Fracture mechanics modeling of popping event during daughter cell separation

Abstract

Most bacteria cells divide by binary fission which is part of a bacteria cell cycle and requires tight regulations and precise coordination. Fast separation of Staphylococcus Aureus (S. Aureus) daughter cells, named as popping event, has been observed in recent experiments. The popping event was proposed to be driven by mechanical crack propagation in the peripheral ring which connected two daughter cells before their separation. It has also been shown that after the fast separation, a small portion of the peripheral ring was left as a hinge. In the article, we develop a fracture mechanics model for the crack growth in the peripheral ring during S. Aureus daughter cell separation. In particular, using finite element analysis, we calculate the energy release rate associated with the crack growth in the peripheral ring, when daughter cells are inflated by a uniform turgor pressure inside. Our results show that with a fixed inflation of daughter cells, the energy release rate depends on the crack length non-monotonically. The energy release rate reaches a maximum value for a crack of an intermediate length. The non-monotonic relationship between the energy release rate and crack length clearly indicates that the crack propagation in the peripheral ring can be unstable. The computed energy release rate as a function of crack length can also be used to explain the existence of a small portion of peripheral ring remained as hinge after the popping event.

Appendix: Geometry and material parameters

Figure 7 shows the geometry of the model of a quarter of a cell directly obtained from previous study (Zhou et al. 2015). Table 1 includes all geometrical and material parameters used in simulations.