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Scientists explain the desire for symmetry as a “new law of nature”

In a paper published this month in the Proceedings of the National Academy of Sciences, the researchers analyzed thousands of protein complexes and RNA structures, as well as a model network of molecules that control genes turning on and off. They found that evolution tends to be symmetrical because the instructions for creating symmetry are easier to embed and follow in the genetic code.

Previously, biologists could not explain the reasons for the wide distribution of symmetry in nature. Researchers have tried to answer this question using computer science.

They proposed an alternative non-adaptive hypothesis based on an algorithmic picture of evolution. She suggests that symmetrical structures predominantly arise not only due to natural selection, but also because they require less specific information to encode, and therefore are much more likely to show up as phenotypic variations through random mutations. The researchers applied arguments from algorithmic information theory to formalize their theory. They tested their predictions against a wealth of biological data, showing that protein complexes, RNA secondary structures, and the regulatory network of model genes show the expected exponential shift towards simpler (and more symmetrical) phenotypes. Less description complexity also correlates with higher resistance to mutations, which can facilitate the evolution of complex modular assemblies from many components. Evolution proceeds through genetic mutations that give rise to new phenotypic variations that can be affected by natural selection. The relationship between genotype space and phenotype space can be expressed as a genotype-phenotype (GP) map (1-3). They can be considered algorithmically, when random genetic mutations search in the space of (evolutionary) algorithms encoded by the GP map for relationships that have been identified, for example, in plants (4), in Dawkins' "biomorphs" (5) and in biomolecules (6).

Oxford University physicist Ard Louie, computer science lecturer at the University of Exeter in England, Chico Camargo, and their colleague Ian Johnston of the University of Bergen in Norway began research into the evolutionary origins of symmetry when the latter was working on his doctoral thesis, running simulations to understand how viruses form their protein coats. He noticed that symmetrical structures arose much more often than pure chance would allow.

The researchers suggested that symmetry is some kind of algorithm for creating simple repeating patterns that is easier to implement and harder to break.

Over the course of a decade, the team applied the same concept to major biological components, studying how proteins assemble into clusters and how RNA folds. The idea of ​​RNA and proteins as small I/O machines that execute algorithmic genetic instructions explains the trend towards symmetry in a way that Darwinian "survival of the fittest" failed to do. Because it is easier to code instructions for building simple, symmetrical structures, nature is left with a disproportionate number of these simpler sets of instructions to choose from when it comes to natural selection.

To explore the preference for simple structures, the researchers used evolutionary modeling, in which fitness is maximized for polyominoes with 16 blocks. With 16 tile types and 64 interface types, the GP card, labeled S16,64, allows the creation of all 13,079,255 possible 16-dimensional polyomino topologies. On fig. 1E shows that the results of evolution are exponentially biased towards 16-dimensional structures with low K˜(p), although each 16-mer has the same fitness.

The tendency towards high symmetry can be further illustrated by examining the prevalence of the two groups with the highest symmetry in evolutionary simulation results. For 16-mers, there are 5 possible structures in class D4 (all square symmetries) and 12 in class C4 (quadruple rotational symmetry). Although these 17 structures represent just over a millionth of all 16-dimensional phenotypes, they represent about 30% of the structures that are fixed during evolution, showing an extremely strong preference for high symmetry. Comparison of histograms in fig. 1C and F shows that polyaminos exhibit qualitatively the same high symmetry bias as seen for proteins.Natural selection explains why 16-measures are chosen, but it does not explain the preference for symmetry. To better understand the mechanisms responsible for the evolutionary preference for high symmetry, the scientists calculated the probability P(p) of obtaining a (polyomino form) p phenotype by uniformly sampling 108 genomes for the S16,64 GP map. On fig. 2 shows that P(p) varies by many orders of magnitude for different p. High P(p) occurs only for structures with low K˜(p), while structures with high K˜(p) have low P(p). This correlation has been tested for a number of different evolutionary parameters, as well as for randomly assigned and fixed fitness functions, and a relationship between frequency and K˜(p) has always been observed that is strikingly similar to that found for a random sample.

While the current article focuses on microscopic structures, the researchers believe that this logic extends to larger, more complex organisms as well. “It would make a lot of sense if nature could reuse the program to create a petal, rather than having a separate program for each of the 100 petals around a sunflower,” Johnston said.

While there is still a gulf between demonstrating a statistical bias towards microscopic symmetry and explaining symmetry in plants and animals, Hollo Gabor, a biologist who studies symmetry at the University of Debrecen in Hungary, says he is excited about the new work. “To explain how such an integral and such a universal feature generally arises in evolution, in nature, is something,” he notes.

Luis Seoane, a complex systems researcher at the Centro Nacional de Biotechnologia in Spain, also not involved in the study, praised the work as "as legitimate as it gets". “There is a war going on between simplicity and complexity, and we live right on the edge of it,” he said.

Scientists explain the desire for symmetry as a “new law of nature”