Physics of protein folding

Abstract Protein physics is grounded on three fundamental experimental facts: protein, this long heteropolymer, has a well defined compact three-dimensional structure; this structure can spontaneously arise from the unfolded protein chain in appropriate environment; and this structure is separated from the unfolded state of the chain by the “all-or-none” phase transition, which ensures robustness of protein structure and therefore of its action. The aim of this review is to consider modern understanding of physical principles of self-organization of protein structures and to overview such important features of this process, as finding out the unique protein structure among zillions alternatives, nucleation of the folding process and metastable folding intermediates. Towards this end we will consider the main experimental facts and simple, mostly phenomenological theoretical models. We will concentrate on relatively small (single-domain) water-soluble globular proteins (whose structure and especially folding are much better studied and understood than those of large or membrane and fibrous proteins) and consider kinetic and structural aspects of transition of initially unfolded protein chains into their final solid (“native”) 3D structures.

[1]  O. Ptitsyn,et al.  Evidence for a molten globule state as a general intermediate in protein folding , 1990, FEBS letters.

[2]  O. Ptitsyn,et al.  Protein folding and protein evolution: common folding nucleus in different subfamilies of c-type cytochromes? , 1998, Journal of molecular biology.

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

[4]  Terrence G. Oas,et al.  The energy landscape of a fast-folding protein mapped by Ala→Gly Substitutions , 1997, Nature Structural Biology.

[5]  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.

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

[7]  A Caflisch,et al.  Acid and thermal denaturation of barnase investigated by molecular dynamics simulations. , 1995, Journal of molecular biology.

[8]  Bengt Nölting,et al.  Mechanism of protein folding , 2000, Proteins.

[9]  G. Kramer,et al.  Co-translational folding. , 1999, Current opinion in structural biology.

[10]  Victor Guallar,et al.  Archives of Biochemistry and Biophysics , 1951, Nature.

[11]  Folding nuclei in 3D protein structures. , 1999, Pacific Symposium on Biocomputing. Pacific Symposium on Biocomputing.

[12]  E. Shakhnovich,et al.  Formation of unique structure in polypeptide chains. Theoretical investigation with the aid of a replica approach. , 1989, Biophysical chemistry.

[13]  P. Wolynes,et al.  Optimal protein-folding codes from spin-glass theory. , 1992, Proceedings of the National Academy of Sciences of the United States of America.

[14]  O. Ptitsyn,et al.  Physical nature of the phase transition in globular proteins , 1986, FEBS letters.

[15]  V. Muñoz,et al.  Folding dynamics and mechanism of β-hairpin formation , 1997, Nature.

[16]  K. Dill,et al.  Protein folding in the landscape perspective: Chevron plots and non‐arrhenius kinetics , 1998, Proteins.

[17]  L Serrano,et al.  Structure of the transition state in the folding process of human procarboxypeptidase A2 activation domain. , 1998, Journal of molecular biology.

[18]  S. Segawa,et al.  Characterization of the transition state of Lysozyme unfolding. I. Effect of protein‐solvent interactions on the transition state , 1984, Biopolymers.

[19]  A. Fersht,et al.  Mapping the transition state and pathway of protein folding by protein engineering , 1989, Nature.

[20]  H. Dyson,et al.  Insights into protein folding from NMR. , 1996, Annual review of physical chemistry (Print).

[21]  J. Onuchic,et al.  How native-state topology affects the folding of dihydrofolate reductase and interleukin-1beta. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[22]  B. Zimm,et al.  Theory of the Phase Transition between Helix and Random Coil in Polypeptide Chains , 1959 .

[23]  O. Ptitsyn,et al.  Molten globule and protein folding. , 1995, Advances in protein chemistry.

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

[25]  E I Shakhnovich,et al.  Theory of cooperative transitions in protein molecules. I. Why denaturation of globular protein is a first‐order phase transition , 1989, Biopolymers.

[26]  A V Finkelstein,et al.  Boltzmann-like statistics of protein architectures. Origins and consequences. , 1995, Sub-cellular biochemistry.

[27]  B. Derrida Random-energy model: An exactly solvable model of disordered systems , 1981 .

[28]  K. Wüthrich NMR of proteins and nucleic acids , 1988 .

[29]  R. B. Merrifield,et al.  The total synthesis of an enzyme with ribonuclease A activity. , 1969, Journal of the American Chemical Society.

