Distorting the sarcomere

One of the goals of cardiovascular science is to create a mathematical model of the heart that can predict ven-tricular function in healthy and diseased states, and that can be used to help improve treatment options for patients with heart disease. To be clinically useful, the model will have to include structural information about the shapes of the chambers and the action of the valves, and about how the electrical activity spreads from the sino-atrial node to the ventricular cells. It will also have to incorporate information about the contractile properties of the myocardial cells in different regions of the heart. In this issue, Ford et al. present a mathematical model that could provide a simpler and better way of predicting how force varies within real ventricular cells during the cardiac cycle. Mathematical modeling of striated muscle was dominated in the latter half of the 20th century by a technique developed by A.F. Huxley (1957). In this approach, the mechanical properties of the muscle are attributed to a single population of myosin heads, each of which independently undergoes cyclic interactions with binding sites on actin filaments. If a myosin head is attached, it is assumed to behave as a Hookean spring so that the force produced by the muscle at any instant can be calculated simply by summing the forces due to the individual bound cross-bridges (the product of a spring constant and the cross-bridge extension in each case). Predicting the mechanical behavior of the muscle during a perturbation thus reduces to calculating how the cross-bridge population distributions (the proportion of cross-bridges attached with each range of spring lengths) evolve after the imposed movement. In Huxley's original formulation, this can be done simply by integrating a single partial differential equation. This general approach has been tremendously successful , and many authors have used the technique to simulate the behavior of different types of skeletal and cardiac muscle. It has become common to incorporate multiple bound states into the actin–myosin cycle, and models of this type can explain many features of experimental data including, for example, the double hyperbolic nature of the force–velocity curve (Månsson, 2010) and the effect of phosphate on iso-metric tension (Pate and Cooke, 1989). The main drawback of these more recent models is that they are quite complex. Månsson's recent publication, for instance , describes simulations performed with 17 free parameters and an attachment rate function that …