Inverse folding with RNA-As-Graphs produces a large pool of candidate sequences with target topologies

We present an RNA-As-Graphs (RAG) based inverse folding algorithm, RAG-IF, to design novel RNA sequences that fold onto target tree graph topologies. The algorithm can be used to enhance our recently reported computational design pipeline (Jain et al., NAR 2018). The RAG approach represents RNA secondary structures as tree and dual graphs, where RNA loops and helices are coarse-grained as vertices and edges, opening the usage of graph theory methods to study, predict, and design RNA structures. Our recently developed computational pipeline for design utilizes graph partitioning (RAG-3D) and atomic fragment assembly (F-RAG) to design sequences to fold onto RNA-like tree graph topologies; the atomic fragments are taken from existing RNA structures that correspond to tree subgraphs. Because F-RAG may not produce the target folds for all designs, automated mutations by RAG-IF algorithm enhance the candidate pool markedly. The crucial residues for mutation are identified by differences between the predicted and the target topology. A genetic algorithm then mutates the selected residues, and the successful sequences are optimized to retain only the minimal or essential mutations. Here we evaluate RAG-IF for 6 RNA-like topologies and generate a large pool of successful candidate sequences with a variety of minimal mutations. We find that RAG-IF adds robustness and efficiency to our RNA design pipeline, making inverse folding motivated by graph topology rather than secondary structure more productive.     

Identification of novel RNA design candidates by clustering the extended RNA-As-Graphs library

BackgroundWe re-evaluate our RNA-As-Graphs clustering approach, using our expanded graph library and new RNA structures, to identify potential RNA-like topologies for design. Our coarse-grained approach represents RNA secondary structures as tree and dual graphs, with vertices and edges corresponding to RNA helices and loops. The graph theoretical framework facilitates graph enumeration, partitioning, and clustering approaches to study RNA structure and its applications.MethodsClustering graph topologies based on features derived from graph Laplacian matrices and known RNA structures allows us to classify topologies into ‘existing’ or hypothetical, and the latter into, ‘RNA-like’ or ‘non RNA-like’ topologies. Here we update our list of existing tree graph topologies and RAG-3D database of atomic fragments to include newly determined RNA structures. We then use linear and quadratic regression, optionally with dimensionality reduction, to derive graph features and apply several clustering algorithms on our tree-graph library and recently expanded dual-graph library to classify them into the three groups.ResultsThe unsupervised PAM and K-means clustering approaches correctly classify 72–77% of all existing graph topologies and 75–82% of newly added ones as RNA-like. For supervised k-NN clustering, the cross-validation accuracy ranges from 57 to 81%.ConclusionsUsing linear regression with unsupervised clustering, or quadratic regression with supervised clustering, provides better accuracies than supervised/linear clustering. All accuracies are better than random, especially for newly added existing topologies, thus lending credibility to our approach.General significanceOur updated RAG-3D database and motif classification by clustering present new RNA substructures and RNA-like motifs as novel design candidates.     

Solution structure of an arabinonucleic acid (ANA)/RNA duplex in a chimeric hairpin: comparison with 2′-fluoro-ANA/RNA and DNA/RNA hybrids

Hybrids of RNA and arabinonucleic acid (ANA) as well as the 2′-fluoro-ANA analog (2′F-ANA) were recently shown to be substrates of the enzyme RNase H. Although RNase H binds to double-stranded RNA, no cleavage occurs with such duplexes. Therefore, knowledge of the structure of ANA/RNA hybrids may prove helpful in the design of future antisense oligonucleotide analogs. In this study, we have determined the NMR solution structures of ANA/RNA and DNA/RNA hairpin duplexes and compared them to the recently published structure of a 2′F-ANA/RNA hairpin duplex. We demonstrate here that the sugars of RNA nucleotides of the ANA/RNA hairpin stem adopt the C3′-endo (north, A-form) conformation, whereas those of the ANA strand adopt a ‘rigid’ O4′-endo (east) sugar pucker. The DNA strand of the DNA/RNA hairpin stem is flexible, but the average DNA/RNA hairpin structural parameters are close to the ANA/RNA and 2′F-ANA/RNA hairpin parameters. The minor groove width of ANA/RNA, 2′F-ANA/RNA and DNA/RNA helices is 9.0 ± 0.5 Å, a value that is intermediate between that of A- and B-form duplexes. These results rationalize the ability of ANA/RNA and 2′F-ANA/RNA hybrids to elicit RNase H activity.     

