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The optical colors of globular clusters (GCs) in most large early-type galaxies are bimodal. Blue and red GCs show a sharp difference in the radial profile of their surface number density in the sense that red GCs are more centrally concentrated than blue GCs. An instant interpretation is that there exist two distinct GC subsystems having different radial distributions. This view, however, was challenged by a scenario in which, due to the nonlinear nature of the GC metallicity-to-color transformation for old ($\gtrsim$10 Gyr) GCs, a broad unimodal metallicity spread can exhibit a bimodal color distribution. Here we show, by simulating the radial trends in the GC color distributions of the four nearby giant elliptical galaxies (M87, M49, M60, and NGC 1399), that the difference in the radial profile between blue and red GCs stems naturally from the metallicity-to-color nonlinearity plus the well-known radial metallicity gradient of GC systems. The model suggests no or little radial variation in GC age even out to $\sim$20${R}_{\rm eff}$. Our results provide a simpler solution to the distinct radial profiles of blue and red GCs that does not necessarily invoke the presence of two GC subsystems and further fortify the nonlinearity scenario for the GC color bimodality phenomenon.