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3D maps of RNA interhelical junctions

Nature Protocols volume 6, pages 1536–1545 (2011)Cite this article

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Abstract

More than 50% of RNA secondary structure is estimated to be A-form helices, which are linked together by various junctions. Here we describe a protocol for computing three interhelical Euler angles describing the relative orientation of helices across RNA junctions. 5′ and 3′ helices, H1 and H2, respectively, are assigned based on the junction topology. A reference canonical helix is constructed using an appropriate molecular builder software consisting of two continuous idealized A-form helices (iH1 and iH2) with helix axis oriented along the molecular Z-direction running toward the positive direction from iH1 to iH2. The phosphate groups and the carbon and oxygen atoms of the sugars are used to superimpose helix H1 of a target interhelical junction onto the corresponding iH1 of the reference helix. A copy of iH2 is then superimposed onto the resulting H2 helix to generate iH2′. A rotation matrix R is computed, which rotates iH2′ into iH2 and expresses the rotation parameters in terms of three Euler angles αh, βh and γh. The angles are processed to resolve a twofold degeneracy and to select an overall rotation around the axis of the reference helix. The three interhelical Euler angles define clockwise rotations around the 5′ (−γh) and 3′ (αh) helices and an interhelical bend angle (βh). The angles can be depicted graphically to provide a 'Ramachandran'-type view of RNA global structure that can be used to identify unusual conformations as well as to understand variations due to changes in sequence, junction topology and other parameters.

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Figure 1: Interhelical Euler angles.
Figure 2: General scheme for computing interhelical Euler angles.
Figure 3: Definition of Euler rotation matrix and angles.
Figure 4: Approaches for mapping interhelical Euler angles.
Figure 5: Topological confinement and distribution of RNA interhelical orientations; 3D interhelical orientation maps showing the individual 2D projections along each plane.

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Acknowledgements

We thank D. Herschlag and V. Chu of Stanford University for stimulating discussions. A.M.M. acknowledges support from a Graduate Research Fellowship from the National Science Foundation (NSF). H.M.A.-H. acknowledges support from a NSF CAREER award (MCB 0644278) and a National Institutes of Health grant (R01GM089846). C.L.B. acknowledges funding for the Center for Multi-scale Modeling Tools for Structural Biology by the National Center for Research Resources (P41RR012255).

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  1. Maximillian H Bailor and Anthony M Mustoe: These authors contributed equally to this work.

Authors and Affiliations

  1. Department of Chemistry and Biophysics, The University of Michigan, Ann Arbor, Michigan, USA

    Maximillian H Bailor, Anthony M Mustoe, Charles L Brooks III & Hashim M Al-Hashimi

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Contributions

All authors contributed to the work presented in this paper. M.H.B. and H.M.A.-H. conceived the original protocol, developed the underlying theory and performed the analysis. A.M.M. developed theory and performed analysis to define the various Euler angle conventions, improve the robustness of the protocol and establish its limits of applicability. C.L.B. performed supporting simulations to assess the robustness of the protocol. M.H.B., A.M.M., C.L.B. and H.M.A.-H. prepared the manuscript.

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Correspondence to Hashim M Al-Hashimi.

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Bailor, M., Mustoe, A., Brooks, C. et al. 3D maps of RNA interhelical junctions. Nat Protoc 6, 1536–1545 (2011). https://doi.org/10.1038/nprot.2011.385

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