Abstract
Understanding protein folding rate is the primary key to unlock the fundamental physics underlying protein structure and its folding mechanism. Especially, the temperature dependence of the folding rate remains unsolved in the literature. Starting from the assumption that protein folding is an event of quantum transition between molecular conformations, we calculated the folding rate for all two-state proteins in a database and studied their temperature dependencies. The non-Arrhenius temperature relation for 16 proteins, whose experimental data had previously been available, was successfully interpreted by comparing the Arrhenius plot with the first-principle calculation. A statistical formula for the prediction of two-state protein folding rate was proposed based on quantum folding theory. The statistical comparisons of the folding rates for 65 two-state proteins were carried out, and the theoretical vs. experimental correlation coefficient was 0.73. Moreover, the maximum and the minimum folding rates given by the theory were consistent with the experimental results.
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Anfinsen CB, Haber E, Sela M, White FH Jr. The kinetics of formation of native ribonuclease during oxidation of the reduced polypeptide chain. Proc Natl Acad Sci USA, 1961, 47: 1309–1314
Anfinsen CB. Principles that govern the folding of protein chains. Science, 1973, 181: 223–230
Levinthal C. Are there pathways for protein folding? J Chim Phys Chim Biol, 1968, 65: 44–45
Qiu L, Pabit SA, Roitberg AE, Hagen SJ. Smaller and faster: the 20 residue Trp-cage protein folds in 4 μs. J Am Chem Soc, 2002, 124: 12952–12953
Kubelka J, Hofrichter J, Eaton WA. The protein folding ‘speed limit’. Curr Opin Struct Biol, 2004, 14: 76–88
Mayor U, Johnson CM, Daggett V, Fersht AR. Protein folding and unfolding in microseconds to nanoseconds by experiment and simulation. Proc Natl Acad Sci USA, 2000, 97: 13518–13522
Reader JS, Van Nuland NA, Thompson GS, Ferguson SJ, Dobson CM, Radford SE. A partially folded intermediate species of the beta-sheet protein apo-pseudoazurin is trapped during proline-limited folding. Protein Sci, 2001, 10: 1216–1224
Phillips DC. The three-dimensional structure of an enzyme molecule. Sci Am, 1966, 215: 78–90
Fersht AR. Nucleation mechanisms in protein folding. Curr Opin Struct Biol, 1997, 7: 3–9
Leopold PE, Montal M, Onuchic JN. Protein folding funnels: a kinetic approach to the sequence-structure relationship. Proc Natl Acad Sci USA, 1992, 89: 8721–8725
Wolynes PG, Onuchic JN, Thirumalai D. Navigating the folding routes. Science, 1995, 267:1619–1620
Dill KA, Chan HS. From levinthal to pathways to funnels. Nat Struct Biol, 1997, 4: 10–19
Wolynes PG. Folding funnels and energy landscapes of larger proteins within the capillarity approximation. Proc Natl Acad Sci USA, 1997, 94: 6170–6175
Bicout DJ, Szabo A. Entropic barriers, transition states, funnels, and exponential protein folding kinetics: A simple model. Protein Sci, 2000, 9: 452–465
Plaxco KW, Simons KT, Baker D. Contact order, transition state placement and the refolding rates of single domain proteins. J Mol Biol, 1998, 227: 985–994
Baker D. A surprising simplicity to protein folding. Nature, 2000, 405: 39–42
Ivankov DN, Finkelstein AV. Prediction of protein folding rates from the amino acid sequence-predicted secondary structure. Proc Natl Acad Sci USA, 2004, 101: 8942–8944
Ouyang Z, Liang J. Predicting protein folding rates from geometric contact and amino acid sequence. Protein Sci, 2008, 17:1256–1263
Segal MR. A novel topology for representing protein folds. Protein Sci, 2009, 18: 686–693
