- Author:
- Shelley Fong <s.fong@auckland.ac.nz>
- Date:
- 2022-01-27 10:10:30+13:00
- Desc:
- Init
- Permanent Source URI:
- https://models.cellml.org/workspace/7fb/rawfile/32c639d056232003fe9f6ac99d22f705f43cbe73/exposure/exposure_frontpage.rst
About this model
====================
This is a bond-graph model of cardiac contraction in the human cardiomyocyte.
**INPUTS:**
- Intracellular calcium transient [Ca]_i
**OUTPUTS:**
- Tension generated by sarcomere
**REACTIONS:**
- R.TRPN_Ca: Binding of Ca to troponin (TRPN)
- R.BU: Spontaneous switching of crossbridge from B (blocked) to U (unbound) states
- R.UW: Spontaneous switching of crossbridge from U to W (pre-powerstroke) states
- R.WS: Spontaneous switching of crossbridge from W to S (powerstroke) states
- R.SU: Spontaneous switching of crossbridge from S to U states
Model status
=============
The current CellML implementation runs in OpenCOR.
Model overview
===================
This model is based on existing kinetic model, where the mathematics are translated into the bond-graph formalism. This describes the model in energetic terms and forces adherence to the laws of thermodynamics.
For the following bond-graphs, all enzymes are shown in maroon.
A '0' node refers to a junction where all chemical potentials are the same. A '1' node refers to all fluxes being the same going in and out of the junction.
.. csv-table:: List of chemical species
:header: "Abbreviation", "Name"
:widths: 5, 15
"Gs", "Gs protein"
Biochemical reactions
~~~~~~~~~~~~~~~~~~~~~
For reaction TRPN_Ca, the rate of Ca unbinding from TRPN is tension dependent. The term was fitted with an exponential function, which is then used as a transformer **TF** in the resultant bond-graph.
.. figure:: exposure/XBstates.png
:width: 100%
:align: center
:alt: BG BUWS
Fig. 1. Bond-graph formulation of calcium binding troponin, with the resulting complex participating in the crossbridge cycle with states B (blocked), U (unbound), W( pre-powerstroke), S (powerstroke).
|
Tension generation
~~~~~~~~~~~~~~~~~~
For differential terms involving tension and displacement, a mass-spring-damper system was used to approximate the model in order to enable translation into bond-graph mathematics.
Length terms were dimensionalised through the resting sarcomere length SL_0, and quantities of crossbridge units were dimensionalised through the estimated number of myosin binding sites per sarcomere.
.. figure:: exposure/BG_dampers.png
:width: 65%
:align: center
:alt: BG dampers
Fig. 1. Bond-graph formulations for distortion states, leading to calculation of active tension (Ta). Each of the three equations are modelled as a 1 node, with sum of potentials of the bonds equalling zero.
|
Parameter finding
~~~~~~~~~~~~~~~~~
A description of the process to find bond-graph parameters is shown in the folder `parameter_finder <parameter_finder>`_, which relies on the:
1. stoichiometry of system
2. kinetic constants for forward/reverse reactions
- If not already, all reactions are made reversible by assigning a small value to the reverse direction.
3. `linear algebra script <https://models.physiomeproject.org/workspace/7f9/file/81651458e3a778c5aabafa5556d3713829682b19/parameter_finder/kinetic_parameters_crossbridge.py>`_.
Here, this solve process is performed in Python.
Original kinetic model
======================
Land et al: `A model of cardiac contraction based on novel measurements of tension development in human cardiomyocytes <https://pubmed.ncbi.nlm.nih.gov/28392437>`_
Additional detail on the binding of TRPN to Ca was taken from
Niederer et al: `A quantitative analysis of cardiac myocyte relaxation: a simulation study <https://models.physiomeproject.org/exposure/d3849e5de91b0b94de79c30548a44a79>`_
