Spike propagation in dendrites with stochastic ion channels (Diba et al. 2006)

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"We investigate the effects of the stochastic nature of ion channels on the faithfulness, precision and reproducibility of electrical signal transmission in weakly active, dendritic membrane under in vitro conditions. ... We numerically simulate the effects of stochastic ion channels on the forward and backward propagation of dendritic spikes in Monte-Carlo simulations on a reconstructed layer 5 pyramidal neuron. We report that in most instances there is little variation in timing or amplitude for a single BPAP, while variable backpropagation can occur for trains of action potentials. Additionally, we find that the generation and forward propagation of dendritic Ca2+ spikes are susceptible to channel variability. This indicates limitations on computations that depend on the precise timing of Ca2+ spikes."
1 . Diba K, Koch C, Segev I (2006) Spike propagation in dendrites with stochastic ion channels. J Comput Neurosci 20:77-84 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Channel/Receptor;
Brain Region(s)/Organism: Neocortex;
Cell Type(s):
Gap Junctions:
Simulation Environment: NEURON;
Model Concept(s): Active Dendrites; Action Potentials;
Implementer(s): Diba, Kamran [diba at andromeda.rutgers.edu];
:26 Ago 2002 Modification of original channel to allow variable time step and to correct an initialization error.
:    Done by Michael Hines(michael.hines@yale.e) and Ruggero Scorcioni(rscorcio@gmu.edu) at EU Advance Course in Computational Neuroscience. Obidos, Portugal

TITLE decay of internal calcium concentration
: Internal calcium concentration due to calcium currents and pump.
: Differential equations.
: Simple model of ATPase pump with 3 kinetic constants (Destexhe 92)
:     Cai + P <-> CaP -> Cao + P  (k1,k2,k3)
: A Michaelis-Menten approximation is assumed, which reduces the complexity
: of the system to 2 parameters: 
:       kt = <tot enzyme concentration> * k3  -> TIME CONSTANT OF THE PUMP
:   kd = k2/k1 (dissociation constant)    -> EQUILIBRIUM CALCIUM VALUE
: The values of these parameters are chosen assuming a high affinity of 
: the pump to calcium and a low transport capacity (cfr. Blaustein, 
: TINS, 11: 438, 1988, and references therein).  
: Units checked using "modlunit" -> factor 10000 needed in ca entry
: VERSION OF PUMP + DECAY (decay can be viewed as simplified buffering)
: All variables are range variables
: This mechanism was published in:  Destexhe, A. Babloyantz, A. and 
: Sejnowski, TJ.  Ionic mechanisms for intrinsic slow oscillations in
: thalamic relay neurons. Biophys. J. 65: 1538-1552, 1993)
: Written by Alain Destexhe, Salk Institute, Nov 12, 1992


    SUFFIX cad2
    USEION ca READ ica, cai WRITE cai
    RANGE ca
    GLOBAL depth,cainf,taur

    (molar) = (1/liter)         : moles do not appear in units
    (mM)    = (millimolar)
    (um)    = (micron)
    (mA)    = (milliamp)
    (msM)   = (ms mM)
    FARADAY = (faraday) (coulomb)

    depth   = .1    (um)        : depth of shell
    taur    = 80   (ms)        : rate of calcium removal
    cainf   = 100e-6(mM)
    cai     (mM)

    ca      (mM) :<1e-5>

    ca = cainf
    cai = ca

    ica     (mA/cm2)
    drive_channel   (mM/ms)
    SOLVE state METHOD derivimplicit


    drive_channel =  - (10000) * ica / (2 * FARADAY * depth)
    if (drive_channel <= 0.) { drive_channel = 0. } : cannot pump inward

    ca' = drive_channel + (cainf-ca)/taur
    cai = ca

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