# Difference between revisions of "Levinthal's Paradox"

Peter Foster, Fall 2011

Energy landscape for the folding of the protein Rhodanese. The landscape on the left shows is the landscape for folding in solution, while the landscape on the right shows the landscape for folding mediated by SR1. Note that the lowest energy corresponds to the fully folded state. Figure taken from Reference 2

## Definition

It is well known that proteins in solution can reliably fold from a random coil to a unique native conformation on a biologically relavent timescale. Levinthal's paradox is an apparent contradiction between the number of possible conformations for a protein chain and the fact that proteins can fold to their native conformation quickly (less than a second). In the proceedings where Levinthal first mentioned the paradox that bears his name (Reference 1), he estimates that for a protein there are 10300 possible conformations. Using the amount of time it actually takes for a protein to fold to its native conformation and assuming the minimal amount of time to sample different conformations, the protein would only be able to sample ~108 different conformations if the protein sampled the conformation space randomly. Because of the relevant timescales, if the protein randomly sampled conformation space, a protein would not be able to correctly fold in a person's lifetime. Herein lies the paradox, since properly folded proteins are needed for the person to exist in the first place.

## Possible Solution

Because of the paradox, it becomes obvious that the protein cannot sample conformation space in a random fashion. Instead, the protein samples the space in a way consistant with statistical mechanics. The probability of sampling a given conformation is weighed by the energy of the conformation. Currently, the generally accepted idea in the field of protein folding is to consider an energy landscape, where every possible conformation is represented by an energy value. The idea is that the energy landscape is generally funnel shaped, with the native conformation having the lowest energy. As the protein folds from its random coil conformation, it travels from conformation to conformation such that with each step, the total energy is lowered. With the idea of a funneled energy landscape, it may seem that it would be possible to calculate the energy landscape of a given amino acid sequence and find the conformation with the lowest energy, corresponding to the native structure. However, in practice this is not the case and we can only predict the native structures for relatively small proteins.

## References

[1] Levinthal, C. 1969. Mossbauer Spectroscopy in Biological Systems. Proceedings of a meeting held at Allerton House. P. Debrunner, J. C. M. Tsibris, and E. Munck, editors. University of Illinois Press, Urbana, IL. Levinthal's Paradox

[2] Hofmann et al. Single-molecule spectroscopy of protein folding in a chaperonin cage. Proceedings of the National Academy of Sciences (2010) vol. 107 (26) pp. 11793