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Gfluctdv.mod
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Gfluctdv.mod
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TITLE Fluctuating conductances
COMMENT
-----------------------------------------------------------------------------
Fluctuating conductance model for synaptic bombardment
======================================================
THEORY
Synaptic bombardment is represented by a stochastic model containing
two fluctuating conductances g_e(t) and g_i(t) descibed by:
Isyn = g_e(t) * [V - E_e] + g_i(t) * [V - E_i]
d g_e / dt = -(g_e - g_e0) / tau_e + sqrt(D_e) * Ft
d g_i / dt = -(g_i - g_i0) / tau_i + sqrt(D_i) * Ft
where E_e, E_i are the reversal potentials, g_e0, g_i0 are the average
conductances, tau_e, tau_i are time constants, D_e, D_i are noise diffusion
coefficients and Ft is a gaussian white noise of unit standard deviation.
g_e and g_i are described by an Ornstein-Uhlenbeck (OU) stochastic process
where tau_e and tau_i represent the "correlation" (if tau_e and tau_i are
zero, g_e and g_i are white noise). The estimation of OU parameters can
be made from the power spectrum:
S(w) = 2 * D * tau^2 / (1 + w^2 * tau^2)
and the diffusion coeffient D is estimated from the variance:
D = 2 * sigma^2 / tau
NUMERICAL RESOLUTION
The numerical scheme for integration of OU processes takes advantage
of the fact that these processes are gaussian, which led to an exact
update rule independent of the time step dt (see Gillespie DT, Am J Phys
64: 225, 1996):
x(t+dt) = x(t) * exp(-dt/tau) + A * N(0,1)
where A = sqrt( D*tau/2 * (1-exp(-2*dt/tau)) ) and N(0,1) is a normal
random number (avg=0, sigma=1)
IMPLEMENTATION
This version has changed from point process nonspecific current to density
PARAMETERS
The mechanism takes the following parameters:
E_e = 0 (mV) : reversal potential of excitatory conductance
E_i = -75 (mV) : reversal potential of inhibitory conductance
g_e0 = 0.0001 (S/cm2) : average excitatory conductance
g_i0 = 0.0005 (S/cm2) : average inhibitory conductance
std_e = 3e-5 (S/cm2) : standard dev of excitatory conductance
std_i = 6e-5 (S/cm2) : standard dev of inhibitory conductance
tau_e = 2.728 (ms) : time constant of excitatory conductance
tau_i = 10.49 (ms) : time constant of inhibitory conductance
Gfluct2: conductance cannot be negative
REFERENCE
Destexhe, A., Rudolph, M., Fellous, J-M. and Sejnowski, T.J.
Fluctuating synaptic conductances recreate in-vivo--like activity in
neocortical neurons. Neuroscience 107: 13-24 (2001).
(electronic copy available at http://cns.iaf.cnrs-gif.fr)
A. Destexhe, 1999
Modified 04/09/08 by RKP so that current can be varied continuously over the course of a simulation
-----------------------------------------------------------------------------
ENDCOMMENT
INDEPENDENT {t FROM 0 TO 1 WITH 1 (ms)}
NEURON {
SUFFIX Gfluctdv
RANGE g_e, g_i, E_e, E_i, g_e0, g_i0, g_e1, g_i1
RANGE std_e, std_i, tau_e, tau_i, D_e, D_i
GLOBAL multex,multin
NONSPECIFIC_CURRENT i
}
UNITS {
(mV) = (millivolt)
(mA) = (milliamp)
(S) = (siemens)
}
PARAMETER {
dt (ms)
E_e = 0 (mV) : reversal potential of excitatory conductance
E_i = -75 (mV) : reversal potential of inhibitory conductance
g_e0 = 0.0001 (S/cm2) : average excitatory conductance
g_i0 = 0.0005 (S/cm2) : average inhibitory conductance
std_e = 3e-5 (S/cm2) : standard dev of excitatory conductance
std_i = 6e-5 (S/cm2) : standard dev of inhibitory conductance
tau_e = 2.728 (ms) : time constant of excitatory conductance
tau_i = 10.49 (ms) : time constant of inhibitory conductance
multex=0
multin=0
}
ASSIGNED {
v (mV) : membrane voltage
i (mA/cm2) : fluctuating current
g_e (S/cm2) : total excitatory conductance
g_i (S/cm2) : total inhibitory conductance
g_e1 (S/cm2) : fluctuating excitatory conductance
g_i1 (S/cm2) : fluctuating inhibitory conductance
D_e (umho umho /ms) : excitatory diffusion coefficient
D_i (umho umho /ms) : inhibitory diffusion coefficient
exp_e
exp_i
amp_e (umho)
amp_i (umho)
}
INITIAL {
g_e1 = 0
g_i1 = 0
if(tau_e != 0) {
D_e = 2 * std_e * std_e / tau_e
exp_e = exp(-dt/tau_e)
amp_e =sqrt(multex)*std_e * sqrt( (1-exp(-2*dt/tau_e)) )
}
if(tau_i != 0) {
D_i = 2 * std_i * std_i / tau_i
exp_i = exp(-dt/tau_i)
amp_i = sqrt(multin)*std_i * sqrt( (1-exp(-2*dt/tau_i)) )
}
}
BREAKPOINT {
SOLVE oup
if(tau_e==0) {
g_e = std_e * normrand(0,1)
}
if(tau_i==0) {
g_i = std_i * normrand(0,1)
}
g_e = multex*g_e0 + g_e1
if(g_e < 0) { g_e = 0 }
g_i = multin* g_i0 + g_i1
if(g_i < 0) { g_i = 0 }
i = g_e * (v - E_e) + g_i * (v - E_i)
}
PROCEDURE oup() { : use Scop function normrand(mean, std_dev)
if(tau_e!=0) {
amp_e =sqrt(multex)*std_e * sqrt( (1-exp(-2*dt/tau_e)) )
g_e1 = exp_e * g_e1 + amp_e * normrand(0,1)
}
if(tau_i!=0) {
amp_i = sqrt(multin)*std_i * sqrt( (1-exp(-2*dt/tau_i)) )
g_i1 = exp_i * g_i1 + amp_i * normrand(0,1)
}
}
PROCEDURE new_seed(seed) { : procedure to set the seed
set_seed(seed)
VERBATIM
printf("Setting random generator with seed = %g\n", _lseed);
ENDVERBATIM
}