[30]  A. Fersht,et al.  Protein folding and unfolding in microseconds to nanoseconds by experiment and simulation. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[31]  R. Dyer,et al.  Fast events in protein folding: relaxation dynamics and structure of the I form of apomyoglobin. , 1997, Biochemistry.

[32]  O. Ptitsyn,et al.  Non-functional conserved residues in globins and their possible role as a folding nucleus. , 1999, Journal of molecular biology.

[33]  A. Fersht,et al.  Transition-state structure as a unifying basis in protein-folding mechanisms: contact order, chain topology, stability, and the extended nucleus mechanism. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[34]  P. Kraulis A program to produce both detailed and schematic plots of protein structures , 1991 .

[35]  Ken A. Dill,et al.  Conformations and Forces in Protein Folding , 1991 .

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

[37]  O. Ptitsyn,et al.  ‘Molten‐globule“ state accumulates in carbonic anhydrase folding , 1984, FEBS letters.

[38]  O. Ptitsyn,et al.  Further evidence on the equilibrium "pre-molten globule state": four-state guanidinium chloride-induced unfolding of carbonic anhydrase B at low temperature. , 1996, Journal of molecular biology.

[39]  L. Mirny,et al.  Universally conserved positions in protein folds: reading evolutionary signals about stability, folding kinetics and function. , 1999, Journal of molecular biology.

[40]  E. Cota,et al.  The folding nucleus of a fibronectin type III domain is composed of core residues of the immunoglobulin-like fold. , 2001, Journal of molecular biology.

[41]  L. Mirny,et al.  Evolutionary conservation of the folding nucleus. , 2000, Journal of molecular biology.

[42]  O. Ptitsyn Thermodynamic parameters of helix-coil transitions in polypeptide chains , 1972, Pure and applied chemistry. Chimie pure et appliquee.

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

[44]  Kevin W Plaxco,et al.  Comparison of the folding processes of distantly related proteins. Importance of hydrophobic content in folding. , 2003, Journal of molecular biology.

[45]  J. Onuchic,et al.  Investigation of routes and funnels in protein folding by free energy functional methods. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[46]  K. Binder,et al.  Spin glasses: Experimental facts, theoretical concepts, and open questions , 1986 .

[47]  L Serrano,et al.  Protein design based on folding models. , 2001, Current opinion in structural biology.

[48]  N. Go,et al.  Studies on protein folding, unfolding and fluctuations by computer simulation. I. The effect of specific amino acid sequence represented by specific inter-unit interactions. , 2009 .

[49]  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.

[50]  Mohamed A. Marahiel,et al.  Conservation of rapid two-state folding in mesophilic, thermophilic and hyperthermophilic cold shock proteins , 1998, Nature Structural Biology.

[51]  O. Ptitsyn,et al.  "Partly folded" state, a new equilibrium state of protein molecules: four-state guanidinium chloride-induced unfolding of beta-lactamase at low temperature. , 1994, Biochemistry.

[52]  V. Muñoz,et al.  Kinetics and Dynamics of Loops, α-Helices, β-Hairpins, and Fast-Folding Proteins , 1999 .

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

[54]  A. Finkelstein,et al.  Rate of β‐structure formation in polypeptides , 1991 .

[55]  G Vriend,et al.  WHAT IF: a molecular modeling and drug design program. , 1990, Journal of molecular graphics.

[56]  E. V. Makeyev,et al.  Folding of firefly luciferase during translation in a cell‐free system. , 1994, The EMBO journal.

[57]  D. Baker,et al.  Critical role of β-hairpin formation in protein G folding , 2000, Nature Structural Biology.

[58]  E. Shakhnovich,et al.  Conserved residues and the mechanism of protein folding , 1996, Nature.

[59]  Karsten Kristiansen,et al.  The formation of a native-like structure containing eight conserved hydrophobic residues is rate limiting in two-state protein folding of ACBP , 1999, Nature Structural Biology.

[60]  Valerie Daggett,et al.  The present view of the mechanism of protein folding , 2003, Nature Reviews Molecular Cell Biology.

[61]  Christopher M. Dobson,et al.  Mutational analysis of acylphosphatase suggests the importance of topology and contact order in protein folding , 1999, Nature Structural Biology.

[62]  P E Wright,et al.  Conformation of peptide fragments of proteins in aqueous solution: implications for initiation of protein folding. , 1988, Biochemistry.

[63]  G. Schwarz ON THE KINETICS OF THE HELIX-COIL TRANSITION OF POLYPEPTIDES IN SOLUTION. , 1965, Journal of molecular biology.

