Set Of Base Pairs Research Articles

New approximation algorithms for RNA secondary structures prediction problems by local search

This paper investigates two combinatorial problems from RNA secondary structure prediction with arbitrary pseudoknots. Given a RNA sequence and a set of base pairs, two parallel and adjacent base pairs constitute a stacking. The Maximum Stacking Base Pairs problem (MSBP) aims at finding a maximum number of based pairs, all of which form stackings, while the Maximum Base Pair Stackings problem (MBPS) is to find a maximum number of stackings. Both problems are NP-hard. We present two new approximation algorithms for the two problems by local search methods. For MSBP, the approximation factor is improved from 52 to 73; as for the MBPS, the approximation factor is improved from 83 to 52.

Computational design and experimental verification of pseudoknotted ribozymes.

The design of new RNA sequences that retain the function of a model RNA structure is a challenge in bioinformatics because of the structural complexity of these molecules. RNA can fold into its secondary and tertiary structures by forming stem-loops and pseudoknots. A pseudoknot is a set of base pairs between a region within a stem-loop and nucleotides outside of this stem-loop; this motif is very important for numerous functional structures. It is important for any computational design algorithm to take into account these interactions to give a reliable result for any structures that include pseudoknots. In our study, we experimentally validated synthetic ribozymes designed by Enzymer, which implements algorithms allowing for the design of pseudoknots. Enzymer is a program that uses an inverse folding approach to design pseudoknotted RNAs; we used it in this study to design two types of ribozymes. The ribozymes tested were the hammerhead and the glmS, which have a self-cleaving activity that allows them to liberate the new RNA genome copy during rolling-circle replication or to control the expression of the downstream genes, respectively. We demonstrated the efficiency of Enzymer by showing that the pseudoknotted hammerhead and glmS ribozymes sequences it designed were extensively modified compared to wild-type sequences and were still active.

Natural versus Artificial Creation of Base Pairs in DNA: Origin of Nucleobases from the Perspectives of Unnatural Base Pair Studies

Since life began on Earth, the four types of bases (A, G, C, and T(U)) that form two sets of base pairs have remained unchanged as the components of nucleic acids that replicate and transfer genetic information. Throughout evolution, except for the U to T modification, the four base structures have not changed. This constancy within the genetic code raises the question of how these complicated nucleotides were generated from the molecules in a primordial soup on the early Earth. At some prebiotic stage, the complementarity of base pairs might have accelerated the generation and accumulation of nucleotides or oligonucleotides. We have no clues whether one pair of nucleobases initially appeared on the early Earth during this process or a set of two base pairs appeared simultaneously. Recently, researchers have developed new artificial pairs of nucleobases (unnatural base pairs) that function alongside the natural base pairs. Some unnatural base pairs in duplex DNA can be efficiently and faithfully amplified in a polymerase chain reaction (PCR) using thermostable DNA polymerases. The addition of unnatural base pair systems could expand the genetic alphabet of DNA, thus providing a new mechanism for the generation novel biopolymers by the site-specific incorporation of functional components into nucleic acids and proteins. Furthermore, the process of unnatural base pair development might provide clues to the origin of the natural base pairs in a primordial soup on the early Earth. In this Account, we describe the development of three representative types of unnatural base pairs that function as a third pair of nucleobases in PCR and reconsider the origin of the natural nucleic acids. As researchers developing unnatural base pairs, they use repeated "proof of concept" experiments. As researchers design new base pairs, they improve the structures that function in PCR and eliminate those that do not. We expect that this process is similar to the one functioning in the chemical evolution and selection of the natural nucleobases. Interestingly, the initial structures designed by each research group were quite similar to those of the latest successful unnatural base pairs. In this regard, it is tempting to form a hypothesis that the base pairs on the primordial Earth, in which the natural purine bases, A and G, and pyrimidine bases, C and T(U), originated from structurally similar compounds, such as hypoxanthine for a purine base predecessor. Subsequently, the initial base pair evolved to the present two sets of base pairs via a keto-enol tautomerization of the initial compounds.

