Landscapes and Funnels

The coarse grained view of protein conformations, as we see, turned out extraordinarily fruitful. It gave us at least a glimpse of physics understanding for otherwise seemingly mysterious properties of proteins. And the potential of this approach is far from exhausted. 

One important conclusion one may draw from thinking about the landscapes is the danger of local minima, which can serve as traps slowing down the finding of the minimal energy native state. To emphasize the necessity of sliding down without significant traps and barriers, yet another metaphor is popular, that of a funnel the landscape should be funnel shaped in order for the native state to be readily accessible. 

Since we know from the coarse grained considerations that the protein-like sequences provide for a very low l3ung ground state energy, corresponding obviously to the very deep valley, we can use the landscape metaphor to hint on the resolution of the Levinthal paradox (see Section 10.3). 

To explain the idea, let s point out that a similar paradox could be formulated for a more trivial case — formation of a crystal, say, crystallization of water how do molecules find their unique positions while they obviously cannot manage to try all of the exponentially large number of possible arrangements Indeed, there are exponentially many configurations, so an attempt to test them all would require an exponentially long time. 

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