Levinthal's Paradox is named after scientist Cyrus Levinthal, who surmised that it should take an eternity for proteins to fold because of the huge number of accessible conformations it has to explore before finding the native state. The fact that it does not take an eternity to occur argues that folding is directed and not random.

A 'back-of-the-envelope' calculation that goes something like this:

  • A protein chain can be thought of as a series of links with, say, two possible angles between them.
  • Say the protein is 100 links (amino acids) long - around the lower limit for size.
  • Let the chain flip the angle between two links every nanosecond (10-9 seconds).
  • The final (folded) state is only one of the 2100 possible states.
  • There are only 1050 seconds since the beginning of the universe

QED? Well (apart from the fact that the numbers above are wrong in detail) this leaves out the important point (as mentioned by Halcyon&on above) that folding proceeds in an orderly, self-directed manner. The particular state the chain is in at any one time determines what states are accessible for the next step. Also, of course, these steps are going on in parallel.

These types of calculations are also presented for 'proof' that proteins could not be evolved. The argument runs as follows; if you chose one random amino acid from the 'set' of 20 for each link in the protein chain you would need <insert large number> of proteins which is <insert humerously large object, such as the earth> in size.

Sadly, this is nonsense - it ignores the fact that the desired end point is a particular protein. It is the design fallacy all over again - "How could this particular object be created by chance?". This is the wrong question. In fact, it doesn't matter which sequence you 'choose' in this imaginary game of statistics. Any sequence is likely to fold and most of those will do something. Okay, so evolving insulin from a boiling soup of chemicals is improbable- but something will emerge.

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