Levinthal's paradox

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.[1] (Often incorrectly cited as a 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.

Theoretically, a computer could calculate all the possible shapes for one sample protein and select the lowest potential energy one. But in practice, however, it is possible that this process takes longer than the age of the universe to do all the calculations.

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.[1] (Often incorrectly cited as a 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.**This paradox is central to computational approaches to protein structure prediction.[3]Theoretically, a computer could calculate all the possible shapes for one sample protein and select the lowest potential energy one. But in practice, however, it is possible that this process takes longer than the age of the universe to do all the calculations.