Chance and Necessity in Evolution: Lessons from RNA

The relationship between sequences and secondary structures or shapes in RNA exhibits robust statistical properties summarized by three notions: (1) the notion of a typical shape (that among all sequences of fixed length certain shapes are realized much more frequently than others), (2) the notion of shape space covering (that all typical shapes are realized in a small neighborhood of any random sequence), and (3) the notion of a neutral network (that sequences folding into the same typical shape form networks that percolate through sequence space). Neutral networks loosen the requirements on the mutation rate for selection to remain effective. The original (genotypic) error threshold has to be reformulated in terms of a phenotypic error threshold. With regard to adaptation, neutrality has two seemingly contradictory effects: It acts as a buffer against mutations ensuring that a phenotype is preserved. Yet it is deeply enabling, because it permits evolutionary change to occur by allowing the sequence context to vary silently until a single point mutation can become phenotypically consequential. Neutrality also influences predictability of adaptive trajectories in seemingly contradictory ways. On the one hand it increases the uncertainty of their genotypic trace. At the same time neutrality structures the access from one shape to another, thereby inducing a topology among RNA shapes which permits a distinction between continuous and discontinuous shape transformations. To the extent that adaptive trajectories must undergo such transformations, their phenotypic trace becomes more predictable.Comment: 37 pages, 14 figures; 1998 CNLS conference; high quality figures at http://www.santafe.edu/~walte

Introduction to protein folding for physicists

The prediction of the three-dimensional native structure of proteins from the knowledge of their amino acid sequence, known as the protein folding problem, is one of the most important yet unsolved issues of modern science. Since the conformational behaviour of flexible molecules is nothing more than a complex physical problem, increasingly more physicists are moving into the study of protein systems, bringing with them powerful mathematical and computational tools, as well as the sharp intuition and deep images inherent to the physics discipline. This work attempts to facilitate the first steps of such a transition. In order to achieve this goal, we provide an exhaustive account of the reasons underlying the protein folding problem enormous relevance and summarize the present-day status of the methods aimed to solving it. We also provide an introduction to the particular structure of these biological heteropolymers, and we physically define the problem stating the assumptions behind this (commonly implicit) definition. Finally, we review the 'special flavor' of statistical mechanics that is typically used to study the astronomically large phase spaces of macromolecules. Throughout the whole work, much material that is found scattered in the literature has been put together here to improve comprehension and to serve as a handy reference.Comment: 53 pages, 18 figures, the figures are at a low resolution due to arXiv restrictions, for high-res figures, go to http://www.pabloechenique.co

Frustration in Biomolecules

Biomolecules are the prime information processing elements of living matter. Most of these inanimate systems are polymers that compute their structures and dynamics using as input seemingly random character strings of their sequence, following which they coalesce and perform integrated cellular functions. In large computational systems with a finite interaction-codes, the appearance of conflicting goals is inevitable. Simple conflicting forces can lead to quite complex structures and behaviors, leading to the concept of "frustration" in condensed matter. We present here some basic ideas about frustration in biomolecules and how the frustration concept leads to a better appreciation of many aspects of the architecture of biomolecules, and how structure connects to function. These ideas are simultaneously both seductively simple and perilously subtle to grasp completely. The energy landscape theory of protein folding provides a framework for quantifying frustration in large systems and has been implemented at many levels of description. We first review the notion of frustration from the areas of abstract logic and its uses in simple condensed matter systems. We discuss then how the frustration concept applies specifically to heteropolymers, testing folding landscape theory in computer simulations of protein models and in experimentally accessible systems. Studying the aspects of frustration averaged over many proteins provides ways to infer energy functions useful for reliable structure prediction. We discuss how frustration affects folding, how a large part of the biological functions of proteins are related to subtle local frustration effects and how frustration influences the appearance of metastable states, the nature of binding processes, catalysis and allosteric transitions. We hope to illustrate how Frustration is a fundamental concept in relating function to structural biology.Comment: 97 pages, 30 figure

Detecting and comparing non-coding RNAs in the high-throughput era.