Chang L, Wang J, Wang W. Composition-based effective chain length for prediction of protein folding rates. Phys Rev E Stat Nonlin Soft Matter Phys, 2010, 82(5 Pt 1): 051930
Chiti F, Taddei N, White PM, Bucciantini M, Magherini F, Stefani M, Dobson CM. Mutational analysis of acylphosphatase suggests the importance of topology and contact order in protein folding. Nat Struct Biol, 1999, 6: 1005–1009
Muñoz V, Eaton WA. A simple model for calculating the kinetics of protein folding from three-dimensional structures. Proc Natl Acad Sci USA, 1999, 96: 11311–11316
Ivankov DN, Finkelstein AV. Theoretical study of a landscape of protein folding-unfolding pathways. Folding rates at midtransition. Biochemistry, 2001, 40: 9957–9961
Alm E, Morozov AV, Kortemme T, Baker D. Simple physical models connect theory and experiment in protein folding kinetics. J Mol Biol, 2002, 322: 463–476
Garbuzynskiy SO, Finkelstein AV, Galzitskaya OV. Outlining folding nuclei in globular proteins. J Mol Biol, 2004, 336: 509–525
Ma BG, Guo JX, Zhang HY. Direct correlation between proteins’ folding rates and their amino acid compositions: an ab initio folding rate prediction. Proteins, 2006, 65: 362–372
Gromiha MM, Thangakani AM, Selvaraj S. FOLD-RATE: prediction of protein folding rates from amino acid sequence. Nucleic Acids Res, 2006, 34 (web server issue): W70–74
Cheng X, Xiao X, Wu ZC, Wang P, Lin WZ. Swfoldrate: predicting protein folding rates from amino acid sequence with sliding window method. Proteins, 2013, 81: 140–148
Ivankov DN, Garbuzynskiy SO, Alm E, Plaxco KW, Baker D, Finkelstein AV. Contact order revisited: influence of protein size on the folding rate. Protein Sci, 2003, 12: 2057–2062
Bryngelson JD, Onuchic JN, Socci ND, Wolynes PG. Funnels, pathways, and the energy landscape of protein folding: a synthesis. Proteins, 1995, 21: 167–195
Chan HS, Dill KA. Protein folding in the landscape perspective: chevron plots and non-Arrhenius kinetics. Proteins, 1998, 30: 2–23
Akmal A, Munoz V. The nature of the free energy barriers to two-state folding. Proteins, 2004, 57: 142–152
Ghosh K, Ozkan B, Dill KA. The ultimate speed limit to protein folding is conformational searching. J Am Chem Soc, 2007, 129: 11920–11927
Yang WY, Gruebele M. Rate-temperature relationship in λ-repressor fragment λ6-85 folding. Biochemistry, 2004, 43: 13018–13025
Zhu Y, Alonso DO, Maki K, Huang CY, Lahr SJ, Daggett V, Roder H, DeGrado WF, Gai F. Ultrafast folding of α3D: a de novo designed three-helix bundle protein. Proc Natl Acad Sci USA, 2003, 100: 15486–15491
Luo LF. Quantum theory on protein folding. Sci China Phys Mech Astron, 2014, 57: 458–468
Chakraborty A, Truhlar DG. Quantum mechanical reaction rate constants by vibrational configuration interaction: the OH+H2->H2O+H reaction as a function of temperature. Proc Natl Acad Sci USA, 2005, 102: 6744–6749
Luo LF. Conformation transitional rate in protein folding. Int J Quant Chem, 1995, 54: 243–247
Luo LF. Protein folding as a quantum transition between conformational states. Front Phys, 2011, 6: 133–140
Zhang Y, Luo LF. The dynamical contact order: protein folding rate parameters based on quantum conformational transitions. Sci China Life Sci, 2011, 54: 386–392
Luo LF. Protein photo-folding and quantum folding theory. Sci China Life Sci, 2012, 55: 533–541
Garbuzynskiy SO, Ivankov DN, Bogatyreva NS, Finkelstein AV. Golden triangle for folding rates of globular proteins. Proc Natl Acad Sci USA, 2013, 110: 147–150
Bernstein FC, Koetzle TF, Williams GJB, Meyer EF Jr, Brice MD, Rodgers JR, Kennard O, Shimanouchi T, Tasumi M. The protein data bank. A computer-based archival file for macromolecular structures. Eur J Biochem, 1977, 80: 319–324
