Fig 1.
Transformation of an RNA 3D molecule into an ordered labeled tree.
(A) The 3D crystal structure of the adenine riboswitch molecule (PDB code: 1Y26) obtained from the Protein Data Bank (PDB) and drawn by PyMOL. The first helix according to the 5′ to 3′ orientation is labeled by H1 and highlighted in blue. The second helix is labeled by H2 and highlighted in green. The third helix is labeled by H3 and highlighted in red. The junction labeled by J1 and hairpin loops labeled by P1 and P2 respectively are highlighted in light grey. J1 is a multi-branch loop where the three helices H1, H2 and H3 connect. P1 and P2 are hairpin loops connected to helices H2 and H3, respectively. (B) The corresponding secondary (2D) structure, obtained from RNAView. Each 2D structural element in (B) is highlighted as in (A). The yellow bar across H1, J1 and H3 denotes a coaxial helical stacking H1H3 in the molecule 1Y26. (C) The ordered labeled tree, T, used to represent the 2D structure R in (B). Each node of T corresponds to a 2D structural element of R where the octagon (squares, triangles respectively) in T represents the junction (helices, hairpin loops respectively) in R.
Fig 2.
Illustration of an alignment between two RNA molecules.
(A) The 3D crystal structure of the adenine riboswitch (PDB code: 1Y26) and its tree representation T1. (B) The 3D crystal structure of the Alu domain of the mammalian signal recognition particle (SRP) (PDB code: 1E8O) and its tree representation T2. (C) When matching T1[i] with T2[j], since t1[i] and t2[j] have different types where t1[i] is a junction and t2[j] is a helix, there are two subcases to be considered. Subcase 1 is illustrated in (i) where t2[j] is aligned to gaps and T1[i] is aligned with T2[j—1]. Subcase 2 is illustrated in (ii) where t1[i] is aligned to gaps, and the subtree rooted at one of the children of t1[i] is aligned with T2[j]. In this example, t1[i] has two children, t1[i1] and t1[i2]. Thus, either the subtree rooted at t1[i1], denoted by 1[i1], is aligned with T2[j] as illustrated in (iia), or the subtree rooted at t1[i2], denoted by T1[i2], is aligned with T2[j] as illustrated in (iib).
Table 1.
The 24 RNA full structures in Dataset1 selected from the Protein Data Bank (PDB) to evaluate the performance of the alignment methods studied in this paper.
Fig 3.
Comparison of the RMSD values obtained by CHSalign_u, CHSalign_p, RSmatch, RNAforester and FOLDALIGN.
The RMSD values of CHSalign_u, CHSalign_p, RSmatch, RNAforester and FOLDALIGN are 1.78 Å, 1.83 Å, 4.41 Å, 6.13 Å and 8.26 Å, respectively. The proposed CHSalign method performs better than the existing alignment tools in terms of RMSD values.
Fig 4.
Comparison of the PR values obtained by CHSalign_u, CHSalign_p, RNAforester, SETTER, RSmatch and FOLDALIGN.
The PR values, as defined in Eq (13), of CHSalign_u, CHSalign_p, RNAforester, SETTER, RSmatch and FOLDALIGN are 1, 0.85, 0.54, 0.42, 0.33 and 0.31, respectively. The proposed CHSalign method performs better than the existing alignment tools in terms of PR values.
Table 2.
The six riboswitches selected from the Protein Data Bank (PDB) to demonstrate the utility of our web server.
Table 3.
Results obtained by aligning seven pairs of riboswitches from Table 2.
Fig 5.
Illustration of the coaxial stacking patterns in the six riboswitches used to demonstrate the utility of our web server.
(A) Artificial purine riboswitch (PDB code: 2G9C) with a three-way junction and a CHS motif of type H1H3 in the junction. (B) Artificial guanine riboswitch (PDB code: 3RKF) with a three-way junction and a CHS motif of type H1H3 in the junction. (C) A. thaliana TPP riboswitch (PDB code: 3D2G) with a three-way junction and a CHS motif of type H1H2 in the junction. (D) E. coli TPP riboswitch (PDB code: 2GDI) with a three-way junction and a CHS motif of type H1H2 in the junction. (E) T. tengcongensis SAM-I riboswitch (PDB code: 2GIS) with a four-way junction and a CHS motif of type H1H4, H2H3 in the junction. (F) H. marismortui SAM-I riboswitch (PDB code: 4B5R) with a four-way junction and a CHS motif of type H1H4, H2H3 in the junction.