- Author:
- WeiweiAi <wai484@aucklanduni.ac.nz>
- Date:
- 2022-07-28 12:05:55+12:00
- Desc:
- Fixed the link
- Permanent Source URI:
- https://models.cellml.org/workspace/8af/rawfile/1b1a07491a4d102536a3f7e25957ca2810d6ed76/Doc/README.rst
About this model
====================
:Original publication: `Rios, E., et al. (1993)`_: "An Allosteric Model of the Molecular Interactions of Excitation-Contraction Coupling in Skeletal Muscle." The Journal of general physiology 102.3 (1993): 449-481.
:DOI: 10.1085/jgp.102.3.449
.. _`Rios, E., et al. (1993)`: https://doi.org/10.1085/jgp.102.3.449
Model status
=============
The current CellML implementation runs in OpenCOR_.
The results have been validated against the data extracted from the figures in the published `Rios, E., et al. (1993)`_. We provide the settings used for the figure reproduction with the simulation results shown under ``Experiments``. The model structure can be found in this documentation. The curation process has been summarized in the `Model history`_ and `Known issues`_.
Model overview
===================
`Rios, E., et al. (1993)`_ proposed a quantitative formulation describing the allosteric transition in MWC model proposed by `Monod, J., Wyman, J., & Changeux, J. P. (1965)`_. The allosteric model includes four independent voltate sensor molecules in contact with the calcium release channel. Two states of the release channel (closed and open) are modelled, as well as two of five possible dispositions of the voltage sensors. The model is therefore a 10-state Markov system, and we refer it as ``MWC-10 model``. In the Appendix, the model is generalized to include 8 sensors with 18 states in total, and we refer the generalized model as ``MWC-18 model``. This workspace holds a CellML_ encoding of the `Rios, E., et al. (1993)`_ ``MWC-10 model`` and ``MWC-18 model``.
.. _`Monod, J., Wyman, J., & Changeux, J. P. (1965)`: https://doi.org/10.1016/S0022-2836(65)80285-6
.. _CellML: https://www.cellml.org/
.. figure:: Doc/model.png
:width: 75%
:align: center
:alt: Schematics of the model
A diagrammatic representation of the `Rios, E., et al. (1993)`_ model.
Modular description
====================
Components
-----------
CellML divides the mathematical model into distinct components, which are able to be re-used. We reuse Markov states model `MarkovS <cellLib/Components/MarkovS.cellml>`_ defined in the workspace cellLib_. `MarkovS`_ defines Markov state change rate, in which ``S1``, ``S2``, and ``S3`` are the state connected with one, two, and three neighbors, respectively.
.. _cellLib: https://models.physiomeproject.org/workspace/6bc
In `Rios, E., et al. (1993)`_ model, the form of the rate constants in transitions can be formalized as follows, where :math:`N` is the number of the sensors, :math:`j` is the number of activated sensors, C is a closed state, and O is an open state:
- The rate constants from :math:`C_{j}` to :math:`C_{j+1}` is :math:`(N-j)*k_C`
- The rate constants from :math:`C_{j+1}` to :math:`C_{j}` is :math:`(j+1)*k^-_C`
- The rate constants from :math:`C_{j}` to :math:`O_{j}` is :math:`k_L/f^j`
- The rate constants from :math:`O_{j}` to :math:`C_{j}` is :math:`k^-_L*f^j`
Hence, the main CellML components are:
- The closed and open states when all the sensors in rest are :math:`C_{0}` to :math:`O_{0}`, which have two neighbors, modelled as `C0_S2 <Components/C0_S2.cellml>`_ and `O0_S2 <Components/O0_S2.cellml>`_.
- The closed and open states when all the sensors being active are :math:`C_{N}` to :math:`O_{N}`, which have two neighbors, modelled as `CN_S2 <Components/CN_S2.cellml>`_ and `ON_S2 <Components/ON_S2.cellml>`_.
- The closed states when some sensors are in rest and some are active, which have three neighbors, modelled as `C_S3 <Components/C_S3.cellml>`_.
- The open states when some sensors are in rest and some are active, which have three neighbors, modelled as `O_S3 <Components/O_S3.cellml>`_.
- The 10-state Markov system, including:
- ``C0`` instantiating `C0_S2`_,
- ``O0`` instantiating `O0_S2`_,
- ``C1`` - ``C3``, instantiating `C_S3`_,
- ``O1`` - ``O3``, instantiating `O_S3`_,
- ``C4`` instantiating `CN_S2`_ ,
- ``O4`` instantiating `ON_S2`_.
- The 18-state Markov system, including:
- ``C0`` instantiating `C0_S2`_,
- ``O0`` instantiating `O0_S2`_,
- ``C1`` - ``C7``, instantiating `C_S3`_,
- ``O1`` - ``O7``, instantiating `O_S3`_,
- ``C8`` instantiating `CN_S2`_ ,
- ``O8`` instantiating `ON_S2`_.
Each of these blocks is itself a CellML model, which enables us to reuse the various components in future studies and models.
Experiments
---------------------
Following best practices, this model separates the mathematics from the parameterisation of the model. The mathematical model is imported into a specific parameterised instance in order to perform numerical simulations. The default parameters are defined in `Para <Components/Para.cellml>`_.
The parameterisation would include defining the stimulus protocol to be applied.
This workspace encodes `MWC_10_experiment <Experiments/MWC_10_test.cellml/view>`_, `MWC_18_experiment <Experiments/MWC_18_test.cellml/view>`_ , and corresponding simulation results.
Simulation settings
-------------------
Simulation settings are encoded in SED-ML_ files for experiment execution. It is common that we may need to vary experimental settings to obtain data under various conditions. Hence, the full experimental settings are encoded in the simulation scripts.
The Python scripts to run simulation and reproduce the figures in the original paper are included under the ``Simulation/src`` folder. The ``runSim.ps1`` is used to run the simulation in PowerShell, while ``plotFigX.py`` (X denotes the figure number) are ready to plot the figures in `MWC_10_experiment`_ and `MWC_18_experiment`_ .
We adopted the same stimulation protocol as discussed in primary Fig 1, where there is 100-ms 20 mV conditioning pulse followed by 100-ms -80 mV holding potential, then the test voltage is applied.
.. _SED-ML: http://sed-ml.org/
Model history
===================
There is no publicly available code for this model.
Known issues
===================
1. The parameters we used to produce the figures are listed in Table 1. The last column is the scaling factor to normalize the open probability P or obtain the absolute value of Q. For Fig 9, we are not sure what 3% /ms in the reference scale refers to, we need to divide our simulation current by 5 to get a closer curve.
.. figure:: Doc/Table1.png
:width: 75%
:align: center
:alt: Parameters
2. In the primary paper, Fig 11 caption says "the parameters are similar to those used for Fig. 9 (908 entries in Table I)" , however, Fig 9 says "Parameters are the same as those listed in Table I for fiber 827 ". We do not know which one is correct, so we tried both. However, neither agrees with the original data well. We also tried other parameter sets and adjusted the test voltages, which are shown under ``Experiments``.
3. Fig 4, 6 and 13 are steady states of ``MWC-10 model`` and ``MWC-18 model``, respectively, which matches the original data very well, except there is a discrepancy in Fig 6 when Fiber 911 setting is applied.
4. Other figures are dynamic behaviors of the models, where we see discrepancy especially in case of perchlorate simulation.
.. _OpenCOR: https://opencor.ws/
