Scientists have found that the key function of a branch of “pure” mathematics can predict how often genetic mutations lead to changes in function.
These rules, established by means of so-called sum functions, also govern certain aspects of protein folding, computer coding, and certain magnetic states in physics.
said lead study author Vibhav Mohanty, theoretical physicist, PhD candidate and MD at Harvard Medical School and MIT.
For each genotype – the DNA letters of a particular gene – there is a phenotype, or end result: a new protein, or even behavior in the case of genes that control other gene pools. The genotype can undergo a number of mutations before the phenotype changes; This accumulation of neutral mutations is the main way evolution takes place.
“We want to understand, how strong is the current mutation phenotype?” Mohanty said. “It seems that this force is too high.” In other words, many “characters,” or base pairs that make up the DNA code, can change before the result changes.
Because these forces are seen not only in genetics, but also in fields such as physics and computer science, Mohani and his colleagues suspect that their roots may lie in the mathematics underlying the potential sequences. This possible sequence is imagined as a multi-dimensional cube, known as a hypercube, and each point on this impossible cube is visualized as a possible genotype. Mohany said that genotypes and similar phenotypes would eventually group together. The question is, what does this group look like?
As it seems, the answer lies in number theory, the area of mathematics concerned with the properties of positive integers. The average phenotypic severity of mutants is shown to be determined by the so-called sum of number functions. This means that by adding the numbers representing each genotype on the cube, you can get the average strength of that genotype.
“Let’s say there are five genotypes related to a certain phenotype,” said Mohanty. So, for example, five DNA sequences, each with a different mutation, but they all still code for the same protein.
The researchers found that adding the numbers used to represent these five sequences gives you the average number of mutations that genotypes can have before their phenotype changes.
This leads to a second interesting discovery: the numbers from the graph form the so-called planmange curves, fractal curves named after French puddings (which look like fancy puddings).
On fractal curves, Mohany said, “If you zoom in on the curve, it seems that it is decreasing, and you can continue zooming in infinitely, indefinitely, indefinitely, and the result will be the same.”
Mohani says these results reveal some interesting secrets about error correction. For example, the natural systems that researchers study tend to handle errors differently than humans do when storing data, such as in digital messages or on CDs or DVDs. In this technological example, all faults are treated equally, while biological systems tend to protect certain sequences more than others.
This is not surprising for genetic sequences, says Muhany, because there can be many linchpin sequences and then other sequences that are more peripheral to key genetic functions.
Understanding the dynamics of these neutral mutations may ultimately be important for disease prevention, says Mohany. Viruses and bacteria evolve rapidly, accumulating many neutralizing mutations in the process. If there was a way to prevent this pathogen from landing a needle mutation in the lucrative haystack among all the straws, researchers might be able to prevent the pathogen’s ability to become more infectious or resistant to antibiotics, for example.
The researchers published their results on July 26 Facade Journal of the Royal Society.