BG_HaiMurphy.cellml

About this model

This is a bond graph model on the contraction of vascular smooth muscle cell. It is based on the work of Hai and Murphy (1988).

INPUTS:
  • Cyclic guanosine monophosphate
OUTPUTS:
  • Stress generated by crossbridge contraction
REACTIONS:
  • Re12m: Phosphorylation of myosin light chain (M) to Mp
  • Re34m: Binding of actin (A) to Mpto form cross bridge (AMp)
  • Re56m: Cross bridge formation by phosphorylation of a latch bridge (AM)
  • Re78m: Detachment of latch bridge into A and M

Model status

The current CellML implementation runs in OpenCOR.

Model overview

This model is based on existing kinetic model by Hai and Murphy (1988), 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.

In this workspace, two forms of the contraction model are presented: the original Hai-Murphy model, and the model altered by Yang et. al. (2005). The latter is used towards coupling with guanylyl cyclase metabolism.

SM_contraction

Fig. 1. Smooth muscle contraction module

For the above bond-graph, 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.

List of chemical species
Abbreviation Name
cGMP Cyclic guanosine monophosphate
M Myosin light chain
Mp Myosin light chain, phosphorylated
A Actin
AM Latch bridge
AMp Cross bridge
Ca Calcium ion

Parameter finding

A description of the process to find bond-graph parameters is shown in the folder 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.
  1. linear algebra script.

Here, this solve process is performed in Python.

Original kinetic model

Hai and Murphy (1988).