  We study a protein-DNA target search model with explicit DNA dynamics
applicable to in vitro experiments. We show that the DNA dynamics plays a
crucial role for the effectiveness of protein "jumps" between sites distant
along the DNA contour but close in 3D space. A strongly binding protein that
searches by 1D sliding and jumping alone, explores the search space less
redundantly when the DNA dynamics is fast on the timescale of protein jumps
than in the opposite "frozen DNA" limit. We characterize the crossover between
these limits using simulations and scaling theory. We also rationalize the slow
exploration in the frozen limit as a subtle interplay between long jumps and
long trapping times of the protein in "islands" within random DNA
configurations in solution.
