Theory of the mobility-shift assay of nonspecific protein-DNA complexes governed by conditional probabilities: The HU:DNA complex Complexes of an 88 bp DNA and the HU protein were studied by both experimental and theoretical electrophoretic mobility-shift analyses. Experimental analysis defined the stoichiometry of binding and estimated an apparent intrinsic dissociation constant (Kd = 1 to 3 X lo-' M) for the HU:DNA complexes. The theory of conditional probabilities was applied to the binding of HU to DNA in order to fix the initial equilibrium composition of mixtures to be assayed theoretically by the mobility-shift procedure. Electrophoretic mobilityshift patterns were obtained by numerical solution of a set of simultaneous transport-reaction equations, in which the chemical kinetic term is formulated in terms of dissociation of the different DNA:HU complexes in gel cages. The computed patterns simulated the experimental patterns describing the titration of a fixed concentration of an 88 bp DNA fragment with dimeric HU. These insightful results provide guidelines for interpretation of the electrophoretic behavior of systems in which a ligand binds nonspecifically to DNA. In particular, the narrow unresolved zone observed both experimentally and theoretically beyond 50-60% saturation is a reaction zone characteristic of noncooperative ligand-binding governed by conditional probabilities. The discrepancy between the theoretically assigned and experimental values of the intrinsic binding constant is attributed to an HU-induced change in the conformation of DNA.