An interdisciplinary team of researchers has uncovered a surprising relationship between pure mathematics, particularly number theory, and genetics. This discovery contributes significantly to our understanding of neutral mutations and their role in the evolution of organisms.
Number theory, a branch of mathematics that examines the properties of positive integers, often seems too abstract to have practical applications in the real world. However, despite its abstract nature, number theory has consistently been applied in unexpected ways in science and engineering, such as the near-universal leaf angles that follow the Fibonacci sequence, and modern encryption methods based on prime number factorization. Now, this same theory has been found to relate unexpectedly to evolutionary genetics.
The research team, comprised of members from institutions like Oxford, Harvard, Cambridge, GUST, MIT, Imperial, and the Alan Turing Institute, has revealed an important connection between the sums-of-digits function from number theory and the mutational robustness of a phenotype in genetics. The mutational robustness of a phenotype describes the average chance that a single mutation won’t change the phenotype, or an organism’s characteristic.
This discovery could have significant impacts on our understanding of evolutionary genetics. A large number of genetic mutations are neutral, meaning they don’t affect an organism’s phenotype. As these mutations accumulate over time, they alter genome sequences at a consistent rate. Because this rate is known, scientists can measure the difference in sequence between two organisms to estimate when their last common ancestor existed.
However, the question remained: What proportion of mutations to a sequence are actually neutral? This is where the idea of phenotype mutational robustness comes into play, defining the average number of mutations that can occur across all sequences without affecting the phenotype.
Professor Ard Louis from the University of Oxford, who headed the research, said, “We’ve known that many biological systems exhibit high phenotype robustness, which is essential for evolution, but we didn’t know the maximum robustness possible.”
The team has provided an answer to this question. They demonstrated that the maximum robustness is proportional to the logarithm of the ratio of all possible sequences that map to a phenotype, with a correction given by the sums-of-digits function, sk(n), which sums the digits of a natural number n in base k. For instance, for n = 123 in base 10, the digit sum would be s10(123) = 1 + 2 + 3 = 6.
Interestingly, they also discovered that the maximum robustness is associated with the Tagaki function, a unique function that is continuous everywhere, but differentiable nowhere, also known as the blancmange curve due to its resemblance to the French dessert.
Dr. Vaibhav Mohanty from Harvard Medical School, the study’s first author, added, “It’s astonishing that we found evidence in the mapping from sequences to RNA secondary structures that nature sometimes achieves the exact maximum robustness boundary. It’s as if biology is aware of the fractal sums-of-digits function.”
Professor Ard Louis further added: “Number theory is not just beautiful in its abstract integer relationships but also illuminates profound mathematical structures in our natural world. We anticipate the discovery of many more fascinating connections between number theory and genetics in the future.”
The study, “Maximum mutational robustness in genotype–phenotype maps follows a self-similar blancmange-like curve” by Vaibhav Mohanty et al., was published in the Journal of The Royal Society Interface on 26 July 2023.
DOI: 10.1098/rsif.2023.0169
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Frequently Asked Questions (FAQs) about Number Theory and Genetics
What is the newly discovered link between pure mathematics and genetics?
Researchers have found a surprising connection between number theory in mathematics and genetics. Specifically, they’ve identified a link between the sums-of-digits function from number theory and the mutational robustness of a phenotype in genetics.
What is phenotype mutational robustness?
Phenotype mutational robustness defines the average number of mutations that can occur across all sequences without affecting the phenotype of an organism.
How can this discovery impact our understanding of evolutionary genetics?
This discovery can enhance our understanding of neutral mutations, which accumulate over time without affecting an organism’s phenotype. By knowing the proportion of these neutral mutations (phenotype mutational robustness), scientists can estimate when the last common ancestor of two organisms existed based on the sequence difference between them.
What is the significance of the sums-of-digits function in this context?
The research team demonstrated that the maximum mutational robustness is proportional to the logarithm of the ratio of all possible sequences that map to a phenotype, with a correction given by the sums-of-digits function. This mathematical function played a key role in their findings.
How is the Tagaki function related to this discovery?
Interestingly, the researchers discovered that the maximum robustness of mutations also correlates with the Tagaki function, a continuous yet non-differentiable function also known as the blancmange curve. This function’s appearance was an unexpected aspect of their findings.
6 comments
neutral mutations, huh? So they change but don’t actually change anything. Sorta like my diet attempts. lol!
just when i thought science couldn’t get any cooler! Phenotype mutational robustness, sums-of-digits function, Tagaki function…its all a bit over my head but sounds epic!
Wow this is mindblowing! Who’d have thought math and genetics could be linked in such a way! Hats off to these researchers.
hmm, not sure how I feel about this. Seems like a bit of a stretch… But then again, what do I know about genetics or number theory!
Always knew number theory was more than just abstract math. Take that, Dickson!
Can’t believe the sums-of-digits function might actually have some real world use… Guess you never know with math.