A Simulation Study Comparing Epidemic Dynamics on Exponential Random Graph and Edge-Triangle Configuration Type Contact Network Models

We compare two broad types of empirically grounded random network models in terms of their abilities to capture both network features and simulated Susceptible-Infected-Recovered (SIR) epidemic dynamics. The types of network models are exponential random graph models (ERGMs) and extensions of the configuration model. We use three kinds of empirical contact networks, chosen to provide both variety and realistic patterns of human contact: a highly clustered network, a bipartite network and a snowball sampled network of a “hidden population”. In the case of the snowball sampled network we present a novel method for fitting an edge-triangle model. In our results, ERGMs consistently capture clustering as well or better than configuration-type models, but the latter models better capture the node degree distribution. Despite the additional computational requirements to fit ERGMs to empirical networks, the use of ERGMs provides only a slight improvement in the ability of the models to recreate epidemic features of the empirical network in simulated SIR epidemics. Generally, SIR epidemic results from using configuration-type models fall between those from a random network model (i.e., an Erdős-Rényi model) and an ERGM. The addition of subgraphs of size four to edge-triangle type models does improve agreement with the empirical network for smaller densities in clustered networks. Additional subgraphs do not make a noticeable difference in our example, although we would expect the ability to model cliques to be helpful for contact networks exhibiting household structure.     

图论在RNA二级结构中的应用

图论是以图为研究对象的数学分支,是一门研究事物对象在图表示法中的特征与性质的学科。鉴于RNA二级结构在功能基因组研究中的重要地位,已发展了用二维图解表示法描述RNA二级结构。文章介绍了用于RNA二级结构图解表示法的两种图,即树图和对偶图的构造规则。并在树图表示基础上产生Laplacian矩阵和相应本征值谱。以有害突变预测和类RNA模体设计的例子,说明图论在RNA二级结构中的应用,同时对可能存在的一些问题做了讨论。     

Theoretical basis for stabilizing messenger RNA through secondary structure design

RNA hydrolysis presents problems in manufacturing, long-term storage, world-wide delivery and in vivo stability of messenger RNA (mRNA)-based vaccines and therapeutics. A largely unexplored strategy to reduce mRNA hydrolysis is to redesign RNAs to form double-stranded regions, which are protected from in-line cleavage and enzymatic degradation, while coding for the same proteins. The amount of stabilization that this strategy can deliver and the most effective algorithmic approach to achieve stabilization remain poorly understood. Here, we present simple calculations for estimating RNA stability against hydrolysis, and a model that links the average unpaired probability of an mRNA, or AUP, to its overall hydrolysis rate. To characterize the stabilization achievable through structure design, we compare AUP optimization by conventional mRNA design methods to results from more computationally sophisticated algorithms and crowdsourcing through the OpenVaccine challenge on the Eterna platform. We find that rational design on Eterna and the more sophisticated algorithms lead to constructs with low AUP, which we term ‘superfolder’ mRNAs. These designs exhibit a wide diversity of sequence and structure features that may be desirable for translation, biophysical size, and immunogenicity. Furthermore, their folding is robust to temperature, computer modeling method, choice of flanking untranslated regions, and changes in target protein sequence, as illustrated by rapid redesign of superfolder mRNAs for B.1.351, P.1 and B.1.1.7 variants of the prefusion-stabilized SARS-CoV-2 spike protein. Increases in in vitro mRNA half-life by at least two-fold appear immediately achievable.     

