- Author:
- David Nickerson <david.nickerson@gmail.com>
- Date:
- 2024-01-11 18:03:04+13:00
- Desc:
- Initial documentation to use in making an exposure
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/af4/rawfile/ca0ee1a16a2b93fbefe9ea6de72d5d0a6b254eed/README.rst
Bond graph example: Nernst-Planck and ion channel gating
========================================================
The figure below shows the bond graph representation of the diffusive solute flux through the membrane and the flux of electrical charge (:math:`q_m^e`) from its capacitive storage in the membrane, with the biochemical equivalent of the membrane potential :math:`u_m^e` (:math:`J.C^{-1}`) being :math:`z_q Fu_m^e` (:math:`J.mol^{-1}`), where :math:`F` (:math:`C.mol^{-1}`) is the Faraday constant and :math:`z_q` is the valence (:math:`z_q=1` for :math:`Na^+`, :math:`z_q=2` for :math:`Ca^{2+}`).
Units have been added to the variables to clarify the transport of moles versus Coulombs and the chemical potentials (:math:`J.mol^{-1}`) versus the electrical potential (:math:`J.C^{-1}`).
Note that the transforming factor :math:`z_qF` ensures that the product of electrical current flow :math:`z_q Fv_m^i` (:math:`C.s^{-1}`) and electrical potential :math:`u_m^e` (:math:`J.C^{-1}`) equals the product of chemical flow :math:`v_m^i` (:math:`mol.s^{-1}`) and chemical potential :math:`z_q Fu_m^e` (:math:`J.mol^{-1}`).
.. figure:: fig1.png
:width: 95%
:align: center
:alt: Schematic and bond graph of the model
The bond graph representation of the diffusive flow :math:`v_m^i` of electrically charged ions through a channel in a membrane across which there is a potential difference :math:`u_m^e`.
The colour of the power flux arrows is blue for mole transfer and brown for charge transfer.
Note on subscripts: ‘1’=cytosol, ‘2’=extracellular, ‘m’=membrane.
The **Views Available** menu to the right provides various options to explore this model here in the Physiome Model Repository.
Of particular interest is the *Launch with OpenCOR* menu item, which will load the simulation experiment shown below directly into the `OpenCOR`_ desktop application.
.. figure:: fig2.png
:width: 95%
:align: center
:alt: OpenCOR showing simulation experiment.
Showing the result of launching the simulation experiment from this exposure in OpenCOR and executing the simulation.
.. _CellML: https://www.cellml.org/
.. _OpenCOR: https://opencor.ws/
.. _SED-ML: https://sed-ml.org