[64]  V Muñoz,et al.  Folding dynamics and mechanism of beta-hairpin formation. , 1997, Nature.

[65]  A. V. Finkelstein,et al.  Theory of cooperative transitions in protein molecules. II. Phase diagram for a protein molecule in solution , 1989, Biopolymers.

[66]  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.

[67]  E. Alm,et al.  Prediction of protein-folding mechanisms from free-energy landscapes derived from native structures. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[68]  N. Go Theory of reversible denaturation of globular proteins. , 2009, International journal of peptide and protein research.

[69]  M Levitt,et al.  Hierarchy of structure loss in MD simulations of src SH3 domain unfolding. , 1999, Journal of molecular biology.

[70]  A. Fersht,et al.  Movement of the position of the transition state in protein folding. , 1995, Biochemistry.

[71]  T. Kiefhaber,et al.  Origin of unusual phi-values in protein folding: evidence against specific nucleation sites. , 2003, Journal of molecular biology.

[72]  J. Hofrichter,et al.  Laser temperature jump study of the helix<==>coil kinetics of an alanine peptide interpreted with a 'kinetic zipper' model. , 1997, Biochemistry.

[73]  R. Zana On the rate‐determining step for helix propagation in the helix–coil transition of polypeptides in solution , 1975 .

[74]  Ralph G. Pearson,et al.  Kinetics and mechanism , 1961 .

[75]  M. Perutz,et al.  Structure of Hæmoglobin: A Three-Dimensional Fourier Synthesis at 5.5-Å. Resolution, Obtained by X-Ray Analysis , 1960, Nature.

[76]  T. Creighton,et al.  Circular and circularly permuted forms of bovine pancreatic trypsin inhibitor. , 1983, Journal of molecular biology.

[77]  V. Daggett,et al.  Mapping the interactions present in the transition state for unfolding/folding of FKBP12. , 1999, Journal of molecular biology.

[78]  F. Blanco,et al.  NMR evidence of a short linear peptide that folds into a .beta.-hairpin in aqueous solution , 1993 .

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

[80]  S. Takada,et al.  Roles of native topology and chain-length scaling in protein folding: a simulation study with a Go-like model. , 2001, Journal of molecular biology.

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

[82]  P. Privalov,et al.  A thermodynamic approach to the problem of stabilization of globular protein structure: a calorimetric study. , 1974, Journal of molecular biology.

[83]  D. Phillips,et al.  The three-dimensional structure of an enzyme molecule. , 1966, Scientific American.

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

[85]  A. Ubbelohde,et al.  Melting and crystal structure , 1940, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[86]  E. Shakhnovich,et al.  Implications of thermodynamics of protein folding for evolution of primary sequences , 1990, Nature.

[87]  S. Jackson,et al.  How do small single-domain proteins fold? , 1998, Folding & design.

[88]  H. Orland,et al.  Mean-Field Model for Protein Folding , 1988 .

[89]  D T Jones,et al.  Protein secondary structure prediction based on position-specific scoring matrices. , 1999, Journal of molecular biology.

[90]  A V Finkelstein,et al.  Cunning simplicity of protein folding landscapes. , 2001, Protein engineering.

[91]  A. Li,et al.  Identification and characterization of the unfolding transition state of chymotrypsin inhibitor 2 by molecular dynamics simulations. , 1996, Journal of molecular biology.

[92]  R. Dyer,et al.  The core of apomyoglobin E-form folds at the diffusion limit , 1998, Nature Structural Biology.

[93]  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.

[94]  T. Creighton,et al.  Protein Folding , 1992 .

[95]  A. Fersht,et al.  Using flexible loop mimetics to extend Φ-value analysis to secondary structure interactions , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[96]  M Karplus,et al.  "New view" of protein folding reconciled with the old through multiple unfolding simulations. , 1997, Science.

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

[98]  Jie Liang,et al.  Are residues in a protein folding nucleus evolutionarily conserved? , 2003, Journal of molecular biology.

[99]  J. Hermans,et al.  Beta poly(L-lysine): a model system for biological self-assembly. , 1974, Journal of molecular biology.

[100]  A. Finkelstein,et al.  Outlining folding nuclei in globular proteins. , 2004, Journal of molecular biology.

[101]  Z. Zeng,et al.  A Simple Parameter Relating Sequences with Folding Rates of Small α Helical Proteins , 2003 .

