RNAdualPF: software to compute the dual partition function with sample applications in molecular evolution theory

The energy-spectrum of bicompatible sequences

Background

Genotype-phenotype maps provide a meaningful filtration of sequence space and RNA secondary structures are particular such phenotypes. Compatible sequences, which satisfy the base-pairing constraints of a given RNA structure, play an important role in the context of neutral evolution. Sequences that are simultaneously compatible with two given structures (bicompatible sequences), are beacons in phenotypic transitions, induced by erroneously replicating populations of RNA sequences. RNA riboswitches, which are capable of expressing two distinct secondary structures without changing the underlying sequence, are one example of bicompatible sequences in living organisms.

Results

We present a full loop energy model Boltzmann sampler of bicompatible sequences for pairs of structures. The sequence sampler employs a dynamic programming routine whose time complexity is polynomial when assuming the maximum number of exposed vertices, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\kappa $$\end{document}κ, is a constant. The parameter \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\kappa $$\end{document}κ depends on the two structures and can be very large. We introduce a novel topological framework encapsulating the relations between loops that sheds light on the understanding of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\kappa $$\end{document}κ. Based on this framework, we give an algorithm to sample sequences with minimum \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\kappa $$\end{document}κ on a particular topologically classified case as well as giving hints to the solution in the other cases. As a result, we utilize our sequence sampler to study some established riboswitches.

Conclusion

Our analysis of riboswitch sequences shows that a pair of structures needs to satisfy key properties in order to facilitate phenotypic transitions and that pairs of random structures are unlikely to do so. Our analysis observes a distinct signature of riboswitch sequences, suggesting a new criterion for identifying native sequences and sequences subjected to evolutionary pressure. Our free software is available at: https://github.com/FenixHuang667/Bifold.

From genotypes to organisms: State-of-the-art and perspectives of a cornerstone in evolutionary dynamics

Understanding how genotypes map onto phenotypes, fitness, and eventually organisms is arguably the next major missing piece in a fully predictive theory of evolution. We refer to this generally as the problem of the genotype-phenotype map. Though we are still far from achieving a complete picture of these relationships, our current understanding of simpler questions, such as the structure induced in the space of genotypes by sequences mapped to molecular structures, has revealed important facts that deeply affect the dynamical description of evolutionary processes. Empirical evidence supporting the fundamental relevance of features such as phenotypic bias is mounting as well, while the synthesis of conceptual and experimental progress leads to questioning current assumptions on the nature of evolutionary dynamics-cancer progression models or synthetic biology approaches being notable examples. This work delves with a critical and constructive attitude into our current knowledge of how genotypes map onto molecular phenotypes and organismal functions, and discusses theoretical and empirical avenues to broaden and improve this comprehension. As a final goal, this community should aim at deriving an updated picture of evolutionary processes soundly relying on the structural properties of genotype spaces, as revealed by modern techniques of molecular and functional analysis.

Genetic robustness of let-7 miRNA sequence-structure pairs

Genetic robustness, the preservation of evolved phenotypes against genotypic mutations, is one of the central concepts in evolution. In recent years a large body of work has focused on the origins, mechanisms, and consequences of robustness in a wide range of biological systems. In particular, research on ncRNAs studied the ability of sequences to maintain folded structures against single-point mutations. In these studies, the structure is merely a reference. However, recent work revealed evidence that structure itself contributes to the genetic robustness of ncRNAs. We follow this line of thought and consider sequence-structure pairs as the unit of evolution and introduce the spectrum of extended mutational robustness (EMR spectrum) as a measurement of genetic robustness. Our analysis of the miRNA let-7 family captures key features of structure-modulated evolution and facilitates the study of robustness against multiple-point mutations.

A Boltzmann Sampler for 1-Pairs with Double Filtration

Recently, a framework considering RNA sequences and their RNA secondary structures as pairs led to some information-theoretic perspectives on how the semantics encoded in RNA sequences can be inferred. This pairing arises naturally from the energy model of RNA secondary structures. Fixing the sequence in the pairing produces the RNA energy landscape, whose partition function was discovered by McCaskill. Dually, fixing the structure induces the energy landscape of sequences. The latter has been considered originally for designing more efficient inverse folding algorithms and subsequently enhanced by facilitating the sampling of sequences. We present here a partition function of sequence/structure pairs, with endowed Hamming distance and base pair distance filtration. This partition function is an augmentation of the previous mentioned (dual) partition function. We develop an efficient dynamic programming routine to recursively compute the partition function with this double filtration. Our framework is capable of dealing with RNA secondary structures as well as 1-structures, where a 1-structure is an RNA pseudoknot structure consisting of "building blocks" of genus 0 or 1. In particular, 0-structures, consisting of only "building blocks" of genus 0, are exactly RNA secondary structures. The time complexity for calculating the partition function of 1-pairs, that is, sequence/structure pairs where the structures are 1-structures, is O(h³b³n⁶), where h, b, n denote the Hamming distance, base pair distance, and sequence length, respectively. The time complexity for the partition function of 0-pairs is O(h²b²n³).

Degeneracy and genetic assimilation in RNA evolution

BACKGROUND

The neutral theory of Motoo Kimura stipulates that evolution is mostly driven by neutral mutations. However adaptive pressure eventually leads to changes in phenotype that involve non-neutral mutations. The relation between neutrality and adaptation has been studied in the context of RNA before and here we further study transitional mutations in the context of degenerate (plastic) RNA sequences and genetic assimilation. We propose quasineutral mutations, i.e. mutations which preserve an element of the phenotype set, as minimal mutations and study their properties. We also propose a general probabilistic interpretation of genetic assimilation and specialize it to the Boltzmann ensemble of RNA sequences.