In recent years there has been a growing interest in the field of non-coding RNA. This surge is a direct consequence of the discovery of a huge number of new non-coding genes and of the finding that many of these transcripts are involved in key cellular functions. In this context, accurately detecting and comparing RNA sequences has become important. Aligning nucleotide sequences is a key requisite when searching for homologous genes. Accurate alignments reveal evolutionary relationships, conserved regions and more generally any biologically relevant pattern. Comparing RNA molecules is, however, a challenging task. The nucleotide alphabet is simpler and therefore less informative than that of amino-acids. Moreover for many non-coding RNAs, evolution is likely to be mostly constrained at the structural level and not at the sequence level. This results in very poor sequence conservation impeding comparison of these molecules. These difficulties define a context where new methods are urgently needed in order to exploit experimental results to their full potential. This review focuses on the comparative genomics of non-coding RNAs in the context of new sequencing technologies and especially dealing with two extremely important and timely research aspects: the development of new methods to align RNAs and the analysis of high-throughput data

Computational Methods For Comparative Non-coding Rna Analysis: From Structural Motif Identification To Genome-wide Functional Classification

Recent advances in biological research point out that many ribonucleic acids (RNAs) are transcribed from the genome to perform a variety of cellular functions, rather than merely acting as information carriers for protein synthesis. These RNAs are usually referred to as the non-coding RNAs (ncRNAs). The versatile regulation mechanisms and functionalities of the ncRNAs contribute to the amazing complexity of the biological system. The ncRNAs perform their biological functions by folding into specific structures. In this case, the comparative study of the ncRNA structures is key to the inference of their molecular and cellular functions. We are especially interested in two computational problems for the comparative analysis of ncRNA structures: the alignment of ncRNA structures and their classification. Specifically, we aim to develop algorithms to align and cluster RNA structural motifs (recurrent RNA 3D fragments), as well as RNA secondary structures. Thorough understanding of RNA structural motifs will help us to disassemble the huge RNA 3D structures into functional modules, which can significantly facilitate the analysis of the detailed molecular functions. On the other hand, efficient alignment and clustering of the RNA secondary structures will provide insights for the understanding of the ncRNA expression and interaction in a genomic scale. In this dissertation, we will present a suite of computational algorithms and software packages to solve the RNA structural motif alignment and clustering problem, as well as the RNA iii secondary structure alignment and clustering problem. The summary of the contributions of this dissertation is as follows. (1) We developed RNAMotifScan for comparing and searching RNA structural motifs. Recent studies have shown that RNA structural motifs play an essential role in RNA folding and interaction with other molecules. Computational identification and analysis of RNA structural motifs remain to be challenging tasks. Existing motif identification methods based on 3D structure may not properly compare motifs with high structural variations. We present a novel RNA structural alignment method for RNA structural motif identi- fication, RNAMotifScan, which takes into consideration the isosteric (both canonical and non-canonical) base-pairs and multi-pairings in RNA structural motifs. The utility and accuracy of RNAMotifScan are demonstrated by searching for Kink-turn, C-loop, Sarcin-ricin, Reverse Kink-turn and E-loop motifs against a 23s rRNA (PDBid: 1S72), which is well characterized for the occurrences of these motifs. (2) We improved upon RNAMotifScan by incorporating base-stacking information and devising a new branch-and-bound algorithm called RNAMotifScanX. Model-based search of RNA structural motif has been focused on finding instances with similar 3D geometry and base-pairing patterns. Although these methods have successfully identified many of the true motif instances, each of them has its own limitations and their accuracy and sensitivity can be further improved. We introduce a novel approach to model the RNA structural motifs, which incorporates both base-pairing and base-stacking information. We also develop a new algorithm to search for known motif instances with the consideration of both base-pairing and base-stacking information. Benchmarking of RNAMotifScanX on searching known RNA structural motifs including kink-turn, C-loop, sarcin-ricin, reverse kink-turn, and E-loop iv clearly show improved performances compared to its predecessor RNAMotifScan and other state-of-the-art RNA structural motif search tools. (3) We develop an RNA structural motif clustering and de novo identification pipeline called RNAMSC. RNA structural motifs are the building blocks of the complex RNA architecture. Identification of non-coding RNA structural motifs is a critical step towards understanding of their structures and functionalities. We present a clustering approach for de novo RNA structural motif identification. We applied our approach on a data set containing 5S, 16S and 23S rRNAs and rediscovered many known motifs including GNRA tetraloop, kink-turn, C-loop, sarcin-ricin, reverse kink-turn, hook-turn, E-loop and tandem-sheared motifs, with higher accuracy than the currently state-of-the-art clustering method. More importantly, several novel structural motif families have been revealed by our novel clustering analysis. (4) We propose an improved RNA structural clustering pipeline that takes into account the length-dependent distribution of the structural similarity measure. We also devise a more efficient and robust CLique finding CLustering algorithm (CLCL), to replace the traditional hierarchical clustering approach. Benchmark of the proposed pipeline on Rfam data clearly demonstrates over 10% performance gain, when compared to a traditional hierarchical clustering pipeline. We applied this new computational pipeline to cluster the posttranscriptional control elements in fly 3’-UTR. The ncRNA elements in the 3’ untranslated regions (3’-UTRs) are known to participate in the genes’ post-transcriptional regulation, such as their stability, translation efficiency, and subcellular localization. Inferring co-expression patterns of the genes by clustering their 3’-UTR ncRNA elements will provide invaluable knowledge for further studies of their functionalities and interactions under specific physiological processes. v (5) We develop an ultra-efficient RNA secondary structure alignment algorithm ERA by using a sparse dynamic programming technique. Current advances of the next-generation sequencing technology have revealed a large number of un-annotated RNA transcripts. Comparative study of the RNA structurome is an important approach to assess the biological functionalities of these RNA transcripts. Due to the large sizes and abundance of the RNA transcripts, an efficient and accurate RNA structure-structure alignment algorithm is in urgent need to facilitate the comparative study. By using the sparse dynamic programming technique, we devised a new alignment algorithm that is as efficient as the tree-based alignment algorithms, and as accurate as the general edit-distance alignment algorithms. We implemented the new algorithm into a program called ERA (Efficient RNA Alignment). Benchmark results indicate that ERA can significantly speedup RNA structure-structure alignments compared to other state-of-the-art RNA alignment tools, while maintaining high alignment accuracy. These novel algorithms have led to the discovery of many novel RNA structural motif instances, which have significantly deepened our understanding to the RNA molecular functions. The genome-wide clustering of ncRNA elements in fly 3’-UTR has predicted a cluster of genes that are responsible for the spermatogenesis process. More importantly, these genes are very likely to be co-regulated by their common 3’-UTR elements. We anticipate that these algorithms and the corresponding software tools will significantly promote the comparative ncRNA research in the futur

