  As wounds heal, embryos develop, cancer spreads, or asthma progresses, the
cellular monolayer undergoes glass transition between solid-like jammed and
fluid-like flowing states. During some of these processes, the cells undergo an
epithelial-to-mesenchymal transition (EMT): they acquire in-plane polarity and
become motile. Thus, how motility drives the glassy dynamics in epithelial
systems is critical for the EMT process. However, no analytical framework that
is indispensable for deeper insights exists. Here, we develop such a theory
inspired by a well-known glass theory. One crucial result of this work is that
the confluency affects the effective persistence time-scale of active force,
described by its rotational diffusivity, $D_r^{\text{eff}}$. $D_r^{\text{eff}}$
differs from the bare rotational diffusivity, $D_r$, of the motile force due to
cell shape dynamics, which acts to rectify the force dynamics:
$D_r^{\text{eff}}$ is equal to $D_r$ when $D_r$ is small and saturates when
$D_r$ is large. We test the theoretical prediction of $D_r^{\text{eff}}$ and
how it affects the relaxation dynamics in our simulations of active Vertex
model. This novel effect of $D_r^{\text{eff}}$ is crucial to understanding the
new and previously published simulation data of active glassy dynamics in
epithelial monolayers.
