Levinthal paradox
Encyclopedia
Levinthal's paradox is a thought experiment
, also constituting a self-reference
in the theory of 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 3300 or 10143 was made in one of his papers. (Often incorrectly cited as a 1968 paper.) For example, a polypeptide of 100 residues
will have 99 peptide bond
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
or picosecond
) rates. The "paradox" is that most small proteins fold spontaneously on a millisecond or even microsecond time scale. This paradox is central to computational approaches to protein structure prediction
.
Levinthal himself was aware that proteins fold spontaneously
and on short timescales. He suggested that the paradox can be resolved if "protein folding is speeded 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." Indeed, the protein folding intermediates
and the partially folded transition state
s were experimentally detected, which explains the fast protein folding
. 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.
Thought experiment
A thought experiment or Gedankenexperiment considers some hypothesis, theory, or principle for the purpose of thinking through its consequences...
, also constituting a self-reference
Self-reference
Self-reference occurs in natural or formal languages when a sentence 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 the theory of protein folding
Protein folding
Protein folding is the process by which a protein structure assumes its functional shape or conformation. It is the physical process by which a polypeptide folds into its characteristic and functional three-dimensional structure from random coil....
. In 1969, Cyrus Levinthal
Cyrus Levinthal
Cyrus Levinthal 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 years before moving to the Massachusetts Institute of Technology in 1957...
noted that, because of the very large number of degrees of freedom
Degrees of freedom (physics and chemistry)
A degree of freedom is an independent physical parameter, often called a dimension, in the formal description of the state of a physical system...
in an unfolded polypeptide chain
Peptide
Peptides are short polymers of amino acid monomers linked by peptide bonds. They are distinguished from proteins on the basis of size, typically containing less than 50 monomer units. The shortest peptides are dipeptides, consisting of two amino acids joined by a single peptide bond...
, the molecule has an astronomical number of possible conformations. An estimate of 3300 or 10143 was made in one of his papers. (Often incorrectly cited as a 1968 paper.) For example, a polypeptide of 100 residues
Amino acid
Amino acids are molecules containing an amine group, a carboxylic acid group and a side-chain that varies between different amino acids. The key elements of an amino acid are carbon, hydrogen, oxygen, and nitrogen...
will have 99 peptide bond
Peptide bond
This article is about the peptide link found within biological molecules, such as proteins. A similar article for synthetic molecules is being created...
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
Nanosecond
A nanosecond is one billionth of a second . One nanosecond is to one second as one second is to 31.7 years.The word nanosecond is formed by the prefix nano and the unit second. Its symbol is ns....
or picosecond
Picosecond
A picosecond is 10−12 of a second. That is one trillionth, or one millionth of one millionth of a second, or 0.000 000 000 001 seconds. A picosecond is to one second as one second is to 31,700 years....
) rates. The "paradox" is that most small proteins fold spontaneously on a millisecond or even microsecond time scale. This paradox is central to computational approaches to protein structure prediction
Protein structure prediction
Protein structure prediction is the prediction of the three-dimensional structure of a protein from its amino acid sequence — that is, the prediction of its secondary, tertiary, and quaternary structure from its primary structure. Structure prediction is fundamentally different from the inverse...
.
Levinthal himself was aware that proteins fold spontaneously
Anfinsen's dogma
Anfinsen's dogma is a postulate in molecular biology championed by the Nobel Prize Laureate Christian B. Anfinsen...
and on short timescales. He suggested that the paradox can be resolved if "protein folding is speeded 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." Indeed, the protein folding intermediates
Reaction intermediate
A reaction intermediate or an intermediate is a molecular entity that is formed from the reactants and reacts further to give the directly observed products of a chemical reaction. Most chemical reactions are stepwise, that is they take more than one elementary step to complete...
and the partially folded transition state
Transition state
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 energy along this reaction coordinate. At this point, assuming a perfectly irreversible reaction, colliding reactant molecules will always...
s were experimentally detected, which explains the fast protein folding
Protein folding
Protein folding is the process by which a protein structure assumes its functional shape or conformation. It is the physical process by which a polypeptide folds into its characteristic and functional three-dimensional structure from random coil....
. This is also described as protein folding directed within funnel-like energy landscapes
Folding funnel
The folding funnel hypothesis is a specific version of the energy landscape theory of protein folding, which assumes that a protein's native state corresponds to its free energy minimum under the solution conditions usually encountered in cells...
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.
See also
- Folding funnelFolding funnelThe folding funnel hypothesis is a specific version of the energy landscape theory of protein folding, which assumes that a protein's native state corresponds to its free energy minimum under the solution conditions usually encountered in cells...
- chaperone — proteins that assist other proteins in folding or unfolding
External links
- http://www-wales.ch.cam.ac.uk/~mark/levinthal/levinthal.html
- http://www.wired.com/wired/archive/9.07/blue_pr.html
- http://web.archive.org/web/20041011182039/http://www.sdsc.edu/~nair/levinthal.html