Scientists Discover 'Pure Math' Is Written Into Evolutionary Genetics

Because so many of us fail to perceive math's beauty, mathematicians find great joy in it. However, nature is a beautiful place where one can witness beauty derived from mathematical correlations.

If we can detect them, the seemingly limitless patterns seen in the natural world are supported by numbers.

Fortunately for us, a disorganized group of scientists has recently discovered another amazing relationship between mathematics and the natural world: number theory, one of the purest branches of mathematics, and genetics, the principles controlling the evolution of life on a molecular level.

Despite its abstract nature, number theory is also a somewhat well-known branch of mathematics for most of us. It includes the arithmetic operations of addition, subtraction, division, and multiplication of integers, or whole numbers, and their inverses.

One well-known example of a series where each number is the sum of the two numbers before it is is the Fibonacci sequence. Patterns of it may be seen in pinecones, pineapples, and sunflower seeds, among other natural objects.

The principal author of the new study, mathematician Ard Louis of Oxford University, says, "The beauty of number theory lies not only in the abstract relationships it uncovers between integers, but also in the deep mathematical structures it illuminates in our natural world."

The genetic mistakes known as mutations, which gradually seep into an organism's DNA and propel evolution, piqued the curiosity of Louis and his colleagues.

While many mutations result in unanticipated benefits or diseases due to single-letter changes in the DNA sequence, other mutations may not affect an organism's phenotype—its outward characteristics—in any noticeable way.

The latter are frequently called neutral mutations, and while they don't seem to affect anything, they are signs of evolution in action. Over time, mutations accumulate steadily and map the genetic links among creatures as they gradually diverge from a common ancestor.

However, in order to maintain their distinctive phenotype, organisms must be able to withstand some mutations while the genetic lottery continues to produce potentially favorable replacements.

Genetic variety is produced through this so-called mutational resilience, which differs among species and is even seen in the proteins found inside of cells.

Sixty-six percent of mutations are harmless and have no influence on the final structure of the studied proteins, which can withstand about two-thirds of random mistakes in their coding sequences.

"Evolution would not be possible without the extraordinarily high phenotypic robustness that many biological systems exhibit," says Louis.

"However, we were unsure of the maximum possible robustness or even if one existed at all."

Louis and colleagues investigated the relationship between a genotype—a distinct genetic sequence that corresponds to a particular phenotype or trait—and short RNA structures and protein folding.

For proteins, the structure is encoded by piecing together the building pieces of the protein, which are spelled out in a brief DNA sequence.

RNA secondary structures, which are free-floating strands of genetic information that aid in the construction of proteins, are smaller than proteins.

Louis and associates conducted numerical simulations to calculate the likelihood that nature would get near to the top boundaries of mutational resilience.

They investigated the mathematically abstract aspects of how many genetic variants map to a given phenotype without altering it, and they demonstrated that naturally occurring proteins and RNA structures might in fact enhance mutational resilience.

Furthermore, the maximal resilience was related to the sum-of-digits fraction, a fundamental idea in number theory, and followed a self-repeating fractal pattern known as a Blancmange curve.

According to Vaibhav Mohanty of Harvard Medical School, "we found clear evidence in the mapping from sequences to RNA secondary structures that nature in some cases achieves the exact maximum robustness bound."

In a way, biology seems to be aware of the fractal sums-of-digits function.

Once more, math seems to be a fundamental aspect of nature that provides the physical universe order, even at the minuscule scale.

The study has been published in the Journal of The Royal Society Interface.