Scientists from the University of Cambridge have produced a mathematical model that can be used to develop optimal training programmes for muscle growth. In the very near future, with the aid of just a little personal data, people could be putting this model to use to build the best possible programmes to meet their goals.

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The Science of Building Muscle

Researchers from the University of Cambridge believe they have created a mathematical model that can predict the optimal way to build muscle. The researchers believe that one day soon the model could be used as part of a software package to allow users to optimise their exercise regimes by providing just a few details about their individual physiology.

The research could be of particular value to athletes, explains Neil Ibata, one of the principal researchers. “So much time and resources could be saved in avoiding low-productivity exercise regimes, and maximising athletes’ potential with regular higher value sessions, given a specific volume that the athlete is capable of achieving.”

The model is based on earlier work the researchers carried out which showed that a component of muscle called titin creates the chemical signals which control muscle growth. They used methods taken from theoretical biophysics to build the model, which amazingly predicts the extent to which a specific amount of exertion will cause a muscle to grow and how long it will take. 

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The paper, featured in the Biophysical Journal, suggests that, for each individual and their muscle growth goal, there is an optimal weight at which to do resistance training. As explained in a press release from Science Daily,

“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.”

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“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, one of the paper’s authors, in the above press release.

A number of variables affect muscle growth: load, repetitions and volume. Why or how much muscle growth takes place, however, still remains unclear. 

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And because muscle cells are made up of microscopic filaments, “part of the explanation for muscle growth must be at the molecular scale,” explains 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.”

One significant problem is the difficulty of obtaining sufficient data. Conducting controlled experiments on muscle growth is not easy, because of differences in individual physiology and behaviour, among other factors. Considering all the factors in play at once and accounting for them adequately is a very tall order.

The researchers, including Terentjev and Ibata, started looking at the mechanisms of mechanosensing — the ability of cells to sense mechanical cues in their environment — several years ago. 

In 2018, they began a project to investigate how the proteins in muscle filaments react to force. They discovered that the main muscle constituents, actin and myosin, do not have binding sites for signalling molecules. As a result, they concluded that the third-most abundant muscle component – titin – must be responsible for signalling the changes in force applied to the muscle.

Without going into too much detail, they were able to show how titin reacts to different amounts of force and, as a result, different amounts of signalling take place. The greater the number of signalling molecules activated, the greater the production of new muscle proteins, leading to an increasing in muscular size.

This research formed the basis of their new mathematical model, which was also validated with data from other long-term studies of muscle hypertrophy.

Interestingly, the study provides clear substantiation for the widely held belief that loads below 70% of an individual’s one-rep max (the amount they can lift once and once only) are sub-optimal for stimulating muscle growth.

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

The model can also be used to address muscular atrophy – i.e. muscle loss – which is a particular concern for those who are bed-bound or even for certain professions, such as astronauts. The model can show both how long a muscle can afford to remain inactive before it begins to deteriorate, and what the optimal recovery regime could be once it does.


In the future, as well as developing an easy-to-use software programme, the researchers also want to improve the model with data for women as well as men, given that most studies of muscle growth tend to favour men.

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