We have shown previously that lac repressor binds specifically and quantitatively to lac operator restriction fragments which have been complexed with histones to form artificial nucleosomes (203 base pair restriction fragment) or core particles (144 base pair restriction fragment. We describe here a quantitative method for determining the equilibrium binding affinities of repressor for these lac reconstitutes. Quantitative analysis shows that the operator-histone reconstitutes may be grouped into two affinity classes: those with an affinity for repressor close to that of naked DNA and those with an affinity 2 or more orders of magnitude less than that of naked DNA. All particles in the lac nucleosome preparations bind repressor with high affinity, but the lac core particle preparations contain particles of both high and low affinities for repressor. Formaldehyde cross-linking causes all high-affinity species to suffer a 100-fold decrease in binding affinity. In contrast, there is no effect of cross-linking on species of low affinity. Therefore, the ability of a particle to be bound tightly by repressor depends on a property of the particle which is eliminated by cross-linking. Control experiments have shown that chemical damage to the operator does not accompany cross-linking. Therefore, the property sensitive to cross-linking must be the ability of the particle to change conformation. We infer that the particles of low native affinity, like cross-linked particles, are of low affinity because of an inability to facilitate repressor binding by means of this conformational change. Dimethyl suberimidate cross-linking experiments show that histone-histone cross-linking is sufficient to preclude high-affinity binding. Thus, the necessary conformational change involves a nucleosome histone core event. We find that the ability of a particle to undergo a repressor-induced facilitating conformational change appears to depend on the position of the operator along the DNA binding path of the nucleosome core. We present a general model which proposes that nucleosomes are divided into domains which function differentially to initiate conformational changes in response to physiological stimuli.