Energy Landscapes for Proteins: From Single Funnels to Multifunctional Systems

This report advances the hypothesis that multifunctional systems may be associated with multifunnel potential and free energy landscapes, with particular focus on biomolecules. It compares systems that exhibit single, double, and multiple competing structures, and contrasts multifunnel landscapes associated with misfolded amyloidogenic oligomers, which presumably do not arise as an evolutionary target. In this context, intrinsically disordered proteins could be considered intrinsically multifunctional molecules, associated with multifunnel landscapes. Potential energy landscape theory enables biomolecules to be treated in a common framework together with self‐organizing and multifunctional systems based on inorganic materials, atomic and molecular clusters, crystal polymorphs, and soft matter.epsr

Energy Landscapes for Proteins: From Single Funnels to Multifunctional Systems

This report advances the hypothesis that multifunctional systems may be associated with multifunnel potential and free energy landscapes, with particular focus on biomolecules. It compares systems that exhibit single, double, and multiple competing structures, and contrasts multifunnel landscapes associated with misfolded amyloidogenic oligomers, which presumably do not arise as an evolutionary target. In this context, intrinsically disordered proteins could be considered intrinsically multifunctional molecules, associated with multifunnel landscapes. Potential energy landscape theory enables biomolecules to be treated in a common framework together with self‐organizing and multifunctional systems based on inorganic materials, atomic and molecular clusters, crystal polymorphs, and soft matter.epsr