Mathematicians Uncover Striking Connection Between Number Theory and Genetics
Mathematics and nature have long been intertwined, with mathematicians finding beauty in the patterns and relationships that exist in the natural world. Now, a team of researchers has discovered another fascinating link between math and nature, specifically between number theory and genetics.
Number theory is one of the more familiar branches of mathematics, encompassing the arithmetic operations of integers. It explores the abstract relationships between whole numbers and their negative counterparts. One well-known example of number theory is the Fibonacci sequence, which can be found in various natural phenomena, such as pinecones and sunflower seeds.
“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,” says Ard Louis, a mathematician from Oxford University and senior author of the study.
The researchers focused on mutations, genetic errors that occur over time and drive evolution. While some mutations have observable effects on an organism’s traits or behaviors, others are considered neutral mutations. Although these mutations do not impact the organism’s phenotype, they play a crucial role in evolutionary processes.
Mutations accumulate steadily over time, allowing scientists to track the genetic relationships between organisms as they diverge from a common ancestor. However, organisms must also maintain “mutational robustness” to preserve their characteristic characteristics amid the genetic lottery.
The team studied proteins and small RNA structures to understand the relationship between genotype and phenotype. By running numerical simulations, they found that mutational robustness can be maximized in naturally occurring proteins and RNA structures.
Surprisingly, the maximum robustness followed a self-repeating fractal pattern known as a Blancmange curve. This pattern was proportional to a basic concept in number theory, called the sum-of-digits fraction.
“We found clear evidence that nature achieves the exact maximum robustness bound in some cases,” says Vaibhav Mohanty from Harvard Medical School. “It’s as if biology knows about the fractal sums-of-digits function.”
This discovery highlights the essential role of mathematics in understanding and explaining the natural world, even at microscopic levels. The study has been published in the Journal of The Royal Society Interface, providing further evidence of the intricate relationship between math and nature.