Muscle machine: How water controls the speed of muscle contraction

Nearly all animals use muscle to move, and it’s been known for a long time that muscle, like all other cells, is composed of about 70% water. But researchers don’t know what sets the range and upper limits of muscle performance. Previous research into how muscle works focused only on how it worked on a molecular level rather than how muscle fibers are shaped, that they are three-dimensional and are full of fluid.

U-M physicist Suraj Shankar together with L. Mahadevan, a professor of physics at Harvard University, created a theoretical model of water’s role in muscle contraction and found that how fluid moves through a muscle fiber determines how quickly a muscle fiber can contract.

They also found that muscle exhibits a new kind of elasticity called odd elasticity that allows muscle to generate power using three dimensional deformations, shown in a common observation that when a muscle fiber contracts lengthwise, it also bulges perpendicularly.

The researchers say this framework can be used to describe many other cells and tissues, which are also largely composed of water, and can be applied to the ultrafast movements of unicellular microorganisms and how they can be controlled. Their findings could also impact the design of soft actuators (a type of material that converts energy into motion), fast artificial muscles, and shape-morphing materials, all of which have very slow contraction speeds because they are triggered externally. Their results are published in the journal Nature Physics.

“Our results suggest that even such basic questions as how quickly muscle can contract or how many ways muscle can generate power have new and unexpected answers when one takes a more integrated and holistic view of muscle as a complex and hierarchically organized material rather than just a bag of molecules,” Shankar said. “Muscle is more than the sum of its parts.”

The researchers envision each muscle fiber as a self-squeezing active sponge, a water-filled, sponge-like material that can contract and squeeze itself through the action of molecular motors, he says.

“Muscle fibers are composed of many components, such as various proteins, cell nuclei, organelles such as mitochondria, and molecular motors such as myosin that convert chemical fuel into motion and drive muscle contraction,” Shankar said. “All of these components form a porous network that is bathed in water. So an appropriate, coarse-grained description for muscle is that of an active sponge.”

But the squeezing process takes time to move water around, so the researchers suspected that this movement of water through the muscle fiber set an upper limit on how rapidly a muscle fiber can twitch.

To test their theory, they modeled muscle movements in multiple organisms across mammals, insects, birds, fish and reptiles, focusing on animals that use muscles for very fast motions. They found that muscles that produce sound, such as the rattle in a rattlesnake’s tail, that can contract ten to hundreds of times per second typically don’t rely on fluid flows. Instead, these contractions are controlled by the nervous system and are more strongly dictated by molecular properties, or the time it takes for molecular motors within cells to bind and generate forces.

But in smaller organisms, such as flying insects who are beating their wings a few hundred to a thousand times per second, these contractions are too fast for neurons to directly control. Here fluid flows are more important.

“In these cases, we found that fluid flows within the muscle fiber are important and our mechanism of active hydraulics is likely to limit the fastest rates of contraction,” Shankar said. “Some insects such as mosquitos seem to be close to our theoretically predicted limit, but direct experimental testing is needed to check and challenge our predictions.”

The researchers also found that when muscle fibers act as an active sponge, the process also causes the muscles to act as an active elastic engine. When something is elastic, such as a rubber band, it stores energy as it tries to resist deformation. Imagine holding a rubber band between two fingers and pulling it back. When you release the rubber band, the band also releases the energy stored when it was being stretched. In this case, energy is conserved — a basic law of physics that dictates that the amount of energy within a closed system should remain the same over time.

But when muscle converts chemical fuel into mechanical work, it can produce energy like an engine, violating the law of the conservation of energy. In this case, muscle shows a new property called “odd elasticity,” where its response when squashed in one direction versus another is not mutual. Unlike the rubber band, when muscle contracts and relaxes along its length, it also bulges out perpendicularly, and its energy does not stay the same. This allows muscle fibers to generate power from repetitive deformations, behaving as a soft engine.

“These results are in contrast to prevailing thought, which focuses on molecular details and neglects the fact that muscles are long and filamentous, are hydrated, and have processes on multiple scales,” Shankar said. “All together, our results suggest a revised view of how muscle functions is essential to understand its physiology. This is also crucial to understanding the origins, extent and limits that underlie the diverse forms of animal movement.”

