TITLE Fluctuating current
COMMENT
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Fluctuating current model for synaptic bombardment
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The present version implements and generate a realization of an Ornstein-Uhlenbeck (OU) process
(see Cox & Miller, 1969; see Tuckwell) to mimick the somatic impact of linearly adding EPSPs and
IPSPs. Thus, it generates and injects in the specified neuronal compartment a fluctuating current
waveform, characterized by a gauss-distributed amplitude, where neighboring amplitude samples are
by definition linearly correlated on a time scale set by the correlation time-length "tau" of the
process.
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) + (1. - exp(-dt/tau)) * (m - x) + sqrt(1.-exp(-2.*dt/tau)) * s * N(0,1)
where N(0,1) is a normal random number (avg=0, sigma=1)..
Please note that only fixed integration time-step methods makes sense, since the stochastic current
synthesized by the present mechanism is produced randomly and on-line. In other words, it is wrong to
assume that neglecting the present integration step, reducing it and resynthesizing the current,
lead to the same overall trajectory in the compartment output voltage.
IMPLEMENTATION
This mechanism is implemented as a nonspecific current defined as a point process.
PARAMETERS
The mechanism takes as input the following parameters:
m = 0. (nA) : steady-state expected value of the current amplitude.
s = 0. (nA) : square root of the steady-state variance of the current amplitude.
tau = 2. (ms) : steady-state correlation time length of the current.
REFERENCES
Rauch, A., La Camera, G., Luescher, H.-R., Senn, W., and Fusi, S. (2003). Neocortical pyramidal cells respond as integrate-and-fire neurons to in vivo-like input currents. J. Neurophysiol. 90(3), 1598-612.
Giugliano, M., Darbon, P., Arsiero, M., Luescher, H.-R., and Streit, J. (2004). Single-neuron discharge properties and network activity in dissociated cultures of neocortex. J. Neurophysiol. 92(2), 977-96.
La Camera, G., Rauch, A., Thurbon, D., Luescher, H.-R., Senn, W., and Fusi, S. (2006). Multiple time scales of temporal response in pyramidal and fast spiking cortical neurons, J. Neurophysiol. 96(6):3448-64.
Arsiero, M., Luescher, H.-R., Lundstrom, B.N., and Giugliano, M. (2007). The Impact of Input Fluctuations on the Frequency-Current Relationships of Layer 5 Pyramidal Neurons in the Rat Medial Prefrontal Cortex. sumbitted.
The present mechanism is inspired by "Gfluct.mod", by A. Destexhe (1999), as taken from ModelDB.
Destexhe, A., Rudolph, M., Fellous, J-M. and Sejnowski, T.J. (2001). Fluctuating synaptic conductances recreate in-vivo-like activity in neocortical neurons. Neuroscience 107: 13-24.
AUTHOR
M. Giugliano, Brain Mind Institute, EPFL Lausanne, May 2006 - mgiugliano@gmail.com
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ENDCOMMENT
INDEPENDENT {t FROM 0 TO 1 WITH 1 (ms)}
NEURON {
POINT_PROCESS Ifluct1
RANGE m, s, tau, x
RANGE new_seed
NONSPECIFIC_CURRENT i
}
UNITS {
(nA) = (nanoamp)
(mV) = (millivolt)
}
PARAMETER {
dt (ms)
m = 0. (nA) : steady-state expected value of the current amplitude
s = 0. (nA) : square root of the steady-state variance of the current amplitude
tau = 2. (ms) : steady-state correlation time length of the current
}
ASSIGNED {
i (nA) : fluctuating current
x : state variable
}
INITIAL {
x = m : to reduce the transient, the state is set to its (expected) steady-state
}
BREAKPOINT {
SOLVE oup
if (tau <= 0) { x = m + s * normrand(0,1) } : white-noise is impossible to generate anyway..
i = - x
}
PROCEDURE oup() { : uses Scop function normrand(mean, std_dev)
if (tau > 0) { x = x + (1. - exp(-dt/tau)) * (m - x) + sqrt(1.-exp(-2.*dt/tau)) * s * 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
}