Yang, Clark, Bryan, Robertson, 2003

Model Status

This is the original unchecked version of the model imported from the previous CellML model repository, 24-Jan-2006.

Model Structure

Contraction in vascular smooth muscle cells can be triggered by mechanical, electrical and chemical stimuli. Several different signal transduction pathways can initiate the contraction, but they all share the common intermediate step of increasing the intracellular calcium concentration ([Ca²⁺]_i). This increase is either due to a Ca²⁺ influx through voltage-gated sarcolemmal Ca²⁺ channels, or a Ca²⁺ release from internal sarcoplasmic reticulum stores. In the cytosol, Ca²⁺ binds to the buffer calmodulin, and the resulting complex (CaCM) activates myosin light chain kinase (MLCK), which in turn phosphorylates myosin light chains in the presence of ATP. This leads to cross-bridge formation and cycling between the myosin heads and the binding sites on the actin filaments, generating the active force needed for muscle contraction. Actin filaments are coupled to the sarcolemma via a viscoelastic system, resulting in changes in cell length. These macroscopic contractile properties of the cell are measured in terms of length-force and force-velocity relationships.

Several mathematical models of cerebrovascular smooth muscle cell function have been previously published; however, each of these has dealt with a single particular aspect of smooth muscle activity: electrophysiology; cytosolic calcium regulation; myosin phosphorylation; and mechanical behaviour have all been considered separately. In this study, Yang et al. combine electrophysiological, biochemical and mechanical experimental data and develop an integrated model of smooth muscle cell function (see the figure below).

The electrochemical model combines a Hodgkin-Huxley type membrane model which captures ionic membrane currents and transmembrane potential, together with a fluid compartment model which describes ionic fluxes, Ca²⁺ buffering and Ca²⁺ handling by the sarcoplasmic reticulum.

The second subsystem model is a chemomechanical model with two coupled units: a model of CaCM-dependent myosin phosphorylation and attached cross-bridge kinetics, and a mechanical model of force generation and mechanical coupling within the cell. A multiple-state kinetic model of myosin phosphorylation represents cross-bridge attachment, and a mechanical model describes active force generation by the contractile actin and myosin filaments and the viscoelastic properties of their coupling to the cell membrane.

The complete original paper reference is cited below:

The myogenic response in isolated rat cerebrovascular arteries: smooth muscle cell model, Jin Yang, John W. Clark Jr., Robert M. Bryan, and Claudia Robertson, 2003, Medical Engineering and Physics , 25, 691-709. (Full text (HTML) and PDF versions of the article are available on the Medical Engineering and Physics website.) PubMed ID: 12900184

Schematic diagrams of: A) the electrochemical model; B) the multi-state kinetic model of CaCM dependent myosin phosphorylation and cross-bridge formation; and C) functional block diagram of the whole integrated smooth muscle cell model.