This Article 
 Bibliographic References 
 Add to: 
Fast Flexible Modeling of RNA Structure Using Internal Coordinates
September/October 2011 (vol. 8 no. 5)
pp. 1247-1257
Samuel Coulbourn Flores, Stanford University, Stanford
Michael A. Sherman, Stanford University, Stanford
Christopher M. Bruns, Stanford University, Stanford
Peter Eastman, Stanford University, Stanford
Russ Biagio Altman, Stanford University, Stanford
Modeling the structure and dynamics of large macromolecules remains a critical challenge. Molecular dynamics (MD) simulations are expensive because they model every atom independently, and are difficult to combine with experimentally derived knowledge. Assembly of molecules using fragments from libraries relies on the database of known structures and thus may not work for novel motifs. Coarse-grained modeling methods have yielded good results on large molecules but can suffer from difficulties in creating more detailed full atomic realizations. There is therefore a need for molecular modeling algorithms that remain chemically accurate and economical for large molecules, do not rely on fragment libraries, and can incorporate experimental information. RNABuilder works in the internal coordinate space of dihedral angles and thus has time requirements proportional to the number of moving parts rather than the number of atoms. It provides accurate physics-based response to applied forces, but also allows user-specified forces for incorporating experimental information. A particular strength of RNABuilder is that all Leontis-Westhof basepairs can be specified as primitives by the user to be satisfied during model construction. We apply RNABuilder to predict the structure of an RNA molecule with 160 bases from its secondary structure, as well as experimental information. Our model matches the known structure to 10.2 Angstroms RMSD and has low computational expense.

[1] A. Roth and R.R. Breaker, “The Structural and Functional Diversity of Metabolite-Binding Riboswitches,” Ann. Rev. Biochemistry, vol. 78, pp. 305-34, 2009.
[2] D.P. Bartel, “MicroRNAs: Genomics, Biogenesis, Mechanism, and Function,” Cell, vol. 116, no. 2, pp. 281-297, 2004.
[3] R.W. Carthew and E.J. Sontheimer, “Origins and Mechanisms of miRNAs and siRNAs,” Cell, vol. 136, no. 4, pp. 642-655, 2009.
[4] S. Katayama et al., “Antisense Transcription in the Mammalian Transcriptome,” Science, vol. 309, no. 5740, pp. 1564-1566, 2005.
[5] P. Carninci et al., “The Transcriptional Landscape of the Mammalian Genome,” Science, vol. 309, no. 5740, pp. 1559-1563, 2005.
[6] A.R. Ferre-D'Amare, K. Zhou, and J.A. Doudna, “A General Module for RNA Crystallization,” J. Molecular Biology, vol. 279, no. 3, pp. 621-631, 1998.
[7] D.K. Treiber and J.R. Williamson, “Exposing the Kinetic Traps in RNA Folding,” Current Opinion in Structural Biology, vol. 9, no. 3, pp. 339-345, 1999.
[8] R. Russell, “RNA Misfolding and the Action of Chaperones,” Frontiers in Bioscience, vol. 13, pp. 1-20, 2008.
[9] R. Das and D. Baker, “Automated De Novo Prediction of Native-Like RNA Tertiary Structures,” Proc Nat'l Academy of Sciences USA, vol. 104, no. 37, pp. 14664-14669, 2007.
[10] M. Parisien and F. Major, “The MC-Fold and MC-Sym Pipeline Infers RNA Structure from Sequence Data,” Nature, vol. 452, no. 7183, pp. 51-55, 2008.
[11] M.A. Jonikas et al., “Coarse-Grained Modeling of Large RNA Molecules with Knowledge-Based Potentials and Structural Filters,” RNA, vol. 15, no. 2, pp. 189-199, 2009.
[12] S. Flores, Y. Wan, R. Russell, and R.B. Altman, “Predicting RNA Structure by Multiple Template Homology Modeling,” Proc. Pacific Symp. Biocomputing, 2010.
