Skip to main content
Biophysical Journal logoLink to Biophysical Journal
. 2002 Jan;82(1 Pt 1):458–463. doi: 10.1016/S0006-3495(02)75410-6

Folding rate prediction using total contact distance.

Hongyi Zhou 1, Yaoqi Zhou 1
PMCID: PMC1302485  PMID: 11751332

Abstract

Linear regression analysis found that either contact order (CO) or long-range order (LRO) parameter has a significant correlation with the logarithms of folding rates. This suggests that sequence separation per contact and total number of contacts are both important in determining the rate of folding. Here, the two factors are incorporated into a new parameter, total contact distance (TCD). Using a database of 28 two-state or weakly three-state folding proteins, TCD is found to be the most accurate among the three parameters (CO, LRO, and TCD) in terms of correlation and prediction. It provides even more accurate prediction than the best neural network results with two descriptors (contact order and stability per residue). The improvement is achieved in all three-structural classes (all alpha, beta, and mixed). The accuracy of total contact distance in predicting folding rates is essentially unchanged if "short"-ranged contacts (absolute value of i - j < or = 14) are not included in calculation. Thus, only long-range contacts with a sequence separation of more than 14 residues are important in determining the rate of folding. This is consistent with the results from the long-range order parameter. One of the significant outliers in prediction is found to be associated with the only protein in the database that involves nonlocal disulfide bonds. Removing the protein leads to a correlation coefficient of 0.89 between experimental observed and predicted folding rates in jackknife cross validation. The corresponding values for CO and LRO are 0.71 and 0.80, respectively.

Full Text

The Full Text of this article is available as a PDF (90.8 KB).

Selected References

These references are in PubMed. This may not be the complete list of references from this article.

