Multiplicity of phenotypes and RNA evolution

2022

J. R. Soc. Interface.

The genotype–phenotype (GP) map of RNA secondary structure links each RNA sequence to its corresponding secondary structure. Previous research has shown that the large-scale structural properties of GP maps, such as the size of neutral sets in genotype space, can influence evolutionary outcomes. In order to use neutral set sizes, efficient and accurate computational methods are needed to compute them. Here, we propose a new method, which is based on free energy estimates and is much faster than existing sample-based methods. Moreover, this approach can give insight into the reasons behind neutral set size variations, for example, why structures with fewer stacks tend to have larger neutral set sizes. In addition, we generalize neutral set size calculations from the previously studied many-to-one framework, where each sequence folds into a single energetically preferred structure, to a fuller many-to-many framework, where several low-energy structures are included. We find that structures with high neutral sets in one framework also tend to have large neutral sets in the other framework for a range of parameters and thus the choice of GP map does not fundamentally affect which structures have the largest neutral set sizes.

Section: Discussionmentioning

confidence: 99%

“…as Ñmfe and ÑðG xÞ respectively. The low-energy set size, N(G ≤ x), is important in its own right because low-energy structures can be close in energy to the mfe structure [21], or even within the resolution of the energy model [22]. A given sequence can therefore fold into several structures.…”

Section: Introductionmentioning

confidence: 99%

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

2022

J. R. Soc. Interface.

“…While individual Boltzmann probabilities are higher when the Boltzmann states are abstract shapes instead of detailed full secondary structures, a single shape cannot fully capture the folding space for a given sequence. Some previous work has already included more than one structure per sequence [ 9 , 12 , 23 ], but many of these studies consider evolutionary dynamics for one specific scenario, rather than quantifying sequence–structure map properties such as phenotypic frequencies, robustness and evolvability systematically for many structures. Establishing a general understanding of the sequence–structure map for this more general case will allow us to understand evolutionary processes for a variety of fitness functions, ranging from a riboswitch, where multiple shapes may be stabilized, to a single-fold molecule, where all suboptimal shapes are selected against.…”

Section: Discussionmentioning

confidence: 99%

“…In practice, a sequence-structure map is interesting if the molecular structure is functionally important and its large-scale analysis is feasible if a fast computational prediction method exists. The secondary structure of RNA sequences fulfils these two criteria [6] and has therefore become one of the best-studied sequence-structure maps (recent examples are [7][8][9][10][11][12]). The secondary structure is the pattern of base pairs between nucleotides, usually not including pseudoknots.…”

Section: Introductionmentioning

confidence: 99%

Insertions and deletions in the RNA sequence–structure map

2021

J. R. Soc. Interface.

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.

“…We use the ViennaRNA [9, 16, 38] package (version 2.4.14) with no isolated base pairs for structure predictions. We only consider sequences with unique mfe structures as folding (due to the discrete nature of the energy model, this is not guaranteed for all sequences [39]), but we do include sequences that have a structure without base pairs as their unique minimum-free-energy state. Due to the high number of 4 30 ∝ 10 18 sequences of length L = 30, we rely on sampling approaches.…”

Section: Methodsmentioning

confidence: 99%

The Boltzmann distributions of folded molecular structures predict likely changes through random mutations

2023

Preprint

New folded molecular structures can only evolve after arising through mutations. This aspect is modelled using genotype-phenotype (GP) maps, which connect sequence changes through mutations to changes in molecular structures. Previous work has shown that the likelihood of appearing through mutations can differ by orders of magnitude from structure to structure and that this can affect the outcomes of evolutionary processes. Thus, we focus on the phenotypic mutation probabilities φqp, i.e. the likelihood that a random mutation changes structure p into structure q. For both RNA secondary structures and the HP protein model, we show that a simple biophysical principle can explain and predict how this likelihood depends on the new structure q: φqpis high if sequences that fold into p as the minimum-free-energy structure are likely to have q as an alternative structure with high Boltzmann frequency. This generalises the existing concept of plastogenetic congruence from individual sequences to the entire neutral spaces of structures. Our result helps us understand why some structural changes are more likely than others, can be used as a basis for estimating these likelihoods via sampling and makes a connection to alternative structures with high Boltzmann frequency, which could be relevant in evolutionary processes.