Revisiting the Effects of Sequence and Structure on the Hydrogen Bonding and π-Stacking Interactions in Nucleic Acids

Calculated electron densities from PBE0/6-31+G(d,p) were analyzed with respect to the hydrogen bonding within a nucleic acid base pair and the π-stacking between sets of base pairs. From published X-ray crystallographic data, base pairs were isolated from a total of 11 DNA and RNA duplexes, and their experimental geometry was maintained throughout the analyses. Focusing solely on Watson-Crick base pairs, from the values of the electron density between interacting nuclei (at the bond critical points), we provide quantitative data on individual weak interactions. For hydrogen bonding, in addition to quantifying the scissoring effect in GC base pairs, the origin of the controversy around the relative stability of AT and AU base pairs is identified and resolved. Thus, it is illustrated how the conclusion as to their relative stability rests on the specific choice of oligonucleotides compared. For π-stacking, sequence effects for tandem AT base pairs are captured, quantified, and explained, and the greater sensitivity of GC, over AT, sequences to the rise parameter is established. The results presented here show that, from experimental geometries and their electron densities, previously determined effects of the sequence and structure of a duplex on the stabilizing interactions can be captured, quantified, and traced back to the geometry of the base pairs.

First-Principles Prediction of the Sequence-Dependent Stability of RNA Hairpin Loop

We develop a statistical mechanical model to predict the sequence-dependent folding stability from the sequence for simple RNA hairpin loops. We use a recently developed 3-vector virtual bond-based RNA folding model which enables rigorous computation of RNA chain entropy. Enumeration of all the possible arrangements of base pairs and the corresponding conformational entropies, through exhaustive self-avoiding random walks of the virtual bonds in a diamond lattice, gives the partition function and free energy for a given RNA sequence. The new model developed here has two unique advantages. First, the model is based on the complete conformational ensemble, including loop conformations that contain all the possible intra-loop base pairs and/or terminal mismatches. Therefore, intra-loop base pairs and mismatches are the results predicted from the model instead of known input information for the model. Second, the model gives accurate estimation for the dramatic entropic changes caused by the formation of the intra-loop base pairs and mismatches. Our first principles calculations for the chain entropy for each given set of base pairs, in combination with the empirical energy function provided from Turner rules, provide ab initio predictions for the sequence-dependent loop stability from RNA sequence. Tests against experimental data indicate that the theory can give improved predictions for the sequence-dependent RNA hairpin loop stability than the nearest-neighbor model.

Problems and Techniques

Problems and Techniques

Computing similarity between RNA structures

The primary structure of a ribonucleic acid (RNA) molecule is a sequence of nucleotides (bases) over the four-letter alphabet {A,C,G,U}. The secondary or tertiary structure of an RNA is a set of base-pairs (nucleotide pairs) which forms bonds between A−U and C−G. For secondary structures, these bonds have been traditionally assumed to be one to one and non-crossing. This paper considers a notion of similarity between two RNA molecule structures taking into account the primary, the secondary and the tertiary structures. We show that, for tertiary structures, it is Max SNP-hard for both minimization and maximization versions. We show a stronger result for the maximization version where it cannot be approximated within ratio 2 log δn in polynomial time, unless NP⊆ DTIME[2 poly log n ] . We then present an algorithm that can be used for practical application. Our algorithm will produce an optimal solution for the case where at least one of the RNA involved is of a secondary structure. We also show an approximation algorithm.

A new algorithm for computing similarity between RNA structures

The primary structure of a ribonucleic acid (RNA) molecule is a sequence of nucleotides (bases) over the four-letter alphabet { A , C , G , U }. The secondary or tertiary structure of an RNA is a set of base-pairs (nucleotide pairs) which form bonds between A – U and C – G . For secondary structures, these bonds have been traditionally assumed to be one-to-one and non-crossing. We consider the edit distance between two RNA structures. This is a notion of similarity, introduced in [Proceedings of the Tenth Symposium on Combinatorial Pattern Matching, Lecture Notes in Computer Science, vol. 1645, Springer, Berlin, 1999, p. 281], between two RNA molecule structures taking into account the primary, the secondary and the tertiary structures. In general this problem is NP-hard for tertiary structures. In this paper, we consider this notion under some constraints. We present an algorithm and then show how to use this algorithm for practical applications.