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