Insertions and deletions in the RNA sequence–structure map

Abstract

Genotype–phenotype maps link genetic changes to their fitness effect and are thus an essential component of evolutionary models. The map between RNA sequences and their secondary structures is a key example and has applications in functional RNA evolution. For this map, the structural effect of substitutions is well understood, but models usually assume a constant sequence length and do not consider insertions or deletions. Here, we expand the sequence–structure map to include single nucleotide insertions and deletions by using the RNAshapes concept. To quantify the structural effect of insertions and deletions, we generalize existing definitions for robustness and non-neutral mutation probabilities. We find striking similarities between substitutions, deletions and insertions: robustness to substitutions is correlated with robustness to insertions and, for most structures, to deletions. In addition, frequent structural changes after substitutions also tend to be common for insertions and deletions. This is consistent with the connection between energetically suboptimal folds and possible structural transitions. The similarities observed hold both for genotypic and phenotypic robustness and mutation probabilities, i.e. for individual sequences and for averages over sequences with the same structure. Our results could have implications for the rate of neutral and non-neutral evolution.

The non-deterministic genotype-phenotype map of RNA secondary structure

“…the temperature T = 37 • C), using the ViennaRNA suboptimal function [7] and the Boltzmann probabilities of these are obtained using the partition function. The energy range for the suboptimals is 15k B T as in [40] to be consistent with the RNAshapes data. The final ND GP map is constructed by mapping each genotype sequence to its ensemble of structures in the energy range (including unfolded structure), as well as their respective normalized probabilities.…”

Fast free-energy-based neutral set size estimates for the RNA genotype–phenotype map

“…A valid secondary structure has a matching closing bracket for each opening bracket, hairpin loops have a minimum length of three bases and there are no pseudo-knots [ 1 ]. Applying these requirements allows us to generate all >1.3 × 10 7 valid structures of length L = 35, following our previous work [ 50 ]: essentially, we start with a list of starting symbols (either a dot or an opening bracket) and extend these recursively. At each step, we append each of the three dot–bracket symbols (dot, opening bracket and closing bracket), unless adding a certain symbol would make it impossible to turn the string into a valid structure of length L = 35 (for example, by opening more brackets than could be closed, closing more brackets than have been opened, creating a hairpin loop below the minimum length, etc.).…”

Random and natural non-coding RNA have similar structural motif patterns but can be distinguished by bulge, loop, and bond counts

“…To begin our analysis, following ref. [30] (and see also [37, 38]), we use the RNAshapes [39, 40] method. According to this method, an RNA dot-bracket SS can be abstracted to one of five levels, of increasing abstraction, by ignoring details such as the length of loops, but including broad shape features.…”

“…It is known that a single strand of RNA can fold into more than one possible structure, and some strands even form different structures in vivo and in vitro [73]. Further, even if a given sequence has a minimum free energy SS which dominates over other suboptimal SS, nonetheless the sequence will assume different SS in accordance with a Boltzmann distribution [38, 74]. As is common practice in biology and bioinformatics — as well as the vast majority of earlier RNA SS studies — here we have simplified the GP map by assuming that the minimum free energy SS predicted by the computational folding package is ‘the’ single phenotype.…”