Mathematical model predicts the best way to build muscle

Figure 1. The “textbook” hierarchy in skeletal muscle anatomy. Global muscle is characterized by its cross section (CSA), which contains a number (Nc) of muscle fibers (multi-core muscle cells or multinucleated myocytes). A given muscle has an almost fixed number of myocytes: between Nc ≈ 1000 for the tensor of the eardrum and Nc> 1,000,000 for the large muscles (gastrocnemius, temporalis, etc. Credit: DOI: 10.1016 / j.bpj.2021.07.023

Researchers have developed a mathematical model that can predict the optimal exercise regimen for building muscle.

Researchers at the University of Cambridge used theoretical biophysical methods to build the model, which can indicate how much specific effort will cause a muscle to grow and how long it will take. The model could form the basis of a software product, where users could optimize their exercise regimes by entering some details of their individual physiology.

The model is based on previous work by the same team, who found that a component of muscle called titin is responsible for generating the chemical signals that affect muscle growth.

The results, reported in the Biophysical Journal, suggest that there is an optimal weight at which to perform resistance training for every person and every muscle growth goal. Muscles can only be near their maximum load for a very short time, and it is the load integrated over time that activates the cell signaling pathway that leads to the synthesis of new muscle proteins. But below a certain value, the load is insufficient to cause much signaling, and the exercise time would have to increase exponentially to compensate. The value of this critical load is likely to depend on the particular physiology of the individual.

We all know that exercise builds muscles. Where do we do? “Surprisingly, not much is known about why or how exercise builds muscle: there is a lot of anecdotal knowledge and wisdom gained, but very little hard or proven data.”said Professor Eugene Terentjev of the Cavendish Laboratory in Cambridge, one of the authors of the article.

When exercising, the greater the load, the more repetitions or the higher the frequency, the greater the increase in muscle size. However, even looking at the whole muscle, why or how much this is happening is not known. The answers to both questions become even more delicate as the focus is placed on a single muscle or its individual fibers.

Muscles are made up of individual filaments, which are only 2 microns long and less than a micrometer in diameter, smaller than the size of the muscle cell. “For this reason, part of the explanation for muscle growth has to be at the molecular level.”, said co-author Neil Ibata. “The interactions between the main structural molecules of muscle were only reconstituted about 50 years ago. How the smaller accessory proteins fit into the picture is still not entirely clear.”

This is because the data is very difficult to come by: people differ considerably in their physiology and behavior, making it almost impossible to perform a controlled experiment on changes in muscle size in a real person. “You can extract muscle cells and examine them individually, but this then ignores other issues like oxygen and glucose levels during exercise.”, Terentjev said. “It’s very difficult to look at everything together.”

Terentjev and his colleagues began to study the mechanisms of mechanodetection, that is, the ability of cells to detect mechanical signals in their environment, several years ago. The research was noticed by the English Institute of Sport, who wanted to know if it could be linked to their observations on muscle rehabilitation. Together, they discovered that muscle hyper / atrophy was directly linked to Cambridge’s work.

In 2018, Cambridge researchers started a project on how muscle filament proteins change under force. They found that the main muscle building blocks, actin and myosin, lack binding sites for signaling molecules.

Whenever part of a molecule is under tension for long enough, it switches to a different state, exposing a region that was previously hidden. If this region can then bind to a small molecule involved in cell signaling, it activates that molecule, generating a chemical signal chain. Titin is a giant protein, much of which stretches when a muscle is stretched, but a small part of the molecule is also under tension during muscle contraction. This part of the titin contains the so-called titin kinase domain, which is the one that generates the chemical signal that affects muscle growth.

The molecule will be more likely to open if it is subjected to more force or if it is held under the same force for longer. Both conditions will increase the number of activated signaling molecules. These molecules then induce the synthesis of more messenger RNA, leading to the production of new muscle proteins, and the cross section of the muscle cell increases.

This awareness led to the current work, started by Ibata, himself a passionate athlete. “I was delighted to better understand both the why and the how of muscle growth”, did he declare. “So much time and resources could be saved by avoiding low productivity exercise regimes and maximizing the potential of athletes with higher value regular sessions, given a specific volume that the athlete is able to achieve.”

Terentjev and Ibata set out to restrict a mathematical model that could give quantitative predictions about muscle growth. They started with a simple model that kept track of titin molecules breaking open under force and starting the signaling cascade. They used microscopy data to determine the probability as a function of force that a unit of titin kinase opens or closes under force and activates a signaling molecule.

They then made the model more complex by including additional information, such as metabolic energy exchange, as well as repetition time and recovery. The model has been validated using previous long-term studies of muscle hypertrophy.

“Our model provides a physiological basis for the idea that muscle growth occurs primarily at 70% of maximum load, which is the idea behind resistance training.”, Terentjev said. “Below, the opening rate of titin kinase drops sharply and prevents mechanosensitive signaling from taking place. Above that, rapid exhaustion prevents a good result, which our model predicted quantitatively.”

“One of the challenges of preparing elite athletes is the common requirement to maximize adaptations while balancing associated tradeoffs such as energy costs.”said Fionn MacPartlin, senior strength and conditioning trainer at the English Institute of Sport. “This work gives us better insight into the potential mechanisms of how muscles feel and respond to load, which can help us design interventions more specifically to achieve these goals.”

The model also addresses the problem of muscle atrophy, which occurs during long periods of bed rest or for astronauts in microgravity, showing both how long a muscle can afford to be inactive before it starts to deteriorate, and what might be the optimal recovery regimen.

Ultimately, the researchers hope to produce a user-friendly software application that could result in individualized exercise regimes for specific goals. The researchers also hope to improve their model by extending their analysis with detailed data for both men and women, as many exercise studies are heavily biased in favor of male athletes.