The Surprising Link between Genetics and Pure Mathematics

Pure Maths and Genes

 

In a groundbreaking study, scientists have uncovered a remarkable connection between genetics and fundamental mathematics. Specifically, they have identified that a branch of pure mathematics holds the key to predicting the impact of genetic mutations on biological functions.

This revelation extends beyond genetics, as the principles governed by the so-called "sum-of-digits function" also influence various domains such as protein folding, computer programming, and specific magnetic states within the field of physics.

Lead writer Vaibhav Mohanty, a theoretical physicist and doctoral candidate at both Harvard Medical School and the Massachusetts Institute of Technology, explains the significance of their research: "Our goal is to decipher the underlying patterns that unify those phenomena determined in nature."

At the heart of their research lies the relationship between genotypes (the DNA sequences of a given gene) and phenotypes (the ensuing proteins or behaviors controlled with the aid of those genes). Remarkably, a genotype can accumulate numerous mutations before undergoing a change in phenotype. This accumulation of neutral mutations serves as a fundamental mechanism in the process of evolution.

Mohanty emphasizes, "We seek to comprehend the resilience of phenotypes to mutations. Surprisingly, this resilience proves to be quite robust." In simpler terms, a significant number of genetic alterations, represented by the "letters" or base pairs of DNA, can occur before observable changes manifest in the output.

This robustness, evident not only in genetics but also in disciplines such as physics and computer science, led Mohanty and his colleagues to explore its mathematical underpinnings within the realm of viable genetic sequences. They envisioned these sequences as existing in a multidimensional cube known as a "hybercube," with each point in this abstract space representing a potential genotype. Genotypes with similar phenotypes naturally clustered together.

The pivotal insight came from the realm of number theory, a branch of mathematics dedicated to the properties of integers. The average robustness of a phenotype to mutations was elucidated through the concept of the "sum-of-digits function." By summing the digits representing each genotype within the cube, researchers could ascertain the genotype's average robustness.

To illustrate, consider five genotypes that map to the same phenotype—a scenario involving five distinct DNA sequences, each carrying unique mutations yet encoding the same protein. The cumulative sum of the digits representing these sequences yields the average number of mutations these genotypes can endure before their phenotypes undergo alterations.

This revelation led to another intriguing discovery: the graphical representation of these sums of digits forms a "blancmange curve," a fractal curve named after a French dessert. In a fractal curve, zooming in reveals a self-replicating pattern identical to the broader view, allowing infinite levels of magnification.

Mohanty's findings shed light on error correction mechanisms. Notably, biological systems, unlike their technological counterparts, tend to prioritize the preservation of certain sequences over others, reflecting the unique nuances of genetic sequences. Understanding the dynamics of these neutral mutations could prove invaluable in disease prevention. Viruses and bacteria rapidly accumulate neutral mutations, and inhibiting their access to advantageous mutations amid the sea of genetic changes could curb their evolution towards increased infectiousness or antibiotic resistance.

In summary, this study uncovers a profound connection between mathematics and genetics, offering new insights into the resilience of genetic phenotypes and potential applications in disease control.