  Cell deformability is an essential determinant for tissue-scale mechanical
nature, such as fluidity and rigidity, and is thus crucial for understanding
tissue homeostasis and stable developmental processes. However, numerical
simulations for the collective dynamics of cells with arbitral cell
deformations akin to mesenchymal, ameboid, and epithelial cells in a
non-confluent situation need high computational costs and are still
challenging. Here we propose a new method that allows us to study significantly
larger numbers of cells than existing methods. Using the method, we
investigated the densely packed active cell population interacting via excluded
volume interactions, and discovered the emergence of two fluid phases in
deformable cell populations, a soft-fluid phase with drastically deformed cell
shapes and a fluid phase with circular cell shapes. The transition between
these two phases is characterized by the percolation of topological defects,
which is experimentally testable.
