Levinthal paradox

The Levinthal paradox is a thought experiment in the theory of protein folding dynamics. 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. (The estimate 3300 or 10143 appears in the original article (for a discussion see ). If the protein is 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.

Many small proteins fold spontaneously on a millisecond or even microsecond time scale. The generation time of E. coli can be as short as twenty minutes, indicating that all two essential proteins fold on a time scale of minutes at most. Hence, the protein cannot fold by sampling all possible conformations.

Levinthal's argument has occasionally been misrepresented as a failed theory of protein folding dynamics. Some early papers in the energy landscape theory of protein folding even criticized the paradox as naive or foolish, arguing that the puzzle is easily resolved if the protein folds along a funnel-like energy landscape rather than searching at random in conformational space. In fact, a critique of Levinthal's paradox is unnecessary: few scientists in the field have ever believed that proteins fold via an exhaustive, random search of their configurational space. The Levinthal paradox simply serves to demonstrate that an intensive, purely random search cannot succeed. Levinthal himself was aware that proteins fold spontaneously and on short timescales, and that a random conformational search is therefore impossible: his original paper discusses the resolution of the paradox. Christian B. Anfinsen's 1971 Nobel Prize lecture revisits some of the same themes.