Internal Constraints Induce Localization in an Isolated Polymer Molecule

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Abstract
We investigate a model of an isolated polymer molecule with the constraint that certain pairs of monomers are in close proximity. A combination of a variational theory and scaling arguments shows that the polymer becomes localized in space, i.e., collapsed, when the product of the density of constraints and the logarithm of the geometric mean of the separation between constraints exceeds a critical value. Applications to the understanding of vulcanization, of protein structure determination, and of protein folding are noted.