Loop Entropy - Wang-Uhlenbeck Entropy

Wang-Uhlenbeck Entropy

The loop entropy formula becomes more complicated with multiples loops, but may be determined for a Gaussian polymer using a matrix method developed by Wang and Uhlenbeck. Let there be contacts among the residues, which define loops of the polymers. The Wang-Uhlenbeck matrix is an symmetric, real matrix whose elements equal the number of common residues between loops and . The entropy of making the specified contacts equals

As an example, consider the entropy lost upon making the contacts between residues 26 and 84 and residues 58 and 110 in a polymer (cf. ribonuclease A). The first and second loops have lengths 58 (=84-26) and 52 (=110-58), respectively, and they have 26 (=84-58) residues in common. The corresponding Wang-Uhlenbeck matrix is

whose determinant is 2340. Taking the logarithm and multiplying by the constants gives the entropy.