iaf_cond_exp_sfa_rr
iaf_cond_exp_sfa_rr - Conductance based leaky integrate-and-fire model with spike-frequency adaptation and relative refractory mechanisms
Description
iaf_cond_exp_sfa_rr is an implementation of a spiking neuron using integrate-and-fire dynamics with conductance-based synapses, with additional spike-frequency adaptation and relative refractory mechanisms as described in 2, page 166.
Incoming spike events induce a post-synaptic change of conductance modelled by an exponential function. The exponential function is normalised such that an event of weight 1.0 results in a peak current of 1 nS.
Outgoing spike events induce a change of the adaptation and relative refractory conductances by q_sfa and q_rr, respectively. Otherwise these conductances decay exponentially with time constants tau_sfa and tau_rr, respectively.
References
- 1
Meffin H, Burkitt AN, Grayden DB (2004). An analytical model for the large, fluctuating synaptic conductance state typical of neocortical neurons in vivo. Journal of Computational Neuroscience, 16:159-175. DOI: https://doi.org/10.1023/B:JCNS.0000014108.03012.81
- 2
Dayan P, Abbott LF (2001). Theoretical neuroscience: Computational and mathematical modeling of neural systems. Cambridge, MA: MIT Press. https://pure.mpg.de/pubman/faces/ViewItemOverviewPage.jsp?itemId=item_3006127
See also
aeif_cond_alpha, aeif_cond_exp, iaf_chxk_2008
Parameters
Name |
Physical unit |
Default value |
Description |
---|---|---|---|
V_th |
mV |
-57.0mV |
Threshold potential |
V_reset |
mV |
-70.0mV |
Reset potential |
t_ref |
ms |
0.5ms |
Refractory period |
g_L |
nS |
28.95nS |
Leak conductance |
C_m |
pF |
289.5pF |
Membrane capacitance |
E_exc |
mV |
0mV |
Excitatory reversal potential |
E_inh |
mV |
-75.0mV |
Inhibitory reversal potential |
E_L |
mV |
-70.0mV |
Leak reversal potential (aka resting potential) |
tau_syn_exc |
ms |
1.5ms |
Synaptic time constant of excitatory synapse |
tau_syn_inh |
ms |
10.0ms |
Synaptic time constant of inhibitory synapse |
q_sfa |
nS |
14.48nS |
Outgoing spike activated quantal spike-frequency adaptation conductance increase |
q_rr |
nS |
3214.0nS |
Outgoing spike activated quantal relative refractory conductance increase |
tau_sfa |
ms |
110.0ms |
Time constant of spike-frequency adaptation |
tau_rr |
ms |
1.97ms |
Time constant of the relative refractory mechanism |
E_sfa |
mV |
-70.0mV |
spike-frequency adaptation conductance reversal potential |
E_rr |
mV |
-70.0mV |
relative refractory mechanism conductance reversal 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_m |
mV |
E_L |
membrane potential |
g_sfa |
nS |
0nS |
inputs from the sfa conductance |
g_rr |
nS |
0nS |
inputs from the rr conductance |
Equations
Source code
neuron iaf_cond_exp_sfa_rr:
state:
r integer = 0 # counts number of tick during the refractory period
V_m mV = E_L # membrane potential
g_sfa nS = 0nS # inputs from the sfa conductance
g_rr nS = 0nS # inputs from the rr conductance
end
equations:
kernel g_inh = exp(-t / tau_syn_inh) # inputs from the inh conductance
kernel g_exc = exp(-t / tau_syn_exc) # inputs from the exc conductance
g_sfa'=-g_sfa / tau_sfa
g_rr'=-g_rr / tau_rr
inline I_syn_exc pA = convolve(g_exc,exc_spikes) * (V_m - E_exc)
inline I_syn_inh pA = convolve(g_inh,inh_spikes) * (V_m - E_inh)
inline I_L pA = g_L * (V_m - E_L)
inline I_sfa pA = g_sfa * (V_m - E_sfa)
inline I_rr pA = g_rr * (V_m - E_rr)
V_m'=(-I_L + I_e + I_stim - I_syn_exc - I_syn_inh - I_sfa - I_rr) / C_m
end
parameters:
V_th mV = -57.0mV # Threshold potential
V_reset mV = -70.0mV # Reset potential
t_ref ms = 0.5ms # Refractory period
g_L nS = 28.95nS # Leak conductance
C_m pF = 289.5pF # Membrane capacitance
E_exc mV = 0mV # Excitatory reversal potential
E_inh mV = -75.0mV # Inhibitory reversal potential
E_L mV = -70.0mV # Leak reversal potential (aka resting potential)
tau_syn_exc ms = 1.5ms # Synaptic time constant of excitatory synapse
tau_syn_inh ms = 10.0ms # Synaptic time constant of inhibitory synapse
q_sfa nS = 14.48nS # Outgoing spike activated quantal spike-frequency adaptation conductance increase
q_rr nS = 3214.0nS # Outgoing spike activated quantal relative refractory conductance increase
tau_sfa ms = 110.0ms # Time constant of spike-frequency adaptation
tau_rr ms = 1.97ms # Time constant of the relative refractory mechanism
E_sfa mV = -70.0mV # spike-frequency adaptation conductance reversal potential
E_rr mV = -70.0mV # relative refractory mechanism conductance reversal potential
# constant external input current
# constant external input current
I_e pA = 0pA
end
internals:
RefractoryCounts integer = steps(t_ref) # refractory time in steps
end
input:
inh_spikes nS <-inhibitory spike
exc_spikes nS <-excitatory spike
I_stim pA <-current
end
output: spike
update:
integrate_odes()
if r != 0: # neuron is absolute refractory
r = r - 1
V_m = V_reset # clamp potential
elif V_m >= V_th:
r = RefractoryCounts
V_m = V_reset # clamp potential
g_sfa += q_sfa
g_rr += q_rr
emit_spike()
end
end
end