Basic region leucine zipper (bZIP) transcription factors involved in DNA recognition are dimeric proteins. The monomers consist of two subdomains, a leucine zipper sequence responsible for dimerization and a highly basic DNA recognition sequence. Leucine zippers are strongly dimerized, and in a bZIP, the basic region can, in the absence of DNA, undergo extensive relative monomer-to-monomer fluctuations. In this work, LZ and bZIP potentials of mean force (PMFs), which provide free energies along reaction coordinates, are simulated with a distance replica exchange method. The method uses restraint potentials to provide sampling along a reaction coordinate and enhances configuration space exploration by exchanging information between neighboring restraint potential configurations. Restraint potentials that are constructed from sums over a number of atom distances are employed. Their use requires a modification of the Weighted Histogram Analysis Method (WHAM) procedure to combine and unbias the data from the different restraint-potential-biased window densities to provide a PMF. These methods are first used to obtain a PMF for separating a leucine zipper (GCN4-pl) of the yeast transcriptional activator GCN4. The PMF indicates a very strong binding free energy that only weakens when the monomers are separated by about 12 A, which is about 6 A beyond their bound, dimer equilibrium distance. PMFs are also obtained for separating the basic subdomain monomer parts of the GCN4 bZIP transcriptional factor, in the absence of DNA. In a monomer separation range spanning the open, crystal-based structure to closer configurations, the basic subdomain PMF is quite flat, implying essentially thermal sampling in this distance range. A PMF generated starting from a "collapsed" state, taken from a previous simulation (J. Phys. Chem. B 2012, 116, 6071), where collapsed refers to the feature that the basic subdomain monomers are also effectively dimerized, shows that this state is bound in free energy, though much less so than the leucine zipper dimer.