  A lattice based model of a protein is used to study the dimerization
equilibrium of the GCN4 leucine zipper. Replica exchange Monte Carlo is used to
determine the free energy of both the monomeric and dimeric forms as a function
of temperature. The method of coincidences is then introduced to explicitly
calculate the entropy loss associated with dimerization, and from it the free
energy difference between monomer and dimer, as well as the corresponding
equilibrium reaction constant. We find that the entropy loss of dimerization is
a strong function of energy (or temperature), and that it is much larger than
previously estimated, especially for high energy states. The results confirm
that it is possible to study the dimerization equilibrium of GCN4 at
physiological concentrations within the reduced representation of the protein
employed.
