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$sim0.1times$ 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.
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