Original Paper
==============

:Original publication:  "Computational modeling of anoctamin 1 calcium-activated chloride channels as pacemaker channels in interstitial cells of Cajal" Am J Physiol Gastrointest Liver Physiol 306: G711–G727, 2014.

:DOI: https://doi.org/10.1152/ajpgi.00449.2013


Model status
=============

The current CellML_ model implementation runs in OpenCOR_.
The CellML model parameters and equations must be updated regarding each specific model variation to reproduce the related simulations; see `Model Experiments` below for more detailed information.
The results have been validated against the data extracted from the figures in the published `Lees-Green, Rachel,  et al (2014)`_; see the section `Model Validation`.
Using the default parameters provided in the paper except for the modification listed in the following sections, Figures 4 and 5 can be reproduced. See `Model Modifications` below.


Model Summary
==============
Interstitial cells of Cajal (ICC) pacemaker activity begins when IP3-mediated Ca\ :sup:`2` release from the ER leads
to depletion of the ER Ca\ :sup:`2` stores, activating SOCE via SOC channels. Ano1 channels colocalized with SOC channels
are activated by the local rise in Ca\ :sup:`2` in microdomains surrounding the open SOC channels, causing depolarization
of the ICC. The depolarization initiates a slow wave by activating voltage-dependent ion channels.
The morphology of the slow wave, including the plateau phase and repolarization, is determined by the balance of
voltage- and Ca\ :sup:`2`-dependent ion currents. The pacemaker cycle concludes when Ca\ :sup:`2` influx via SOC channels and uptake via SERCA pumps
is sufficient to refill the ER stores, resulting in deactivation of the SOC channels and Ano1 channels.

.. figure:: Doc/Schematic_diagram_ICC.png
   :width: 70%
   :alt: Schematic diagram of ICC.


Model Equations
===============
The model is implemented using a Hodgkin-Huxley type formulation, where the cell membrane lipid bilayer is expresses capacitance (Cm),
and the ion channels in the membrane express conductance. The change in the transmembrane potential (Vm) over time depends on
the sum of the individual ion currents through each class of ion channel in the cell current:


.. math::

   \frac{dVm}{dt} = - \frac{I_{tot}}{C_{m}}

where there are 12 different ion channels contributing to the total current I\ :sub:`tot`\.

Model Variations
================
A high chloride environment ( :math:`E_{Cl} = - 20.2` mV,  :math:`C_{Cl} = 78` mM) is categorized into four different variations:

- High-Cl (NaV): Ion current specific to Voltage-gated Na channel

- High-Cl (NSCC): Ion currents specific to Ca\ :sup:`2`-activated nonselective channel

- High-Cl (CaV): Ion current specific to Voltage-gated  `Ca` channel

A low chloride environment is modelled (:math:`E_{Cl} = - 49.7` mV, :math:`C_{Cl} = 25.85` mM) where the low chloride simulations are categorized into two different variations:

- Low-Cl (NaV) : Ion currents specific to Voltage-gated Na channel

- Low-Cl (NSCC): Ion currents specific to Ca\ :sup:`2`-activated nonselective channel


Model Experiments
=================
This workspace contains two sets of experiments and corresponding simulation results. 
The first sets reproduce the four variations for the high chloride concentration and therefore :math:`E_{Cl}=-20 mV`, and the results are demonstrated in Figure. 4.
The second sets of variations represent the low chloride environment with the :math:`E_{Cl}=-50 mV` (Figure 5 in the original paper). 

- Figure 4A-4E  (HIGH-CL(NaV): Sodium  Voltage Activated Channel): the file HCl-NaV.json_ contains the HIGH-CL(NAV) model's parameters and initial conditions. The wild-type (WT) simulation's result (full model simulation) is saved in 'Fig4_1a.csv'. For the Ano1 knockout (KO) scenarios, data is saved in 'Fig4_1b.csv'.

- Figure 4B-4F (HIGH-CL(NSV): Non-Selective Voltage  Activated Channel): the file HCl-NSV.json_ contains the HIGH-CL(NSV) model's parameters and initial conditions. The data relating to HIGH-CL(NSV) wild-type simulation is saved in 'Fig4_2a.csv'. For the Ano1 knockout (KO) scenarios, data is saved in 'Fig4_2b.csv'.