RESULTS

We show that degenerate sequences i.e. sequences with more than one structure at the MFE level have the highest evolvability among all sequences and are central to evolutionary innovation. Degenerate sequences also tend to cluster together in the sequence space. The selective pressure in an evolutionary simulation causes the population to move towards regions with more degenerate sequences, i.e. regions at the intersection of different neutral networks, and this causes the number of such sequences to increase well beyond the average percentage of degenerate sequences in the sequence space. We also observe that evolution by quasineutral mutations tends to conserve the number of base pairs in structures and thereby maintains structural integrity even in the presence of pressure to the contrary.

CONCLUSIONS

We conclude that degenerate RNA sequences play a major role in evolutionary adaptation.

SARNAclust: Semi-automatic detection of RNA protein binding motifs from immunoprecipitation data

RNA-protein binding is critical to gene regulation, controlling fundamental processes including splicing, translation, localization and stability, and aberrant RNA-protein interactions are known to play a role in a wide variety of diseases. However, molecular understanding of RNA-protein interactions remains limited; in particular, identification of RNA motifs that bind proteins has long been challenging, especially when such motifs depend on both sequence and structure. Moreover, although RNA binding proteins (RBPs) often contain more than one binding domain, algorithms capable of identifying more than one binding motif simultaneously have not been developed. In this paper we present a novel pipeline to determine binding peaks in crosslinking immunoprecipitation (CLIP) data, to discover multiple possible RNA sequence/structure motifs among them, and to experimentally validate such motifs. At the core is a new semi-automatic algorithm SARNAclust, the first unsupervised method to identify and deconvolve multiple sequence/structure motifs simultaneously. SARNAclust computes similarity between sequence/structure objects using a graph kernel, providing the ability to isolate the impact of specific features through the bulge graph formalism. Application of SARNAclust to synthetic data shows its capability of clustering 5 motifs at once with a V-measure value of over 0.95, while GraphClust achieves only a V-measure of 0.083 and RNAcontext cannot detect any of the motifs. When applied to existing eCLIP sets, SARNAclust finds known motifs for SLBP and HNRNPC and novel motifs for several other RBPs such as AGGF1, AKAP8L and ILF3. We demonstrate an experimental validation protocol, a targeted Bind-n-Seq-like high-throughput sequencing approach that relies on RNA inverse folding for oligo pool design, that can validate the components within the SLBP motif. Finally, we use this protocol to experimentally interrogate the SARNAclust motif predictions for protein ILF3. Our results support a newly identified partially double-stranded UUUUUGAGA motif similar to that known for the splicing factor HNRNPC.

RNA-protein binding is critical to gene regulation, and aberrant RNA-protein interactions play a role in a wide variety of diseases. However, molecular understanding of these interactions remains limited because of the difficulty of ascertaining the motifs that bind each protein. To address this challenge, we have developed a novel algorithm, SARNAclust, to computationally identify combined structure/sequence motifs from immunoprecipitation data. SARNAclust can deconvolve multiple motifs simultaneously and determine the importance of specific features through a graph kernel and bulge graph formalism. We have verified SARNAclust to be effective on synthetic motif data and also tested it on ENCODE eCLIP datasets, identifying known motifs and novel predictions. We have experimentally validated SARNAclust for two proteins, SLBP and ILF3, using RNA Bind-n-Seq measurements. Applying SARNAclust to ENCODE data provides new evidence for previously unknown regulatory interactions, notably splicing co-regulation by ILF3 and the splicing factor hnRNPC.

Adaptive multiscapes: an up-to-date metaphor to visualize molecular adaptation

Background

Wright’s metaphor of the fitness landscape has shaped and conditioned our view of the adaptation of populations for almost a century. Since its inception, and including criticism raised by Wright himself, the concept has been surrounded by controversy. Among others, the debate stems from the intrinsic difficulty to capture important features of the space of genotypes, such as its high dimensionality or the existence of abundant ridges, in a visually appealing two-dimensional picture. Two additional currently widespread observations come to further constrain the applicability of the original metaphor: the very skewed distribution of phenotype sizes (which may actively prevent, due to entropic effects, the achievement of fitness maxima), and functional promiscuity (i.e. the existence of secondary functions which entail partial adaptation to environments never encountered before by the population).

Results

Here we revise some of the shortcomings of the fitness landscape metaphor and propose a new “scape” formed by interconnected layers, each layer containing the phenotypes viable in a given environment. Different phenotypes within a layer are accessible through mutations with selective value, while neutral mutations cause displacements of populations within a phenotype. A different environment is represented as a separated layer, where phenotypes may have new fitness values, other phenotypes may be viable, and the same genotype may yield a different phenotype, representing genotypic promiscuity. This scenario explicitly includes the many-to-many structure of the genotype-to-phenotype map. A number of empirical observations regarding the adaptation of populations in the light of adaptive multiscapes are reviewed.

Conclusions

Several shortcomings of Wright’s visualization of fitness landscapes can be overcome through adaptive multiscapes. Relevant aspects of population adaptation, such as neutral drift, functional promiscuity or environment-dependent fitness, as well as entropic trapping and the concomitant impossibility to reach fitness peaks are visualized at once. Adaptive multiscapes should aid in the qualitative understanding of the multiple pathways involved in evolutionary dynamics.

Reviewers

This article was reviewed by Eugene Koonin and Ricard Solé.