We report that the density profiles of globular cluster (GC) systems in a sample of 17 early-type galaxies (ETGs) show breaks at the radii where the gravitational acceleration exerted by the stars equals the galactic acceleration scale a 0 known from the radial acceleration relation or the modified Newtonian dynamics (MOND). The match with the other characteristic radii in the galaxy is not that close. We propose possible explanations in the frameworks of the Lambda cold dark matter (ΛCDM) model and MOND. We find tentative evidence that in the ΛCDM context, GCs reveal not only the masses of the dark halos through the richness of the GC systems but also the concentrations through the break radii of the GC systems.