  In order to study the effect of cell elastic properties on the behavior of
assemblies of motile cells, this paper describes an alternative to the cell
phase field (CPF) \cite{Palmieri2015} we have previously proposed. The CPF is a
multi-scale approach to simulating many cells which tracked individual cells
and allowed for large deformations. Though results were largely in agreement
with experiment that focus on the migration of a soft cancer cell in a
confluent layer of normal cells \cite{Lee2012}, simulations required large
computing resources, making more detailed study unfeasible. In this work we
derive a sharp interface limit of CPF, including all interactions and
parameters. This new model offers over $200$ fold speedup when compared to our
original CPF implementation. We demonstrate that this model captures similar
behavior and allows us to obtain new results that were previously intractable.
We obtain the full velocity distribution for a large range of degrees of
confluence, $\rho$, and show regimes where its tail is heavier and lighter than
a normal distribution. Furthermore, we fully characterize the velocity
distribution with a single parameter, and its dependence on $\rho$ is fully
determined. Finally, cell motility is shown to linearly decrease with
increasing $\rho$, consistent with previous theoretical results.
