Number Theory’s Genetic Insight
A diverse group of mathematicians, engineers, physicists, and medical scientists has unveiled an unforeseen connection between fundamental mathematics and genetics, shedding light on neutral mutation structure and evolutionary patterns in organisms.
Number theory, the exploration of positive integer properties, represents a quintessential form of mathematics. Its apparent abstraction may seem incompatible with the natural realm. However, number theory repeatedly reveals unexpected applications across science and engineering, from Fibonacci-influenced leaf angles to modern encryption based on prime number factorization. Now, researchers have unveiled an unanticipated bridge between number theory and evolutionary genetics.
The team, comprising members from prestigious institutions like Oxford, Harvard, Cambridge, GUST, MIT, Imperial, and the Alan Turing Institute, has unearthed a profound link between the sums-of-digits concept in number theory and a pivotal genetic attribute—the mutational robustness of phenotypes. This attribute gauges the likelihood that a point mutation won’t alter a phenotype (an organism’s trait).
Number Theory’s Genetic Insight: evolutionary genetics
This revelation holds significant implications for evolutionary genetics. Neutral mutations, often accumulating without impacting phenotype viability, drive steady genome sequence changes over time. This change rate aids in deducing the time of a common ancestor between organisms by comparing sequence percentage differences.
Nevertheless, the existence of neutral mutations has raised a crucial question: what proportion of sequence mutations are neutral? Referred to as phenotype mutational robustness, this property defines the average mutations that can occur across sequences without influencing phenotypes.
Leading the study, Professor Ard Louis from the University of Oxford stated, “We’ve long known that various biological systems demonstrate remarkably high phenotype robustness, a prerequisite for evolution. However, the maximum achievable robustness remained uncertain.”
Number Theory’s Genetic Insight: the maximum robustness
The team addressed this question, establishing that the maximum robustness is proportionate to the logarithm of the fraction of all possible sequences corresponding to a phenotype. Additionally, a correction factor, indicated by the sums of digits function sk(n), contributes to this maximum. For instance, for n = 123 in base 10, the digit sum is s10(123) = 1 + 2 + 3 = 6.
Another intriguing discovery was the relationship between maximum robustness and the renowned Takagi function—a continuous yet non-differentiable fractal function. This function, known as the blancmange curve due to its resemblance to a French dessert, is interconnected with maximum robustness.
RNA secondary structures
Dr. Vaibhav Mohanty (Harvard Medical School), the study’s lead author, remarked, “Most surprising is the clear evidence we found in the mapping of sequences to RNA secondary structures, where nature in some cases achieves the exact maximum robustness. It’s as if biology incorporates the fractal sums-of-digits function.”
Therefore, professor Ard Louis emphasized, “Number theory’s beauty transcends abstract integer relationships, delving into profound mathematical structures within our natural surroundings. We foresee numerous fascinating connections between number theory and genetics waiting to be uncovered in the future.”
Read the original article on sciencedaily.
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