Levinthal's paradox is a

thought experiment A thought experiment is a hypothetical situation in which a hypothesis, theory, or principle is laid out for the purpose of thinking through its consequences. History The ancient Greek ''deiknymi'' (), or thought experiment, "was the most anci ...

, also constituting a

self-reference Self-reference occurs in natural or formal languages when a sentence, idea or formula refers to itself. The reference may be expressed either directly—through some intermediate sentence or formula—or by means of some encoding. In philoso ...

in the theory of

protein folding Protein folding is the physical process by which a protein chain is translated to its native three-dimensional structure, typically a "folded" conformation by which the protein becomes biologically functional. Via an expeditious and reproduci ...

. In 1969,

Cyrus Levinthal Cyrus Levinthal (May 2, 1922 – November 4, 1990) was an American molecular biologist. Biography Levinthal graduated with a Ph.D. in physics from University of California, Berkeley and taught physics at the University of Michigan for seven ...

noted that, because of the very large number of

degrees of freedom Degrees of freedom (often abbreviated df or DOF) refers to the number of independent variables or parameters of a thermodynamic system. In various scientific fields, the word "freedom" is used to describe the limits to which physical movement or ...

in an unfolded

polypeptide chain Peptides (, ) are short chains of amino acids linked by peptide bonds. Long chains of amino acids are called proteins. Chains of fewer than twenty amino acids are called oligopeptides, and include dipeptides, tripeptides, and tetrapeptides. A p ...

, the molecule has an astronomical number of possible conformations. An estimate of 10³⁰⁰ was made in one of his papers (often incorrectly cited as the 1968 paper). For example, a polypeptide of 100 residues will have 99

peptide bond In organic chemistry, a peptide bond is an amide type of covalent chemical bond linking two consecutive alpha-amino acids from C1 (carbon number one) of one alpha-amino acid and N2 (nitrogen number two) of another, along a peptide or protein cha ...

s, 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 A nanosecond (ns) is a unit of time in the International System of Units (SI) equal to one billionth of a second, that is, of a second, or 10 seconds. The term combines the SI prefix ''nano-'' indicating a 1 billionth submultiple of an SI unit ( ...

picosecond A picosecond (abbreviated as ps) is a unit of time in the International System of Units (SI) equal to 10−12 or (one trillionth) of a second. That is one trillionth, or one millionth of one millionth of a second, or 0.000 000 000 ...

) 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 Protein structure prediction is the inference of the three-dimensional structure of a protein from its amino acid sequence—that is, the prediction of its secondary and tertiary structure from primary structure. Structure prediction is different ...

. 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 In thermodynamics, nucleation is the first step in the formation of either a new thermodynamic phase or structure via self-assembly or self-organization within a substance or mixture. Nucleation is typically defined to be the process that deter ...

points in the folding process". Indeed, the protein folding intermediates and the partially folded

transition state In chemistry, the transition state of a chemical reaction is a particular configuration along the reaction coordinate. It is defined as the state corresponding to the highest potential energy along this reaction coordinate. It is often marked wi ...

s were experimentally detected, which explains the fast

. This is also described as protein folding directed within funnel-like energy landscapes. Some computational approaches to protein structure prediction have sought to identify and simulate the mechanism of protein folding. 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.

Suggested explanations

* According to

Edward Trifonov Edward Nikolayevich Trifonov ( he, אדוארד טריפונוב, russian: Эдуapд Тpифoнoв; b. March 31, 1937) is a Russian-born Israeli molecular biophysicist and a founder of Israeli bioinformatics. In his research, he specializes in ...

and Igor Berezovsky, the proteins fold by subunits (modules) of the size of 25–30 amino acids.

References

External links

* 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 {{DEFAULTSORT:Levinthal's Paradox Protein structure Physical paradoxes Thought experiments

Suggested explanations

See also

References

External links