  Many biological systems such as cell aggregates, tissues or bacterial
colonies behave as unconventional systems of particles that are strongly
constrained by volume exclusion and shape interactions. Understanding how these
constraints lead to macroscopic self-organized structures is a fundamental
question in e.g. developmental biology. To this end, various types of
computational models have been developed: phase fields, cellular automata,
vertex models, level-set, finite element simulations, etc. We introduce a new
framework based on optimal transport theory to model particle systems with
arbitrary dynamical shapes and deformability. Our method builds upon the
pioneering work of Brenier on incompressible fluids and its recent applications
to materials science. It lets us specify the shapes of individual cells and
supports a wide range of interaction mechanisms, while automatically taking
care of the volume exclusion constraint at an affordable numerical cost. We
showcase the versatility of this approach by reproducing several classical
systems in computational biology. Our Python code is freely available at:
www.github.com/antoinediez/ICeShOT
