Loop entropy
Loop entropy is the entropy lost upon bringing together two residues of a polymer within a prescribed distance. For a single loop, the entropy varies logarithmically with the number of residues formula_1 in the loop where formula_3 is the Boltzmann constant and formula_4 is a coefficient that depends on the properties of the polymer. This entropy formula corresponds to a power-law distribution formula_5 for the probability of the residues contacting. The loop entropy may also vary with the position of the contacting residues. Residues near the ends of the polymer are more likely to contact (quantitatively, have  a lower formula_4) than those in the middle (i.e., far from the ends), primarily due to excluded volume effects. 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 formula_7 contacts among the residues, which define formula_7 loops of the polymers. The Wang-Uhlenbeck matrix formula_9 is an formula_10 symmetric, real matrix whose elements formula_11 equal the number of common residues between loops formula_12 and formula_13. 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 formula_16 gives the entropy.