Loop entropy is the entropy lost upon bringing together two residues of a polymer in the loop

is the Boltzmann constant is a coefficient that depends on the properties of the polymer. This entropy formula corresponds to a power-law distribution for the probability of the residues contacting.

) 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. 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 gives the entropy.

References

• Wang, M. C., & Uhlenbeck, G. E. (1945). On the theory of the Brownian motion II. Reviews of Modern Physics, 17(2-3), 323.http://216.92.172.113/courses/phys39/simulations/Uhlenbeck%20Brownian%20Motion%20Rev%20Mod%20Phys%201945.pdf