TITLE Fluctuating conductances
COMMENT

chris deister: This mod file was written by A. Destexhe (thank you), I
used and modified the file to approximate a noisy leak conductance. So
I got rid of inhibition (g_i) etc. resulting in only one conductance
not two. std_e and tau_e were controlled by me in the sim and usually
set to 0.001 and 5, respectively and is set in the hoc files.
20101021 ModelDB Administrator: Ted Carnevale identified three bugs
in the BREAKPOINT block. One bug would have affected simulations
run with tau_e == 0. The second bug was "latent" i.e. it would
only emerge if a naive fix were applied to the first bug
in which case it would cause simulations run with tau_e == 0 to be
wildly incorrect. The third bug was that, under certain conditions,
a minor range variable would not be updated at each fadvance.
All three bugs have now been fixed.
Also note that the current and conductance units in this mechanism
are all "absolute" i.e. not density units. This is because the original
implementation by Destexhe was as a POINT_PROCESS, but the authors are
using it here as a density mechanism without having converted to density
units. In its present form the mechanism works in the sense that
it can produce valid simulations. However, its current and conductance
values should be interpreted as having density units, i.e. mA/cm2 and S/cm2,
respectively. In other words, the net current delivered by the mechanism
to any compartment is the product of the numerical value of its i
(interpreted as mA/cm2) and the compartment surface area (in cm2).
Likewise, the net conductance presented by this mechanism to any
compartment is the product of its ge (interpreted as S/cm2) and the
compartment surface area. See ModelDB for the author's
original version of syn.mod.
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 OrnsteinUhlenbeck (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 * (1exp(2*dt/tau)) ) and N(0,1) is a normal
random number (avg=0, sigma=1)
IMPLEMENTATION
This mechanism is implemented as a nonspecific current defined as a
point process.
PARAMETERS
The mechanism takes the following parameters:
E_e = 70 (mV) : reversal potential of excitatory conductance
E_i = 75 (mV) : reversal potential of inhibitory conductance
g_e0 = 0.0121 (umho) : average excitatory conductance
g_i0 = 0.0573 (umho) : average inhibitory conductance
std_e = 0.0030 (umho) : standard dev of excitatory conductance
std_i = 0.0066 (umho) : 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
A. Destexhe, Laval University, 1999

ENDCOMMENT
INDEPENDENT {t FROM 0 TO 1 WITH 1 (ms)}
NEURON {
SUFFIX Gfluct
RANGE g_e, E_e, g_e0,g_e1
RANGE std_e, tau_e, D_e
RANGE new_seed
NONSPECIFIC_CURRENT i
}
UNITS {
(nA) = (nanoamp)
(mV) = (millivolt)
(umho) = (micromho)
}
PARAMETER {
dt (ms)
E_e = 0 (mV) : reversal potential of excitatory conductance
g_e0 = 0.0121 (umho) : average excitatory conductance
std_e = 0.0030 (umho) : standard dev of excitatory conductance
tau_e = 2.728 (ms) : time constant of excitatory conductance
}
ASSIGNED {
v (mV) : membrane voltage
i (nA) : fluctuating current
g_e (umho) : total excitatory conductance
g_e1 (umho) : fluctuating excitatory conductance
D_e (umho umho /ms) : excitatory diffusion coefficient
exp_e
amp_e (umho)
xtemp (1)
}
INITIAL {
g_e1 = 0
if(tau_e != 0) {
D_e = 2 * std_e * std_e / tau_e
exp_e = exp(dt/tau_e)
amp_e = std_e * sqrt( (1exp(2*dt/tau_e)) )
}
}
BREAKPOINT {
SOLVE oup
i = g_e * (v  E_e)
}
PROCEDURE oup() {
xtemp = normrand(0,1)
if(tau_e==0) {
g_e1 = std_e * xtemp
g_e = g_e1
} else {
g_e1 = exp_e * g_e1 + amp_e * xtemp
g_e = g_e0 + g_e1
}
}
PROCEDURE new_seed(seed) { : procedure to set the seed
set_seed(seed)
VERBATIM
printf("Setting random generator with seed = %g\n", _lseed);
ENDVERBATIM
}
