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_ex	mV	0mV	Excitatory reversal Potential
E_in	mV	-75.0mV	Inhibitory reversal Potential
E_L	mV	-70.0mV	Leak reversal Potential (aka resting potential)
tau_syn_ex	ms	1.5ms	Synaptic Time Constant Excitatory Synapse
tau_syn_in	ms	10.0ms	Synaptic Time Constant for 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
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

\[\frac{ dg_{sfa} } { dt }= \frac{ -g_{sfa} } { \tau_{sfa} }\]

\[\frac{ dg_{rr} } { dt }= \frac{ -g_{rr} } { \tau_{rr} }\]

\[\frac{ dV_{m} } { dt }= \frac 1 { C_{m} } \left( { (-I_{L} + I_{e} + I_{stim} - I_{syn,exc} - I_{syn,inh} - I_{sfa} - I_{rr}) } \right)\]

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 = 0 nS     # inputs from the sfa conductance
     g_rr nS = 0 nS      # inputs from the rr conductance
   end

   equations:
     kernel g_in = exp(-t/tau_syn_in) # inputs from the inh conductance
     kernel g_ex = exp(-t/tau_syn_ex) # inputs from the exc conductance

     g_sfa' = -g_sfa / tau_sfa
     g_rr' = -g_rr / tau_rr

     inline I_syn_exc pA = convolve(g_ex, spikesExc) * ( V_m - E_ex )
     inline I_syn_inh pA = convolve(g_in, spikesInh) * ( V_m - E_in )
     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 = -57.0 mV      # Threshold Potential
     V_reset mV = -70.0 mV   # Reset Potential
     t_ref ms = 0.5 ms       # Refractory period
     g_L nS = 28.95 nS       # Leak Conductance
     C_m pF = 289.5 pF       # Membrane Capacitance
     E_ex mV = 0 mV          # Excitatory reversal Potential
     E_in mV = -75.0 mV      # Inhibitory reversal Potential
     E_L mV = -70.0 mV       # Leak reversal Potential (aka resting potential)
     tau_syn_ex ms = 1.5 ms  # Synaptic Time Constant Excitatory Synapse
     tau_syn_in ms = 10.0 ms # Synaptic Time Constant for Inhibitory Synapse
     q_sfa nS = 14.48 nS     # Outgoing spike activated quantal spike-frequency adaptation conductance increase
     q_rr nS = 3214.0 nS     # Outgoing spike activated quantal relative refractory conductance increase.
     tau_sfa ms = 110.0 ms   # Time constant of spike-frequency adaptation.
     tau_rr ms = 1.97 ms     # Time constant of the relative refractory mechanism.
     E_sfa mV = -70.0 mV     # spike-frequency adaptation conductance reversal potential
     E_rr mV = -70.0 mV      # relative refractory mechanism conductance reversal potential

     # constant external input current
     I_e pA = 0 pA
   end

   internals:
     RefractoryCounts integer = steps(t_ref) # refractory time in steps
   end

   input:
     spikesInh nS <- inhibitory spike
     spikesExc nS <- excitatory spike
     I_stim pA <- continuous
   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: # neuron is not absolute refractory
       r = RefractoryCounts
       V_m = V_reset # clamp potential
       g_sfa += q_sfa
       g_rr += q_rr
       emit_spike()
     end
   end
 end

Characterisation