Structural Alignment of Pseudoknotted RNA

Abstract

Abstract. In this paper, we address the problem of discovering novel non-coding RNA (ncRNA) using primary sequence, and secondary structure conservation, focusing on ncRNA families with pseudo-knotted structures. Our main technical result is an efficient algorithm for computing an optimum structural alignment of an RNA sequence against a genomic substring. This algorithm finds two applications. First, by scanning a genome, we can identify novel (homologous) pseudoknotted ncRNA, and second, we can infer the secondary structure of the target aligned sequence. We test an implementation of our algorithm (PAL), and show that it has near-perfect behavior for predicting the structure of many known pseudoknots. Additionally, it can detect the true homologs with high sensitivity and specificity in controlled tests. We also use PAL to search entire viral genome and mouse genome for novel homologs of some viral, and eukaryotic pseudoknots respectively. In each case, we have found strong support for novel homologs.

A MEMORY EFFICIENT ALGORITHM FOR STRUCTURAL ALIGNMENT OF RNAs WITH EMBEDDED SIMPLE PSEUDOKNOTS

“…An embedded simple pseudoknot structure is defined as follows [13]. M is an embedded simple pseudoknot structure if ∃ 1≤ x 1 < y 1 <…< x s < y s ≤ m such that 1.…”

“…Let B[p,q,r,i,j,k] be the optimal alignment score between P(i,j,k) of S and P(p,q,r) of another length-n subsequence T[p 0 …r 0 ] whose structure is unknown. Consider the case of (i, j)∈M L , the following recurrence equation [13] gives the value for B. The case for (i, j)∈M R is similar.…”

“…Some focuses on this simpler structure. Dost et al [13] developed a tool called PAL using dynamic programming approach that supports secondary structures with embedded simple pseudoknots. By restricting their supporting structure to be a subset of the structures having 2-crossing properties, their dynamic programming algorithm runs faster and uses less memory with time complexity of O(mn 4 ) and space complexity of O(mn 3 ).…”

“…The best known algorithm for solving this problem (Dost et al [13]) runs in O(mn4) time with space complexity of O(mn3), which requires too much memory making it infeasible for comparing ncRNAs (non-coding RNAs) with length several hundreds or more. We propose a memory efficient algorithm to solve the same problem.…”

Fixed Parameter Tractable Alignment of RNA Structures Including Arbitrary Pseudoknots

“…Among the algorithms supporting pseudoknots, there are several grammarbased approaches for motif finding, which try to align a sequence with given structure to a sequence with unknown structure (usually a genomic sequence) [14,15]. In these approaches, the class of supported pseudoknots depends on the expressivity of the underlying grammar formalism.…”