[13] S. Flores and R.B. Altman, “Turning Limited Experimental Information Into 3D Models of RNA,” RNA, vol. 16, pp. 1769-1778, 2010.
[14] C.R. Sweet et al., “Normal Mode Partitioning of Langevin Dynamics for Biomolecules,” J. Chemical Physics, vol. 128, no. 14, pp. 145101-145113, 2008.
[15] C.D. Schwieters and G.M. Clore, “Internal Coordinates for Molecular Dynamics and Minimization in Structure Determination and Refinement,” J. Magnetic Resonance, vol. 152, no. 2, pp. 288-302, 2001.
[16] C. Levinthal, “Molecular Model-Building by Computer,” Scientific Am., vol. 214, no. 6, pp. 42-52, 1966.
[17] M. Levitt, C. Sander, and P.S. Stern, “Protein Normal-Mode Dynamics: Trypsin Inhibitor, Crambin, Ribonuclease and Lysozyme,” J. Molecular Biology, vol. 181, no. 3, pp. 423-447, 1985.
[18] T. Noguti and N. Go, “Efficient Monte Carlo Method for Simulation of Fluctuating Conformations of Native Proteins,” Biopolymers, vol. 24, no. 3, pp. 527-546, 1985.
[19] Z. Li and H.A. Scheraga, “Monte Carlo-Minimization Approach to the Multiple-Minima Problem in Protein Folding,” Proc. Nat'l Academy of Sciences USA, vol. 84, no. 19, pp. 6611-6615, 1987.
[20] A.K. Mazur, V.E. Dorofeev, and R.A. Abagyan, “Derivation and Testing of Explicit Equations of Motion for Polymers Described by Internal Coordinates,” J. Computational Physics, vol. 92, no. 2, pp. 261-272, 1991.
[21] A. Jain, N. Vaidehi, and G. Rodriguez, “A Fast Recursive Algorithm for Molecular Dynamics Simulation,” J. Computational Physics, vol. 106, no. 2, pp. 258-268, 1993.
[22] N. Vaidehi, A. Jain, and W.A.I. Goddard, “Constant Temperature Constrained Molecular Dynamics: The Newton-Euler Inverse Mass Operator Method,” J. Physical Chemistry, vol. 100, no. 25, pp. 10508-10517, June 1996.
[23] A.M. Mathiowetz et al., “Protein Simulations Using Techniques Suitable for Very Large Systems: The Cell Multipole Method for Nonbond Interactions and the Newton-Euler Inverse Mass Operator Method for Internal Coordinate Dynamics,” Proteins: Structure, Function, and Genetics, vol. 20, no. 3, pp. 227-247, 1994.
[24] N. Vaidehi and W.A. Goddard, “Domain Motions in Phosphoglycerate Kinase Using Hierarchical NEIMO Molecular Dynamics Simulations,” J. Physical Chemistry A, vol. 104, no. 11, pp. 2375-2383, 2000.
[25] L.M. Rice and A.T. Brunger, “Torsion Angle Dynamics: Reduced Variable Conformational Sampling Enhances Crystallographic Structure Refinement,” Proteins, vol. 19, no. 4, pp. 277-90, 1994.
[26] P. Guntert, C. Mumenthaler, and K. Wuthrich, “Torsion Angle Dynamics for NMR Structure Calculation with the New Program DYANA,” J. Molecular Biology, vol. 273, no. 1, pp. 283-298, 1997.
[27] J.P. Schmidt et al., “The Simbios National Center: Systems Biology in Motion,” Proc. IEEE, vol. 96, no. 8, pp. 1266-1280, Aug. 2008.
[28] M.A. Sherman, “Simbody Home Page,”, 2009.
[29] K.E. Brenan, S.L. Campbell, and L.R. Petzold, Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations, vol. 8, p. 210, North Holland, 1989.