Kabsch W, Sander C. Dictionary of protein secondary structure: pattern recognition of hydrogen-bonded and geometrical features. Biopolymers, 1983, 22: 2577–2637
Dimitriadis G, Drysdale A, Myers JK, Arora P, Radford SE, Oas TG, Smith DA. Microsecond folding dynamics of the F13W G29A mutant of the B domain of staphylococcal protein A by laser-induced temperature jump. Proc Natl Acad Sci USA, 2004, 101: 3809–3814
Kuhlman B, Luisi DL, Evans PA, Raleigh DP. Global analysis of the effects of temperature and denaturant on the folding and unfolding kinetics of the N-terminal domain of the protein L9. J Mol Biol, 1998, 284: 1661–1670
Nguyen H, Jager M, Moretto A, Gruebele M, Kelly JW. Tuning the free-energy landscape of a WW domain by temperature, mutation, and truncation. Proc Natl Acad Sci USA, 2003, 100: 3948–2953
Manyusa S, Whitford D. Defining folding and unfolding reactions of apocytochrome b5 using equilibrium and kinetic fluorescence measurements. Biochemistry, 1999, 38: 9533–9540
Bunagan MR, Yang X, Saven JG, Gai F. Ultrafast folding of a computationally designed Trp-cage mutant: Trp2-cage. J Phys Chem B, 2006, 110: 3759–3763
Jäger M, Nguyen H, Crane JC, Kelly JW, Gruebele M. The folding mechanism of a beta-sheet: the WW domain. J Mol Biol, 2001, 311: 373–393
Wang T, Zhu YJ, Gai F. Folding of a three-helix bundle at the folding speed limit. J Phys Chem B, 2004, 108: 3694–3697
Spector S, Raleigh DP. Submillisecond folding of the peripheral subunit-binding domain. J Mol Biol, 1999, 293: 763–768
Richardson JS. The anatomy and taxonomy of protein structure. Adv Protein Chem, 1981, 34: 167–339
Liu F, Gruebele M. Tuning λ6-85 towards downhill folding at its melting temperature. J Mol Biol, 2007, 370: 574–584
Luo LF, Lu J. Temperature dependence of protein folding deduced from quantum transition. arXiv: 1102.3748 [q-bio.BM], 2011, Available from: http://arxiv.org/abs/1102.3748
Ghosh K, Dill K. Cellular proteomes have broad distributions of protein stability. Biophys J, 2010, 99: 3996–4002
Zhao JD, Luo LF. A theory of quantum conformation transition for tubulin vibration. Biosystems, in press
Kostrowicki J, Scheraga HA. Application of the diffusion equation method for global optimization to oligopeptides. J Phys Chem, 1992, 96: 7442–7449
Wang M, Tang Y, Sato S, Vugmeyster L, McKnight CJ, Raleigh DP. Dynamic NMR line-shape analysis demonstrates that the villin headpiece subdomain folds on the microsecond time scale. J Am Chem Soc, 2003, 125: 6032–6033
Lindorff-Larsen K, Piana S, Dror RO, Shaw DE. How fast-folding proteins fold. Science, 2011, 334: 517–520
Kubelka J, Chiu TK, Davies DR, Eaton WA, Hofrichter J. Sub-microsecond protein folding. J Mol Biol, 2006, 359: 546–553
Horng JC, Moroz V, Raleigh DP. Rapid cooperative two-state folding of a miniature α-β protein and design of a thermostable variant. J Mol Biol, 2003, 326: 1261–1270
Gillespie B, Vu DM, Shah PS, Marshall SA, Dyer RB, Mayo SL, Plaxco KW. NMR and temperature-jump measurements of de novo designed proteins demonstrate rapid folding in the absence of explicit selection for kinetics. J Mol Biol, 2003, 330: 813–819
Neuweiler H, Sharpe TD, Rutherford TJ, Johnson CM, Allen MD, Ferguson N, Fersht AR. The folding mechanism of BBL: plasticity of transition-state structure observed within an ultrafast folding protein family. J Mol Biol, 2009, 390: 1060–1073
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Lv, J., Luo, L. Statistical analyses of protein folding rates from the view of quantum transition. Sci. China Life Sci. 57, 1197–1212 (2014). https://doi.org/10.1007/s11427-014-4728-9
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DOI: https://doi.org/10.1007/s11427-014-4728-9