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

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

iaf_cond_exp_nestml

f-I curve

iaf_cond_exp_nestml