DOI: 10.5061/dryad.sj3tx969f
title: Data from: Maximum mutational robustness in genotype-phenotype maps follows a self-similar blancmange-like curve

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 organised 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 (GP) maps for RNA secondary structure and the 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.
description: This data contains the data and code required to generate
 presented in "Maximum Mutational Robustness in Genotype-Phenotype
 Maps Follows a Self-similar Blancmange-like Curve" by Mohanty et al.,
 published in Journal of the Royal Society Interface.
 The exact maximum robustness curve corresponding to the
 robustness of the bricklayer's graphs, as well as the interpolated
 curve, can be generated from the RoBound Calculator, available free of
 charge and open source on GitHub
 (https://github.com/vaibhav-mohanty/RoBound-Calculator).
 All bounds (e.g. Figure 1, 9, 10, and 11 as well as the bounds
 shown in Figure 3 or 7) can be calculated using the RoBound Calculator
 (https://github.com/vaibhav-mohanty/RoBound-Calculator).
 In Figure 3, the RNA and HP model neutral component sizes and
 robustness values are provided in the files hp5x5_components.csv,
 hp24_components.csv, rna12_components.csv, and rna15_components.csv. These
 results obtainedd from Greenbury et al., "Genetic Correlations
 Greatly Increase Mutational Robustness and Can Both Reduce and Enhance
 Evolvability," PLOS Computational Biology, 2016.
 In Figure 4, we show the deviation of RNA12 and RNA15 neutral
 networks from the maximum (bricklayer's) robustness. This data is
 obtained from rna12.csv (alternatively rna12.mat) and rna15.csv
 (alternatively rna15.mat), which were also results obtained from Greenbury
 et al., "Genetic Correlations Greatly Increase Mutational Robustness
 and Can Both Reduce and Enhance Evolvability," PLOS Computational
 Biology, 2016. The code to produce the figure is found in
 nc_err_corr.m In Figure 7, the bounds can be
 calculated using the RoBound Calculator
 (https://github.com/vaibhav-mohanty/RoBound-Calculator). The raw data is
 obtained from using ViennaRNA (https://www.tbi.univie.ac.at/RNA/) to
 calculate the dot-bracket structures. These structures are then fed into
 the RNASHAPES software
 (https://bibiserv.cebitec.uni-bielefeld.de/rnashapes) to generate the
 coarse-grained data. The data files rna12abstract.mat and
 rna15abstract.mat contain the frequency and robustness values for the
 neutral networks at various levels of coarse-graining.
 In Figure 8, the RNA12 transition probabilites between
 phenotypes can be obtained from rna12_theta.csv, which provides the phi_pq
 matrix when each column's sum is normalized to 1. The script
 phi_critical_ranges.m produces Figure 8. Figures 2,
 5, and 6 are schematics and have no associated data.
description: CSV files can be opened easily. MATLAB (or associated python
 packages) can open the .mat files. MATLAB or Octave can be used to load
 the .m scripts.