TITLE Fluctuating conductances
COMMENT
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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 mechanism is implemented as a nonspecific current defined as a
point process.
PARAMETERS
The mechanism takes the following parameters:
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
Gfluct3: 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
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ENDCOMMENT
INDEPENDENT {t FROM 0 TO 1 WITH 1 (ms)}
NEURON {
POINT_PROCESS orn
RANGE g_e, g_e_max, cc_peak, g_e_baseline
RANGE std_e, tau_e, D_e
NONSPECIFIC_CURRENT i
THREADSAFE : only true if every instance has its own distinct Random
POINTER donotuse
}
UNITS {
(nA) = (nanoamp)
(mV) = (millivolt)
(umho) = (micromho)
}
PARAMETER {
dt (ms)
E_e = 0 (mV) : reversal potential of excitatory conductance
g_e_max = 75e-3 (umho) : average excitatory conductance
cc_peak = 0 : (affinity*odor cc)
g_e_baseline = 0 (umho) : background noise
std_e = 1e-3 (umho) : standard dev of excitatory conductance
tau_e = 400 (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)
donotuse
}
STATE { O C D }
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( (1-exp(-2*dt/tau_e)) )
}
O = 0
C = 1
D = 0
}
BREAKPOINT {
LOCAL SORN
SOLVE oup
SOLVE states METHOD derivimplicit
if(tau_e==0) {
g_e = std_e * normrand123()
}
SORN = O * (1-D)
g_e = g_e1 + SORN * cc_peak * g_e_max + g_e_baseline
if(g_e < 0) {
g_e = 0
}
i = g_e * (v - E_e)
}
DERIVATIVE states {
LOCAL KO, KC1, KC2, KD1, KD2
KO = 1/100
KC1 = 1/100
KC2 = 1e-4
KD1 = 1/6000
KD2 = 1/100
O' = KO*(1-C-O)
C' = KC1*(1-C)*C + KC2*(1-C)
D' = KD1*O*(1-D) - KD2*D*(1-O)
}
PROCEDURE oup() { : use Scop function normrand(mean, std_dev)
if(tau_e!=0) {
g_e1 = exp_e * g_e1 + amp_e * normrand123()
}
}
NET_RECEIVE(dummy) {
C = 0
}
VERBATIM
double nrn_random_pick(void* r);
Rand* nrn_random_arg(int agpos);
ENDVERBATIM
FUNCTION normrand123() {
VERBATIM
if (_p_donotuse) {
/*
:Supports separate independent but reproducible streams for
: each instance. However, the corresponding hoc Random
: distribution MUST be set to Random.negexp(1)
*/
_lnormrand123= nrn_random_pick(_p_donotuse);
}else{
/* only can be used in main thread */
if (_nt != nrn_threads) {
hoc_execerror("multithread random in NetStim"," only via hoc Random");
}
ENDVERBATIM
: the old standby. Cannot use if reproducible parallel sim
: independent of nhost or which host this instance is on
: is desired, since each instance on this cpu draws from
: the same stream
normrand123 = normrand(0,1)
VERBATIM
}
ENDVERBATIM
}
PROCEDURE noiseFromRandom() {
VERBATIM
{
void** pv = (void**)(&_p_donotuse);
if (ifarg(1)) {
*pv = nrn_random_arg(1);
}else{
*pv = (void*)0;
}
}
ENDVERBATIM
}