Nearly all animals use muscle to move, and it’s been known for a long time that muscle, like all other cells, is composed of about 70% water. But researchers don’t know what sets the range and upper limits of muscle performance. Previous research into how muscle works focused only on how it worked on a molecular level rather than how muscle fibers are shaped, that they are three-dimensional and are full of fluid.

U-M physicist Suraj Shankar together with L. Mahadevan, a professor of physics at Harvard University, created a theoretical model of water’s role in muscle contraction and found that how fluid moves through a muscle fiber determines how quickly a muscle fiber can contract.

They also found that muscle exhibits a new kind of elasticity called odd elasticity that allows muscle to generate power using three dimensional deformations, shown in a common observation that when a muscle fiber contracts lengthwise, it also bulges perpendicularly.

The researchers say this framework can be used to describe many other cells and tissues, which are also largely composed of water, and can be applied to the ultrafast movements of unicellular microorganisms and how they can be controlled. Their findings could also impact the design of soft actuators (a type of material that converts energy into motion), fast artificial muscles, and shape-morphing materials, all of which have very slow contraction speeds because they are triggered externally. Their results are published in the journal Nature Physics.

“Our results suggest that even such basic questions as how quickly muscle can contract or how many ways muscle can generate power have new and unexpected answers when one takes a more integrated and holistic view of muscle as a complex and hierarchically organized material rather than just a bag of molecules,” Shankar said. “Muscle is more than the sum of its parts.”

The researchers envision each muscle fiber as a self-squeezing active sponge, a water-filled, sponge-like material that can contract and squeeze itself through the action of molecular motors, he says.

“Muscle fibers are composed of many components, such as various proteins, cell nuclei, organelles such as mitochondria, and molecular motors such as myosin that convert chemical fuel into motion and drive muscle contraction,” Shankar said. “All of these components form a porous network that is bathed in water. So an appropriate, coarse-grained description for muscle is that of an active sponge.”

But the squeezing process takes time to move water around, so the researchers suspected that this movement of water through the muscle fiber set an upper limit on how rapidly a muscle fiber can twitch.

To test their theory, they modeled muscle movements in multiple organisms across mammals, insects, birds, fish and reptiles, focusing on animals that use muscles for very fast motions. They found that muscles that produce sound, such as the rattle in a rattlesnake’s tail, that can contract ten to hundreds of times per second typically don’t rely on fluid flows. Instead, these contractions are controlled by the nervous system and are more strongly dictated by molecular properties, or the time it takes for molecular motors within cells to bind and generate forces.

But in smaller organisms, such as flying insects who are beating their wings a few hundred to a thousand times per second, these contractions are too fast for neurons to directly control. Here fluid flows are more important.

“In these cases, we found that fluid flows within the muscle fiber are important and our mechanism of active hydraulics is likely to limit the fastest rates of contraction,” Shankar said. “Some insects such as mosquitos seem to be close to our theoretically predicted limit, but direct experimental testing is needed to check and challenge our predictions.”

The researchers also found that when muscle fibers act as an active sponge, the process also causes the muscles to act as an active elastic engine. When something is elastic, such as a rubber band, it stores energy as it tries to resist deformation. Imagine holding a rubber band between two fingers and pulling it back. When you release the rubber band, the band also releases the energy stored when it was being stretched. In this case, energy is conserved — a basic law of physics that dictates that the amount of energy within a closed system should remain the same over time.

But when muscle converts chemical fuel into mechanical work, it can produce energy like an engine, violating the law of the conservation of energy. In this case, muscle shows a new property called “odd elasticity,” where its response when squashed in one direction versus another is not mutual. Unlike the rubber band, when muscle contracts and relaxes along its length, it also bulges out perpendicularly, and its energy does not stay the same. This allows muscle fibers to generate power from repetitive deformations, behaving as a soft engine.

“These results are in contrast to prevailing thought, which focuses on molecular details and neglects the fact that muscles are long and filamentous, are hydrated, and have processes on multiple scales,” Shankar said. “All together, our results suggest a revised view of how muscle functions is essential to understand its physiology. This is also crucial to understanding the origins, extent and limits that underlie the diverse forms of animal movement.”