  In development and homeostasis, multi-cellular systems exhibit spatial and
temporal heterogeneity in their biochemical and mechanical properties.
Nevertheless, it remains unclear how spatiotemporally heterogeneous forces
affect the dynamical and mechanical properties of confluent tissue. To address
this question, we study the dynamical behavior of the two-dimensional cellular
vertex model for epithelial monolayers in the presence of fluctuating cell-cell
interfacial tensions, which is a biologically relevant source of mechanical
spatiotemporal heterogeneity. In particular, we investigate the effects of the
amplitude and persistence time of fluctuating tension on the tissue dynamics.
We unexpectedly find that the long-time diffusion constant describing cell
rearrangements depends non-monotonically on the persistence time, while it
increases monotonically as the amplitude increases. Our analysis indicates that
at low and intermediate persistence times tension fluctuations drive motion of
vertices and promote cell rearrangements, while at the highest persistence
times the tension in the network evolves so slowly that rearrangements become
rare.
