iaf_cond_alpha

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

Description

iaf_cond_alpha 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 alpha function. The alpha function is normalised such that an event of weight 1.0 results in a peak current of 1 nS at \(t = \tau_{syn}\).

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

Bernander O, Douglas RJ, Martin KAC, Koch C (1991). Synaptic background activity influences spatiotemporal integration in single pyramidal cells. Proceedings of the National Academy of Science USA, 88(24):11569-11573. DOI: https://doi.org/10.1073/pnas.88.24.11569

3

Kuhn A, Rotter S (2004) Neuronal integration of synaptic input in the fluctuation- driven regime. Journal of Neuroscience, 24(10):2345-2356 DOI: https://doi.org/10.1523/JNEUROSCI.3349-03.2004

See also

iaf_cond_exp

Authors

Schrader, Plesser

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

   equations:
     kernel g_in = (e/tau_syn_in) * t * exp(-t/tau_syn_in)
     kernel g_ex = (e/tau_syn_ex) * t * exp(-t/tau_syn_ex)

     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. 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

iaf_cond_alpha_nestml

f-I curve

iaf_cond_alpha_nestml