WPI professor Sam Walcott developed a molecular model that explains and accurately predicts muscle force, offering new opportunities for medical innovation. 

In honor of our upcoming Arts & Sciences Week, WPI is showcasing research that demonstrates how mathematics is advancing medical science.  

A new mathematical model developed at Worcester Polytechnic Institute (WPI) could enhance our understanding and treatment of heart disease. Created by Sam Walcott, director of bioinformatics and computational biology, the model simulates how microscopic structures within muscle cells generate force, using principles from both physics and biology to describe the interaction of individual molecules. It also reveals how subtle changes at the molecular level can lead to serious cardiac conditions. The research could inform the next generation of energy-efficient prosthetics. 

Walcott collaborated with Edward (Ned) Debold, professor of kinesiology at UMass Amherst, and Walter Herzog, professor of kinesiology at the University of Calgary. Using rabbit muscle tissue, Debold conducted molecular-scale experiments to study how individual muscle proteins respond under different conditions, while Herzog examined how whole muscle cells generate force. Their combined experiments provided data that Walcott then used for his model. 

“We have developed a mathematical model that describes how muscle cells generate force by accounting for how the molecules in the cell interact,” Walcott explains. “This connection between the cellular and molecular scale is important because, for example, genetic heart disease often causes subtle changes in one or two types of molecules in the heart muscle, yet drastic changes in heart function.” 

Walcott’s research has big potential for the future of medical science. For example, a relatively new discovery in the world of muscle contraction research is thick filament activation, which is a kind of “on/off-switch” for muscle molecules. Walcott’s mathematical models account for this process and suggest how it might affect muscle function. 

When you tense your muscle and stretch it (as if you're beginning to lose an arm-wrestling contest), your muscle can produce more force than without the stretch, a phenomenon called force enhancement. Similarly, if you tense your muscle and shorten it (as if you're beginning to win an arm-wrestling contest), your muscle can generate less force, a phenomenon called force depression. These phenomena, discovered in 1952, lack a molecular explanation. Remarkably, though one might expect force depression and  

enhancement to arise from the same process, there are differences between them—for example, force enhancement is not associated with an increased number of force-generating muscle molecules, while force depression is associated with a decrease in those molecules. 

A leading idea for how force enhancement arises is that a molecular "spring" gets engaged as you activate your muscle. When the muscle is then stretched, the spring is also stretched, thereby generating some extra force in addition to the force-generating molecules in the muscle. Walcott and his collaborators proposed that, when the muscle is shortened, the spring contracts. This then decreases the force in the muscle. Thick filament activation proposes that the force-generating molecules switch "off" when force drops, so this drop in force decreases the number of force-generating molecules. This explains both the drop in force observed in force depression and also why the number of force-generating molecules decreases. 

The model, which was originally designed to describe the Herzog lab’s cellular experiments, was also able to successfully predict the results of the Debold lab’s molecular-scale experiments. This suggests that we can, in fact, connect the behavior of molecules with the function of muscle cells. 

These discoveries mark an exciting step in the world of medicine and biomechanical design, like heart disease research and prosthetics. “Designing prosthetics requires thinking about how muscles use energy, since one wants the prosthetic to be both functional and efficient,” Walcott explains. “If we understand how muscle molecules interact, we can understand how they use energy and how the muscle overall uses energy.” 

Walcott’s research was supported by a $1.4 million grant from the National Institute of General Medical Sciences (NIGMS), an institute of the NIH. This project also highlights the interdisciplinary focus of WPI’s Bioinformatics and Computational Biology program, where students and faculty use math and data to explore the frontiers of biological research.