  In vivo and in vitro cells rely on the support of an underlying biocompatible
substrate, such as the extracellular matrix or a culture substrate, to spread
and proliferate. The mechanical and chemical properties of such structures play
a central role in the dynamical and statistical properties of the tissue. At
the cell scale, these substrates are highly disordered. Here, we investigate
how spatial heterogeneities of the cell-substrate interaction influence the
motility of the cells in a model confluent tissue. We use the Self-Propelled
Voronoi model and describe the disorder as a spatially dependent preferred
geometry of the individual cells. We found that when the characteristic length
scale of the preferred geometry is smaller than the cell size, the tissue is
less rigid than its homogeneous counterpart, with a consequent increase in cell
motility. This result is in sharp contrast to what has been reported for
tissues with heterogeneity in the mechanical properties of the individual
cells, where the disorder favors rigidity. Using the fraction of rigid cells,
we observe a collapse of the motility data for different model parameters and
provide evidence that the rigidity transition in the model tissue is
accompanied by the emergence of a spanning cluster of rigid cells.
