A Powerful Model of Relaxation

Modeling what triggers heart cells to relax

When a heart beats, millions of muscle cells contract in unison to pump blood to the body; then they relax, allowing the heart to refill. Though scientists have carefully characterized the mechanisms that govern contraction, they are less certain about the dynamics of relaxation. But a new mathematical model of calcium ion concentration in cardiac muscle—published in March 2006 in Biophysical Journal—has resolved at least one controversy.


“There’s been a lot of emphasis on contraction, because it’s the first thing you measure experimentally,” says Nicolas Smith, PhD, senior lecturer in the Bioengineering Institute and Department of Engineering Science at the University of Auckland in New Zealand. “But it’s just as important that the heart relaxes. We wanted to be very clear that we were characterizing the relaxation properties just as well as the contraction properties in this model.”


Here’s what a heartbeat looks like from within a cell: An electric signal spurs the release of calcium ions, which bind to motor proteins and activate contraction; then, the calcium ions are pumped away, and the cell relaxes. The rise in calcium clearly governs contraction, but scientists still debate the key trigger for relaxation. Some have suggested that relaxation depends more heavily on mechanical factors (when the cell reaches a critical length or tension), rather than on biochemical factors (a drop in calcium levels).


Smith and his colleagues combed the literature and found decades worth of experimental data (from humans, chickens, rats, mice, ferrets, rabbits, cows and cats) on calcium concentration and binding, as well as cell velocity, length, and tension during a heart beat. They combined these diverse data into a series of mathematical equations that simulate cellular contraction and relaxation. Then they simulated the tension changes in the beat of a heart cell—and found that their predictions closely approximated tension changes measured in the lab (data that had not been used to build the model).


Their simulation also showed that cell relaxation depends predominantly on the drop in calcium levels. “In some ways this is less exciting than more esoteric ideas of length dependence and tension dependence, because it’s actually quite simple. But it does clear up a lot of the debate,” Smith says.


Smith and his colleagues are extending their model to study life-threatening biochemical changes that arise during ischemic heart disease (where oxygen is not getting to the heart). In ischemia, heart tissue becomes acidic, which wreaks havoc on calcium signaling. An unchecked overload of calcium will cause the heart to perpetually contract—a deadly deficiency of relaxation.
The model is limited to the cellular level, Smith notes, as modeling at the molecular or atomic scale would take too much computing power. But, he adds, “Because of the way we for-mulated it, it would be absolutely clear how we would interface with a much more detailed protein model.” The model can also be embedded into tissue-level and whole-heart models of contraction.


“This paper is unique because the authors searched the literature pretty extensively to come up with the estimates for different muscle responses,” comments John Jeremy Rice, PhD, a researcher in the Functional Genomics and Systems Biology Group at IBM’s T.J. Watson Research Center in New York. “Often models get published that are very limited in scope, because authors are only interested in fitting their particular dataset. But these authors tried to match a diverse set of data.”


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