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

Martin, Nora S; Ahnert, Sebastian E.

doi:10.1098/rsif.2022.0072

Cited by 5 publications

(11 citation statements)

References 64 publications

(261 reference statements)

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“…3, or not, as shown in section S1 of the SI. This result agrees with existing computational data for the RNAshapes model (SI of ref [6]) and is consistent with our previous work showing correlations between various phenotypic frequency definitions in RNA [22]. It is also consistent with theoretical arguments [23] for a Boltzmann-like trend in phenotypic frequencies, where energetically unfavourable features are associated with an exponential decrease in phenotypic frequencies.…”

Section: Resultssupporting

confidence: 93%

“…Finally, the fact that the shared number of compatible sequences only gives an upper bound for ϕ qp values is consistent with our previous result for neutral set sizes, where the number of base pairs and hence compatible sequences was found to be only weakly predictive of neutral set size [13]. We found that thermodynamic considerations are also necessary since the fraction of compatible sequences that actually adopt the structure as a mfe structure differs considerably from structure to structure [13].…”

Section: Supplementary Informationsupporting

confidence: 90%

“…Sampling approaches used for the RNA data in Fig. 2 : ϕ pq and p pq for a given initial structure p are approximated from two separate sequence samples, which are both generated with our adaptation [22] of Weiß and Ahnert’s site-scanning method [35] (parameters: 100 sitescanning processing with 10 5 steps and subsequent subsampling of one in 50 sequences). Our adaptation includes base pair swaps and is therefore more suitable for sampling from neutral sets, not just their connected components.…”

Section: Methodsmentioning

confidence: 99%

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

Martin

Ahnert

2023

Preprint

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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.

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Section: Resultssupporting

confidence: 93%

Section: Supplementary Informationsupporting

confidence: 90%

Section: Methodsmentioning

confidence: 99%

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

Martin

Ahnert

2023

Preprint

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“…This GP map feature was also shown to create a negative correlation between plasticity and robustness [15]. The work from Meyers and Fontana as well as further more recent work [16][17][18][19][20][21] that includes plasticity, has improved our understanding of the plastic GP map but has not fully addressed how concepts such as robustness, evolvability and neutral spaces can be quantified for the non-deterministic case in a way that is consistent with averages over their deterministic counterparts. Thermal fluctuations are ubiquitous in molecular environments, which means that many-to-many GP maps that include plasticity are more biologically realistic in the context of molecular evolution.…”

Section: Introductionmentioning

confidence: 99%

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

García-Galindo

Ahnert

Martin³

2023

Preprint

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Selection and variation are both key aspects in the evolutionary process. Previous research on the mapping between molecular sequence (genotype) and molecular fold (phenotype) has shown the presence of several structural properties in different biological contexts, implying that these might be universal in evolutionary spaces. The deterministic genotype-phenotype (GP) map that links short RNA sequences to minimum free energy secondary structures has been studied extensively because of its computational tractability and biologically realistic nature. However, this mapping ignores the phenotypic plasticity of RNA. We define a GP map that incorporates non-deterministic phenotypes, and take RNA as a case study; we use the Boltzmann probability distribution of folded structures and examine the structural properties of non-deterministic (ND) GP maps for RNA sequences of length 12 and coarse-grained RNA structures of length 30 (RNAshapes30). A framework is presented to study robustness, evolvability and neutral spaces in the non-deterministic map. This framework is validated by demonstrating close correspondence between the non-deterministic quantities and sample averages of their deterministic counterparts. When using the non-deterministic framework we observe the same structural properties as in the deterministic GP map, such as bias, negative correlation between genotypic robustness and evolvability, and positive correlation between phenotypic robustness and evolvability.

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“…7 is based on sampling, as explained in the following and tested in the SM: first a structure sample of 10 4 distinct structures was selected as in ref. [20], by randomly drawing from a list of all valid secondary structures of L = 30. To exclude non-foldable structures, a structure was only included in the sample if a sequence folding into the structure was found after ten iterations of ViennaRNA's inverse folding function.…”

mentioning

confidence: 99%

Thermodynamics and neutral sets in the RNA sequence-structure map

Martin¹,

Ahnert²

2022

EPL

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The sequence-structure map of biological macromolecules, also referred to as a genotype-phenotype (GP) map, shapes evolutionary processes by determining how mutations affect molecular structures. RNA secondary structure constitutes a central model in the field, both because of the availability of efficient folding algorithms and the biological importance of RNA structures. Despite the immense knowledge about the characteristics of the RNA GP map, there is not enough understanding of how these characteristics emerge from the underlying energetics of RNA folding. In this paper, we fill this gap with a computational study of the connection between the energy gap between the lowest-energy structures, here referred to as the stability, and the characteristics of the GP map. We focus on neutral sets, i.e., sequences that share a structure, and on connected neutral components within neutral sets. We find first that both mean stability and the stability change through point mutations are linked to the size of neutral sets and neutral components and secondly that the typical stability change through mutations depends on structural characteristics. These results contribute to a deeper understanding of the RNA GP map and are relevant for evolutionary processes since stability may be under selection.

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

Cited by 5 publications

References 64 publications

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

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

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

Thermodynamics and neutral sets in the RNA sequence-structure map

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