RNA and protein folding: common themes and variations.

Visualizing the navigation of an ensemble of unfolded molecules through the bumpy energy landscape in search of the native state gives a pictorial view of biomolecular folding. This picture, when combined with concepts in polymer theory, provides a unified theory of RNA and protein folding. Just as for proteins, the major folding free energy barrier for RNA scales sublinearly with the number of nucleotides, which allows us to extract the elusive prefactor for RNA folding. Several folding scenarios can be anticipated by considering variations in the energy landscape that depend on sequence, native topology, and external conditions. RNA and protein folding mechanism can be described by the kinetic partitioning mechanism (KPM) according to which a fraction (Phi) of molecules reaches the native state directly, whereas the remaining fraction gets kinetically trapped in metastable conformations. For two-state folders Phi approximately 1. Molecular chaperones are recruited to assist protein folding whenever Phi is small. We show that the iterative annealing mechanism, introduced to describe chaperonin-mediated folding, can be generalized to understand protein-assisted RNA folding. The major differences between the folding of proteins and RNA arise in the early stages of folding. For RNA, folding can only begin after the polyelectrolyte problem is solved, whereas protein collapse requires burial of hydrophobic residues. Cross-fertilization of ideas between the two fields should lead to an understanding of how RNA and proteins solve their folding problems.

[1]  D. O. Jordan Physico-Chemical Properties of Nucleic Acids , 1950, Nature.

[2]  A Adams,et al.  Tertiary structure in transfer ribonucleic acids. , 1966, Cold Spring Harbor symposia on quantitative biology.

[3]  M. Eigen,et al.  Co-operative non-enzymic base recognition. 3. Kinetics of the helix-coil transition of the oligoribouridylic--oligoriboadenylic acid system and of oligoriboadenylic acid alone at acidic pH. , 1971, Journal of molecular biology.

[4]  D. Crothers,et al.  Conformational changes of transfer ribonucleic acid. Equilibrium phase diagrams. , 1972, Biochemistry.

[5]  O. Uhlenbeck,et al.  Thermodynamics and kinetics of the helix‐coil transition of oligomers containing GC base pairs , 1973 .

[6]  M. Bina-Stein,et al.  Conformational changes of transfer ribonucleic acid. The pH phase diagram under acidic conditions. , 1974, Biochemistry.

[7]  D. Crothers,et al.  Conformational changes of transfer RNA. The role of magnesium(II). , 1976, Biochemistry.

[8]  D M Crothers,et al.  Equilibrium binding of magnesium(II) by Escherichia coli tRNAfMet. , 1976, Biochemistry.

[9]  A. Rich,et al.  Introduction to transfer RNA , 1977 .

[10]  T. Cech,et al.  In vitro splicing of the ribosomal RNA precursor of tetrahymena: Involvement of a guanosine nucleotide in the excision of the intervening sequence , 1981, Cell.

[11]  T. Cech,et al.  Self-splicing RNA: Autoexcision and autocyclization of the ribosomal RNA intervening sequence of tetrahymena , 1982, Cell.

[12]  J. R. Fresco,et al.  Mechanistic studies of ribonucleic acid renaturation by a helix-destabilizing protein. , 1982, Biochemistry.

[13]  N. Pace,et al.  The RNA moiety of ribonuclease P is the catalytic subunit of the enzyme , 1983, Cell.

[14]  T. Cech,et al.  Fate of an intervening sequence ribonucleic acid: excision and cyclization of the Tetrahymena ribosomal ribonucleic acid intervening sequence in vivo. , 1983, Biochemistry.

[15]  T. Cech,et al.  Specific interaction between the self-splicing RNA of Tetrahymena and its guanosine substrate: implications for biological catalysis by RNA , 1984, Nature.

[16]  S. Altman,et al.  Catalytic activity of an RNA molecule prepared by transcription in vitro. , 1984, Science.

[17]  P. Wolynes,et al.  Spin glasses and the statistical mechanics of protein folding. , 1987, Proceedings of the National Academy of Sciences of the United States of America.

[18]  M. Mézard,et al.  Spin Glass Theory and Beyond , 1987 .

[19]  N. Oppenheimer,et al.  Structure and mechanism , 1989 .

[20]  Peter G. Wolynes,et al.  A simple statistical field theory of heteropolymer collapse with application to protein folding , 1990 .

[21]  K. Dill Dominant forces in protein folding. , 1990, Biochemistry.

