About: Compactness   Sponge Permalink

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One of the important factors for humans or computers trying to fold proteins is achieving compactness. A newly-formed string of amino acids in a cell has a preferred three-dimensional shape (its “native structure”) and the components in the interior of the folded molecule like to be snugged up together tightly, without spaces between them. In Foldit, you can get some idea of whether your protein has such spaces, called voids, by selecting “Show Voids” from the view options menu. Few players use this view to fold, but it's useful checking the quality of a fold.

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  • Compactness
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  • One of the important factors for humans or computers trying to fold proteins is achieving compactness. A newly-formed string of amino acids in a cell has a preferred three-dimensional shape (its “native structure”) and the components in the interior of the folded molecule like to be snugged up together tightly, without spaces between them. In Foldit, you can get some idea of whether your protein has such spaces, called voids, by selecting “Show Voids” from the view options menu. Few players use this view to fold, but it's useful checking the quality of a fold.
  • The Compactness Theorem states that if T is a collection of first-order statements and every finite subset of T is consistent, then T is itself consistent. A set of statements is consistent if it has a model.
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  • One of the important factors for humans or computers trying to fold proteins is achieving compactness. A newly-formed string of amino acids in a cell has a preferred three-dimensional shape (its “native structure”) and the components in the interior of the folded molecule like to be snugged up together tightly, without spaces between them. In Foldit, you can get some idea of whether your protein has such spaces, called voids, by selecting “Show Voids” from the view options menu. Few players use this view to fold, but it's useful checking the quality of a fold.
  • The Compactness Theorem states that if T is a collection of first-order statements and every finite subset of T is consistent, then T is itself consistent. A set of statements is consistent if it has a model. By abuse of terminology, the following related fact is also frequently referred to as "compactness." Let M be a -saturated model, be a definable set, and be a collection of definable subsets of , with of size less than . If covers D, then some finite subset of covers D. This fact follows from the definition of -saturation. Compactness is used to prove the existence of -saturated models, however.
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