  This letter reports on the first computation, from data obtained in lattice
QCD with $u,d,s$ and $c$ quarks in the sea, of the running strong coupling via
the ghost-gluon coupling renormalized in the MOM Taylor scheme. We provide with
estimates of $\ams(m_\tau^2)$ and $\ams(m_Z^2)$ in very good agreement with
experimental results. Including a dynamical c quark makes safer the needed
running of $\ams$.
