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

:Original publication: On the dynamical structure of calcium oscillations
:Published By: National Academy of Sciences
:DOI: https://doi.org/10.1073/pnas.1614613114


Reference paper
===============
:Reference: A stochastic model of calcium puffs based on single-channel data
:Published By: Biophysical Journal
:DOI: https://doi.org/10.1016/j.bpj.2013.07.034

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.
The main results that reproduced by CellML implementation: Cell model simulations Fig. 1 (A, C, E).

Model Summary
==============

The model acts via the stimulation of phospholipase C to make IP3, which binds to IP3 receptors (IPRs) on the membrane of the ER/SR. IPRs are also Ca2+ channels, and binding of IP3 opens these channels to allow a rapid flow of Ca2+ out
of the ER/SR and a consequent rise in cytosolic calcium concentration. Pumping Ca2+ by Ca2+ ATPases back into the ER/SR restarts the process, allowing for cyclical Ca2+ release from the ER/SR and oscillations in cytosolic calcium concentration.

Oscillations in the concentration of cytosolic calcium are
an important control mechanism in many cell types. The model predicts that cells with Class I Ca2+ oscillations
can control the oscillation period by modulating (among
other things) how fast the rate of calcium activation of the IPR
responds to changes in calcium concentration.

Model Components
================
The model is implemented using the current formulation which is based on :ref:`Reference paper`. There are four main Components in the model:


1. Cytoplasm Ca2+ concentration (Ca2+):

- Jserca  : the uptake of Ca2+ into the SR by SERCA pumps.
- Jin  : Sum of main Ca2+ influxes including Jrocc (receptor-operated Ca2+ channel), Jsocc (store-operated Ca2+ channel).
- Jpm : the flux through plasma pump.
- JIPR : the flux through the IPRs, which is the most complex component contains at least 7 subcomponents.

2. Endoplasmic reticulum (ER) Ca2+ concentration(ca_e):

- Jserca  : the uptake of Ca2+ into the SR by SERCA pumps.
- JIPR : the flux through the IPRs

3. IPRs activation rate (h)

4. IP3 concentration (p)


Model Issues
===================
There were not any noticeable issues in the model. The only problem that we can mention here is that there wasn't any clear protocol about the IP3 behavior before and after pulse responses, the initial value for IP3 concentrations, and other system state variables.

Model Validations
===================
Applying the default parameters in the model, we were able to reproduce the model predictions. However, we should consider that there is not a clear protocol to define the IP3 pulse responses in the original article. Initial values are not defined as well. The following definition is used to produce the current IP3 pulse response:
In the absence of the IP3 pulse response, there is a constant IP3 concentration in the model (ps =0.12).  To inter the IP3 pulse response, we applied the model equation mentioned in the supporting information document:

.. math::
   \frac{dp}{dt} = \tau (p-ps)

To have a decaying function of IP3 pulse response, we need to define the initial value greater than the IP3 resting value (ps = 0.12).


.. image::Doc/Figure_1.png
    :width: 100%
    :align: center
    :alt: Different pulse responses to the Calcium model.

Model Simulation
================

Simulation setting:
-------------------
Simulation settings are encoded in SED-ML_ documents for the experiment execution.
The python script (Fig1_sim.py) to run the simulation (Sneyd_2016.sedml).

Simulation process:
-------------------
Execute 'Fig1_sim.py' in the Python console in OpenCOR_. This can be done
with the following commands at the prompt in the OpenCOR_ Python console:

In [1]: cd path/to/folder_this_file_is_in

In [2]: run Fig1_sim.py

To reproduce Figure 1, after collection of the required data, run the Python script Fig1_Plot.py.