Homogeneous synaptic input. Biologial Cybernetics 95:1-19. DOI: https://doi.org/10.1007/s00422-006-0068-6

[2]

Hanuschkin A, Kunkel S, Helias M, Morrison A, Diesmann M (2010). A general and efficient methof for incorporating precise spike times in globally time-driven simulations. Frontiers in Neuroinformatics. DOI: https://doi.org/10.3389/fninf.2010.00113

[3]

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

[4]

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

Neuron, Integrate-And-Fire, Current-Based