  Using Herschel data from the Open Time Key Project the Herschel Virgo Cluster
Survey (HeViCS), we investigated the relationship between the metallicity
gradients expressed by metal abundances in the gas phase as traced by the
chemical composition of HII regions, and in the solid phase, as traced by the
dust-to-gas mass ratio. We derived the radial gradient of the dust-to-gas mass
ratio for all galaxies observed by HeViCS whose metallicity gradients are
available in the literature. They are all late type Sbc galaxies, namely
NGC4254, NGC4303, NGC4321, and NGC4501. We examined different dependencies on
metallicity of the CO-to-H$_2$ conversion factor (\xco), used to transform the
$^{12}$CO observations into the amount of molecular hydrogen. We found that in
these galaxies the dust-to-gas mass ratio radial profile is extremely sensitive
to choice of the \xco\ value, since the molecular gas is the dominant component
in the inner parts. We found that for three galaxies of our sample, namely
NGC4254, NGC4321, and NGC4501, the slopes of the oxygen and of the dust-to-gas
radial gradients agree up to $\sim$0.6-0.7R$_{25}$ using \xco\ values in the
range 1/3-1/2 Galactic \xco. For NGC4303 a lower value of \xco$\sim0.1\times$
10$^{20}$ is necessary. We suggest that such low \xco\ values might be due to a
metallicity dependence of \xco (from close to linear for NGC4254, NGC4321, and
NGC4501 to superlinear for NGC4303), especially in the radial regions
R$_G<$0.6-0.7R$_{25}$ where the molecular gas dominates. On the other hand, the
outer regions, where the atomic gas component is dominant, are less affected by
the choice of \xco, and thus we cannot put constraints on its value.
