Biological tissues, and more particularly epithelia are very particular kinds of material. Not only do they behave like solids and liquids at the same time (think shaving foam), they are also governed by the behaviour of their constituent individual cells. Biological processes (a bunch of incredibly complex chemical reactions) and physics are intertwined so that complex forms emerge from initially smooth tissues.

Along advanced imaging techniques and genetic manipulation of model organism, biophysical modeling is key in understanding these shape changes, or morphogenesis. We studied the role of programmed cell death, or apoptosis in the formation of a fold in the fruit fly pupae (an intermediate stage between larva and adult). In a recently published article we demonstrated that apoptotic cells had an active role in shaping this fold (which will later become a joint in the adult fly's leg). Cells die on a ring around the socket shaped tissue (one cell thick, and about 200 µm in diameter), they contract and pull on their neighbours, initiating changes in the tissue properties.

In this presentation, I will describe how we use python to develop a numerical model of this epithelium. The leg-joint module is based on Tiago Peixoto's graph-tool library, and uses SciPy optimization routines to perform the gradient descent at the core of the dynamical simulation. The following topics will be discussed:

• Visualization: plain matplotlib vs vispy vs Blender.

• Performance: can we go from 24 hrs per simulation to less than 1? The pure python vectorization and BoostPython/CGAL routes.

• Future plans: towards a biological tissue physics engine.

The code is showcased in a series of Jupyter Notebooks that can be browsed here.