Rapid ab initio prediction of RNA pseudoknots via graph tree decomposition

The prediction of RNA secondary structure including pseudoknots remains a challenge due to the intractable computation of the sequence conformation from nucleotide interactions under free energy models. Optimal algorithms often assume a restricted class for the predicted RNA structures and yet still require a high-degree polynomial time complexity, which is too expensive to use. Heuristic methods may yield time-efficient algorithms but they do not guarantee optimality of the predicted structure. This paper introduces a new and efficient algorithm for the prediction of RNA structure with pseudoknots for which the structure is not restricted. Novel prediction techniques are developed based on graph tree decomposition. In particular, based on a simplified energy model, stem overlapping relationships are defined with a graph, in which a specialized maximum independent set corresponds to the desired optimal structure. Such a graph is tree decomposable; dynamic programming over a tree decomposition of the graph leads to an efficient optimal algorithm. The final structure predictions are then based on re-ranking a list of suboptimal structures under a more comprehensive free energy model. The new algorithm is evaluated on a large number of RNA sequence sets taken from diverse resources. It demonstrates overall sensitivity and specificity that outperforms or is comparable with those of previous optimal and heuristic algorithms yet it requires significantly less time than the compared optimal algorithms. The preliminary version of this paper appeared in the proceedings of the 6th Workshop on Algorithms for Bioinformatics (WABI 2006).     

Stacks in canonical RNA pseudoknot structures

In this paper we study the distribution of stacks/loops in k-non-crossing, τ-canonical RNA pseudoknot structures (〈k,τ〉-structures). Here, an RNA structure is called k-non-crossing if it has no more than k-1 mutually crossing arcs and τ-canonical if each arc is contained in a stack of length at least τ. Based on the ordinary generating function of 〈k,τ〉-structures [G. Ma, C.M. Reidys, Canonical RNA pseudoknot structures, J. Comput. Biol. 15 (10) (2008) 1257] we derive the bivariate generating function , where T_k,τ(n,t) is the number of 〈k,τ〉-structures having exactly t stacks and study its singularities. We show that for a specific parametrization of the variable u, T_k,τ(x,u) exhibits a unique, dominant singularity. The particular shift of this singularity parametrized by u implies a central limit theorem for the distribution of stack-numbers. Our results are of importance for understanding the ‘language’ of minimum-free energy RNA pseudoknot structures, generated by computer folding algorithms.     

Local Connectivity of Neutral Networks

This paper studies local connectivity of neutral networks of RNA secondary and pseudoknot structures. A neutral network denotes the set of RNA sequences that fold into a particular structure. It is called locally connected, if in the limit of long sequences, the distance of any two of its sequences scales with their distance in the n-cube. One main result of this paper is that is the threshold probability for local connectivity for neutral networks, considered as random subgraphs of n-cubes. Furthermore, we analyze local connectivity for finite sequence length and different alphabets. We show that it is closely related to the existence of specific paths within the neutral network. We put our theoretical results into context with folding algorithms into minimum-free energy RNA secondary and pseudoknot structures. Finally, we relate our structural findings with dynamics by discussing the role of local connectivity in the context of neutral evolution.     

Asymptotic Enumeration of RNA Structures with Pseudoknots

In this paper, we present the asymptotic enumeration of RNA structures with pseudoknots. We develop a general framework for the computation of exponential growth rate and the asymptotic expansion for the numbers of k-noncrossing RNA structures. Our results are based on the generating function for the number of k-noncrossing RNA pseudoknot structures, , derived in Bull. Math. Biol. (2008), where k−1 denotes the maximal size of sets of mutually intersecting bonds. We prove a functional equation for the generating function and obtain for k=2 and k=3, the analytic continuation and singular expansions, respectively. It is implicit in our results that for arbitrary k singular expansions exist and via transfer theorems of analytic combinatorics, we obtain asymptotic expression for the coefficients. We explicitly derive the asymptotic expressions for 2- and 3-noncrossing RNA structures. Our main result is the derivation of the formula .     

