A Kinetic Approach to the Prediction of RNA Secondary Structures

Abstract

A new approach to the prediction of secondary RNA structures based on the analysis of the kinetics of molecular self-organisation is proposed herein. The Markov process is used to describe structural reconstructions during secondary structure formation. This process is modelled by a Monte-Carlo method. Examples of the calculation by this method of the secondary structures kinetic ensemble are given. Distribution of time-dependent probabilities within the ensembles is obtained.

An effective method for search for the equilibrium ensemble is also suggested. This method is based on the construction of a tree of all possible secondary structures of RNA. By ascribing a probability for each structure (according to its free energy) the Boltzmann equilibrium ensemble can be obtained.     

A 3D Graphical Representation of RNA Secondary Structures

Abstract

In this paper, we proposed a 3-D graphical representation of RNA secondary structures. Based on this representation, we outline an approach by constructing a 3-component vector whose components are the normalized leading eigenvalues of the L/L matrices associated with RNA secondary structure. The examination of similarities/dissimilarities among the secondary structure at the 3′-terminus of different viruses illustrates the utility of the approach.     

On A Six-Dimensional Representation of RNA Secondary Structures

Abstract

In this paper, we proposed a 6-D representation of RNA secondary structures. The use of the 6-D representation is illustrated by constructing structure invariants. Comparisons with the similarity/dissimilarity results based on 6-D representation for a set of RNA secondary structures, are considered to illustrate the use of our structure invariants based on the entries in derived sequence matrices restricted to a selected width of a band along the main diagonal.     

Physical Studies on a Nucleoprotein from the Ribosome of E. coli

Abstract

Bacterial 5S RNA and its cognate proteins constitute an attractive system to study nucleoprotein interactions. The molecular weights of the components involved are modest and they can be prepared in the quantities necessary to permit the application of material-intensive techniques like NMR and X-ray crystallography.

5S RNA is being examined by proton NMR at 500 MHz with special attention paid to the downfield NH proton region. A substantial number of assignments can be suggested in this region based on nuclear Overhauser results. The binding of protein L25 (E. coli) to the RNA gives rise to a highly characteristic set of perturbations in the spectrum of the RNA. The data suggest a localized and assignable alteration in RNA structure upon formation of the complex.

In addition we have grown large crystals of RNAs related to 5S RNA and their complexes with a cognate protein. The properties of these crystals and the progress made in analyzing their structure are discussed.     

Algorithm independent properties of RNA secondary structure predictions

Algorithms predicting RNA secondary structures based on different folding criteria – minimum free energies (mfe), kinetic folding (kin), maximum matching (mm) – and different parameter sets are studied systematically. Two base pairing alphabets were used: the binary GC and the natural four-letter AUGC alphabet. Computed structures and free energies depend strongly on both the algorithm and the parameter set. Statistical properties, such as mean number of base pairs, mean numbers of stacks, mean loop sizes, etc., are much less sensitive to the choice of parameter set and even of algorithm. Some features of RNA secondary structures, such as structure correlation functions, shape space covering and neutral networks, seem to depend only on the base pairing logic (GC or AUGC alphabet). Received: 16 May 1996 / Accepted: 10 July 1996     

Fuzzy Kernel Clustering of RNA Secondary Structure Ensemble Using a Novel Similarity Metric

Abstract

Measuring the (dis)similarity between RNA secondary structures is critical for the study of RNA secondary structures and has implications to RNA functional characterization. Although a number of methods have been developed for comparing RNA structural similarities, their applications have been limited by the complexity of the required computation. In this paper, we present a novel method for comparing the similarity of RNA secondary structures generated from the same RNA sequence, i.e., a secondary structure ensemble, using a matrix representation of the RNA structures. Relevant features of the RNA secondary structures can be easily extracted through singular value decomposition (SVD) of the representing matrices. We have mapped the feature vectors of the singular values to a kernel space, where (dis)similarities among the mapped feature vectors become more evident, making clustering of RNA secondary structures easier to handle. The pair-wise comparison of RNA structures is achieved through computing the distance between the singular value vectors in the kernel space. We have applied a fuzzy kernel clustering method, using this similarity metric, to cluster the RNA secondary structure ensembles. Our application results suggest that our fuzzy kernel clustering method is highly promising for classifications of RNA structure ensembles, because of its low computational complexity and high clustering accuracy.     

