iaf_cond_beta

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

Description

iaf_cond_beta 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 a beta function. The beta function is normalised such that an event of weight 1.0 results in a peak current of 1 nS at \(t = \tau_{rise\_[ex|in]}\).

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

[4]

Rotter S, Diesmann M (1999). Exact simulation of time-invariant linear systems with applications to neuronal modeling. Biologial Cybernetics 81:381-402. DOI: https://doi.org/10.1007/s004220050570

[5]

Roth A and van Rossum M (2010). Chapter 6: Modeling synapses. in De Schutter, Computational Modeling Methods for Neuroscientists, MIT Press.

See also

iaf_cond_exp, iaf_cond_alpha

Parameters

Name	Physical unit	Default value	Description
E_L	mV	-70mV	Leak reversal potential (aka resting potential)
C_m	pF	250pF	Capacitance of the membrane
t_ref	ms	2ms	Refractory period
V_th	mV	-55mV	Threshold potential
V_reset	mV	-60mV	Reset potential
E_ex	mV	0mV	Excitatory reversal potential
E_in	mV	-85mV	Inhibitory reversal potential
g_L	nS	16.6667nS	Leak conductance
tau_syn_rise_I	ms	0.2ms	Synaptic time constant excitatory synapse
tau_syn_decay_I	ms	2ms	Synaptic time constant for inhibitory synapse
tau_syn_rise_E	ms	0.2ms	Synaptic time constant excitatory synapse
tau_syn_decay_E	ms	2ms	Synaptic time constant for inhibitory synapse
F_E	nS	0nS	Constant external input conductance (excitatory).
F_I	nS	0nS	Constant external input conductance (inhibitory).
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_in	real	0	inputs from the inhibitory conductance
g_in$	real	g_I_const * (1 / tau_syn_rise_I - 1 / tau_syn_decay_I)
g_ex	real	0	inputs from the excitatory conductance
g_ex$	real	g_E_const * (1 / tau_syn_rise_E - 1 / tau_syn_decay_E)

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

The model source code can be found in the NESTML models repository here: iaf_cond_beta.

Characterisation

Synaptic response

f-I curve