Coarse-grained modeling of large RNA molecules with knowledge-based potentials and structural filters

Understanding the function of complex RNA molecules depends critically on understanding their structure. However, creating three-dimensional (3D) structural models of RNA remains a significant challenge. We present a protocol (the nucleic acid simulation tool [NAST]) for RNA modeling that uses an RNA-specific knowledge-based potential in a coarse-grained molecular dynamics engine to generate plausible 3D structures. We demonstrate NAST's capabilities by using only secondary structure and tertiary contact predictions to generate, cluster, and rank structures. Representative structures in the best ranking clusters averaged 8.0 ± 0.3 Å and 16.3 ± 1.0 Å RMSD for the yeast phenylalanine tRNA and the P4-P6 domain of the Tetrahymena thermophila group I intron, respectively. The coarse-grained resolution allows us to model large molecules such as the 158-residue P4-P6 or the 388-residue T. thermophila group I intron. One advantage of NAST is the ability to rank clusters of structurally similar decoys based on their compatibility with experimental data. We successfully used ideal small-angle X-ray scattering data and both ideal and experimental solvent accessibility data to select the best cluster of structures for both tRNA and P4-P6. Finally, we used NAST to build in missing loops in the crystal structures of the Azoarcus and Twort ribozymes, and to incorporate crystallographic data into the Michel–Westhof model of the T. thermophila group I intron, creating an integrated model of the entire molecule. Our software package is freely available at https://simtk.org/home/nast.     

Central and local limit theorems for RNA structures

A k-noncrossing RNA pseudoknot structure is a graph over {1,…,n} without 1-arcs, i.e. arcs of the form (i,i+1) and in which there exists no k-set of mutually intersecting arcs. In particular, RNA secondary structures are 2-noncrossing RNA structures. In this paper we prove a central and a local limit theorem for the distribution of the number of 3-noncrossing RNA structures over n nucleotides with exactly h bonds. Our analysis employs the generating function of k-noncrossing RNA pseudoknot structures and the asymptotics for the coefficients. The results of this paper explain the findings on the number of arcs of RNA secondary structures obtained by molecular folding algorithms and are of relevance for prediction algorithms of k-noncrossing RNA structures.     

Short, synthetic and selectively 13C-labeled RNA sequences for the NMR structure determination of protein–RNA complexes

We report an optimized synthesis of all canonical 2′-O-TOM protected ribonucleoside phosphoramidites and solid supports containing [¹³C₅]-labeled ribose moieties, their sequence-specific introduction into very short RNA sequences and their use for the structure determination of two protein–RNA complexes. These specifically labeled sequences facilitate RNA resonance assignments and are essential to assign a high number of sugar–sugar and intermolecular NOEs, which ultimately improve the precision and accuracy of the resulting structures. This labeling strategy is particularly useful for the study of protein–RNA complexes with single-stranded RNA in solution, which is rapidly an increasingly relevant research area in biology.     

Generic properties of combinatory maps: Neutral networks of RNA secondary structures

Random graph theory is used to model and analyse the relationship between sequences and secondary structures of RNA molecules, which are understood as mappings from sequence space into shape space. These maps are non-invertible since there are always many orders of magnitude more sequences than structures. Sequences folding into identical structures formneutral networks. A neutral network is embedded in the set of sequences that arecompatible with the given structure. Networks are modeled as graphs and constructed by random choice of vertices from the space of compatible sequences. The theory characterizes neutral networks by the mean fraction of neutral neighbors (λ). The networks are connected and percolate sequence space if the fraction of neutral nearest neighbors exceeds a threshold value (λ>λ*). Below threshold (λ<λ*), the networks are partitioned into a largest “giant” component and several smaller components. Structure are classified as “common” or “rare” according to the sizes of their pre-images, i.e. according to the fractions of sequences folding into them. The neutral networks of any pair of two different common structures almost touch each other, and, as expressed by the conjecture ofshape space covering sequences folding into almost all common structures, can be found in a small ball of an arbitrary location in sequence space. The results from random graph theory are compared to data obtained by folding large samples of RNA sequences. Differences are explained in terms of specific features of RNA molecular structures. Deicated to professor Manfred Eigen     

Squaring theory with practice in RNA design

Ribonucleic acid (RNA) design offers unique opportunities for engineering genetic networks and nanostructures that self-assemble within living cells. Recent years have seen the creation of increasingly complex RNA devices, including proof-of-concept applications for in vivo three-dimensional scaffolding, imaging, computing, and control of biological behaviors. Expert intuition and simple design rules-the stability of double helices, the modularity of noncanonical RNA motifs, and geometric closure-have enabled these successful applications. Going beyond heuristics, emerging algorithms may enable automated design of RNAs with nucleotide-level accuracy but, as illustrated on a recent RNA square design, are not yet fully predictive. Looking ahead, technological advances in RNA synthesis and interrogation are poised to radically accelerate the discovery and stringent testing of design methods.     

