- Author:
- David Nickerson <david.nickerson@gmail.com>
- Date:
- 2024-01-11 16:29:35+13:00
- Desc:
- Adding figures for documentation
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/af0/rawfile/7166e945597fcd88fa2f8ba467597e42c7230d1c/README.rst
Bond graph example: A simple biochemical reaction
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For biochemical systems :math:`q_j^i` is the molar quantity of a chemical species :math:`i` in solution in compartment :math:`j` and :math:`u_j^i` is its chemical potential.
A biochemical reaction in one compartment ('c'), with forward and reverse affinities :math:`A^f` and :math:`A^r`, is shown below along with its bond graph representation.
Note the usual representation for energy storage, but the dissipative reaction term (:math:`Re_r`) now requires explicit dependence on the chemical potential of the reactants and products, rather than depending only on the potential across the dissipation 'resistor'.
Therefore, the corresponding :math:`Re` component must have two ports, in contrast to the standard one-port :math:`R` component.
Flow 1:nodes are therefore needed on either side of the reaction, when multiple species are involved, to provide the two ports.
.. figure:: fig1.png
:width: 95%
:align: center
:alt: Schematic and bond graph of the model
A biochemical reaction where :math:`A^f` and :math:`A^r` are the forward and reverse affinities (a), and its bond graph representation (b).
The 0:nodes represent the chemical potentials :math:`u_1^i` and :math:`u_2^i` associated with the chemical species :math:`q_1^i` and :math:`q_2^i` stored in compartments 1 and 2.
The reaction :math:`Re_r` (the dissipative term for a biochemical system) has associated chemical flux :math:`v_r` that depends explicitly on the chemical potentials of the reactant (:math:`q_c^1`) and product (:math:`q_c^2`) since in this simple case :math:`u_R^f = A^f = u_c^1` and :math:`u_R^r = A^r = u_c^2`.
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
