Modeling mechanical dynamics in chain-mediated bacterial sliding

Investigating the mechanical dynamics of bacterial motility has led to a deeper understanding of the behaviors and lifecycle of many bacterial species. We discuss chain driven sliding motility where the bacteria maintain connections between daughter cells following division, resulting in long chains that expand across the viscous substrate. These chains grow exponentially, suggesting the chain tips may accelerate to very fast speeds. We devise multiple mathematical frameworks encapsulating the key physical dynamics and interactions to investigate the dynamics of bacterial chains and the biological implications of this motility.

Our first framework, the rigid rod model, provides a set of equations describing the chain growth dynamics. Analysis of these equations reveals the stress maintaining cell-cell linkages increases unsustainably at an exponential rate. We devise a perturbation analysis of the rigid rod model in order to predict the critical stress associated with mechanical failure of these linkages. A phenomenological population model reveals that repeated chain breakages limit the expansion of the entire population to linear growth.

Through experimental observation and computer simulations, we identify two key mechanical instabilities that emerge in growing bacterial chains. The first is sharp localized kinking that leads to the chain breakage mentioned above. In the second dynamic, the chain buckles due to compressive drag forces resulting in the emergence of large curvatures throughout the chain. We devise a continuum mechanics framework to examine the curvature dynamics in the growing chain. Through linear stability analysis of the rigid rod model and the continuum mechanics framework, we predict the dominant instability dynamic based on the physical properties of the chain and its environment. We use rigid rod model simulations to investigate the biological implications of these dynamics.

Lastly, we introduce a number of methods that extend the rigid rod model to allow for the investigation of interacting chains. We consider methods that implement forces due to the entanglement of cell body appendages as well as collision dynamics. In total these models provide generic frameworks for investigating mechanical dynamics of growing bacterial chains. Our models provide testable predictions and suggest biological motivations for the typical behaviors that are observed in these cell chains.