Kinking and buckling instability in growing bacterial chains

Many gram-positive bacteria like Bacillus subtilis and Clostridium species, exhibit a growing chain-mediated sliding motility that is driven entirely by the force of cell growth. Particularly, the bacteria maintain cell-cell linkage after cell division and form long chains of many cells. The cells in a chain are continuously pushed outward by the mechanical force of cell growth. As the cell number in a chain grows, the cells toward the tip of the chain accelerate, and can in principle reach very high speeds. Although this seems to suggest a highly efficient motility mechanism, recent modeling work predicted mechanical stress builds up in the growing chain and the resulting chain breakage beyond a critical chain length, which ultimately sets a mechanical limitation in the maximum speed of the chain-mediated sliding. In this work we developed models to show that under different conditions the chain can either form sharp kinks or smooth buckles under the increasing stress. This can explain differential behaviors observed in different bacterial species. Our model further predicted how kinking and buckling affect the susceptibility of the chain to breakage. Our model provides a theoretical framework for predicting the dynamics and efficiency of growing chain-mediated bacterial sliding, and suggest cell properties that can optimize sliding efficiency.