- Figure 4C-4G (HIGH-CL(NSCC): Non-Selective Ca Activated Channel): the file HCl-NSCC.json_ contains the HIGH-CL(NSCC) model's parameters and initial conditions. The  WT and KO results are saved in 'Fig4_3a.csv' and 'Fig4_3b.csv', respectively.

- Figure 4D-4H (HIGH-CL(CaV): Ca Voltage Activated Channel): the file HCl-CaV.json_ contains the HIGH-CL(CaV) model's parameters and initial conditions. The data for WT and KO scenarios is saved in 'Fig4_4a.csv' and 'Fig4_4b.csv', respectively.

- Figure 5A-5C  (LOW-CL(NaV): Sodium  Voltage Activated Channel) : the file LCl-NaV.json_ contains the LOW-CL(NAV) model's parameters and initial conditions. The data for WT and KO scenarios is saved in 'Fig5_1a.csv' and 'Fig5_1b.csv', respectively.

- Figure 5B-5D (LOW-CL(NSCC): Non-Selective Ca Activated Channel): the file LCl-NSCC.json_ contains the LOW-CL(NSCC) model's parameters and initial conditions. The data for WT and KO scenarios is saved in 'Fig5_2a.csv' and 'Fig5_2b.csv', respectively.

.. _HCl-NaV.json: https://models.physiomeproject.org/workspace/762/file/8a27d6b243d418a476421012e6a6bcbe80639b6d/Simulations/HCl_NaV.json
.. _HCl-NSV.json: https://models.physiomeproject.org/workspace/762/file/8a27d6b243d418a476421012e6a6bcbe80639b6d/Simulations/HCl_NSV.json
.. _HCl-NSCC.json: https://models.physiomeproject.org/workspace/762/file/8a27d6b243d418a476421012e6a6bcbe80639b6d/Simulations/HCl_NSCC.json
.. _HCl-CaV.json: https://models.physiomeproject.org/workspace/762/file/8a27d6b243d418a476421012e6a6bcbe80639b6d/Simulations/HCl_CaV.json
.. _LCl-NaV.json: https://models.physiomeproject.org/workspace/762/file/8a27d6b243d418a476421012e6a6bcbe80639b6d/Simulations/LCl_NSV.json
.. _LCl-NSCC.json: https://models.physiomeproject.org/workspace/762/file/8a27d6b243d418a476421012e6a6bcbe80639b6d/Simulations/LCl_NSCC.json

Model Modifications
===================
In the case of reproducibility and reusability, there are a couple of issues with the model equations and model default parameters. We point them as below:

- There are no definitions of the fluxes for some ion channels; definitions are defined from the references and compared to the similar descriptions of the other fluxes with similar behaviour in the original work and confirmed through the MATLAB updated model of ICC.

- To reproduce Figure 5A-5C: the K parameter for voltage-dependent gating equation for the NaV channel inactivation F_NaV is changed from -4.5 mV to 4.5 mV as the K parameter for voltage-dependent gating equation in the case of inactivation is always positive.

.. figure:: Doc/Issue_LCl_NaV.png
   :width: 60%
   :alt: LCl_NaV.

To reproduce Figure 5B-5D: the conductance value for the CaV channel is reduced to g = 3.72 nS from the original value g = 4 nS. As shown in the below diagram at g = 4 nS, there are damped oscillations that indicate that the dominant eigenvalue has a negative real value for stable system. These damped oscillations switch to the slow-wave oscillations for g = 3.72 nS.

.. figure:: Doc/Issue_LCL_NSCC.png
   :width: 60%
   :alt: LCl_NSCC


Model Validations
=================
The results have been validated against the data extracted from the figures in the published `Lees-Green, Rachel,  et al (2014)`_.
Reproduction of Figure 4:

.. figure:: Doc/Figure4.png
      :width: 100%
      :alt: Fig 4


Reproduction of figure 5, with modifications listed in `Model Modifications` performed:

.. figure:: Doc/Figure5.png
     :width: 60%
     :alt: Fig 5


.. _CellML: https://www.cellml.org/
.. _OpenCOR: https://opencor.ws/
.. _SED-ML: https://sed-ml.org
.. _`Lees-Green, Rachel,  et al (2014)`: https://doi.org/10.1152/ajpgi.00449.2013