TAR inter-helical conformation as a function of [Mg]:[TAR] stoichiometry. Order tensor orientations (Sxx, Syy, Szz) for stem I (red) and II (blue) in (a) TAR(free) (b) TAR(3.0 Mg) and (c) TAR(4.5 Mg). Ribbon representation of the relative orientation of stem I (in red) and II (in blue) determined by superimposing stem-specific principal axes for (d) TAR(free), (e) TAR(3.0 Mg) and (f) TAR(4.5 Mg), where the helix axis of stem I is oriented towards the reader. The helix axis of stem II is superimposed for all three conformations along the molecular z direction. (g) The average and allowed range of determined inter-helical angles (a). Order matrix analysis36,37 was carried out independently for stems I and II for both TAR(3.0 Mg) and TAR(4.5 Mg), closely following the procedure previously described for TAR(free)21(see Table 1). In all cases, repeating order matrix analyses when excluding data measured in terminal residues in various permutations had a negligible effect on the average values of derived structural and dynamic parameters. Stems I and II were rotated into the principal axis system (PAS) using the program Insight II, and one orientation among four degenerate solutions could be selected based on linkage geometry considerations.21 In particular, the translational disposition of the two stems was determined by fixing the distance between atoms U40 (P) and C39(O3′) at 1.59 Å . With the latter translational constraint, two of the four inter-stem orientations generated through 180° rotations about the Sxx and Syy directions could be discarded because they lead to anti-parallel stem alignments that is inconsistent with the secondary structure and sequence (terminal residues G17–C45 in stem I are oriented towards residues G26– C39 in stem II). Among the two remaining solutions involving180° rotation about Szz, one of the solutions could be discarded because it lead to a considerable distance between A22(O3′) and G26(P) (~35 Å and 33 Å for TAR(3.5 Mg) and TAR(4.5 Mg), respectively) which cannot be connected using a three-residue bulge (the same distance in A-form helices is only ~17 Å).