Levinthal's paradox

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Levinthal's paradox is a thought experiment in the field of computational protein structure prediction where an algorithmic search for a minimum energy configuration is vastly slower than the actual process by which stable configurations are reached in protein folding.


In 1969, Cyrus Levinthal noted that, because of the very large number of degrees of freedom in an unfolded polypeptide chain, the molecule has an astronomical number of possible conformations. An estimate of 10300 was made in one of his papers[1] (often incorrectly cited as the 1968 paper[2]). For example, a polypeptide of 100 residues will have 99 peptide bonds, and therefore 198 different phi and psi bond angles. If each of these bond angles can be in one of three stable conformations, the protein may misfold into a maximum of 3198 different conformations (including any possible folding redundancy). Therefore, if a protein were to attain its correctly folded configuration by sequentially sampling all the possible conformations, it would require a time longer than the age of the universe to arrive at its correct native conformation. This is true even if conformations are sampled at rapid (nanosecond or picosecond) rates. The "paradox" is that most small proteins fold spontaneously on a millisecond or even microsecond time scale. The solution to this paradox has been established by computational approaches to protein structure prediction.[3]

Levinthal himself was aware that proteins fold spontaneously and on short timescales. He suggested that the paradox can be resolved if "protein folding is sped up and guided by the rapid formation of local interactions which then determine the further folding of the peptide; this suggests local amino acid sequences which form stable interactions and serve as nucleation points in the folding process".[4] Indeed, the protein folding intermediates and the partially folded transition states were experimentally detected, which explains the fast protein folding. This is also described as protein folding directed within funnel-like energy landscapes.[5][6][7] Some computational approaches to protein structure prediction have sought to identify and simulate the mechanism of protein folding.[8]

Levinthal also suggested that the native structure might have a higher energy, if the lowest energy was not kinetically accessible. An analogy is a rock tumbling down a hillside that lodges in a gully rather than reaching the base.[9]

Suggested explanations[edit]

  • According to Edward Trifonov and Igor Berezovsky, the proteins fold by subunits (modules) of the size of 25–30 amino acids.[10]

See also[edit]


  1. ^ Levinthal, Cyrus (1969). "How to Fold Graciously". Mossbauer Spectroscopy in Biological Systems: Proceedings of a Meeting Held at Allerton House, Monticello, Illinois: 22–24. Archived from the original on 2010-10-07.
  2. ^ Levinthal, Cyrus (1968). "Are there pathways for protein folding?" (PDF). Journal de Chimie Physique et de Physico-Chimie Biologique. 65: 44–45. Bibcode:1968JCP....65...44L. doi:10.1051/jcp/1968650044. Archived from the original (PDF) on 2009-09-02.
  3. ^ Zwanzig R, Szabo A, Bagchi B (1992-01-01). "Levinthal's paradox". Proc Natl Acad Sci USA. 89 (1): 20–22. Bibcode:1992PNAS...89...20Z. doi:10.1073/pnas.89.1.20. PMC 48166. PMID 1729690.
  4. ^ Rooman, Marianne Rooman; Yves Dehouck; Jean Marc Kwasigroch; Christophe Biot; Dimitri Gilis (2002). "What is paradoxical about Levinthal Paradox?" (PDF). Journal of Biomolecular Structure and Dynamics. 20 (3): 327–329. doi:10.1080/07391102.2002.10506850. PMID 12437370. S2CID 6839744.[permanent dead link]
  5. ^ Dill K; H.S. Chan (1997). "From Levinthal to pathways to funnels". Nat. Struct. Biol. 4 (1): 10–19. doi:10.1038/nsb0197-10. PMID 8989315. S2CID 11557990.
  6. ^ Durup, Jean (1998). "On "Levinthal paradox" and the theory of protein folding". Journal of Molecular Structure. 424 (1–2): 157–169. doi:10.1016/S0166-1280(97)00238-8.
  7. ^ s˘Ali, Andrej; Shakhnovich, Eugene; Karplus, Martin (1994). "How does a protein fold?" (PDF). Nature. 369 (6477): 248–251. Bibcode:1994Natur.369..248S. doi:10.1038/369248a0. PMID 7710478. S2CID 4281915.[permanent dead link]
  8. ^ Karplus, Martin (1997). "The Levinthal paradox: yesterday and today". Folding & Design. 2 (4): S69–S75. doi:10.1016/S1359-0278(97)00067-9. PMID 9269572.
  9. ^ Hunter, Philip (2006). "Into the fold". EMBO Rep. 7 (3): 249–252. doi:10.1038/sj.embor.7400655. PMC 1456894. PMID 16607393.
  10. ^ Berezovsky, Igor N.; Trifonov, Edward N. (2002). "Loop fold structure of proteins: Resolution of Levinthal's paradox" (PDF). Journal of Biomolecular Structure & Dynamics. 20 (1): 5–6. doi:10.1080/07391102.2002.10506817. ISSN 0739-1102. PMID 12144347. S2CID 33174198. Archived from the original (PDF) on 2005-02-12.

External links[edit]