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_exc

mV

0mV

Excitatory reversal potential

E_inh

mV

-75.0mV

Inhibitory reversal potential

E_L

mV

-70.0mV

Leak reversal potential (aka resting potential)

tau_syn_exc

ms

1.5ms

Synaptic time constant of excitatory synapse

tau_syn_inh

ms

10.0ms

Synaptic time constant of 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

r

integer

0

counts number of tick during the refractory period

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 = 0nS # inputs from the sfa conductance
    g_rr nS = 0nS # inputs from the rr conductance
  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
    g_sfa'=-g_sfa / tau_sfa
    g_rr'=-g_rr / tau_rr
    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_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 = -57.0mV # 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_exc mV = 0mV # Excitatory reversal potential
    E_inh mV = -75.0mV # Inhibitory reversal potential
    E_L mV = -70.0mV # Leak reversal potential (aka resting potential)
    tau_syn_exc ms = 1.5ms # Synaptic time constant of excitatory synapse
    tau_syn_inh ms = 10.0ms # Synaptic time constant of 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
    # 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
      g_sfa += q_sfa
      g_rr += q_rr
      emit_spike()
    end
  end

end

Characterisation