Pairwise alignment of protein interaction networks.

With an ever-increasing amount of available data on protein-protein interaction (PPI) networks and research revealing that these networks evolve at a modular level, discovery of conserved patterns in these networks becomes an important problem. Although available data on protein-protein interactions is currently limited, recently developed algorithms have been shown to convey novel biological insights through employment of elegant mathematical models. The main challenge in aligning PPI networks is to define a graph theoretical measure of similarity between graph structures that captures underlying biological phenomena accurately. In this respect, modeling of conservation and divergence of interactions, as well as the interpretation of resulting alignments, are important design parameters. In this paper, we develop a framework for comprehensive alignment of PPI networks, which is inspired by duplication/divergence models that focus on understanding the evolution of protein interactions. We propose a mathematical model that extends the concepts of match, mismatch, and gap in sequence alignment to that of match, mismatch, and duplication in network alignment and evaluates similarity between graph structures through a scoring function that accounts for evolutionary events. By relying on evolutionary models, the proposed framework facilitates interpretation of resulting alignments in terms of not only conservation but also divergence of modularity in PPI networks. Furthermore, as in the case of sequence alignment, our model allows flexibility in adjusting parameters to quantify underlying evolutionary relationships. Based on the proposed model, we formulate PPI network alignment as an optimization problem and present fast algorithms to solve this problem. Detailed experimental results from an implementation of the proposed framework show that our algorithm is able to discover conserved interaction patterns very effectively, in terms of both accuracies and computational cost.     

Dynamic signal processing by ribozyme-mediated RNA circuits to control gene expression

Organisms have different circuitries that allow converting signal molecule levels to changes in gene expression. An important challenge in synthetic biology involves the de novo design of RNA modules enabling dynamic signal processing in live cells. This requires a scalable methodology for sensing, transmission, and actuation, which could be assembled into larger signaling networks. Here, we present a biochemical strategy to design RNA-mediated signal transduction cascades able to sense small molecules and small RNAs. We design switchable functional RNA domains by using strand-displacement techniques. We experimentally characterize the molecular mechanism underlying our synthetic RNA signaling cascades, show the ability to regulate gene expression with transduced RNA signals, and describe the signal processing response of our systems to periodic forcing in single live cells. The engineered systems integrate RNA–RNA interaction with available ribozyme and aptamer elements, providing new ways to engineer arbitrary complex gene circuits.     

Dynamic Motions of the HIV-1 Frameshift Site RNA

The HIV-1 frameshift site (FS) plays a critical role in viral replication. During translation, the HIV-1 FS transitions from a 3-helix to a 2-helix junction RNA secondary structure. The 2-helix junction structure contains a GGA bulge, and purine-rich bulges are common motifs in RNA secondary structure. Here, we investigate the dynamics of the HIV-1 FS 2-helix junction RNA. Interhelical motions were studied under different ionic conditions using NMR order tensor analysis of residual dipolar couplings. In 150 mM potassium, the RNA adopts a 43°(±4°) interhelical bend angle (β) and displays large amplitude, anisotropic interhelical motions characterized by a 0.52(±0.04) internal generalized degree of order (GDO_int) and distinct order tensor asymmetries for its two helices (η = 0.26(±0.04) and 0.5(±0.1)). These motions are effectively quenched by addition of 2 mM magnesium (GDO_int = 0.87(±0.06)), which promotes a near-coaxial conformation (β = 15°(±6°)) of the two helices. Base stacking in the bulge was investigated using the fluorescent purine analog 2-aminopurine. These results indicate that magnesium stabilizes extrahelical conformations of the bulge nucleotides, thereby promoting coaxial stacking of helices. These results are highly similar to previous studies of the HIV transactivation response RNA, despite a complete lack of sequence similarity between the two RNAs. Thus, the conformational space of these RNAs is largely determined by the topology of their interhelical junctions.     

