49,812 research outputs found

    Expected degree for RNA secondary structure networks

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    Consider the network of all secondary structures of a given RNA sequence, where nodes are connected when the corresponding structures have base pair distance one. The expected degree of the network is the average number of neighbors, where average may be computed with respect to the either the uniform or Boltzmann probability. Here we describe the first algorithm, RNAexpNumNbors, that can compute the expected number of neighbors, or expected network degree, of an input sequence. For RNA sequences from the Rfam database, the expected degree is significantly less than the CMFE structure, defined to have minimum free energy over all structures consistent with the Rfam consensus structure. The expected degree of structural RNAs, such as purine riboswitches, paradoxically appears to be smaller than that of random RNA, yet the difference between the degree of the MFE structure and the expected degree is larger than that of random RNA. Expected degree does not seem to correlate with standard structural diversity measures of RNA, such as positional entropy, ensemble defect, etc. The program {\tt RNAexpNumNbors} is written in C, runs in cubic time and quadratic space, and is publicly available at http://bioinformatics.bc.edu/clotelab/RNAexpNumNbors.Comment: 25 pages, 5 figures, 5 table

    Effects of neutral selection on the evolution of molecular species

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    We introduce a new model of evolution on a fitness landscape possessing a tunable degree of neutrality. The model allows us to study the general properties of molecular species undergoing neutral evolution. We find that a number of phenomena seen in RNA sequence-structure maps are present also in our general model. Examples are the occurrence of "common" structures which occupy a fraction of the genotype space which tends to unity as the length of the genotype increases, and the formation of percolating neutral networks which cover the genotype space in such a way that a member of such a network can be found within a small radius of any point in the space. We also describe a number of new phenomena which appear to be general properties of neutrally evolving systems. In particular, we show that the maximum fitness attained during the adaptive walk of a population evolving on such a fitness landscape increases with increasing degree of neutrality, and is directly related to the fitness of the most fit percolating network.Comment: 16 pages including 4 postscript figures, typeset in LaTeX2e using the Elsevier macro package elsart.cl

    Neutral networks of genotypes: Evolution behind the curtain

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    Our understanding of the evolutionary process has gone a long way since the publication, 150 years ago, of "On the origin of species" by Charles R. Darwin. The XXth Century witnessed great efforts to embrace replication, mutation, and selection within the framework of a formal theory, able eventually to predict the dynamics and fate of evolving populations. However, a large body of empirical evidence collected over the last decades strongly suggests that some of the assumptions of those classical models necessitate a deep revision. The viability of organisms is not dependent on a unique and optimal genotype. The discovery of huge sets of genotypes (or neutral networks) yielding the same phenotype --in the last term the same organism--, reveals that, most likely, very different functional solutions can be found, accessed and fixed in a population through a low-cost exploration of the space of genomes. The 'evolution behind the curtain' may be the answer to some of the current puzzles that evolutionary theory faces, like the fast speciation process that is observed in the fossil record after very long stasis periods.Comment: 7 pages, 7 color figures, uses a modification of pnastwo.cls called pnastwo-modified.cls (included

    A tractable genotype-phenotype map for the self-assembly of protein quaternary structure

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    The mapping between biological genotypes and phenotypes is central to the study of biological evolution. Here we introduce a rich, intuitive, and biologically realistic genotype-phenotype (GP) map, that serves as a model of self-assembling biological structures, such as protein complexes, and remains computationally and analytically tractable. Our GP map arises naturally from the self-assembly of polyomino structures on a 2D lattice and exhibits a number of properties: redundancy\textit{redundancy} (genotypes vastly outnumber phenotypes), phenotype bias\textit{phenotype bias} (genotypic redundancy varies greatly between phenotypes), genotype component disconnectivity\textit{genotype component disconnectivity} (phenotypes consist of disconnected mutational networks) and shape space covering\textit{shape space covering} (most phenotypes can be reached in a small number of mutations). We also show that the mutational robustness of phenotypes scales very roughly logarithmically with phenotype redundancy and is positively correlated with phenotypic evolvability. Although our GP map describes the assembly of disconnected objects, it shares many properties with other popular GP maps for connected units, such as models for RNA secondary structure or the HP lattice model for protein tertiary structure. The remarkable fact that these important properties similarly emerge from such different models suggests the possibility that universal features underlie a much wider class of biologically realistic GP maps.Comment: 12 pages, 6 figure

    Encoding folding paths of RNA switches

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    RNA co-transcriptional folding has long been suspected to play an active role in helping proper native folding of ribozymes and structured regulatory motifs in mRNA untranslated regions. Yet, the underlying mechanisms and coding requirements for efficient co-transcriptional folding remain unclear. Traditional approaches have intrinsic limitations to dissect RNA folding paths, as they rely on sequence mutations or circular permutations that typically perturb both RNA folding paths and equilibrium structures. Here, we show that exploiting sequence symmetries instead of mutations can circumvent this problem by essentially decoupling folding paths from equilibrium structures of designed RNA sequences. Using bistable RNA switches with symmetrical helices conserved under sequence reversal, we demonstrate experimentally that native and transiently formed helices can guide efficient co-transcriptional folding into either long-lived structure of these RNA switches. Their folding path is controlled by the order of helix nucleations and subsequent exchanges during transcription, and may also be redirected by transient antisense interactions. Hence, transient intra- and intermolecular base pair interactions can effectively regulate the folding of nascent RNA molecules into different native structures, provided limited coding requirements, as discussed from an information theory perspective. This constitutive coupling between RNA synthesis and RNA folding regulation may have enabled the early emergence of autonomous RNA-based regulation networks.Comment: 9 pages, 6 figure

    Statistical mechanics of RNA folding: importance of alphabet size

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    We construct a minimalist model of RNA secondary-structure formation and use it to study the mapping from sequence to structure. There are strong, qualitative differences between two-letter and four or six-letter alphabets. With only two kinds of bases, there are many alternate folding configurations, yielding thermodynamically stable ground-states only for a small set of structures of high designability, i.e., total number of associated sequences. In contrast, sequences made from four bases, as found in nature, or six bases have far fewer competing folding configurations, resulting in a much greater average stability of the ground state.Comment: 7 figures; uses revtex

    A complex adaptive systems approach to the kinetic folding of RNA

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    The kinetic folding of RNA sequences into secondary structures is modeled as a complex adaptive system, the components of which are possible RNA structural rearrangements (SRs) and their associated bases and base pairs. RNA bases and base pairs engage in local stacking interactions that determine the probabilities (or fitnesses) of possible SRs. Meanwhile, selection operates at the level of SRs; an autonomous stochastic process periodically (i.e., from one time step to another) selects a subset of possible SRs for realization based on the fitnesses of the SRs. Using examples based on selected natural and synthetic RNAs, the model is shown to qualitatively reproduce characteristic (nonlinear) RNA folding dynamics such as the attainment by RNAs of alternative stable states. Possible applications of the model to the analysis of properties of fitness landscapes, and of the RNA sequence to structure mapping are discussed.Comment: 23 pages, 4 figures, 2 tables, to be published in BioSystems (Note: updated 2 references
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