In [2]:
import IPython.core.display as disp
%run nb_init.py

2015-01-26 09:46:39,187 -leg_joint -INFO -successfully imported leg_joint


# A model of leg joint formation in the drosophila pupa¶

## Objectives of the model¶

We are building a minimal model of the apical junctions network in the drosophila leg disk epithelium. We want do be able to model not only topological modifications of the apical juncitions but also geometrical changes, as we seek to understand how cell death -- or apoptosis -- leads to the appearance of a fold in the developing leg disk and further on the leg articulation.

Bellow is a vue of the leg disk apical junctions via a fluorescent cadherin marker.

In [3]:
disp.SVG(lj.data.get_image('apical_view_junctions.svg'))

Out[3]:

View of the apical junctions of the leg disk.

E-Cadh GFP - maximum intensity projection of a 3D confocal stack - full width of the image is about 200 µm

## The reference framework: a 2D model of wing disk apical junctions network¶

Our model is a 3D generalization of the model developed by Farhadifar et al..

The objective of this project is to model an other imaginal disk, the leg disk. Both tissues are very close biologicaly, as they pertain to the same stage of the drosophila development.

In [9]:
disp.Image(lj.data.get_image('faradifar_model.jpeg'))

Out[9]:

This vertex model computes each cell energy based on its geometrical properties:

• its area
• its perimeter
• the length of the junctions (the frontier) between two cells

The junction network configuration is found by minimizing this energy locally each time a topological change occurs in the tissue, such as a cell division or an intercalation event.