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

Parameters

Name	Physical unit	Default value	Description
V_th	mV	-55mV	Threshold potential
V_reset	mV	-60mV	Reset potential
t_ref	ms	2ms	Refractory period
g_L	nS	16.6667nS	Leak conductance
C_m	pF	250pF	Membrane capacitance
E_exc	mV	0mV	Excitatory reversal potential
E_inh	mV	-85mV	Inhibitory reversal potential
E_L	mV	-70mV	Leak reversal potential (aka resting potential)
tau_syn_exc	ms	0.2ms	Synaptic time constant of excitatory synapse
tau_syn_inh	ms	2ms	Synaptic time constant of inhibitory synapse
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

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_inh = (e / tau_syn_inh) * t * exp(-t / tau_syn_inh)
    kernel g_exc = (e / tau_syn_exc) * t * exp(-t / tau_syn_exc)
    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_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 = -55mV # Threshold potential
    V_reset mV = -60mV # Reset potential
    t_ref ms = 2ms # Refractory period
    g_L nS = 16.6667nS # Leak conductance
    C_m pF = 250pF # Membrane capacitance
    E_exc mV = 0mV # Excitatory reversal potential
    E_inh mV = -85mV # Inhibitory reversal potential
    E_L mV = -70mV # Leak reversal potential (aka resting potential)
    tau_syn_exc ms = 0.2ms # Synaptic time constant of excitatory synapse
    tau_syn_inh ms = 2ms # Synaptic time constant of inhibitory synapse
    # 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
      emit_spike()
    end
  end

end

Characterisation

Synaptic response