[22]  C. Branden,et al.  Introduction to protein structure , 1991 .

[23]  G. Lorimer,et al.  Purified chaperonin 60 (groEL) interacts with the nonnative states of a multitude of Escherichia coli proteins , 1992, Protein science : a publication of the Protein Society.

[24]  D Thirumalai,et al.  Kinetics and thermodynamics of folding in model proteins. , 1993, Proceedings of the National Academy of Sciences of the United States of America.

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

[26]  Sebastian Doniach Statistical mechanics, protein structure, and protein substrate interactions , 1994 .

[27]  G. Lorimer,et al.  Dynamics of the chaperonin ATPase cycle: implications for facilitated protein folding. , 1994, Science.

[28]  Sarah A. Woodson,et al.  In vivo facilitation of Tetrahymena group I intron splicing in Escherichia coli pre-ribosomal RNA. , 1995, RNA.

[29]  K. Weeks,et al.  Protein facilitation of group I intron splicing by assembly of the catalytic core and the 5′ splice site domain , 1995, Cell.

[30]  D. Herschlag RNA Chaperones and the RNA Folding Problem (*) , 1995, The Journal of Biological Chemistry.

[31]  D. Thirumalai,et al.  From Minimal Models to Real Proteins: Time Scales for Protein Folding Kinetics , 1995 .

[32]  K. Weeks,et al.  Efficient protein-facilitated splicing of the yeast mitochondrial bI5 intron. , 1995, Biochemistry.

[33]  D. Thirumalai,et al.  Kinetics of protein folding: Nucleation mechanism, time scales, and pathways , 1995 .

[34]  Kinetic and thermodynamic analysis of proteinlike heteropolymers: Monte Carlo histogram technique , 1995, chem-ph/9507003.

[35]  J. Onuchic,et al.  Funnels, pathways, and the energy landscape of protein folding: A synthesis , 1994, Proteins.

[36]  T. Kiefhaber,et al.  Kinetic traps in lysozyme folding. , 1995, Proceedings of the National Academy of Sciences of the United States of America.

[37]  D. Draper,et al.  Parallel worlds , 1996, Nature Structural Biology.

[38]  C. Kundrot,et al.  Crystal Structure of a Group I Ribozyme Domain: Principles of RNA Packing , 1996, Science.

[39]  K. Weeks,et al.  Assembly of a Ribonucleoprotein Catalyst by Tertiary Structure Capture , 1996, Science.

[40]  J. Onuchic,et al.  Protein folding funnels: the nature of the transition state ensemble. , 1996, Folding & design.

[41]  E. Shakhnovich,et al.  Chain Length Scaling of Protein Folding Time. , 1996, Physical review letters.

[42]  Devarajan Thirumalai,et al.  Kinetics of Folding of Proteins and RNA , 1996 .

[43]  E Westhof,et al.  New loop-loop tertiary interactions in self-splicing introns of subgroup IC and ID: a complete 3D model of the Tetrahymena thermophila ribozyme. , 1996, Chemistry & biology.

[44]  Ashwin,et al.  Dynamics of Random Hydrophobic-Hydrophilic Copolymers with Implications for Protein Folding. , 1996, Physical review letters.

[45]  D Thirumalai,et al.  Chaperonin-facilitated protein folding: optimization of rate and yield by an iterative annealing mechanism. , 1996, Proceedings of the National Academy of Sciences of the United States of America.

[46]  P. Zarrinkar,et al.  Slow folding kinetics of RNase P RNA. , 1996, RNA.

[47]  D. Thirumalai,et al.  The nucleation-collapse mechanism in protein folding: evidence for the non-uniqueness of the folding nucleus. , 1997, Folding & design.

[48]  C M Dobson,et al.  Fast and slow tracks in lysozyme folding: insight into the role of domains in the folding process. , 1997, Journal of molecular biology.

[49]  J. Onuchic,et al.  Theory of protein folding: the energy landscape perspective. , 1997, Annual review of physical chemistry.

[50]  A. Horwich,et al.  GroEL‐Mediated protein folding , 1997, Protein science : a publication of the Protein Society.

[51]  P. Wolynes,et al.  Folding funnels and energy landscapes of larger proteins within the capillarity approximation. , 1997, Proceedings of the National Academy of Sciences of the United States of America.

[52]  T. Pan,et al.  Intermediates and kinetic traps in the folding of a large ribozyme revealed by circular dichroism and UV absorbance spectroscopies and catalytic activity , 1997, Nature Structural Biology.

