  The dust-to-metals ratio describes the fraction of the heavy elements
contained in dust grains, and its variation provides key insights into the life
cycle of dust. We measure the dust-to-metals ratio in M101, a nearby galaxy
with a radial metallicity (Z) gradient spanning $\sim$1 dex. We fit the dust
spectral energy distribution from 100 to 500 $\mu m$ with five variants of the
modified blackbody dust emission model in which we vary the temperature
distribution and how emissivity depends on wavelength. Among them, the model
with a single temperature blackbody modified by a broken power-law emissivity
gives the statistically best fit and physically most plausible results. Using
these results, we show that the dust-to-gas ratio is proportional to $\rm
Z^{1.7}$. This implies that the dust-to-metals ratio is not constant in M101,
but decreases as a function of radius, equivalent to a lower fraction of metals
trapped in dust at low metallicity (large radius). The dust-to-metals ratio in
M101 remains at or above what would be predicted by the minimum depletion level
of metals observed in the Milky Way. Our current knowledge of
metallicity-dependent CO-to-H$_2$ conversion factor suggests that variations in
the conversion factor cannot be responsible for the dust-to-metals ratio trends
we observe. This change of dust-to-metals ratio is significantly correlated
with molecular hydrogen fraction, which suggests that the accretion of gas
phase metals onto existing dust grains could be a mechanism contributing to a
variable dust-to-metals ratio.
