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Using Herschel data from the Open Time Key Project the Herschel Virgo ClusterSurvey (HeViCS), we investigated the relationship between the metallicitygradients expressed by metal abundances in the gas phase as traced by thechemical composition of HII regions, and in the solid phase, as traced by thedust-to-gas mass ratio. We derived the radial gradient of the dust-to-gas massratio for all galaxies observed by HeViCS whose metallicity gradients areavailable in the literature. They are all late type Sbc galaxies, namelyNGC4254, NGC4303, NGC4321, and NGC4501. We examined different dependencies onmetallicity 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 inthese galaxies the dust-to-gas mass ratio radial profile is extremely sensitiveto choice of the \xco\ value, since the molecular gas is the dominant componentin the inner parts. We found that for three galaxies of our sample, namelyNGC4254, NGC4321, and NGC4501, the slopes of the oxygen and of the dust-to-gasradial gradients agree up to $\sim$0.6-0.7R$_{25}$ using \xco\ values in therange 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 ametallicity dependence of \xco (from close to linear for NGC4254, NGC4321, andNGC4501 to superlinear for NGC4303), especially in the radial regionsR$_G<$0.6-0.7R$_{25}$ where the molecular gas dominates. On the other hand, theouter regions, where the atomic gas component is dominant, are less affected bythe choice of \xco, and thus we cannot put constraints on its value.

The Herschel Virgo Cluster Survey. IX. Dust-to-gas mass ratio and metallicity gradients in four Virgo spiral galaxies