Model of the four-state Vascular Smooth Muscle crossbridge dynamics (Hai and Murphy, 1988).
Description
This model represents the four-state VSM crossbridge dynamics presented by Hai and Murphy (AJP 254:C99-106, 1988). Myosin phosphorylation and binding to actin are described by the system of 4 ODEs as presented below. In the steady state, the fraction of myosin bound to actin both in the phosphorylated and dephosphorylated state correlates directly to the level of activation of the VSM in the vessel. The fixed parameters used here are as presented in Koenigsberger et al. (Biophys J 91:1663-1674, 2006).
Figure: Fraction of of each state after elapsed time. Initially all four states are fractionally equal (0.25). M is unphosphorylated free myosin, Mp is phosphorylated free myosin, AM is dephosphorylated attached crossbridges, and AMp is phosphorylated attached crossbridges.
Equations
The equations for this model may be viewed by running the JSim model applet and clicking on the Source tab at the bottom left of JSim's Run Time graphical user interface. The equations are written in JSim's Mathematical Modeling Language (MML). See the Introduction to MML and the MML Reference Manual. Additional documentation for MML can be found by using the search option at the Physiome home page.
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Hai CM and Murphy RA, Cross-bridge phosphorylation and regulation of latch state in smooth muscle. AJP-Cell Physiology 254:C99-C106, 1988. Koenigsberger M, Sauser R, Beny JL, and Meister JJ., Effects of arterial wall stress on vasomotion. Biophysical Journal 91:1663-1674, 2006.
Please cite https://www.imagwiki.nibib.nih.gov/physiome in any publication for which this software is used and send one reprint to the address given below:
The National Simulation Resource, Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle WA 98195-5061.
Model development and archiving support at https://www.imagwiki.nibib.nih.gov/physiome provided by the following grants: NIH U01HL122199 Analyzing the Cardiac Power Grid, 09/15/2015 - 05/31/2020, NIH/NIBIB BE08407 Software Integration, JSim and SBW 6/1/09-5/31/13; NIH/NHLBI T15 HL88516-01 Modeling for Heart, Lung and Blood: From Cell to Organ, 4/1/07-3/31/11; NSF BES-0506477 Adaptive Multi-Scale Model Simulation, 8/15/05-7/31/08; NIH/NHLBI R01 HL073598 Core 3: 3D Imaging and Computer Modeling of the Respiratory Tract, 9/1/04-8/31/09; as well as prior support from NIH/NCRR P41 RR01243 Simulation Resource in Circulatory Mass Transport and Exchange, 12/1/1980-11/30/01 and NIH/NIBIB R01 EB001973 JSim: A Simulation Analysis Platform, 3/1/02-2/28/07.