mat2_psc_exp – Non-resetting leaky integrate-and-fire neuron model with exponential PSCs and adaptive threshold
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Description
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``mat2_psc_exp`` is an implementation of a leaky integrate-and-fire model
with exponential shaped postsynaptic currents (PSCs). Thus, postsynaptic
currents have an infinitely short rise time.
The threshold is lifted when the neuron is fired and then decreases in a
fixed time scale toward a fixed level [3]_.
The threshold crossing is followed by a total refractory period
during which the neuron is not allowed to fire, even if the membrane
potential exceeds the threshold. The membrane potential is NOT reset,
but continuously integrated.
The linear subthreshold dynamics is integrated by the Exact
Integration scheme [1]_. The neuron dynamics is solved on the time
grid given by the computation step size. Incoming as well as emitted
spikes are forced to that grid.
An additional state variable and the corresponding differential
equation represents a piecewise constant external current.
The general framework for the consistent formulation of systems with
neuron like dynamics interacting by point events is described in
[1]_. A flow chart can be found in [2]_.
The current implementation requires tau_m != tau_syn_{ex,in} to avoid
a degenerate case of the ODE describing the model [1]_. For very
similar values, numerics will be unstable.
The following state variables can be read out with the multimeter device:
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V_m mV Non-resetting membrane potential
V_th mV Two-timescale adaptive threshold
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Parameters
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The following parameters can be set in the status dictionary:
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C_m pF Capacity of the membrane
E_L mV Resting potential
tau_m ms Membrane time constant
tau_syn_ex ms Time constant of postsynaptic excitatory currents
tau_syn_in ms Time constant of postsynaptic inhibitory currents
t_ref ms Duration of absolute refractory period (no spiking)
V_m mV Membrane potential
I_e pA Constant input current
t_spike ms Point in time of last spike
tau_1 ms Short time constant of adaptive threshold
tau_2 ms Long time constant of adaptive threshold
alpha_1 mV Amplitude of short time threshold adaption [3]_
alpha_2 mV Amplitude of long time threshold adaption [3]_
omega mV Resting spike threshold (absolute value, not
relative to E_L as in [3]_)
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References
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.. [1] Rotter S and 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] Diesmann M, Gewaltig M-O, Rotter S, Aertsen A (2001). State
space analysis of synchronous spiking in cortical neural
networks. Neurocomputing 38-40:565-571.
DOI:https://doi.org/10.1016/S0925-2312(01)00409-X
.. [3] Kobayashi R, Tsubo Y and Shinomoto S (2009). Made-to-order
spiking neuron model equipped with a multi-timescale adaptive
threshold. Frontiers in Computuational Neuroscience 3:9.
DOI: https://doi.org/10.3389/neuro.10.009.2009
Sends
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SpikeEvent
Receives
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SpikeEvent, CurrentEvent, DataLoggingRequest
Examples using this model
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.. listexamples:: mat2_psc_exp