The mechanism of pattern formation in the developing Drosophila retina

The biological patterning of the Drosophila retina in vivo has striking resemblance to liquid bubbles, in which the surface mechanics due to N-cadherin within a sub-group of retina cells can be mimicked by surface tension. In this work, the aggregating patterns were reasonably simplified into 2D clusters consisting of 2-6 identical bubbles confined within a shrinking boundary. By using a hybrid fluid dynamics model proposed for liquid foams, the aggregating process of 2-6 retina cells was studied. Assuming the minimal perimeter for patterning cells to be the condition of stability patterns, the stable converged patterns we simulated in this work are the same as the experimental observations. More importantly, a new pattern of 6 cells was obtained which was found physically more stable than the other two reported by Hayashi and Carthew. Aggregating perimeters of cells, i.e. the surface energy, showed a good linear fit with the cell numbers.