Microcolony Dynamics: Motion from Growth, Order, and Incompressibility

Abstract

Rod-shaped bacteria such as E. coli reproduce by expanding along their long axis and splitting into pairs of daughter cells. If conditions are favourable for growth, they will continue in this way, doubling repeatedly until they hit some limiting factor, such as a lack of nutrients or a buildup of toxic waste products. Long before they reach this stage, however, they must contend with another limited resource: space. As these bacteria lengthen, they push their neighbours aside to make room for their added volume. The result is a constantly shifting mass of tightly packed cells, each one rotating and reorienting itself in an ongoing competition for space.

In the past decade and a half, the physics governing this behaviour has garnered considerable attention, and a robust literature has developed, drawing on hydrodynamic theories of liquid crystals and their active matter counterparts (so-called "active nematics"). However, these models have relied exclusively on gradient effects to drive the dynamics of the system, and these are insufficient to describe the behaviour of real microcolonies, which exhibit asymmetric growth dynamics even in the absence of spatial gradients.

This thesis seeks to address this shortcoming. We do so by developing a novel model of microcolony dynamics, based in part on earlier models from the literature on nutrient-limited growth. We begin by showing that the physics in these models can be recast as a variational problem: minimizing the total kinetic energy. We then modify this variational problem to account for cell morphology, biasing the direction of a cell's motion based on its orientation. The result is a new model of microcolony growth that exhibits asymmetric spreading. Next, we develop numerical schemes to simulate our system, combining techniques from finite difference methods, level set methods, and unfitted finite element methods. These schemes are validated against analytical solutions. Finally, we use these numerical implementations to explore the behaviour of our model in more complex scenarios where exact solutions are lacking. Our findings suggest that this novel mechanism can reproduce several behaviours observed in real microcolonies, such as spontaneous alignment in semi-confined domains, as well as fingering and defect generation at a microcolony's boundary. We conclude by proposing some strategies to synthesize our model with other models in the active nematic literature.