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Maximum mutational robustness in genotype–phenotype maps follows a self-similar blancmange-like curve

Phenotype robustness, defined as the average mutational robustness of all the genotypes that map to a given phenotype, plays a key role in facilitating neutral exploration of novel phenotypic variation by an evolving population. By applying results from coding theory, we prove that the maximum pheno...

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Autores principales: Mohanty, Vaibhav, Greenbury, Sam F., Sarkany, Tasmin, Narayanan, Shyam, Dingle, Kamaludin, Ahnert, Sebastian E., Louis, Ard A.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: The Royal Society 2023
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10369032/
https://www.ncbi.nlm.nih.gov/pubmed/37491910
http://dx.doi.org/10.1098/rsif.2023.0169
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author Mohanty, Vaibhav
Greenbury, Sam F.
Sarkany, Tasmin
Narayanan, Shyam
Dingle, Kamaludin
Ahnert, Sebastian E.
Louis, Ard A.
author_facet Mohanty, Vaibhav
Greenbury, Sam F.
Sarkany, Tasmin
Narayanan, Shyam
Dingle, Kamaludin
Ahnert, Sebastian E.
Louis, Ard A.
author_sort Mohanty, Vaibhav
collection PubMed
description Phenotype robustness, defined as the average mutational robustness of all the genotypes that map to a given phenotype, plays a key role in facilitating neutral exploration of novel phenotypic variation by an evolving population. By applying results from coding theory, we prove that the maximum phenotype robustness occurs when genotypes are organized as bricklayer’s graphs, so-called because they resemble the way in which a bricklayer would fill in a Hamming graph. The value of the maximal robustness is given by a fractal continuous everywhere but differentiable nowhere sums-of-digits function from number theory. Interestingly, genotype–phenotype maps for RNA secondary structure and the hydrophobic-polar (HP) model for protein folding can exhibit phenotype robustness that exactly attains this upper bound. By exploiting properties of the sums-of-digits function, we prove a lower bound on the deviation of the maximum robustness of phenotypes with multiple neutral components from the bricklayer’s graph bound, and show that RNA secondary structure phenotypes obey this bound. Finally, we show how robustness changes when phenotypes are coarse-grained and derive a formula and associated bounds for the transition probabilities between such phenotypes.
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spelling pubmed-103690322023-07-27 Maximum mutational robustness in genotype–phenotype maps follows a self-similar blancmange-like curve Mohanty, Vaibhav Greenbury, Sam F. Sarkany, Tasmin Narayanan, Shyam Dingle, Kamaludin Ahnert, Sebastian E. Louis, Ard A. J R Soc Interface Life Sciences–Physics interface Phenotype robustness, defined as the average mutational robustness of all the genotypes that map to a given phenotype, plays a key role in facilitating neutral exploration of novel phenotypic variation by an evolving population. By applying results from coding theory, we prove that the maximum phenotype robustness occurs when genotypes are organized as bricklayer’s graphs, so-called because they resemble the way in which a bricklayer would fill in a Hamming graph. The value of the maximal robustness is given by a fractal continuous everywhere but differentiable nowhere sums-of-digits function from number theory. Interestingly, genotype–phenotype maps for RNA secondary structure and the hydrophobic-polar (HP) model for protein folding can exhibit phenotype robustness that exactly attains this upper bound. By exploiting properties of the sums-of-digits function, we prove a lower bound on the deviation of the maximum robustness of phenotypes with multiple neutral components from the bricklayer’s graph bound, and show that RNA secondary structure phenotypes obey this bound. Finally, we show how robustness changes when phenotypes are coarse-grained and derive a formula and associated bounds for the transition probabilities between such phenotypes. The Royal Society 2023-07-26 /pmc/articles/PMC10369032/ /pubmed/37491910 http://dx.doi.org/10.1098/rsif.2023.0169 Text en © 2023 The Authors. https://creativecommons.org/licenses/by/4.0/Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) , which permits unrestricted use, provided the original author and source are credited.
spellingShingle Life Sciences–Physics interface
Mohanty, Vaibhav
Greenbury, Sam F.
Sarkany, Tasmin
Narayanan, Shyam
Dingle, Kamaludin
Ahnert, Sebastian E.
Louis, Ard A.
Maximum mutational robustness in genotype–phenotype maps follows a self-similar blancmange-like curve
title Maximum mutational robustness in genotype–phenotype maps follows a self-similar blancmange-like curve
title_full Maximum mutational robustness in genotype–phenotype maps follows a self-similar blancmange-like curve
title_fullStr Maximum mutational robustness in genotype–phenotype maps follows a self-similar blancmange-like curve
title_full_unstemmed Maximum mutational robustness in genotype–phenotype maps follows a self-similar blancmange-like curve
title_short Maximum mutational robustness in genotype–phenotype maps follows a self-similar blancmange-like curve
title_sort maximum mutational robustness in genotype–phenotype maps follows a self-similar blancmange-like curve
topic Life Sciences–Physics interface
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10369032/
https://www.ncbi.nlm.nih.gov/pubmed/37491910
http://dx.doi.org/10.1098/rsif.2023.0169
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