[30] E. Eich, “Results for a Coordinate Projection Method Applied to Mechanical Systems with Algebraic Constraints,” SIAM J. Numerical Analysis, vol. 30, no. 5, pp. 1467-1482, 1993.
[31] K.L. Johnson, Contact Mechanics, ch. 4 (Section 4.2). Cambridge Univ. Press, 1985.
[32] K.H. Hunt and F.R.E. Crossley, “Coefficient of Restitution Interpreted as Damping in Vibroimpact,” ASME J. Applied Mechanics, Series E, vol. 42, pp. 440-445, 1975.
[33] J.M. Wang, P. Cieplak, and P.A. Kollman, “How Well Does a Restrained Electrostatic Potential (RESP) Model Perform in Calculating Conformational Energies of Organic and Biological Molecules?,” J. Computational Chemistry, vol. 21, pp. 1049-1074, 2000.
[34] S. Nosé, “A Unified Formulation of the Constant Temperature Molecular Dynamics Methods,” J. Chemical Physics, vol. 81, pp. 511-519, 1984.
[35] W. Hoover, “Canonical Dynamics: Equilibrium Phase-Space Distributions,” Physical Rev. A, vol. 31, pp. 1695-1697, 1985.
[36] JP Ryckaert, G. Ciccotti, and H.J.C. Berendsen, “Numerical Integration of the Cartesian Equations of Motion of a System with Constraints: Molecular Dynamics of N-Alkanes,” J. Computational Physics, vol. 23, no. 3, pp. 327-341, 1977.
[37] H.C. Andersen, “Rattle: A “Velocity” Version of the Shake Algorithm for Molecular Dynamics Calculations,” J. Computational Physics, vol. 52, no. 1, pp. 24-34, 1983.
[38] S. Miyamoto and P.A. Kollman, “Settle: An Analytical Version of the SHAKE and RATTLE Algorithm for Rigid Water Models,” J. Computational Chemistry, vol. 13, no. 8, pp. 952-962, 1992.
[39] B. Hess, H. Bekker, H.J.C. Berendsen, and J.G.E.M. Fraaije, “LINCS: A Linear Constraint Solver for Molecular Simulations,” J. Computational Chemistry, vol. 18, no. 12, pp. 1463-1472, 1997.
[40] S. Flores et al., “The Database of Macromolecular Motions: New Features Added at the Decade Mark,” Nucleic Acids Res, vol. 34, Database Issue, pp. D296-D301, 2006.
[41] S.C. Flores et al., “HingeMaster: Normal Mode Hinge Prediction Approach and Integration of Complementary Predictors,” Proteins, vol. 73, no. 2, pp. 299-319, 2008.
[42] N.B. Leontis, J. Stombaugh, and E. Westhof, “The Non-Watson-Crick Base Pairs and Their Associated Isostericity Matrices,” Nucleic Acids Res, vol. 30, no. 16, pp. 3497-3531, 2002.
[43] J. Stroud, “The Make-Na Server,” , 2010.
[44] M.A. Jonikas, R.J. Radmer, and R.B. Altman, “Knowledge-Based Instantiation of Full Atomic Detail Into Coarse-Grain RNA 3D Structural Models,” Bioinformatics, vol. 25, no. 24, pp. 3259-3266, 2009.
[45] W.T. Astbury, “The Structure of Biological Tissues as Revealed by X-Ray Diffraction Analysis and Electron Microscopy,” British J. Radiology, vol. 22, pp. 355-365, 1949.

Index Terms:
Internal coordinate mechanics, molecular, structure, dynamics, RNA, modeling, prediction, linear, scaling.
Samuel Coulbourn Flores, Michael A. Sherman, Christopher M. Bruns, Peter Eastman, Russ Biagio Altman, "Fast Flexible Modeling of RNA Structure Using Internal Coordinates," IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 8, no. 5, pp. 1247-1257, Sept.-Oct. 2011, doi:10.1109/TCBB.2010.104
Usage of this product signifies your acceptance of the Terms of Use.