    Calcium buffering models explanatory note:

    Model Published in:

    Anwar H, Hong S, De Schutter E (2010) Controlling Ca2+-activated K+
    channels with models of Ca2+ buffering in Purkinje cell. Cerebellum *

    * Available as Open Access

    PubMed link: http://www.ncbi.nlm.nih.gov/pubmed/20981513

    Email contact: anwar@oist.jp

    Model description:

    In this work, we compare the dynamics of different buffering models
    during generation of a dendritic Ca2+ spike in a single compartment
    model of a Purkinje cell dendrite.  The Ca2+ buffering models used are
    1) a single Ca2+ pool, 2) two Ca2+ pools respectively for the fast and
    slow transients, 3) a detailed calcium model with buffers, pump
    (Schmidt et al., 2003), and diffusion and 4) a calcium model with
    buffers, pump and diffusion compensation. The parameters of single
    pool and double pool are tuned, using Neurofitter (Van Geit et al.,
    2007), to approximate the behavior of detailed calcium dynamics over
    range of 0.5 µM to 8 µM of intracellular calcium. The diffusion
    compensation is modeled using a buffer-like mechanism called DCM. To
    use DCM robustly for different diameter compartments, its parameters
    are estimated, using Neurofitter (Van Geit et al., 2007), as a
    function of compartment diameter (0.8 µm-20 µm).

    Scripts Explanation:

    Go to the folder containing the model scripts. Run nrnivmodl. Then
    type nrngui CaBufferingModels.hoc

    A panel with six buttons will appear on the screen.

    1.  Detailed Calcium dynamics model: Click on this button to see the
    behavior of detailed calcium dynamics model. It will display nine
    plots arranged in three rows and three columns. The plot on the top
    left corner shows calcium transients with peak amplitude of 0.5 µM, 1
    µM and 2 µM. These transients were generated using a voltage step
    command (as shown in Figure 1a in Anwar et al., 2010) with different
    maximal conductance values of P-type Ca2+ channel. All the other plots
    show corresponding behavior of buffers and pump current. These plots
    are same as Figure 2 in Anwar et al., 2010.

    2.  Calcium transients using different buffering models: Click on this
    button to see the calcium transients with peak amplitude of 2 µM,
    generated using single pool, double pool, detailed calcium dynamics
    model and DCM. The parameters of single pool, double pool and DCM were
    fitted using Neurofitter (Van Geit et al., 2007) as described in Anwar
    et al., 2010. This plot is similar to Figure 3c and Figure 6 in Anwar
    et al., 2010 except that the Ca2+ transient in these scripts are shown
    for diameter 4 µm.

    3.  Calcium spikes using single pool model: Click on this button to
    see the calcium spikes generated using single pool model. The maximal
    conductance values for P-type and T-type Ca2+ channels and BK-type and
    SK-type Ca2+ activated K+ channels were tuned using Neurofitter (Van
    Geit et al., 2007) and are presented in Anwar et al., 2010. Note that
    the parameter values used for single pool in this plot are different
    than those used in plot showing calcium transients. The parameter
    values of single pool used to generate calcium spikes in this plot are
    obtained using experimental trace (shown in Figure 1b in Anwar et al.,
    2010) as a voltage command. This plot exists in Figure 7d in Anwar et
    al., 2010.

    4.  Calcium spikes using double pool model: Click on this button to
    see the calcium spikes generated using double pool model. The maximal
    conductance values for P-type and T-type Ca2+ channels and BK-type and
    SK-type Ca2+ activated K+ channels were tuned using Neurofitter (Van
    Geit et al., 2007) and are presented in Anwar et al., 2010. Note that
    the parameter values used for double pool in this plot are different
    than those used in plot showing calcium transients. The parameter
    values of double pool used to generate calcium spikes in this plot are
    obtained using experimental trace (shown in Figure 1b in Anwar et al.,
    2010) as a voltage command. This plot exists in Figure 7d in Anwar et
    al., 2010.

    5.  Calcium spikes using detailed model: Click on this button to see
    the calcium spikes generated using detailed model. The maximal
    conductance values for P-type and T-type Ca2+ channels and BK-type and
    SK-type Ca2+ activated K+ channels were tuned using Neurofitter (Van
    Geit et al., 2007) and are presented in Anwar et al., 2010. This plot
    exists in Figure 7c in Anwar et al., 2010.

    6.  Calcium spikes using DCM: Click on this button to see the calcium
    spikes generated using DCM. The maximal conductance values for P-type
    and T-type Ca2+ channels and BK-type and SK-type Ca2+ activated K+
    channels were tuned using Neurofitter (Van Geit et al., 2007) and are
    presented in Anwar et al., 2010. This plot exists in Figure 7c in
    Anwar et al., 2010.

    References

    Anwar H, Hong S, De Schutter E (2010) Controlling Ca2+-activated K+
    channels with models of Ca2+ buffering in Purkinje cell. Cerebellum,
    in print.

    van Geit W, Achard P, de Schutter E (2007) Neurofitter: a parameter
    tuning package for a wide range of electrophysiological neuron
    models. Front Neuroinform 1:1

    Schmidt H, Stiefel K, Racay P, Schwaller B, Eilers J (2003) Mutational
    analysis of dendritic Ca2+ kinetics in rodent Purkinje cells: role of
    parvalbumin and calbindin D28k. J Physiol 551:13-32

     Changelog

     cdp3.mod and cdp5.mod are updated due to issue mentioned in https://github.com/neuronsimulator/nrn/pull/1955.
     CONSTANT block has no effect in the initialization of ion variables.