Levinthal's paradox

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{{cite journal

|last=Levinthal|first=Cyrus|year=1969|title=How to Fold Graciously|

journal=Mossbauer Spectroscopy in Biological Systems: Proceedings of a Meeting Held at Allerton House, Monticello, Illinois|pages=22–24|

url=http://www-miller.ch.cam.ac.uk/levinthal/levinthal.html

|archiveurl = https://web.archive.org/web/20101007174851/http://www-miller.ch.cam.ac.uk/levinthal/levinthal.html |archivedate = 2010-10-07}} (often incorrectly cited as the 1968 paper{{cite journal

|last=Levinthal|first=Cyrus|year=1968|title=Are there pathways for protein folding?|journal=Journal de Chimie Physique et de Physico-Chimie Biologique|volume=65|pages=44–45|doi=10.1051/jcp/1968650044|bibcode=1968JCP....65...44L|url=http://www.biochem.wisc.edu/courses/biochem704/Reading/Levinthal1968.pdf|archiveurl = https://web.archive.org/web/20090902211239/http://www.biochem.wisc.edu/courses/biochem704/Reading/Levinthal1968.pdf|archivedate = 2009-09-02}}). For example, a polypeptide of 100 residues will have 200 different phi and psi{{Broken anchor|date=2025-06-10|bot=User:Cewbot/log/20201008/configuration|target_link=Dihedral angle#Dihedral angles of biological molecules|reason= The anchor (Dihedral angles of biological molecules) has been deleted.|diff_id=689317788}} bond angles, two within each residue. If each of these bond angles can be in one of three stable conformations, the protein may misfold into a maximum of 3²⁰⁰ different conformations (including any possible folding redundancy), not even considering the peptide linkages between each residue or the conformations of the side-chains. 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.{{cite journal |vauthors=Zwanzig R, Szabo A, Bagchi B |title=Levinthal's paradox |journal=Proc Natl Acad Sci USA |date=1992-01-01 |volume=89 |issue=1 |pages=20–22 |pmc=48166 |pmid=1729690 |doi=10.1073/pnas.89.1.20|bibcode=1992PNAS...89...20Z |doi-access=free }}

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".{{cite journal |author1=Rooman, Marianne Rooman |author2=Yves Dehouck |author3=Jean Marc Kwasigroch |author4=Christophe Biot |author5=Dimitri Gilis |year=2002 |title=What is paradoxical about Levinthal Paradox? |journal=Journal of Biomolecular Structure and Dynamics |volume=20 |issue=3 |pages=327–329 |pmid=12437370 |doi=10.1080/07391102.2002.10506850 |s2cid=6839744 }} 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.{{cite journal|author1=Dill K |author2=H.S. Chan |year=1997 |title=From Levinthal to pathways to funnels|journal=Nat. Struct. Biol. |volume=4 |pages=10–19 | pmid = 8989315 |doi=10.1038/nsb0197-10 |issue=1 |s2cid=11557990 }}{{cite journal|author= Durup, Jean |year=1998| title=On "Levinthal paradox" and the theory of protein folding|journal= Journal of Molecular Structure |volume= 424| issue= 1–2| pages=157–169|doi= 10.1016/S0166-1280(97)00238-8}}{{cite journal |year=1994 |title=How does a protein fold? |journal=Nature |volume=369 |pages=248–251 |url=http://courses.theophys.kth.se/SI2700/sali1.pdf |doi=10.1038/369248a0 |issue=6477 |last1=s˘Ali |first1=Andrej |last2=Shakhnovich |first2=Eugene |last3=Karplus |first3=Martin |pmid=7710478 |bibcode=1994Natur.369..248S |s2cid=4281915 }}{{dead link|date=December 2017 |bot=InternetArchiveBot |fix-attempted=yes }} Some computational approaches to protein structure prediction have sought to identify and simulate the mechanism of protein folding.{{cite journal|author= Karplus, Martin |year=1997| title=The Levinthal paradox: yesterday and today|journal= Folding & Design |volume=2| pages=S69–S75 |doi=10.1016/S1359-0278(97)00067-9|pmid= 9269572|issue= 4|doi-access=free}}

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.{{cite journal| author=Hunter, Philip |year=2006 |title=Into the fold| journal=EMBO Rep. |volume=7 |issue=3| pages=249–252 |doi=10.1038/sj.embor.7400655 | pmid=16607393| pmc= 1456894}}

Levinthal's paradox was cited on the first page of the Scientific Background to the 2024 Nobel Prize in Chemistry (awarded to David Baker, Demis Hassabis, and John M. Jumper for computational protein design and protein structure prediction) by way of demonstrating the sheer scale of the problem given the astronomical number of permutations.https://www.nobelprize.org/uploads/2024/10/advanced-chemistryprize2024.pdf

According to Edward Trifonov and Igor Berezovsky, proteins fold by subunits (modules) of the size of 25–30 amino acids.{{cite journal|last1 = Berezovsky|first1 = Igor N.|last2 = Trifonov|first2 = Edward N.|title = Loop fold structure of proteins: Resolution of Levinthal's paradox|journal = Journal of Biomolecular Structure & Dynamics|year = 2002|volume = 20|pages = 5–6|issn = 0739-1102|url = http://paradox.harvard.edu/~igor/PUBL_BER/PUB22.pdf|issue = 1|doi = 10.1080/07391102.2002.10506817|url-status = dead|archiveurl = https://web.archive.org/web/20050212130449/http://paradox.harvard.edu/~igor/PUBL_BER/PUB22.pdf|archivedate = 2005-02-12|pmid = 12144347|s2cid = 33174198}}

• Chaperone{{snd}} proteins that assist other proteins in folding or unfolding
• Folding funnel
• Anfinsen's dogma

{{reflist|2}}

• http://www-wales.ch.cam.ac.uk/~mark/levinthal/levinthal.html
• https://www.wired.com/wired/archive/9.07/blue_pr.html
• https://web.archive.org/web/20041011182039/http://www.sdsc.edu/~nair/levinthal.html

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Category:Eponymous paradoxes

Category:Protein structure

Category:Physical paradoxes

Category:Thought experiments