TSEE: an elastic embedding method to visualize the dynamic gene expression patterns of time series single-cell RNA sequencing data

Background

Time series single-cell RNA sequencing (scRNA-seq) data are emerging. However, the analysis of time series scRNA-seq data could be compromised by 1) distortion created by assorted sources of data collection and generation across time samples and 2) inheritance of cell-to-cell variations by stochastic dynamic patterns of gene expression. This calls for the development of an algorithm able to visualize time series scRNA-seq data in order to reveal latent structures and uncover dynamic transition processes.

Results

In this study, we propose an algorithm, termed time series elastic embedding (TSEE), by incorporating experimental temporal information into the elastic embedding (EE) method, in order to visualize time series scRNA-seq data. TSEE extends the EE algorithm by penalizing the proximal placement of latent points that correspond to data points otherwise separated by experimental time intervals. TSEE is herein used to visualize time series scRNA-seq datasets of embryonic developmental processed in human and zebrafish. We demonstrate that TSEE outperforms existing methods (e.g. PCA, tSNE and EE) in preserving local and global structures as well as enhancing the temporal resolution of samples. Meanwhile, TSEE reveals the dynamic oscillation patterns of gene expression waves during zebrafish embryogenesis.

Conclusions

TSEE can efficiently visualize time series scRNA-seq data by diluting the distortions of assorted sources of data variation across time stages and achieve the temporal resolution enhancement by preserving temporal order and structure. TSEE uncovers the subtle dynamic structures of gene expression patterns, facilitating further downstream dynamic modeling and analysis of gene expression processes. The computational framework of TSEE is generalizable by allowing the incorporation of other sources of information.

     

Secondary Structures of Tetrahymena Thermophila rRNA IVS Sequence Involved in Its Self-Splicing Reactions: A New Computer Analysis

Abstract

The secondary structures of Tetrahymena thermophila rRNA IVS sequence involved in the self-splicing reactions, are theoretically investigated with a refined computer method previously proposed, able to select a set of the deepest free energy RNA secondary structures under constraints of model hypotheses and experimental evidences. The secondary structures obtained are characterized by the close proximity of self-reactions sites and account for double mutations experiments, and differential digestion data.     

Synthesis and Characterization of Artificial Ribonucleases

Abstract

RNA cleaving molecules were synthesized by conjugating components of ribonucleases A and T1 catalytic centers (imidazole, aliphatic amino and/or carboxy residues) to intercalating and cationic structures. The artificial ribonucleases were shown cleave RNA at Py-Pu sites in single-stranded regions.     

Relationship Between Chromatin High-order Folding and Nucleosomal Linker Twist in Nuclei of Human HeLa S3 Cells

Abstract

We have used the intercalative agent ethidium bromide to examine the association between chromatin high-order folding and the twist of internucleosomal DNA regions. The analysis was carried out on intact nuclei isolated from human HeLa S3 cells. Our data shows that alterations in the nucleosomal linker twist significantly influence the way in which a chain of nucleosomes folds to form different higher-order structures. The assay used allowed us to identify the existence of two chromatin fractions differing in their extent of high-order folding. We have also found that active gene sequences are preferentially associated with the chromatin fraction corresponding to the more extended conformation. A model is proposed to account for the effect of variations in the nucleosome linker twist on the state of chromatin folding.     

Properties and Anti-HIV Activity of Nicked Dumbbell Oligonucleotides

Abstract

We have designed a new type of oligodeoxyribonucleotide. These oligodeoxyribonucleotides form two hairpin loop structures with base pairs (sense and antisense) in the double helical stem at the 3′ and 5′-ends (nicked dumbbell oligonucleotides). The nicked dumbbell oligonucleotides are molecules with free ends that are more resistant to exonuclease attack. Furthermore, the nicked dumbbell oligonucleotide containing phosphorothioate (P=S) bonds in the hairpin loops has increased nuclease resistance, as compared to the unmodified nicked oligonucleotide. The binding of the nicked dumbbell oligonucleotide to RNA is lower than that of a single-stranded DNA. We also describe the anti-HIV activity of nicked dumbbell oligonucleotides.

     

Statistical Description of Nucleic Acid Secondary Structure Folding

Abstract

A simple statistical model describing the folding of nucleic acids is proposed. For long sequences the real configuration of the secondary structure is a quasi equilibrium state that cannot be characterised by minimal free energy. This is because the time required to achieve complete thermal equilibrium considerably exceeds the life-time of the molecule. The formation of the secondary structure is represented as a random walk process in the space of all possible molecular configurations. TTie quasi equilibrium structure is obtained by successive linking and disruptions of helix segments with probabilities determined by the rate constants of corresponding unimolecular reactions. The probabilities of configurations consisting of all possible compatible helices are calculated. Structures of some t - RNAs and ribosomal RNAs are analysed.