[102]  G. Rose,et al.  Is protein folding hierarchic? I. Local structure and peptide folding. , 1999, Trends in biochemical sciences.

[103]  David Baker,et al.  Experiment and theory highlight role of native state topology in SH3 folding , 1999, Nature Structural Biology.

[104]  A. Fersht,et al.  Characterizing transition states in protein folding: an essential step in the puzzle. , 1995, Current opinion in structural biology.

[105]  R. Dyer,et al.  Fast events in protein folding: relaxation dynamics of secondary and tertiary structure in native apomyoglobin. , 1997, Proceedings of the National Academy of Sciences of the United States of America.

[106]  D Baker,et al.  Critical role of beta-hairpin formation in protein G folding. , 2000, Nature structural biology.

[107]  K. Kuwajima,et al.  Equilibrium and kinetics of the thermal unfolding of alpha-lactalbumin. The relation to its folding mechanism. , 1978, Biophysical chemistry.

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

[109]  D Baker,et al.  Mechanisms of protein folding. , 2001, Current opinion in structural biology.

[110]  P. Privalov Stability of proteins. Proteins which do not present a single cooperative system. , 1982, Advances in protein chemistry.

[111]  R. Dyer,et al.  Fast events in protein folding: helix melting and formation in a small peptide. , 1996, Biochemistry.

[112]  Christopher M. Dobson,et al.  Protein Folding: Solid evidence for molten globules , 1994, Current Biology.

[113]  Oxana V. Galzitskaya,et al.  α-Helix and β-Hairpin Folding from Experiment, Analytical Theory and Molecular Dynamics Simulations , 2002 .

[114]  O. Ptitsyn,et al.  [Stages in the mechanism of self-organization of protein molecules]. , 1973, Doklady Akademii nauk SSSR.

[115]  L. Serrano,et al.  A short linear peptide that folds into a native stable β-hairpin in aqueous solution , 1994, Nature Structural Biology.

[116]  [Physical reasons for rapid self-organization of a stable spatial protein structure: solution of the Levinthal paradox]. , 1997 .

[117]  T. Creighton,et al.  Folding pathway of a circular form of bovine pancreatic trypsin inhibitor. , 1984, Journal of Molecular Biology.

[118]  Ronald W. Barrett,et al.  Small Peptides as Potent Mimetics of the Protein Hormone Erythropoietin , 1996, Science.

[119]  P E Wright,et al.  Folding of immunogenic peptide fragments of proteins in water solution. II. The nascent helix. , 1988, Journal of molecular biology.

[120]  S. Takada Go-ing for the prediction of protein folding mechanisms. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[121]  A. Finkelstein,et al.  A theoretical search for folding/unfolding nuclei in three-dimensional protein structures. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[122]  S Sugai,et al.  Rapid formation of secondary structure framework in protein folding studied by stopped‐flow circular dichroism , 1987, FEBS letters.

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

[124]  Rate of protein folding near the point of thermodynamic equilibrium between the coil and the most stable chain fold: Influence of chain knotting on the rate of folding , 1998 .

[125]  C. Anfinsen,et al.  The kinetics of formation of native ribonuclease during oxidation of the reduced polypeptide chain. , 1961, Proceedings of the National Academy of Sciences of the United States of America.

[126]  O. Ptitsyn,et al.  Alpha-Lactalbumin: compact state with fluctuating tertiary structure? , 1981, FEBS letters.

[127]  Wallace Wurth,et al.  Fundamentals of Biochemistry: , 1936, Nature.

[128]  David Baker,et al.  Important role of hydrogen bonds in the structurally polarized transition state for folding of the src SH3 domain , 1998, Nature Structural &Molecular Biology.

[129]  Luis Serrano,et al.  The folding transition state between SH3 domains is conformationally restricted and evolutionarily conserved , 1999, Nature Structural Biology.

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

[131]  M Karplus,et al.  The fundamentals of protein folding: bringing together theory and experiment. , 1999, Current opinion in structural biology.

[132]  D J Bicout,et al.  Entropic barriers, transition states, funnels, and exponential protein folding kinetics: A simple model , 2008, Protein science : a publication of the Protein Society.

[133]  Igor N Berezovsky,et al.  Loop Fold Structure of Proteins: Resolution of Levinthal's Paradox , 2002, Journal of biomolecular structure & dynamics.

[134]  A. Fersht,et al.  The structure of the transition state for folding of chymotrypsin inhibitor 2 analysed by protein engineering methods: evidence for a nucleation-condensation mechanism for protein folding. , 1995, Journal of molecular biology.

