202110221009 Levinthal's paradox

Levinthal's paradox¹ 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. 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 mis-fold into a maximum of $3^{198}$ 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. It may imply that there's a specific algorithmic process that's followed that we have not been able to discover as of now.