iaf_psc_exp_dend
iaf_psc_exp_dend  Leaky integrateandfire neuron model with exponential PSCs
Description
iaf_psc_exp is an implementation of a leaky integrateandfire model with exponentialkernel postsynaptic currents (PSCs) according to 1. 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.
Note
If tau_m is very close to tau_syn_ex or tau_syn_in, numerical problems may arise due to singularities in the propagator matrics. If this is the case, replace equalvalued parameters by a single parameter.
For details, please see IAF_neurons_singularity.ipynb
in
the NEST source code (docs/model_details
).
References
 1
Tsodyks M, Uziel A, Markram H (2000). Synchrony generation in recurrent networks with frequencydependent synapses. The Journal of Neuroscience, 20,RC50:15. URL: https://infoscience.epfl.ch/record/183402
See also
iaf_cond_exp
Parameters
Name 
Physical unit 
Default value 
Description 

C_m 
pF 
250pF 
Capacity of the membrane 
tau_m 
ms 
10ms 
Membrane time constant 
tau_syn_inh 
ms 
2ms 
Time constant of inhibitory synaptic current 
tau_syn_exc 
ms 
2ms 
Time constant of excitatory synaptic current 
t_ref 
ms 
2ms 
Duration of refractory period 
E_L 
mV 
70mV 
Resting potential 
V_reset 
mV 
70mV  E_L 
reset value of the membrane potential 
Theta 
mV 
55mV  E_L 
Threshold, RELATIVE TO RESTING POTENTIAL (!). 
I_e 
pA 
0pA 
constant external input current 
State variables
Name 
Physical unit 
Default value 
Description 

r 
integer 
0 
counts number of tick during the refractory period 
V_abs 
mV 
0mV 

I_dend 
pA 
0pA 
third factor, to be read out by synapse during weight update 
Equations
Source code
neuron iaf_psc_exp_dend:
state:
r integer = 0 # counts number of tick during the refractory period
V_abs mV = 0mV
I_dend pA = 0pA # third factor, to be read out by synapse during weight update
end
equations:
kernel I_kernel_inh = exp(t / tau_syn_inh)
kernel I_kernel_exc = exp(t / tau_syn_exc)
recordable inline V_m mV = V_abs + E_L # Membrane potential.
inline I_syn pA = convolve(I_kernel_exc,exc_spikes)  convolve(I_kernel_inh,inh_spikes)
V_abs'=V_abs / tau_m + (I_syn + I_e + I_stim) / C_m
end
parameters:
C_m pF = 250pF # Capacity of the membrane
tau_m ms = 10ms # Membrane time constant
tau_syn_inh ms = 2ms # Time constant of inhibitory synaptic current
tau_syn_exc ms = 2ms # Time constant of excitatory synaptic current
t_ref ms = 2ms # Duration of refractory period
E_L mV = 70mV # Resting potential
V_reset mV = 70mV  E_L # reset value of the membrane potential
Theta mV = 55mV  E_L # Threshold, RELATIVE TO RESTING POTENTIAL (!).
# I.e. the real threshold is (E_L_+V_th_)
# constant external input current
I_e pA = 0pA
end
internals:
RefractoryCounts integer = steps(t_ref) # refractory time in steps
end
input:
exc_spikes pA <excitatory spike
inh_spikes pA <inhibitory spike
I_stim pA <current
end
output: spike
update:
I_dend *= 0.95
if r == 0: # neuron not refractory, so evolve V
integrate_odes()
else:
r = r  1 # neuron is absolute refractory
end
if V_abs >= Theta: # threshold crossing
r = RefractoryCounts
V_abs = V_reset
emit_spike()
end
end
end