Identifying novel and functional RNA structures remains a significant challenge in RNA motif design and is crucial for developing RNA-based therapeutics. Here we introduce a computational topology-based approach with unsupervised machine-learning algorithms to estimate the database size and content of RNA-like graph topologies. Specifically, we apply graph theory enumeration to generate all 110,667 possible 2D dual graphs for vertex numbers ranging from 2 to 9. Among them, only 0.11% (121 dual graphs) correspond to approximately 200,000 known RNA atomic fragments/substructures (collected in 2021) using the RNA-as-Graphs (RAG) framework. The remaining 99.89% of the dual graphs may be RNA-like or non-RNA-like. To determine which dual graphs in the 99.89% hypothetical set are more likely to be associated with RNA structures, we apply computational topology descriptors using the Persistent Spectral Graphs (PSG) method to characterize each graph using 19 PSG-based features and use clustering algorithms that partition all possible dual graphs into two clusters. The cluster with the higher percentage of known dual graphs for RNA is defined as the "RNA-like" cluster, while the other is considered as "non-RNA-like". The distance between each dual graph and the center of the RNA-like cluster represents the likelihood of it belonging to RNA structures. From validation, our PSG-based RNA-like cluster includes 97.3% of the 121 known RNA dual graphs, suggesting good performance. Furthermore, 46.017% of the hypothetical RNAs are predicted to be RNA-like. Among the top 15 graphs identified as high-likelihood candidates for novel RNA motifs, 4 were confirmed from the RNA dataset collected in 2022. Significantly, we observe that all the top 15 RNA-like dual graphs can be separated into multiple subgraphs, whereas the top 15 non-RNA-like dual graphs tend not to have any subgraphs (subgraphs preserve pseudoknots and junctions). Moreover, a significant topological difference between top RNA-like and non-RNA-like graphs is evident when comparing their topological features (e.g., Betti-0 and Betti-1 numbers). These findings provide valuable insights into the size of the RNA motif universe and RNA design strategies, offering a novel framework for predicting RNA graph topologies and guiding the discovery of novel RNA motifs, perhaps anti-viral therapeutics by subgraph assembly.

SUMMARY: We launch a webserver for RNA structure prediction and design corresponding to tools developed using our RNA-As-Graphs (RAG) approach. RAG uses coarse-grained tree graphs to represent RNA secondary structure, allowing the application of graph theory to analyze and advance RNA structure discovery. Our webserver consists of three modules: (a) RAG Sampler: samples tree graph topologies from an RNA secondary structure to predict corresponding tertiary topologies, (b) RAG Builder: builds three-dimensional atomic models from candidate graphs generated by RAG Sampler, and (c) RAG Designer: designs sequences that fold onto novel RNA motifs (described by tree graph topologies). Results analyses are performed for further assessment/selection. The Results page provides links to download results and indicates possible errors encountered. RAG-Web offers a user-friendly interface to utilize our RAG software suite to predict and design RNA structures and sequences. AVAILABILITY AND IMPLEMENTATION: The webserver is freely available online at: http://www.biomath.nyu.edu/ragtop/. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Incorporating the cognate instead of non-cognate substrates is crucial for DNA polymerase function. Here we analyze molecular dynamics simulations of DNA polymerase μ (pol μ) bound to different non-cognate incoming nucleotides including A:dCTP, A:dGTP, A(syn):dGTP, A:dATP, A(syn):dATP, T:dCTP, and T:dGTP to study the structure-function relationships involved with aberrant base pairs in the conformational pathway; while a pol μ complex with the A:dTTP base pair is available, no solved non-cognate structures are available. We observe distinct differences of the non-cognate systems compared to the cognate system. Specifically, the motions of active-site residue His329 and Asp330 distort the active site, and Trp436, Gln440, Glu443 and Arg444 tend to tighten the nucleotide-binding pocket when non-cognate nucleotides are bound; the latter effect may further lead to an altered electrostatic potential within the active site. That most of these "gate-keeper" residues are located farther apart from the upstream primer in pol μ, compared to other X family members, also suggests an interesting relation to pol μ's ability to incorporate nucleotides when the upstream primer is not paired. By examining the correlated motions within pol μ complexes, we also observe different patterns of correlations between non-cognate systems and the cognate system, especially decreased interactions between the incoming nucleotides and the nucleotide-binding pocket. Altered correlated motions in non-cognate systems agree with our recently proposed hybrid conformational selection/induced-fit models. Taken together, our studies propose the following order for difficulty of non-cognate system insertions by pol μ: T:dGTP<A(syn):dATP<T:dCTP<A:dGTP<A(syn):dGTP<A:dCTP

