Input Fluctuations effects on f-I curves (Arsiero et al. 2007)

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"... We examined in vitro frequency versus current (f-I) relationships of layer 5 (L5) pyramidal cells of the rat medial prefrontal cortex (mPFC) using fluctuating stimuli. ...our results show that mPFC L5 pyramidal neurons retain an increased sensitivity to input fluctuations, whereas their sensitivity to the input mean diminishes to near zero. This implies that the discharge properties of L5 mPFC neurons are well suited to encode input fluctuations rather than input mean in their firing rates, with important consequences for information processing and stability of persistent activity at the network level."
1 . Arsiero M, L├╝scher HR, Lundstrom BN, Giugliano M (2007) The impact of input fluctuations on the frequency-current relationships of layer 5 pyramidal neurons in the rat medial prefrontal cortex. J Neurosci 27:3274-84 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Neuron or other electrically excitable cell;
Brain Region(s)/Organism: Prefrontal cortex (PFC);
Cell Type(s): Neocortex L5/6 pyramidal GLU cell;
Channel(s): I Sodium; I Potassium;
Gap Junctions:
Simulation Environment: NEURON;
Model Concept(s): Simplified Models; Action Potentials; Spike Frequency Adaptation;
Search NeuronDB for information about:  Neocortex L5/6 pyramidal GLU cell; I Sodium; I Potassium;
TITLE Fluctuating current


    Fluctuating current model for synaptic bombardment

 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
 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.


  This mechanism is implemented as a nonspecific current defined as a point process.


  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.


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.

M. Giugliano, Brain Mind Institute, EPFL Lausanne, May 2006 -



    RANGE m, s, tau, x
    RANGE new_seed

    (nA) = (nanoamp) 
    (mV) = (millivolt)

     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

    i     (nA)          : fluctuating current
    x                   : state variable

    x = m               : to reduce the transient, the state is set to its (expected) steady-state

    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
      printf("Setting random generator with seed = %g\n", _lseed);

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