  1. Alm E., Baker D. Prediction of protein-folding mechanisms from free-energy landscapes derived from native structures. Proc Natl Acad Sci U S A. 1999 Sep 28;96(20):11305–11310. doi: 10.1073/pnas.96.20.11305. [DOI] [PMC free article] [PubMed] [Google Scholar]
  2. Aronsson G., Brorsson A. C., Sahlman L., Jonsson B. H. Remarkably slow folding of a small protein. FEBS Lett. 1997 Jul 14;411(2-3):359–364. doi: 10.1016/s0014-5793(97)00730-8. [DOI] [PubMed] [Google Scholar]
  3. Burton R. E., Huang G. S., Daugherty M. A., Fullbright P. W., Oas T. G. Microsecond protein folding through a compact transition state. J Mol Biol. 1996 Oct 25;263(2):311–322. doi: 10.1006/jmbi.1996.0577. [DOI] [PubMed] [Google Scholar]
  4. Clarke J., Cota E., Fowler S. B., Hamill S. J. Folding studies of immunoglobulin-like beta-sandwich proteins suggest that they share a common folding pathway. Structure. 1999 Sep 15;7(9):1145–1153. doi: 10.1016/s0969-2126(99)80181-6. [DOI] [PubMed] [Google Scholar]
  5. Debe D. A., Goddard W. A., 3rd First principles prediction of protein folding rates. J Mol Biol. 1999 Dec 3;294(3):619–625. doi: 10.1006/jmbi.1999.3278. [DOI] [PubMed] [Google Scholar]
  6. Dinner A. R., Karplus M. The roles of stability and contact order in determining protein folding rates. Nat Struct Biol. 2001 Jan;8(1):21–22. doi: 10.1038/83003. [DOI] [PubMed] [Google Scholar]
  7. Ferguson N., Capaldi A. P., James R., Kleanthous C., Radford S. E. Rapid folding with and without populated intermediates in the homologous four-helix proteins Im7 and Im9. J Mol Biol. 1999 Mar 12;286(5):1597–1608. doi: 10.1006/jmbi.1998.2548. [DOI] [PubMed] [Google Scholar]
  8. Fersht A. R. Transition-state structure as a unifying basis in protein-folding mechanisms: contact order, chain topology, stability, and the extended nucleus mechanism. Proc Natl Acad Sci U S A. 2000 Feb 15;97(4):1525–1529. doi: 10.1073/pnas.97.4.1525. [DOI] [PMC free article] [PubMed] [Google Scholar]
  9. Galzitskaya O. V., Finkelstein A. V. A theoretical search for folding/unfolding nuclei in three-dimensional protein structures. Proc Natl Acad Sci U S A. 1999 Sep 28;96(20):11299–11304. doi: 10.1073/pnas.96.20.11299. [DOI] [PMC free article] [PubMed] [Google Scholar]
  10. Gromiha M. M., Selvaraj S. Comparison between long-range interactions and contact order in determining the folding rate of two-state proteins: application of long-range order to folding rate prediction. J Mol Biol. 2001 Jun 29;310(1):27–32. doi: 10.1006/jmbi.2001.4775. [DOI] [PubMed] [Google Scholar]
  11. Guijarro J. I., Morton C. J., Plaxco K. W., Campbell I. D., Dobson C. M. Folding kinetics of the SH3 domain of PI3 kinase by real-time NMR combined with optical spectroscopy. J Mol Biol. 1998 Feb 27;276(3):657–667. doi: 10.1006/jmbi.1997.1553. [DOI] [PubMed] [Google Scholar]
  12. Jackson S. E. How do small single-domain proteins fold? Fold Des. 1998;3(4):R81–R91. doi: 10.1016/S1359-0278(98)00033-9. [DOI] [PubMed] [Google Scholar]
  13. Khorasanizadeh S., Peters I. D., Butt T. R., Roder H. Folding and stability of a tryptophan-containing mutant of ubiquitin. Biochemistry. 1993 Jul 13;32(27):7054–7063. doi: 10.1021/bi00078a034. [DOI] [PubMed] [Google Scholar]
  14. Kragelund B. B., Højrup P., Jensen M. S., Schjerling C. K., Juul E., Knudsen J., Poulsen F. M. Fast and one-step folding of closely and distantly related homologous proteins of a four-helix bundle family. J Mol Biol. 1996 Feb 16;256(1):187–200. doi: 10.1006/jmbi.1996.0076. [DOI] [PubMed] [Google Scholar]
  15. Kuhlman B., Luisi D. L., Evans P. A., Raleigh D. P. 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 Dec 18;284(5):1661–1670. doi: 10.1006/jmbi.1998.2246. [DOI] [PubMed] [Google Scholar]
  16. Ladurner A. G., Fersht A. R. Glutamine, alanine or glycine repeats inserted into the loop of a protein have minimal effects on stability and folding rates. J Mol Biol. 1997 Oct 17;273(1):330–337. doi: 10.1006/jmbi.1997.1304. [DOI] [PubMed] [Google Scholar]