Riboswitches are RNAs that modulate gene expression by ligand-induced conformational changes. However, the way in which sequence dictates alternative folding pathways of gene regulation remains unclear. In this study, we compute energy landscapes, which describe the accessible secondary structures for a range of sequence lengths, to analyze the transcriptional process as a given sequence elongates to full length. In line with experimental evidence, we find that most riboswitch landscapes can be characterized by three broad classes as a function of sequence length in terms of the distribution and barrier type of the conformational clusters: low-barrier landscape with an ensemble of different conformations in equilibrium before encountering a substrate; barrier-free landscape in which a direct, dominant "downhill" pathway to the minimum free energy structure is apparent; and a barrier-dominated landscape with two isolated conformational states, each associated with a different biological function. Sharing concepts with the "new view" of protein folding energy landscapes, we term the three sequence ranges above as the sensing, downhill folding, and functional windows, respectively. We find that these energy landscape patterns are conserved in various riboswitch classes, though the order of the windows may vary. In fact, the order of the three windows suggests either kinetic or thermodynamic control of ligand binding. These findings help understand riboswitch structure/function relationships and open new avenues to riboswitch design.

BACKGROUND: In 2004, we presented a web resource for stimulating the search for novel RNAs, RNA-As-Graphs (RAG), which classified, catalogued, and predicted RNA secondary structure motifs using clustering and build-up approaches. With the increased availability of secondary structures in recent years, we update the RAG resource and provide various improvements for analyzing RNA structures. DESCRIPTION: Our RAG update includes a new supervised clustering algorithm that can suggest RNA motifs that may be "RNA-like". We use this utility to describe RNA motifs as three classes: existing, RNA-like, and non-RNA-like. This produces 126 tree and 16,658 dual graphs as candidate RNA-like topologies using the supervised clustering algorithm with existing RNAs serving as the training data. A comparison of this clustering approach to an earlier method shows considerable improvements. Additional RAG features include greatly expanded search capabilities, an interface to better utilize the benefits of relational database, and improvements to several of the utilities such as directed/labeled graphs and a subgraph search program. CONCLUSIONS: The RAG updates presented here augment the database's intended function - stimulating the search for novel RNA functionality - by classifying available motifs, suggesting new motifs for design, and allowing for more specific searches for specific topologies. The updated RAG web resource offers users a graph-based tool for exploring available RNA motifs and suggesting new RNAs for design.

SUMMARY: Our RNA-As-Graph-Pools (RagPools) web server offers a theoretical companion tool for RNA in vitro selection and related problems. Specifically, it suggests how to construct RNA sequence/structure pools with user-specified properties and assists in analyzing resulting distributions. This utility follows our recently developed approach for engineering sequence pools that links RNA sequence space regions with corresponding structural distributions via a 'mixing matrix' approach combined with a graph theory analysis of RNA secondary-structure space; the mixing matrix specifies nucleotide transition rates, and graph theory links sequences to simple graphical objects representing RNA motifs. The companion RagPools web server ('Designer' component) provides optimized starting sequences, mixing matrices and associated weights in response to a user-specified target pool structure distribution. In addition, RagPools ('Analyzer' component) analyzes the motif distribution of pools generated from user-specified starting sequences and mixing matrices. Thus, RagPools serves as a guide to researchers who aim to synthesize RNA pools with desired properties and/or experiment in silico with various designs by our approach. AVAILABILITY: The web server is accessible on the web at http://rubin2.biomath.nyu.edu

Article Share on Searching for 2D RNA geometries in bacterial genomes Authors: Uri Laserson New York University, New York, NY New York University, New York, NYView Profile , Hin Hark Gan New York University, New York, NY New York University, New York, NYView Profile , Tamar Schlick New York University, New York, NY New York University, New York, NYView Profile Authors Info & Claims SCG '04: Proceedings of the twentieth annual symposium on Computational geometryJune 2004 Pages 373–377https://doi.org/10.1145/997817.997819Published:08 June 2004Publication History 5citation310DownloadsMetricsTotal Citations5Total Downloads310Last 12 Months1Last 6 weeks1 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteGet Access