[53]  A V Finkelstein,et al.  Rate of protein folding near the point of thermodynamic equilibrium between the coil and the most stable chain fold. , 1997, Folding & design.

[54]  D. Thirumalai,et al.  Folding of RNA involves parallel pathways. , 1997, Journal of molecular biology.

[55]  E. Westhof,et al.  Hierarchy and dynamics of RNA folding. , 1997, Annual review of biophysics and biomolecular structure.

[56]  K. Dill,et al.  From Levinthal to pathways to funnels , 1997, Nature Structural Biology.

[57]  D. Thirumalai,et al.  Kinetic partitioning mechanism as a unifying theme in the folding of biomolecules , 1997, cond-mat/9704067.

[58]  A. Fersht,et al.  A structural model for GroEL-polypeptide recognition. , 1997, Proceedings of the National Academy of Sciences of the United States of America.

[59]  K. Weeks Protein-facilitated RNA folding. , 1997, Current opinion in structural biology.

[60]  A. Fersht Nucleation mechanisms in protein folding. , 1997, Current opinion in structural biology.

[61]  R. Hochstrasser,et al.  Protein fluctuations are sensed by stimulated infrared echoes of the vibrations of carbon monoxide and azide probes. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

[62]  D. Thirumalai,et al.  Fishing for folding nuclei in lattice models and proteins. , 1998, Folding & design.

[63]  E I Shakhnovich,et al.  Folding nucleus: specific or multiple? Insights from lattice models and experiments. , 1998, Folding & design.

[64]  S. Woodson,et al.  Folding intermediates of a self-splicing RNA: mispairing of the catalytic core. , 1998, Journal of molecular biology.

[65]  A. Fersht Structure and mechanism in protein science , 1998 .

[66]  V. Muñoz,et al.  Kinetics and Dynamics of Loops, α-Helices, β-Hairpins, and Fast-Folding Proteins , 1998 .

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

[68]  I. Tinoco,et al.  RNA folding causes secondary structure rearrangement. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

[69]  D Thirumalai,et al.  Native secondary structure formation in RNA may be a slave to tertiary folding. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

[70]  Stanley B. Prusiner,et al.  Nobel Lecture: Prions , 1998 .

[71]  J. Weissman,et al.  GroEL-GroES-mediated protein folding requires an intact central cavity. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

[72]  Tobin R. Sosnick,et al.  The burst phase in ribonuclease A folding and solvent dependence of the unfolded state , 1998, Nature Structural Biology.

[73]  D. K. Treiber,et al.  Fast folding mutants of the Tetrahymena group I ribozyme reveal a rugged folding energy landscape. , 1998, Journal of molecular biology.

[74]  RNA Folding at Millisecond Intervals by Synchrotron Hydroxyl Radical Footprinting , 1998 .

[75]  V. Pande,et al.  Pathways for protein folding: is a new view needed? , 1998, Current opinion in structural biology.

[76]  D. Draper,et al.  On the role of magnesium ions in RNA stability , 1998, Biopolymers.

[77]  I. Tinoco,et al.  How RNA folds. , 1999, Journal of molecular biology.

[78]  A. Ferré-D’Amaré,et al.  RNA folds: insights from recent crystal structures. , 1999, Annual review of biophysics and biomolecular structure.

[79]  D Thirumalai,et al.  Exploring the kinetic requirements for enhancement of protein folding rates in the GroEL cavity. , 1999, Journal of molecular biology.

[80]  M. Gruebele,et al.  Observation of strange kinetics in protein folding. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[81]  D. Thirumalai,et al.  Deciphering the timescales and mechanisms of protein folding using minimal off-lattice models. , 1999, Current opinion in structural biology.

[82]  T. Pan,et al.  Mg2+-dependent folding of a large ribozyme without kinetic traps , 1999, Nature Structural Biology.

[83]  A. Lambowitz,et al.  18 Group I and Group II Ribozymes as RNPs: Clues to the Past and Guides to the Future , 1999 .

[84]  D. Herschlag,et al.  New pathways in folding of the Tetrahymena group I RNA enzyme. , 1999, Journal of molecular biology.

[85]  S W Englander,et al.  Chaperonin function: folding by forced unfolding. , 1999, Science.

