Mathematicians enjoy the beauty of mathematics that many of us don’t see. But nature is a wonderful world in which to observe the beauty created by mathematical relations.
The natural world offers seemingly endless patterns based on numbers – if we can recognize them.
Fortunately for us, a diverse team of researchers has just discovered another amazing connection between mathematics and nature. Between one of the purest forms of mathematics, number theory, and the mechanisms that govern the evolution of life on molecular scales, is genetics.
abstract as it may be, Number theory It may also be one of the most popular forms of mathematics for many of us. It includes multiplication, subtraction, division, and addition (arithmetic functions) of whole numbers, or whole numbers and their negative counterparts.
famous Fibonacci sequence This is just one example, where each number in the sequence is the sum of the two preceding numbers. Its patterns can be found all over nature, in pinecones, pineapples, and sunflower seeds.
“The beauty of number theory lies not only in the abstract relationships it reveals among the integers, but also in the profound mathematical structures it illuminates in our natural world.” Explain Oxford mathematician Ard Lewis is lead author of the new study.
Of interest to Lewis and his colleagues were mutations, genetic errors that slip into an organism’s genome over time and lead to evolution.
Some mutations can be a single letter change in the genetic sequence that causes disease or produces some unexpected advantage, while others cannot have any noticeable effect on the appearance, traits or behaviors (phenotype) of the organism.
The latter are sometimes referred to as neutral mutations, and although they have no discernible effect, they are indicators of evolution at work. Mutations accumulate at a steady rate over time, mapping genetic relationships between organisms as they slowly diverge from a common ancestor.
However, organisms must be able to tolerate some mutations, to maintain their distinctive phenotype while the genetic lottery continues to distribute the variants that Uh, maybe not be useful.
That’s what it’s called Mutational durability Genetic diversity is born, but it varies between species, and can even be observed in intracellular proteins.
The studied proteins can tolerate about two-thirds of the random errors in their coding sequences 66% of mutations neutral and has no effect on its final look.
“We have known for some time that many biological systems exhibit remarkably high apparent strength, without which evolution would not be possible.” Explain Louis.
“But we didn’t know what the absolute maximum force was possible, or if there was a limit.”
To investigate, Lewis and his colleagues looked to folding protein And Small RNA structures As examples of how a unique genetic sequence, known as a genotype, can map to a particular phenotype or trait.
In the case of proteins, a short DNA sequence outlines the protein’s building blocks, which, when grouped together, encode their shape.
Smaller than proteins are the secondary structures of RNA; Free-floating strands of genetic code that help build proteins.
Lewis and his colleagues wondered how close nature would be to reaching the upper bounds of mutational force, so they ran numerical simulations to calculate the probabilities.
They studied the abstract mathematical features of how many genetic variations map to a particular phenotype without changing it, and showed that mutational power can indeed be maximized in naturally occurring proteins and RNA structures.
Moreover, the maximum robustness follows a self-recurring fractal pattern called a Blancmange curveand was consistent with the basic concept of number theory, called Break the sum of the numbers.
“We found clear evidence in mapping from sequences to RNA secondary structures that in some cases nature achieves the exact upper limit of strength.” He says Vaibhav Mohanty, of Harvard Medical School.
“It is as if biology knows about the function of the sum of rational numbers.”
Once again, mathematics seems to be an essential element of nature, giving structure to the physical world, even on microscopic levels.
The study was published in Interface Journal of the Royal Society.
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