"Pure mathematics" explains evolutionary genetics

We are fortunate that a diverse group of scientists have just discovered another exciting link between mathematics and nature: between genetics, one of the most important branches of biology, and number theory, one of the purest branches of mathematics.

Although it may seem abstract, number theory is probably one of the branches of mathematics that most of us are familiar with. It includes the arithmetic operations of adding, multiplying, subtracting and dividing integers or integers and their negative equivalents.

A well-known example is the Fibonacci sequence, where each number is the sum of the two numbers before it. Its patterns can be seen in a variety of natural objects, including sunflower seeds, pineapples, and pinecones.

According to Oxford mathematician Ard Lewis, lead author of the new study, “The beauty of number theory lies not only in the abstract relationships it reveals between integers, but also in the deep mathematical structures it highlights in our natural world.”

Genetic errors known as mutations, which creep into an organism's DNA over time and promote evolution, were of interest to Lewis and his colleagues.

Some mutations can lead to disease or unexpected benefit by changing a single letter in the genetic sequence, while other changes may have no noticeable effect on the phenotype (appearance, features, or behaviors) of the organism.

These latter mutations are sometimes referred to as neutral mutations, and although they do not appear to have any effects, they are evidence that evolution is active. As species gradually diverge from a common ancestor, mutations accumulate over time at a constant rate, strengthening the genetic links between them.

However, in order to maintain a distinct phenotype while the genetic lottery continues to distribute alternatives that may or may not be favourable, organisms must be able to tolerate certain changes.

Genetic diversity is produced by so-called mutational plasticity, which varies between species and can be seen even in proteins found inside cells.

About 66% of mutations are benign and have no effect on the final structure of the studied proteins, which can tolerate about two-thirds of random errors in their coding sequences.

Lewis explains that evolution is inconceivable without the high phenotypic plasticity exhibited by many biological systems.

But we were not sure how much flexibility could be achieved or even if such flexibility existed.

Lewis and his colleagues looked to protein folding and small RNA structures as examples of how a distinct genetic sequence, often known as a genotype, can map to a particular phenotype or characteristic in order to better understand

In the case of proteins, the concise DNA sequence enumerates the component parts of the protein, which when put together encode its shape.

RNA secondary structures, which are free strands of genetic information that aid in protein synthesis, are smaller than proteins.

Lewis and his colleagues used numerical simulations to calculate probabilities in order to determine how close nature is to the limits of mutational plasticity.

They studied the amorphous mathematical properties of the number of genetic changes that can map to a given phenotype without changing it, and demonstrated that mutational flexibility can be maximized in naturally occurring proteins and RNA structures.

Furthermore, the maximum elasticity was related to the fraction of the sum of numbers, a fundamental idea in number theory, and followed a self-repeating fractal pattern known as the Blancman curve.

According to Vaibhav Mohanty of Harvard Medical School, “We found clear evidence in mapping from sequences to RNA secondary structures that nature sometimes achieves a precise maximum in strength.”

It seems as if biology is aware of the function of fractal sums of numbers.

Again, computation appears to be a fundamental aspect of nature that provides organization of the physical world even on small scales.