Modeling of Protein Interactions Involved in Cardiac Tension Development

Model Status

This model contains partial differentials and as such can not currently be solved by existing CellML tools.

Model Structure

Mathematical modelling of the protein interactions responsible for cardiac tension development can improve the understanding of the physiological and pathophysiological processes occuring in the heart. The principal components of muscular tension development are the proteins actin, myosin, troponin and tropomyosin. The tension is produced by cross-bridge cycling of actin and myosin using the hydrolyisis of adenosine triphosphate (ATP) as an energy source. The cross-bridge cycle is initiated by the binding of intracellular calcium to troponin and the resulting configuration changes of tropomyosin.

The first effort to mathematically model active tension development in muscle was published in 1938 by A. V. Hill. Since then, several other models have been published, including the five models of Rice et al., 1999. Combining and extending existing models, Sachse et al. develop a hybrid model of protein interactions in cardiac tension development (see the figure below). This model includes dependencies on intracellular calcium concentration, sarcomere stretch, and stretch velocity, as well as cooperativity mechanisms.

The complete original paper reference is cited below:

Modeling of Protein Interactions Involved in Cardiac Tension Development, F. B. Sachse, K. G. Glanzel, and G. Seemann, 2003, International Journal of Bifurcation and Chaos , 13, 3561-3578. (A PDF version of the article is available to subscribers on the International Journal of Bifurcation and Chaos website.)

State diagram of the model. Two state variables quantify the calcium binding to troponin C (T). Two further state variables describe the configuration of tropomyosin (TM). Ten state variables represent the interaction of actin and myosin as well as the hydrolysis of adenosine triphosphate (ATP). M and A represent myosin and actin respectively. Transition between states is depicted by an arrow.

The authors suggest that this hybrid model of cardiac tension development provides an interface to other models of cardiac electromechanics. The model can be coupled with models of cellular electrophysiology and passive mechanics of myocardium allowing the incorporation of mechano-electrical feedback mechanisms. Results of simulations with the model can be used to elucidate cooperativity mechanisms, pathophysiological changes, and the metabolism of tension development.