  17. Muñoz V., Eaton W. A. A simple model for calculating the kinetics of protein folding from three-dimensional structures. Proc Natl Acad Sci U S A. 1999 Sep 28;96(20):11311–11316. doi: 10.1073/pnas.96.20.11311. [DOI] [PMC free article] [PubMed] [Google Scholar]
  18. Otzen D. E., Kristensen O., Proctor M., Oliveberg M. Structural changes in the transition state of protein folding: alternative interpretations of curved chevron plots. Biochemistry. 1999 May 18;38(20):6499–6511. doi: 10.1021/bi982819j. [DOI] [PubMed] [Google Scholar]
  19. Plaxco K. W., Simons K. T., Baker D. Contact order, transition state placement and the refolding rates of single domain proteins. J Mol Biol. 1998 Apr 10;277(4):985–994. doi: 10.1006/jmbi.1998.1645. [DOI] [PubMed] [Google Scholar]
  20. Plaxco K. W., Simons K. T., Ruczinski I., Baker D. Topology, stability, sequence, and length: defining the determinants of two-state protein folding kinetics. Biochemistry. 2000 Sep 19;39(37):11177–11183. doi: 10.1021/bi000200n. [DOI] [PubMed] [Google Scholar]
  21. Plaxco K. W., Spitzfaden C., Campbell I. D., Dobson C. M. A comparison of the folding kinetics and thermodynamics of two homologous fibronectin type III modules. J Mol Biol. 1997 Aug 1;270(5):763–770. doi: 10.1006/jmbi.1997.1148. [DOI] [PubMed] [Google Scholar]
  22. Scalley M. L., Baker D. Protein folding kinetics exhibit an Arrhenius temperature dependence when corrected for the temperature dependence of protein stability. Proc Natl Acad Sci U S A. 1997 Sep 30;94(20):10636–10640. doi: 10.1073/pnas.94.20.10636. [DOI] [PMC free article] [PubMed] [Google Scholar]
  23. Schindler T., Herrler M., Marahiel M. A., Schmid F. X. Extremely rapid protein folding in the absence of intermediates. Nat Struct Biol. 1995 Aug;2(8):663–673. doi: 10.1038/nsb0895-663. [DOI] [PubMed] [Google Scholar]
  24. Schindler T., Schmid F. X. Thermodynamic properties of an extremely rapid protein folding reaction. Biochemistry. 1996 Dec 24;35(51):16833–16842. doi: 10.1021/bi962090j. [DOI] [PubMed] [Google Scholar]
  25. Schönbrunner N., Koller K. P., Kiefhaber T. Folding of the disulfide-bonded beta-sheet protein tendamistat: rapid two-state folding without hydrophobic collapse. J Mol Biol. 1997 May 2;268(2):526–538. doi: 10.1006/jmbi.1997.0960. [DOI] [PubMed] [Google Scholar]
  26. Spector S., Kuhlman B., Fairman R., Wong E., Boice J. A., Raleigh D. P. Cooperative folding of a protein mini domain: the peripheral subunit-binding domain of the pyruvate dehydrogenase multienzyme complex. J Mol Biol. 1998 Feb 20;276(2):479–489. doi: 10.1006/jmbi.1997.1522. [DOI] [PubMed] [Google Scholar]
  27. Spector S., Raleigh D. P. Submillisecond folding of the peripheral subunit-binding domain. J Mol Biol. 1999 Nov 5;293(4):763–768. doi: 10.1006/jmbi.1999.3189. [DOI] [PubMed] [Google Scholar]
  28. Van Nuland N. A., Meijberg W., Warner J., Forge V., Scheek R. M., Robillard G. T., Dobson C. M. Slow cooperative folding of a small globular protein HPr. Biochemistry. 1998 Jan 13;37(2):622–637. doi: 10.1021/bi9717946. [DOI] [PubMed] [Google Scholar]
  29. Viguera A. R., Serrano L. Loop length, intramolecular diffusion and protein folding. Nat Struct Biol. 1997 Nov;4(11):939–946. doi: 10.1038/nsb1197-939. [DOI] [PubMed] [Google Scholar]
  30. Villegas V., Azuaga A., Catasús L., Reverter D., Mateo P. L., Avilés F. X., Serrano L. Evidence for a two-state transition in the folding process of the activation domain of human procarboxypeptidase A2. Biochemistry. 1995 Nov 21;34(46):15105–15110. doi: 10.1021/bi00046a017. [DOI] [PubMed] [Google Scholar]
  31. van Nuland N. A., Chiti F., Taddei N., Raugei G., Ramponi G., Dobson C. M. Slow folding of muscle acylphosphatase in the absence of intermediates. J Mol Biol. 1998 Nov 6;283(4):883–891. doi: 10.1006/jmbi.1998.2009. [DOI] [PubMed] [Google Scholar]

Articles from Biophysical Journal are provided here courtesy of The Biophysical Society

RESOURCES