MOTIVATION: Understanding RNA's structural diversity is vital for identifying novel RNA structures and pursuing RNA genomics initiatives. By classifying RNA secondary motifs based on correlations between conserved RNA secondary structures and functional properties, we offer an avenue for predicting novel motifs. Although several RNA databases exist, no comprehensive schemes are available for cataloguing the range and diversity of RNA's structural repertoire. RESULTS: Our RNA-As-Graphs (RAG) database describes and ranks all mathematically possible (including existing and candidate) RNA secondary motifs on the basis of graphical enumeration techniques. We represent RNA secondary structures as two-dimensional graphs (networks), specifying the connectivity between RNA secondary structural elements, such as loops, bulges, stems and junctions. We archive RNA tree motifs as 'tree graphs' and other RNAs, including pseudoknots, as general 'dual graphs'. All RNA motifs are catalogued by graph vertex number (a measure of sequence length) and ranked by topological complexity. The RAG inventory immediately suggests candidates for novel RNA motifs, either naturally occurring or synthetic, and thereby might stimulate the prediction and design of novel RNA motifs. AVAILABILITY: The database is accessible on the web at http://monod.biomath.nyu.edu/rna

BACKGROUND: The proliferation of structural and functional studies of RNA has revealed an increasing range of RNA's structural repertoire. Toward the objective of systematic cataloguing of RNA's structural repertoire, we have recently described the basis of a graphical approach for organizing RNA secondary structures, including existing and hypothetical motifs. DESCRIPTION: We now present an RNA motif database based on graph theory, termed RAG for RNA-As-Graphs, to catalogue and rank all theoretically possible, including existing, candidate and hypothetical, RNA secondary motifs. The candidate motifs are predicted using a clustering algorithm that classifies RNA graphs into RNA-like and non-RNA groups. All RNA motifs are filed according to their graph vertex number (RNA length) and ranked by topological complexity. CONCLUSIONS: RAG's quantitative cataloguing allows facile retrieval of all classes of RNA secondary motifs, assists identification of structural and functional properties of user-supplied RNA sequences, and helps stimulate the search for novel RNAs based on predicted candidate motifs.

A truncated Newton minimization package, TNPACK, was described in ACM Transactions on Mathematical Software 14 , 1 (Mar. 1992), pp.46–111. Modifications to enhance performance, especially for large-scale minimization of molecular potential functions, are described here. They involve three program segments of TNPACK: negative curvature test, modified Cholesky factorization, and line-search stopping rule.

We report the development of second-derivative FORTRAN routines to supplement Algorithm 566 developed by J. More´ et al. ( ACM Trans. Math. Softw. 7, 14-41, 136–140, 1981). Algorithm 566 provides function and gradient subroutines of 18 test functions for multivariate minimization. Our supplementary Hessian segments enable users to test optimization software that requires second derivative information. Eigenvalue analysis throughout the minimization is now possible, with the goal of better understanding progress by different minimization algorithms and the relation of progress to eigenvalue distribution and condition number.

We present a FORTRAN package of subproWams for minimizmg multivariate functions without

article Free Access Share on TNPACK—a truncated Newton minimization package for large-scale problems: II. Implementation examples Authors: Tamar Schlick New York Univ., New York, NY New York Univ., New York, NYView Profile , Aaron Fogelson Univ. of Utah, Salt Lake City Univ. of Utah, Salt Lake CityView Profile Authors Info & Claims ACM Transactions on Mathematical SoftwareVolume 18Issue 1pp 71–111https://doi.org/10.1145/128745.150975Published:01 March 1992Publication History 39citation656DownloadsMetricsTotal Citations39Total Downloads656Last 12 Months27Last 6 weeks2 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF

We present a FORTRAN package of subprograms for minimizing multivariate functions without constraints by a truncated Newton algorithm. The algorithm is especially suited for problems involving a large number of variables. Truncated Newton methods allow approximate, rather than exact, solutions to the Newton equations. Truncation is accomplished in the present version by using the preconditioned Conjugate Gradient algorithm (PCG) to solve approximately the Newton equations. The preconditioner M is factored in PCG using a sparse modified Cholesky factorization based on the Yale Sparse Matrix Package. In this paper we briefly describe the method and provide details for program usage.