© 2021 authors. Published by the American Physical Society.The quark mass function is computed both by solving the quark propagator Dyson-Schwinger equation and from lattice simulations implementing overlap and domain-wall fermion actions for valence and sea quarks, respectively. The results are examined and are seen to produce a very congruent picture, showing a remarkable agreement for the explored range of current-quark masses. The effective running interaction is based on a process-independent charge rooted on a particular truncation of the Dyson-Schwinger equations in the gauge sector, establishing a link from there to the quark sector and inspiring a correlation between the emergence of gluon and hadron masses.