Fracture mechanics of bacterial colonies growing in soft gels

Abstract

When submerged in agarose gels, growing Escherichia coli (E. coli) form lenticular colonies. In this thesis I first present a study on the origin of this morphology. Using single plane illumination microscopy, I record the full 3D morphology of growing E. coli colonies for the first time. By adding fiducial markers to the gel, I measured the displacement of the gel surrounding the growing colonies. These measurements revealed that as E. coli undergo binary fission, growing from a single bacterium into a colony of ∼ 10⁶ cells, they fracture the gel around them. However, this fracture process cannot be described by simple linear elastic fracture mechanics. Instead, fractures opened up by expanding colonies undergo a transition in propagation mode, changing from one where the gel is fractured over the entire crack surface, to one where the gel is fractured in a single plane. To my knowledge, this is the first time this transition has been measured, showing the potential of using bacteria to explore small scale fracture mechanics. The observed transition in fracture mode is consistent with cavitation theory, suggesting that at small scales the pressure required for colony growth is independent of the gel’s fracture energy. This independence may mean that bacteria can grow in far tougher materials than would previously have been expected. In a second study I develop an apparatus that can inject oil bubbles into agarose at the same length and time scales as bacterial colonies grow, effectively creating a physical simulation of colony growth. With this apparatus I show that there is little difference between fractures propagated by a Newtonian fluid and those propagated by a colony of E. coli. In fact, what morphological differences could be observed can be plausibly explained by the difference in interfacial energy between the agarose-E. coli and agarose-oil interface. This means that in the future hydraulic fracture theories may be applied wholesale to predictions of bacterial infiltration into materials. In a final study, the elastic and fracture properties of agarose were measured using a custom apparatus to perform Rivlin and Thomas’s pure shear test. The fracture energy was found to be in reasonable agreement with the theory of Lake and Thomas, being of order 0.4 J m−² for 2 % agarose. The fracture energy was found to be independent of the fracture rate below cross head speeds of 0.01 mm s−¹, meaning that the viscous dissipation in the gel surrounding the colonies is small and that the measurements made in this study are applicable to predictions of the slowly growing colony morphology