Researchers developed mathematical model for building muscle

 Researchers have developed a mathematical model that can predict the optimum exercise regime for building muscle.

Surprisingly, not very much is known about why or how exercise builds muscles: there’s a lot of anecdotal knowledge and acquired wisdom, but very little in the way of hard or proven data

Eugene Terentjev

The researchers, from the University of Cambridge, used methods of theoretical biophysics to construct the model, which can tell how much a specific amount of exertion 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 optimise their exercise regimes by entering a few details of their individual physiology.

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

The results, reported in the Biophysical Journal, suggest that there is an optimal weight at which to do resistance training for each person and each muscle growth target. Muscles can only be near their maximal load for a very short time, and it is the load integrated over time which activates the cell signalling pathway that leads to synthesis of new muscle proteins. But below a certain value, the load is insufficient to cause much signalling, and 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 muscle. Or do we? “Surprisingly, not very much is known about why or how exercise builds muscles: there’s a lot of anecdotal knowledge and acquired wisdom, but very little in the way of hard or proven data,” said Professor Eugene Terentjev from Cambridge’s Cavendish Laboratory, one of the paper’s authors.

When exercising, the higher the load, the more repetitions or the greater the frequency, then the greater the increase in muscle size. However, even when looking at the whole muscle, why or how much this happens isn’t known. The answers to both questions get even trickier as the focus goes down to a single muscle or its individual fibres.

Muscles are made up of individual filaments, which are only 2 micrometres long and less than a micrometre across, smaller than the size of the muscle cell. “Because of this, part of the explanation for muscle growth must be at the molecular scale,” said co-author Neil Ibata. “The interactions between the main structural molecules in muscle were only pieced together around 50 years ago. How the smaller, accessory proteins fit into the picture is still not fully clear.”

This is because the data is very difficult to obtain: people differ greatly in their physiology and behaviour, making it almost impossible to conduct a controlled experiment on muscle size changes in a real person. “You can extract muscle cells and look at those individually, but that then ignores other problems like oxygen and glucose levels during exercise,” said Terentjev. “It’s very hard to look at it all together.”

Terentjev and his colleagues started looking at the mechanisms of mechanosensing – the ability of cells to sense mechanical cues in their environment – several years ago. The research was noticed by the English Institute of Sport, who were interested in whether it might relate to their observations in muscle rehabilitation. Together, they found that muscle hyper/atrophy was directly linked to the Cambridge work.

In 2018, the Cambridge researchers started a project on how the proteins in muscle filaments change under force. They found that main muscle constituents, actin and myosin, lack binding sites for signalling molecules, so it had to be the third-most abundant muscle component – titin – that was responsible for signalling the changes in applied force.

Whenever part of a molecule is under tension for a sufficiently long time, it toggles into a different state, exposing a previously hidden region. If this region can then bind to a small molecule involved in cell signalling, it activates that molecule, generating a chemical signal chain. Titin is a giant protein, a large part of which is extended when a muscle is stretched, but a small part of the molecule is also under tension during muscle contraction. This part of 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 under more force, or when kept under the same force for longer. Both conditions will increase the number of activated signalling molecules. These molecules then induce the synthesis of more messenger RNA, leading to production of new muscle proteins, and the cross-section of the muscle cell increases.

This realisation led to the current work, started by Ibata, himself a keen athlete. “I was excited to gain a better understanding of both the why and how of muscle growth,” he said.