[135]  G J Williams,et al.  The Protein Data Bank: a computer-based archival file for macromolecular structures. , 1977, Journal of molecular biology.

[136]  O. V. Galzitskaya,et al.  Folding Nuclei in Proteins , 2001, Molecular Biology.

[137]  A. Fersht,et al.  Structure of the transition state for folding of a protein derived from experiment and simulation. , 1996, Journal of molecular biology.

[138]  Sensitivity of the Folding Pathway to the Details of Amino Acid Sequence , 2002, Molecular Biology.

[139]  E I Shakhnovich,et al.  Specific nucleus as the transition state for protein folding: evidence from the lattice model. , 1994, Biochemistry.

[140]  G J Williams,et al.  The Protein Data Bank: a computer-based archival file for macromolecular structures. , 1978, Archives of biochemistry and biophysics.

[141]  A. Fersht,et al.  The folding of an enzyme. I. Theory of protein engineering analysis of stability and pathway of protein folding. , 1992, Journal of molecular biology.

[142]  Stefan M. Larson,et al.  Evolutionary conservation in protein folding kinetics. , 2000, Journal of molecular biology.

[143]  O. Ptitsyn,et al.  An early intermediate of refolding α‐lactalbumin forms within 20 ms , 1987 .

[144]  Andreas Matouschek,et al.  Transient folding intermediates characterized by protein engineering , 1990, Nature.

[145]  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.

[146]  J. Kendrew,et al.  A Three-Dimensional Model of the Myoglobin Molecule Obtained by X-Ray Analysis , 1958, Nature.

[147]  H. Okayama,et al.  Primary structure of rat chromogranin A and distribution of its mRNA , 1988, FEBS letters.

[148]  E I Shakhnovich,et al.  Is burst hydrophobic collapse necessary for protein folding? , 1995, Biochemistry.

[149]  F M Poulsen,et al.  Folding of a four-helix bundle: studies of acyl-coenzyme A binding protein. , 1995, Biochemistry.

[150]  Benjamin A. Shoemaker,et al.  Exploring structures in protein folding funnels with free energy functionals: the transition state ensemble. , 1999, Journal of molecular biology.

[151]  N. C. Price,et al.  Conformational studies on plasminogen activator inhibitor (PAI-1) in active, latent, substrate, and cleaved forms. , 1995, Biochemistry.

[152]  N. Go Theoretical studies of protein folding. , 1983, Annual review of biophysics and bioengineering.

[153]  Serrano,et al.  Structure of the transition state for folding of the 129 aa protein CheY resembles that of a smaller protein, CI-2. , 1995, Folding & design.

[154]  M. Karplus,et al.  Kinetics of protein folding. A lattice model study of the requirements for folding to the native state. , 1994, Journal of molecular biology.

[155]  David Baker,et al.  Simple physical models connect theory and experiment in protein folding kinetics. , 2002, Journal of molecular biology.

[156]  V. Muñoz,et al.  A simple model for calculating the kinetics of protein folding from three-dimensional structures. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[157]  P. Privalov Stability of proteins: small globular proteins. , 1979, Advances in protein chemistry.

[158]  Benjamin A. Shoemaker,et al.  Exploring structures in protein folding funnels with free energy functionals: the denatured ensemble. , 1999, Journal of molecular biology.

[159]  C. Levinthal Are there pathways for protein folding , 1968 .

[160]  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.

[161]  M. Proctor,et al.  Structural changes in the transition state of protein folding: alternative interpretations of curved chevron plots. , 1999, Biochemistry.

[162]  O. Ptitsyn,et al.  α‐lactalbumin: compact state with fluctuating tertiary structure? , 1981, FEBS letters.

[163]  Matthews Cr Effect of point mutations on the folding of globular proteins. , 1987 .

[164]  D. Goldenberg,et al.  Mutational analysis of a protein-folding pathway , 1989, Nature.

[165]  A V Finkelstein,et al.  Can protein unfolding simulate protein folding? , 1997, Protein engineering.

[166]  Effect of point mutations on the folding of globular proteins. , 1987, Methods in enzymology.

[167]  F. Hartl,et al.  Principles of protein folding in the cellular environment. , 1999, Current opinion in structural biology.

[168]  Eugene I. Shakhnovich,et al.  Free energy landscape for protein folding kinetics: Intermediates, traps, and multiple pathways in theory and lattice model simulations , 1994 .