[86]  D. Thirumalai,et al.  Magnesium-dependent folding of self-splicing RNA: exploring the link between cooperativity, thermodynamics, and kinetics. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[87]  D. Baker,et al.  Chain collapse can occur concomitantly with the rate-limiting step in protein folding , 1999, Nature Structural Biology.

[88]  Andrew B. Martin,et al.  Single-molecule protein folding: diffusion fluorescence resonance energy transfer studies of the denaturation of chymotrypsin inhibitor 2. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[89]  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.

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

[91]  Eugene I. Shakhnovich,et al.  Kinetics, thermodynamics and evolution of non-native interactions in a protein folding nucleus , 2000, Nature Structural Biology.

[92]  Karen L. Buchmueller,et al.  A collapsed non-native RNA folding state , 2000, Nature Structural Biology.

[93]  D. Thirumalai,et al.  Dynamics of collapse of flexible polyampholytes , 2000 .

[94]  Lisa J. Lapidus,et al.  Fast kinetics and mechanisms in protein folding. , 2000, Annual review of biophysics and biomolecular structure.

[95]  R. Gutell,et al.  Function of tyrosyl-tRNA synthetase in splicing group I introns: an induced-fit model for binding to the P4-P6 domain based on analysis of mutations at the junction of the P4-P6 stacked helices. , 2000, Journal of molecular biology.

[96]  D. Bartel,et al.  One sequence, two ribozymes: implications for the emergence of new ribozyme folds. , 2000, Science.

[97]  S. Woodson Recent insights on RNA folding mechanisms from catalytic RNA , 2000, Cellular and Molecular Life Sciences CMLS.

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

[99]  D. Thirumalai,et al.  Maximizing RNA folding rates: a balancing act. , 2000, RNA.

[100]  C. Ralston,et al.  Folding mechanism of the Tetrahymena ribozyme P4-P6 domain. , 2000, Biochemistry.

[101]  K. Weeks,et al.  Protein-dependent transition states for ribonucleoprotein assembly. , 2001, Journal of molecular biology.

[102]  Dynamics of Collapse of Flexible Polyelectrolytes in Poor Solvents , 2000, cond-mat/0001094.

[103]  D. Perl,et al.  Role of the chain termini for the folding transition state of the cold shock protein. , 2001, Biochemistry.

[104]  D. Thirumalai,et al.  Role of counterion condensation in folding of the Tetrahymena ribozyme. I. Equilibrium stabilization by cations. , 2001, Journal of molecular biology.

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

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

[107]  D. J. Naylor,et al.  Dual Function of Protein Confinement in Chaperonin-Assisted Protein Folding , 2001, Cell.

[108]  D. K. Treiber,et al.  Beyond kinetic traps in RNA folding. , 2001, Current opinion in structural biology.

[109]  D. Thirumalai,et al.  Chaperonin-mediated protein folding. , 2001, Annual review of biophysics and biomolecular structure.

[110]  D. Thirumalai,et al.  Role of counterion condensation in folding of the Tetrahymena ribozyme. II. Counterion-dependence of folding kinetics. , 2001, Journal of molecular biology.

[111]  J. Lorsch RNA Chaperones Exist and DEAD Box Proteins Get a Life , 2002, Cell.

[112]  Satoshi Takahashi,et al.  Conformational landscape of cytochrome c folding studied by microsecond-resolved small-angle x-ray scattering , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[113]  Folding plasticity , 2002, Nature Structural Biology.

[114]  A. Lambowitz,et al.  A DEAD-Box Protein Functions as an ATP-Dependent RNA Chaperone in Group I Intron Splicing , 2002, Cell.

[115]  Jeanette Tångrot,et al.  Complete change of the protein folding transition state upon circular permutation , 2002, Nature Structural Biology.

[116]  R. Schroeder,et al.  RNA chaperone StpA loosens interactions of the tertiary structure in the td group I intron in vivo. , 2002, Genes & development.

[117]  Kevin W Plaxco,et al.  Equilibrium collapse and the kinetic 'foldability' of proteins. , 2002, Biochemistry.

[118]  H. Roder,et al.  Early kinetic intermediate in the folding of acyl-CoA binding protein detected by fluorescence labeling and ultrarapid mixing , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[119]  V. Muñoz,et al.  Experimental Identification of Downhill Protein Folding , 2002, Science.

[120]  Jennifer A. Doudna,et al.  The chemical repertoire of natural ribozymes , 2002, Nature.

[121]  X. Zhuang,et al.  Correlating Structural Dynamics and Function in Single Ribozyme Molecules , 2002, Science.