Toward multiplexing the application of solvent accessibility probes for the investigation of RNA three-dimensional structures by electrospray ionization-Fourier transform mass spectrometry

Multiple solvent accessibility probes can be applied simultaneously to investigate the three-dimensional structure of complex RNA substrates when electrospray ionization-Fourier transform mass spectrometry (ESI-FTMS) is employed in place of polyacrylamide gel electrophoresis (PAGE). We show that classic chemical probes, such as dimethylsulfate, kethoxal, and 1-cyclohexyl-3-(2-morpholinoethyl)carbodiimide metho-p-toluenesulfonate, can be combined in probing mixtures designed to assess the full spectrum of base pairing and steric protection for the most abundant ribonucleotides included in RNA. After probe-independent hydrolysis of the alkylated substrate, the mixture of oligonucleotide products is mass mapped by ESI-FTMS analysis, which enables the unambiguous identification of probed bases from the unique mass signatures provided by the different chemical modifiers. In this bottom-up approach, any theoretical limit to the size of the possible target RNA will be determined by the effectiveness of the hydrolysis procedure rather than by the performance of the detection technique. Control experiments performed on the stem-loop 4 of human immunodeficiency virus type 1 have shown no adverse interactions between the reagents combined in the probing cocktails. No significant discrepancies between the alkylation patterns offered by the cocktails and the individual reagents could be detected, indicating that multiplexing the probe application does not necessarily lead to structural distortion but provides valid data on base accessibility and protection. To demonstrate the ruggedness of this approach, optimized cocktails were finally employed to assess the stability of the folded structure of mouse mammary tumor virus pseudoknot in the presence of different amounts of Mg2+. Multiplexing the probe application constitutes an essential step toward high-throughput applications, which will take advantage of a strategy that maximizes the information attainable from a single experiment, while minimizing time and sample consumption over PAGE-based methods.     

Combinatorics of RNA Structures with Pseudoknots

In this paper, we derive the generating function of RNA structures with pseudoknots. We enumerate all k-noncrossing RNA pseudoknot structures categorized by their maximal sets of mutually intersecting arcs. In addition, we enumerate pseudoknot structures over circular RNA. For 3-noncrossing RNA structures and RNA secondary structures we present a novel 4-term recursion formula and a 2-term recursion, respectively. Furthermore, we enumerate for arbitrary k all k-noncrossing, restricted RNA structures i.e. k-noncrossing RNA structures without 2-arcs i.e. arcs of the form (i,i+2), for 1≤i≤n−2.     

A pseudoknot improves selection efficiency in ribosome display

The size and diversity of ribosome display libraries depends upon stability of the complex formed between the ribosome, mRNA and translated protein. To investigate if mRNA secondary structure improves stability of the complex, we tested a pseudoknot, originating from the genomic RNA of infectious bronchitis virus (IBV), a member of the positive-stranded coronavirus group. We used the previously-isolated anti-DNA scFv, 3D8, as a target protein. During in vitro translation in rabbit reticulocyte lysate, we observed that incorporation of the pseudoknot into the mRNA resulted in production of a translational intermediate that corresponded to the expected size for ribosomal arrest at the pseudoknot. Complexes containing the mRNA pseudoknot exhibited a higher efficiency of affinity selection than that those without, indicating that the pseudoknot improves stability of the mRNA-ribosome-antibody complex in a eukaryotic translation system. Thus, in order to improve the efficiency of selection, this relatively short pseudoknot sequence could be incorporated into ribosome display.     

Ligand-inducible formation of RNA pseudoknot

Here, we demonstrate that a series of naphthyridine derivatives, naphthyridine carbamate tetramer (NCTn), can bind to the RNA CGG/CGG triad comprised of two single-stranded regions of a hairpin loop and a tail. Complete suppression of the binding by a single mutation indicated simultaneous binding of NCTn between hairpin loop and single stranded tail, leading to the formation of NCTn-induced pseudoknot.     

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.     

Different role of functional domains of hTR in DNA binding to telomere and telomerase reconstruction

Even if template sequence of hTR played an essential role in telomere binding, a 326 nucleotide fragment of hTR containing template, pseudoknot, and CR4-5 domains is critical for both binding with telomeric DNA and reconstitution of telomerase activity. A functional study with antisense oligonucleotides suggested that targeted disruption of the template region efficiently abrogated both telomeric DNA binding and telomerase activity, whereas disruption of the CR4-5 region induced only loss of telomerase activity. hTR interacts with telomeric DNA via structural region composed of the template, pseudoknot, and CR4-5 domains, however, each structural domain plays a distinct role in telomere binding and telomerase activity reconstitution.