Recent observations show that the Milky Way's metallicity distribution function (MDF) changes its shape as a function of radius. This new evidence of radial migration within the stellar disc sets additional constraints on Galactic models. By performing controlled test particle simulations in a detailed, observationally motivated model of the Milky Way, we show that the spiral arms are able to imprint their signature in the radial migration, shaping the MDF in the outskirts of the Galactic disc with a minimal participation of the bar. Conversely, this work has the potential to characterise some structural and dynamical parameters of the spiral arms based on radial migration and the shape of the MDF. Finally, by performing a chemical-tagging to the simulations, we can reproduce the MDF curves as seen by APOGEE, showing that a fundamental factor influencing their shape is the Galactic potential.