  We generalise the framework of Dyson-Schwinger and Bethe-Salpeter equations
for four-quark states to accommodate the case of unequal quark masses. As a
first application, we consider the quantum numbers $I(J^{PC})=0(1^{++})$ of the
$X(3872)$ and study the four-quark states with quark contents
$cq\bar{q}\bar{c}$ and $cs\bar{s}\bar{c}$. Their Bethe-Salpeter amplitudes are
represented by a basis of heavy-light meson-meson, hadro-charmonium and
diquark-antidiquark operators, which allows for a dynamical distinction between
different internal configurations.
  In both cases we find the heavy-light meson-meson component to be dominant.
For the putative $X(3872)$ we obtain a mass of $3916(74)$ MeV; the
corresponding $cs\bar{s}\bar{c}$ state is predicted at $4068(61)$ MeV.