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

[123]  V. Pande,et al.  Absolute comparison of simulated and experimental protein-folding dynamics , 2002, Nature.

[124]  Christina Waldsich,et al.  RNA folding in vivo. , 2002, Current opinion in structural biology.

[125]  Linlin Qiu,et al.  Fast chain contraction during protein folding: "foldability" and collapse dynamics. , 2003, Physical review letters.

[126]  Karen L. Buchmueller,et al.  Near native structure in an RNA collapsed state. , 2003, Biochemistry.

[127]  D. Selkoe Folding proteins in fatal ways , 2003, Nature.

[128]  X. Xie,et al.  Protein Conformational Dynamics Probed by Single-Molecule Electron Transfer , 2003, Science.

[129]  Kevin W Plaxco,et al.  Contact order revisited: Influence of protein size on the folding rate , 2003, Protein science : a publication of the Protein Society.

[130]  Tao Pan,et al.  RNA folding: models and perspectives. , 2003, Current opinion in structural biology.

[131]  Dmitry N Ivankov,et al.  Chain length is the main determinant of the folding rate for proteins with three‐state folding kinetics , 2003, Proteins.

[132]  Rhiju Das,et al.  The fastest global events in RNA folding: electrostatic relaxation and tertiary collapse of the Tetrahymena ribozyme. , 2003, Journal of molecular biology.

[133]  Valerie Daggett,et al.  The complete folding pathway of a protein from nanoseconds to microseconds , 2003, Nature.

[134]  Mu Xiao,et al.  Concerted folding of a Candida ribozyme into the catalytically active structure posterior to a rapid RNA compaction. , 2003, Nucleic acids research.

[135]  D. Thirumalai,et al.  Thermal denaturation and folding rates of single domain proteins: size matters , 2003, q-bio/0310020.

[136]  Martin Gruebele,et al.  Folding at the speed limit , 2003, Nature.

[137]  Matthias Rief,et al.  Single-molecule folding. , 2003, Current opinion in structural biology.

[138]  R. Elber,et al.  Kinetics of cytochrome C folding: Atomically detailed simulations , 2003, Proteins.

[139]  E. Rhoades,et al.  Watching proteins fold one molecule at a time , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[140]  Eric Westhof,et al.  Assembly of core helices and rapid tertiary folding of a small bacterial group I ribozyme , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[141]  J. Onuchic,et al.  Theory of Protein Folding This Review Comes from a Themed Issue on Folding and Binding Edited Basic Concepts Perfect Funnel Landscapes and Common Features of Folding Mechanisms , 2022 .

[142]  Compaction of a bacterial group I ribozyme coincides with the assembly of core helices. , 2004, Biochemistry.

[143]  M. Gruebele,et al.  Heterogeneous folding of the trpzip hairpin: full atom simulation and experiment. , 2004, Journal of molecular biology.

[144]  Sebastian Doniach,et al.  Principles of RNA compaction: insights from the equilibrium folding pathway of the P4-P6 RNA domain in monovalent cations. , 2004, Journal of molecular biology.

[145]  A. Finkelstein,et al.  Prediction of protein folding rates from the amino acid sequence-predicted secondary structure , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[146]  K. Weeks,et al.  Structural basis for the self-chaperoning function of an RNA collapsed state. , 2004, Biochemistry.

[147]  Cecilia Clementi,et al.  Quantifying the roughness on the free energy landscape: entropic bottlenecks and protein folding rates. , 2004, Journal of the American Chemical Society.

[148]  Nam-Kyung Lee,et al.  Folding of the Tetrahymena ribozyme by polyamines: importance of counterion valence and size. , 2004, Journal of molecular biology.

[149]  Changbong Hyeon,et al.  Extracting stacking interaction parameters for RNA from the data set of native structures. , 2005, Journal of molecular biology.

[150]  D. Thirumalai,et al.  Probing the "annealing" mechanism of GroEL minichaperone using molecular dynamics simulations. , 2005, Journal of molecular biology.

[151]  Kevin M Weeks,et al.  RNA SHAPE chemistry reveals nonhierarchical interactions dominate equilibrium structural transitions in tRNA(Asp) transcripts. , 2005, Journal of the American Chemical Society.

[152]  D. Thirumalai,et al.  Counterion charge density determines the position and plasticity of RNA folding transition states. , 2006, Journal of molecular biology.

[153]  How do proteins fold and why , 2007 .