REVERSIBLE, THERMOTROPIC ALTERATION OF NUCLEAR MEMBRANE STRUCTURE AND NUCLEOCYTOPLASMIC RNA TRANSPORT IN TETRAHYMENA

We examine the effect of cooling upon the freeze-etch ultrastructure of nuclear membranes, as well as upon nucleocytoplasmic RNA transport in the unicellular eukaryote Tetrahymena pyriformis. Chilling produces smooth, particle-free areas on both faces of the two freeze-fractured macronuclear membranes. Upon return to optimum growth temperature the membrane-associated particles revert to their normal uniform distribution and the smooth areas disappear. Chilling lowers the incorporation of [¹⁴C]uridine into whole cells and their cytoplasmic RNA. Cooling from the optimum growth temperature of 28° to 18°C (or above) decreases [¹⁴C]uridine incorporation into cells more than into their cytoplasmic RNA; chilling to below 18°C but above 10°C causes the reverse. [¹⁴C]Uridine incorporation into whole cells and their cytoplasmic RNA reflects overall RNA synthesis and nucleocytoplasmic RNA transport, respectively. RNA transport decreases strongly between 20° and 16°C, which is also the temperature range where morphologically detectable nuclear membrane transitions occur. This suggests that the nuclear envelope limits the rate of nucleocytoplasmic RNA transport at low temperatures. We hypothesize that a thermotropic lipid phase transition switches nuclear pore complexes from an "open" to a "closed" state with respect to nucleocytoplasmic RNA transport.     

Exploring the repertoire of RNA secondary motifs using graph theory; implications for RNA design

Understanding the structural repertoire of RNA is crucial for RNA genomics research. Yet current methods for finding novel RNAs are limited to small or known RNA families. To expand known RNA structural motifs, we develop a two-dimensional graphical representation approach for describing and estimating the size of RNA’s secondary structural repertoire, including naturally occurring and other possible RNA motifs. We employ tree graphs to describe RNA tree motifs and more general (dual) graphs to describe both RNA tree and pseudoknot motifs. Our estimates of RNA’s structural space are vastly smaller than the nucleotide sequence space, suggesting a new avenue for finding novel RNAs. Specifically our survey shows that known RNA trees and pseudoknots represent only a small subset of all possible motifs, implying that some of the ‘missing’ motifs may represent novel RNAs. To help pinpoint RNA-like motifs, we show that the motifs of existing functional RNAs are clustered in a narrow range of topological characteristics. We also illustrate the applications of our approach to the design of novel RNAs and automated comparison of RNA structures; we report several occurrences of RNA motifs within larger RNAs. Thus, our graph theory approach to RNA structures has implications for RNA genomics, structure analysis and design.     

Visualizing the dynamic behavior of poliovirus plus-strand RNA in living host cells

Dynamic analysis of viral nucleic acids in host cells is important for understanding virus–host interaction. By labeling endogenous RNA with molecular beacon, we have realized the direct visualization of viral nucleic acids in living host cells and have studied the dynamic behavior of poliovirus plus-strand RNA. Poliovirus plus-strand RNA was observed to display different distribution patterns in living Vero cells at different post-infection time points. Real-time imaging suggested that the translocation of poliovirus plus-strand RNA is a characteristic rearrangement process requiring intact microtubule network of host cells. Confocal-FRAP measurements showed that 49.4 ± 3.2% of the poliovirus plus-strand RNA molecules diffused freely (with a D-value of 9.6 ± 1.6 × 10⁻¹⁰ cm²/s) within their distribution region, while the remaining (50.5 ± 2.9%) were almost immobile and moved very slowly only with change of the RNA distribution region. Under the electron microscope, it was found that virus-induced membrane rearrangement is microtubule-associated in poliovirus-infected Vero cells. These results reveal an entrapment and diffusion mechanism for the movement of poliovirus plus-strand RNA in living mammalian cells, and demonstrate that the mechanism is mainly associated with microtubules and virus-induced membrane structures.