iaf_cond_exp

iaf_cond_exp - Simple conductance based leaky integrate-and-fire neuron model

Description

iaf_cond_exp is an implementation of a spiking neuron using IAF dynamics with conductance-based synapses. 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 conductance of 1 nS.

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

See also

iaf_psc_delta, iaf_psc_exp, iaf_cond_exp

Author

Sven Schrader

Parameters

Name	Physical unit	Default value	Description
V_th	mV	-55.0mV	Threshold Potential
V_reset	mV	-60.0mV	Reset Potential
t_ref	ms	2.0ms	Refractory period
g_L	nS	16.6667nS	Leak Conductance
C_m	pF	250.0pF	Membrane Capacitance
E_ex	mV	0mV	Excitatory reversal Potential
E_in	mV	-85.0mV	Inhibitory reversal Potential
E_L	mV	-70.0mV	Leak reversal Potential (aka resting potential)
tau_syn_ex	ms	0.2ms	Synaptic Time Constant Excitatory Synapse
tau_syn_in	ms	2.0ms	Synaptic Time Constant for Inhibitory Synapse
I_e	pA	0pA	constant external input current

State variables

Name	Physical unit	Default value	Description
V_m	mV	E_L	membrane potential

Equations

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

Source code

neuron iaf_cond_exp:
   state:
     r integer = 0     # counts number of tick during the refractory period
     V_m mV = E_L     # membrane potential
   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

     inline I_syn_exc pA = convolve(g_ex, spikeExc) * ( V_m - E_ex )
     inline I_syn_inh pA = convolve(g_in, spikeInh) * ( V_m - E_in )
     inline I_leak pA = g_L * ( V_m - E_L )
     V_m' = ( -I_leak - I_syn_exc - I_syn_inh + I_e + I_stim ) / C_m
   end

   parameters:
     V_th mV = -55.0 mV     # Threshold Potential
     V_reset mV = -60.0 mV  # Reset Potential
     t_ref ms = 2.0 ms      # Refractory period
     g_L nS = 16.6667 nS    # Leak Conductance
     C_m pF = 250.0 pF      # Membrane Capacitance
     E_ex mV = 0 mV         # Excitatory reversal Potential
     E_in mV = -85.0 mV     # Inhibitory reversal Potential
     E_L mV = -70.0 mV      # Leak reversal Potential (aka resting potential)
     tau_syn_ex ms = 0.2 ms # Synaptic Time Constant Excitatory Synapse
     tau_syn_in ms = 2.0 ms # Synaptic Time Constant for Inhibitory Synapse

     # constant external input current
     I_e pA = 0 pA
   end

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

   input:
     spikeInh nS <- inhibitory spike
     spikeExc 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
       emit_spike()
     end

   end

 end

Characterisation

Synaptic response

f-I curve