All-atom Monte Carlo simulation of GCAA RNA folding.

We report a detailed all-atom simulation of the folding of the GCAA RNA tetraloop. The GCAA tetraloop motif is a very common and thermodynamically stable secondary structure in natural RNAs. We use our simulation methods to study the folding behavior of a 12-base GCAA tetraloop structure with a four-base helix adjacent to the tetraloop proper. We implement an all-atom Monte Carlo (MC) simulation of RNA structural dynamics using a Go potential. Molecular dynamics (MD) simulation of RNA and protein has realistic energetics and sterics, but is extremely expensive in terms of computational time. By coarsely treating non-covalent energetics, but retaining all-atom sterics and entropic effects, all-atom MC techniques are a useful method for the study of protein and now RNA. We observe a sharp folding transition for this structure, and in simulations at room temperature the state histogram shows three distinct minima: an unfolded state (U), a more narrow intermediated state (I), and a narrow folded state (F). The intermediate consists primarily of structures with the GCAA loop and some helix hydrogen bonds formed. Repeated kinetic folding simulations reveal that the number of helix base-pairs forms a simple 1D reaction coordinate for the I-->N transition.

[1]  D. Turner,et al.  Context dependence of hydrogen bond free energy revealed by substitutions in an RNA hairpin. , 1992, Science.

[2]  H. Heus,et al.  Structural features that give rise to the unusual stability of RNA hairpins containing GNRA loops. , 1991, Science.

[3]  D. Baker,et al.  Contact order, transition state placement and the refolding rates of single domain proteins. , 1998, Journal of molecular biology.

[4]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[5]  J. Onuchic,et al.  Topological and energetic factors: what determines the structural details of the transition state ensemble and "en-route" intermediates for protein folding? An investigation for small globular proteins. , 2000, Journal of molecular biology.

[6]  Eric J. Sorin,et al.  Does native state topology determine the RNA folding mechanism? , 2004, Journal of molecular biology.

[7]  C. Brooks,et al.  From folding theories to folding proteins: a review and assessment of simulation studies of protein folding and unfolding. , 2001, Annual review of physical chemistry.

[8]  P. Zarrinkar,et al.  Kinetic intermediates in RNA folding. , 1994, Science.

[9]  E. Shakhnovich,et al.  The ensemble folding kinetics of protein G from an all-atom Monte Carlo simulation , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[10]  G. Hummer,et al.  An extension of the rigorous base-unit oriented description of nucleic acid structures. , 1994, Journal of biomolecular structure & dynamics.

[11]  A. Fersht,et al.  Demonstration of a low-energy on-pathway intermediate in a fast-folding protein by kinetics, protein engineering, and simulation. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[12]  Gerard T. Barkema,et al.  Monte Carlo Methods in Statistical Physics , 1999 .

[13]  S. Edwards,et al.  The Theory of Polymer Dynamics , 1986 .

[14]  Daniel Herschlag,et al.  RNA simulations: probing hairpin unfolding and the dynamics of a GNRA tetraloop. , 2002, Journal of molecular biology.

[15]  V S Pande,et al.  Folding pathway of a lattice model for proteins. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[16]  H. Heus,et al.  A network of heterogeneous hydrogen bonds in GNRA tetraloops. , 1996, Journal of molecular biology.

[17]  S. Woodson,et al.  Fast folding of a ribozyme by stabilizing core interactions: evidence for multiple folding pathways in RNA. , 2000, Journal of molecular biology.

[18]  Haruo Abe,et al.  Noninteracting local‐structure model of folding and unfolding transition in globular proteins. II. Application to two‐dimensional lattice proteins , 1981, Biopolymers.

[19]  Yiqing Shen,et al.  Configurational diffusion down a folding funnel describes the dynamics of DNA hairpins , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[20]  S. Balasubramanian,et al.  Non-Arrhenius kinetics for the loop closure of a DNA hairpin , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[21]  E. Shakhnovich,et al.  The folding thermodynamics and kinetics of crambin using an all-atom Monte Carlo simulation. , 2000, Journal of molecular biology.

[22]  N. Go,et al.  Noninteracting local‐structure model of folding and unfolding transition in globular proteins. I. Formulation , 1981, Biopolymers.

[23]  J. Skolnick,et al.  Comparison of lattice Monte Carlo dynamics and Brownian dynamics folding pathways of α-helical hairpins , 1991 .

[24]  D. Baker,et al.  A surprising simplicity to protein folding , 2000, Nature.

[25]  C R Woese,et al.  Architecture of ribosomal RNA: constraints on the sequence of "tetra-loops". , 1990, Proceedings of the National Academy of Sciences of the United States of America.

[26]  A Libchaber,et al.  Sequence dependent rigidity of single stranded DNA. , 2000, Physical review letters.

[27]  V. Pande,et al.  On the transition coordinate for protein folding , 1998 .

[28]  A. Fersht,et al.  Protein Folding and Unfolding at Atomic Resolution , 2002, Cell.

[29]  C. Bustamante,et al.  Overstretching B-DNA: The Elastic Response of Individual Double-Stranded and Single-Stranded DNA Molecules , 1996, Science.

[30]  X. Zhuang,et al.  A single-molecule study of RNA catalysis and folding. , 2000, Science.

[31]  A Libchaber,et al.  Kinetics of conformational fluctuations in DNA hairpin-loops. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

[32]  M. Gruebele Protein folding: the free energy surface. , 2002, Current opinion in structural biology.

[33]  O. Uhlenbeck Tetraloops and RNA folding , 1990, Nature.

[34]  G. Favrin,et al.  Monte Carlo update for chain molecules: Biased Gaussian steps in torsional space , 2001, cond-mat/0103580.

[35]  L. Mirny,et al.  Protein folding theory: from lattice to all-atom models. , 2001, Annual review of biophysics and biomolecular structure.

[36]  D. Thirumalai,et al.  Early events in RNA folding. , 2001, Annual review of physical chemistry.

[37]  Taekjip Ha,et al.  Mg2+-dependent conformational change of RNA studied by fluorescence correlation and FRET on immobilized single molecules , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[38]  D. K. Treiber,et al.  Exposing the kinetic traps in RNA folding. , 1999, Current opinion in structural biology.

[39]  Eric J. Sorin,et al.  Insights into nucleic acid conformational dynamics from massively parallel stochastic simulations. , 2003, Biophysical journal.